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Solution of generalized shifted linear systems with complex symmetric matrices
NASA Astrophysics Data System (ADS)
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green's function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1-9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126-140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
NASA Technical Reports Server (NTRS)
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Freund, Roland
Complex symmetric matrices with strongly stable iterates
Complex-valued symmetric matrices are studied. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. A sharp criterion is provided for identifying those symmetric matrices whose spectral norm is not exceeding one: such strongly stable matrices are usually sought in connection with convergent difference approximations to partial differential equations. As an example, the derived criterion is applied to conclude the strong stability of a Lax-Wendroff scheme.
Tadmor, E.
Complex PT-symmetric nonlinear Schr�dinger equation and Burgers equation.
The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schr�dinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schr�dinger equations (known as the Gross-Pitaevskii equation in Bose-Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail. PMID:23509385
Yan, Zhenya
Complex extensions of semisimple symmetric spaces
Microsoft Academic Search
Let G\\/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G\\/H) contains a maximal G-invariant neighbourhood ? of the zero section where the adapted-complex structure exists. Such ? is endowed with a canonical\\u000a G-invariant pseudo-K�hler metric of the same signature as the metric on G\\/H. We use the polar map to define a G-invariant pseudo-K�hler metric on distinguished G-invariant
Laura Geatti
Symmetrical perturbation analysis of complex two-dimensional photonic crystals
We study complex photonic crystals with unit cells that include different dielectric cylinders. A symmetrical perturbation approach is developed here which predicts how the band spectrum of the complex structures evolves from the most symmetrical prophase. As a specific example, we apply this symmetrical approach to the analysis of square lattices with alternating layers of dielectric cylinders perpendicular to one
N. Malkova; S. Kim; V. Gopalan
Linear programming using symmetric triangular intuitionistic fuzzy numbers
This paper introduces Symmetric Triangular Intuitionistic Fuzzy Numbers (STriFNs) and also proposes a new type of intuitionistic fuzzy arithmetic operations on STriIFNs. A special ranking function for ordering STriIFNs has been introduced. A solution methodology for Intuitionistic Fuzzy Linear Programming Problems (IFLPPs) with STriIFNs as parameters has been proposed by using Intuitionistic Fuzzy Simplex Method and the arithmetic operations on STriIFNs. Finally, an illustrative numerical example is presented to demonstrate the proposed approach.
Parvathi, R.; Malathi, C.
Invisibility in {PT}-symmetric complex crystals
Bragg scattering in sinusoidal {PT}-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel functions of first kind. The analytical results indicate that unidirectional invisibility, recently predicted for such crystals by coupled-mode theory (Z Lin et al 2011 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.106.213901), breaks down for crystals containing a large number of unit cells. In particular, for a given modulation depth in a shallow sinusoidal potential, three regimes are encountered as the crystal thickness is increased. At short lengths the crystal is reflectionless and invisible when probed from one side (unidirectional invisibility), whereas at intermediate lengths the crystal remains reflectionless but not invisible; for longer crystals both unidirectional reflectionless and invisibility properties are broken.
Longhi, Stefano
Symmetrical analysis of complex two-dimensional hexagonal photonic crystals
We study complex hexagonal photonic crystals with unit cells that include different dielectric cylinders. A general symmetrical perturbation approach for a hexagonal lattice with up to three basis rods is presented that systematically develops other structural derivatives including comblike structures. We show how the band spectrum of these complex structures evolves from the most symmetrical prophase. The results are in
N. Malkova; S. Kim; T. Dilazaro; V. Gopalan
Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q =0
We present representation theoretical interpretations of quasi-symmetric functions and noncommutative symmetric functions in terms of quantum linear groups and Hecke algebras at q = 0. We obtain in this way a noncommutative realization of quasi-symmetric functions analogous to the plactic symmetric functions of Lascoux and Schutzenberger. The generic case leads to a notion of quantum Schur function.
Daniel Krob; Jean-Yves Thibon
Linear chains in a monolithic symmetric trap for quantum information processing
Linear ion chains are being used [1] to simulate quantum magnet Ising interactions, phase transitions, and spin frustrations. We will present results for trapping linear ion chains in a monolithic two-level trap that utilizes the flexibility, complexity and scalability provided by VLSI silicon microfabrication. This trap provides optimized features and dimensions for trapping equally spaced ion chains while minimizing light scattering and exposed dielectrics that sometimes limit surface electrode ion traps. The ions are trapped symmetrically between two electrode layers. This geometry provides a strong pseudopotential well and radial field symmetry, resulting in stable ion mode frequencies and chains. [4pt] [1] K. Kim, et al, Phys. Rev. Lett. 103, 120502 (2009)
Shaikh, Fayaz; Slusher, Richart
Multigrid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear sigma-model
We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear sigma-model [ = SU(2) principal chirral model
Robert G. Edwards; Sabino Jos�ferreira; Jonathan Goodman; Alan D. Sokal
A CAD\\/CAPP interface for complex rotationally symmetric parts
A new methodology for interfacing Computer-Aided Design (CAD) and Computer-Aided Process Planning (CAPP) based on automatic feature recognition is proposed in the domain of complex rotationally symmetric parts. The interface system consists of three stages: (1) Initial Graphics Exchange Specification (1GES) data translation, (2) polygonal decomposition or splitting, (3) automatic recognition of precedences and features. In the data translation stage,
A relationship between linear complexity and kapa-error linear complexity
The -error linear complexity of a periodic sequence of pe- riod is defined as the smallest linear complexity that can be obtained by changing or fewer bits of the sequence per period. This correspondence shows a relationship between the linear complexity and the minimum value for which the -error linear complexity is strictly less than the linear complexity.
Kaoru Kurosawa; Fumio Sato; Takahiro Sakata; Wataru Kishimoto
Model-size reduction for the non-linear dynamic analysis of quasi-symmetric structures
A numerical technique is developed to reduce the size of models describing the nonlinear dynamic response of quasi-symmetric structures (i.e., structures with unsymmetric geometry). The response vectors of the structure are approximated by a linear combination of the symmetric and antisymmetric vectors at each time step. The mathematical formulation and numerical implementation of the method are described in detail, and results for a shallow laminated anisotropic panel of quadrilateral planform are presented in graphs and normalized contour plots.
Noor, Ahmed K.; Peters, Jeanne M.
Solitons supported by complex PT-symmetric Gaussian potentials
SciTech Connect
The existence and stability of fundamental, dipole, and tripole solitons in Kerr nonlinear media with parity-time-symmetric Gaussian complex potentials are reported. Fundamental solitons are stable not only in deep potentials but also in shallow potentials. Dipole and tripole solitons are stable only in deep potentials, and tripole solitons are stable in deeper potentials than for dipole solitons. The stable regions of solitons increase with increasing potential depth. The power of solitons increases with increasing propagation constant or decreasing modulation depth of the potentials.
Hu Sumei [Laboratory of Photonic Information Technology, South China Normal University, Guangzhou 510631 (China); Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000 (China); Ma Xuekai; Lu Daquan; Yang Zhenjun; Zheng Yizhou; Hu Wei [Laboratory of Photonic Information Technology, South China Normal University, Guangzhou 510631 (China)
Symmetric linear systems - An application of algebraic systems theory
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Hazewinkel, M.; Martin, C.
Stationary modes and integrals of motion in nonlinear lattices with a { {PT}}-symmetric linear part
We consider finite-dimensional nonlinear systems with a linear part described by a parity-time ({ {PT}}-)symmetric operator. We investigate bifurcations of stationary nonlinear modes from the eigenstates of the linear operator and consider a class of { {PT}}-symmetric nonlinearities allowing the existence of families of nonlinear modes. We pay particular attention to situations when the underlying linear { {PT}}-symmetric operator is characterized by the presence of degenerate eigenvalues or an exceptional-point singularity. In each of the cases we construct formal expansions for small-amplitude nonlinear modes. We also report a class of nonlinearities allowing the system to admit one or several integrals of motion, which turn out to be determined by the pseudo-hermiticity of the nonlinear operator.
Zezyulin, D. A.; Konotop, V. V.
A carbon nanotube\\/polymer strain sensor with linear and anti-symmetric piezoresistivity
In this article, a strain sensor made from an epoxy-based nanocomposite using a kind of multi-walled carbon nanotubes (MWNTs), i.e., LMWNT-10, was investigated. It was found that the piezoresistivity of this strain sensor is linear and anti-symmetric in tensile and compressive states within a large strain range, which is different from that of the strain sensor using another type of
Gang Yin; Ning Hu; Yoshifumi Karube; Yaolu Liu; Yuan Li; Hisao Fukunaga
Gallager-type bounds for non-binary linear block codes over memoryless symmetric channels
The performance analysis of non-binary linear block codes is studied under ML decoding where it is assumed that the transmission takes place over memoryless symmetric channels. Gallager-type bounds are derived, and the proposed bounds are exemplified for expurgated regular ensembles of non-binary low-density parity-check (LDPC) codes. These bounds are also compared with classical and recent improved sphere-packing bounds, indicating that
Eran Hof; Igal Sason; Shlomo Shamai
Symmetrical and unsymmetrical dizinc complexes as models for the active sites of hydrolytic enzymes.
Dinuclear carboxylate-bridged zinc complexes of one symmetric and one asymmetric phenolate-based ligand catalyse the transesterification of 2-hydroxypropyl-p-nitrophenyl phosphate (HPNP) at different rates, with an unsymmetrical complex being more active than a symmetric one. PMID:18274677
Jarenmark, Martin; Kappen, Sascha; Haukka, Matti; Nordlander, Ebbe
Convergence of a Matrix Splitting Algorithm for the Symmetric Monotone Linear Complementarity Problem. (Reannouncement with New Availability Information).
National Technical Information Service (NTIS)
A matrix splitting algorithm for the linear complementarity problem is considered, where the matrix is symmetric positive semidefinite. It is shown that if the splitting is regular, then the iterates generated by the algorithm are well defined and converg...
Z. Q. Luo P. Tseng
Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials
We report the existence, stability, and rich dynamics of dissipative lattice solitons in optical media described by the cubic-quintic complex Ginzburg-Landau model with parity-time (PT) symmetric potentials. We focus on studying the generic spatial soliton propagation scenarios by changing (a) the linear loss coefficient in the complex Ginzburg-Landau model, (b) the amplitudes, and (c) the periods of real and imaginary parts of the complex-valued PT-symmetric optical lattice potential. Generically, it is found that if the period of the real part of the PT-symmetric optical lattice potential is close to ?, the spatial solitons are tightly bound and they can propagate straightly along the lattice, while if the period of the real part of the PT-symmetric optical lattice potential is larger than ?, the launched solitons are loosely bound and they can exhibit either a transverse (lateral) drift or a persistent swing around the input launching point due to gradient force arising from the spatially inhomogeneous loss. These latter features are intimately related to the dissipative nature of the system under consideration because they do not arise in the conservative counterpart of the dynamical model. These generic propagation scenarios can be effectively managed by properly changing the profile of the spatially inhomogeneous loss.
He, Yingji; Mihalache, Dumitru
Buckling Behavior of Long Symmetrically Laminated Plates Subjected to Shear and Linearly Varying Axial Edge Loads
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates that are subjected to linearly varying edge loads, uniform shear loads, or combinations of these loads is presented. The study focuses on the effects of the shape of linearly varying edge load distribution, plate orthotropy, and plate flexural anisotropy on plate buckling behavior. In addition, the study exmines the interaction of linearly varying edge loads and uniform shear loads with plate flexural anisotropy and orthotropy. Results obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates are presented for [+/- theta](sub s), thin graphite-epoxy laminates that are representative of spacecraft structural components. Also, numerous generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These charts show explicitly the effects of flexural orthotropy and flexural anisotropy on plate buckling behavior for linearly varying edge loads, uniform shear loads, or combinations of these loads. The most important finding of the present study is that specially orthotropic and flexurally anisotropic plates that are subjected to an axial edge load distribution that is tension dominated can support shear loads that are larger in magnitude than the shear buckling load.
Nemeth, Michael P.
Symmetry breaking puzzles in inner-shell photoionization of symmetric linear molecules
Core-level photoionization of small molecules, followed by Auger decay, generally leads to molecular fragmentation. Modern momentum imaging (COLTRIMS) techniques, combined with coincident measurement of all charged particles produced by a single photoabsorption event, allow one to reconstruct photo- and Auger electron angular distributions in the body frame, which are generally far richer than conventionally measured laboratory-frame angular distributions. In this talk, I will discuss two cases where such measurements on symmetric linear target molecules have revealed interesting symmetry paradoxes. The first case involves K-shell ionization of molecular nitrogen where experimental measurements raise familiar questions about whether the photoprocess creates a localized hole at one of two equivalent, but spatially well-separated sites or rather a delocalized hole, smeared over the equivalent sites, preserving the symmetry of the molecule. The second example involves carbon 1s ejection from the symmetric CO2 molecule and the origin of observed asymmetry in the molecular-frame photoelectron angular distributions. In both cases, theoretical calculations assist in interpreting the experimental findings.
Rescigno, Thomas
A shared minimum-error discrimination among three linearly dependent mirror-symmetric qubit states
We discuss how a shared minimum-error discrimination (SMD) may be implemented by two remote partners Alice and Bob. Here Bob is given a qubit prepared in one of three linearly dependent mirror-symmetric states with a priori probability. Alice has the knowledge of Bob's signal states, but Bob has not. We show that the shared generalized measurement could be realized by Alice performing a suitable unitary evolution from acting on her system to acting on Bob's system, and remotely rotating the optimal measurement directions to coincide with Bob's basis vectors. In this case, Bob could perform a local orthogonal measurement to determine his signal states with the smallest possible error and without inconclusive answers. A quantum network, which is realizable with current technology, is suggested to implement this SMD.
Chen, Libing; Lu, Hong
On the stability of the non-symmetric BEM/FEM coupling in linear elasticity
In this paper we discuss the use of single and double layer boundary integral equations for the numerical solution of linear elasticity problems with boundary conditions of mixed type, and the one-equation coupling of finite and boundary element methods to solve a free space transmission problem. In particular we present a sufficient and necessary condition which ensures stability of the coupled approach for any choice of finite and boundary elements. These results justify the coupling of collocation and Galerkin one-equation boundary element methods with finite elements as used in many engineering and industrial applications. Hence one may avoid the use of the symmetric formulation of boundary integral equations, which is, although well established from a mathematical point of view and also used in some engineering applications, not so much accepted in particular in industrial applications.
Steinbach, Olaf
An efficient EM-ICP algorithm for symmetric consistent non-linear registration of point sets
PubMed Central
In this paper, we present a new algorithm for non-linear registration of point sets. We estimate both forward and backward deformations fields best superposing the two point sets of interest and we make sure that they are consistent with each other by designing a symmetric cost function where they are coupled. Regularisation terms are included in this cost function to enforce deformation smoothness. Then we present a two-step iterative algorithm to optimise this cost function, where the two fields and the fuzzy matches between the two sets are estimated in turn. Building regularisers using the RKHS theory allows to obtain fast and efficient closed-form solutions for the optimal fields. The resulting algorithm is efficient and can deal with large point sets.
Combes, Benoit; Prima, Sylvain
Polymer complexes XXXVII novel models and structural of symmetrical poly-Schiff base on heterobinuclear complexes of dioxouranium(VI)
Some binary and ternary novel complexes of dioxouranium(VI) with 5-vinylsalicylaldehyde (VSH) have been prepared and characterized by various physico-chemical techniques. The amine exchange reactions of coordinated poly-Schiff bases in these complexes have been also carried out which give symmetrical tetradentate poly-Schiff base complexes. Metal exchange reaction of these dioxouranium(VI) complexes with copper(II) gives the corresponding Cu(II) complexes. Reaction of tetradentate
A. Z El-Sonbati; A. A El-Bindary; I. G. A Rashed
Computational complexity of LCPs associated with positive definite symmetric matrices
Murty in a recent paper has shown that the computational effort required to solve a linear complementarity problem (LCP), by either of the two well known complementary pivot methods is not bounded above by a polynomial in the size of the problem. In that paper, by constructing a class of LCPs�one of ordern forn = 2�he has shown that to
Yahya Fathi
Low-complexity narrowband adaptive beamforming based on symmetrically distributed arrays
Based on the symmetrically distributed array (SDA) structure and the resultant generalised conjugate symmetric property of its optimum weight vector, a transformation matrix is introduced to preprocess the received array data, after which the original complex-valued optimum weight vector is reduced to a real-valued one, so that in the following weight adaptation we can simply remove imaginary part of the weight vector. As a result of this regularization, improved performance is achieved with much lower computational complexity. There is an undetermined phase factor in the transformation matrix and two different cases are studied with beamforming examples provided for each case, supported by simulation results.
Zhang, Lei; Liu, Wei; Langley, Richard J.
Symmetric topological complexity of projective and lens spaces
For real projective spaces, (a) the Euclidean immersion dimension, (b) the\\u000aexistence of axial maps, and (c) the topological complexity are known to be\\u000athree facets of the same problem. But when it comes to embedding dimension, the\\u000aclassical work of Berrick, Feder and Gitler leaves a small indeterminacy when\\u000atrying to identify the existence of Euclidean embeddings of these
Jesus Gonzalez; Peter Landweber
Collision-induced absorption in mixtures of symmetrical linear and tetrahedral molecules - Methane-nitrogen
The far infrared absorption of a CH4-N2 mixture was measured at 297, 195, and 162 K from 30 to 650/cm. The spectral invariants gamma1 and alpha1, proportional, respectively, to the zeroth and first spectral moments, due to bimolecular collisions between CH4 and N2 were obtained from these data and compared with theoretical values. The theory for collision-induced dipoles between a tetrahedral and a diatomic or symmetrical linear molecule includes contributions not previously considered. Whereas the theoretical values of gamma1 are only somewhat greater than experiment at all temperatures, the theoretical values of alpha1 are significantly lower than the experimental values. From the theoretical spectral moments for the various induced dipole components, the parameters of the BC shape were computed, and theoretical spectra were constructed. Good agreement was obtained at the lower frequencies, but with increasing frequencies the theoretical spectra were increasingly less intense than the experimental spectra. Although the accuracy of the theoretical results may suffer from the lack of a reliable potential function, it does not appear that this high frequency discrepancy can be removed by any conceivable modification in the potential.
Birnbaum, G.; Borysow, A.; Buechele, A.
Fluorescence study of protein�lipid complexes with a new symmetric squarylium probe
The novel symmetric squarylium derivative SQ-1 has been synthesized and tested for its sensitivity to the formation of protein�lipid complexes. SQ-1 binding to the model membranes composed of zwitterionic lipid phosphatidylcholine (PC) and its mixtures with anionic lipid cardiolipin (CL) in different molar ratios was found to be controlled mainly by hydrophobic interactions. Lysozyme (Lz) and ribonuclease A (RNase) exerted
Valeriya M. Ioffe; Galyna P. Gorbenko; Todor Deligeorgiev; Nikolai Gadjev; Aleksey Vasilev
A Linear Time Algorithm for Constructing Maximally Symmetric Straight Line Drawings of Triconnected Planar Graphs
Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we employ two steps. The first step is to find appropriate automorphisms. The second step is to draw the graph to display the automorphisms. Our aim in this paper is to construct maximally symmetric straight line drawings
Seok-hee Hong; Brendan D. Mckay; Peter Eades
Preconditioning the bidomain model with almost linear complexity
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog ?( n) (for some constant ?) which is optimal complexity for such problems.
Pierre, Charles
The next linear collider damping ring complex
We report progress on the design of the Next Linear Collider (NLC) Damping Rings complexes. The purpose of the damping rings is to provide low emittance electron and positron bunch trains to the NLC linacs, at a rate of 120 Hz. As an option to operate at the higher rate of 180 Hz, two 1.98 GeV main damping rings per beam are proposed, and one positron pre-damping ring. The main damping rings store up to 0.8 amp in 3 trains of 190 bunches each and have normalized extracted beam emittances {gamma}{var_epsilon}x = 3 mm-mrad and {gamma}{var_epsilon}y = 0.02 mm-mrad. The optical designs, based on a theoretical minimum emittance lattice (TME), are described, with an analysis of dynamic aperture and non-linear effects. Key subsystems and components are described, including the wiggler, the vacuum systems and photon stop design, and the higher-order-mode damped RF cavities. Impedance and instabilities are discussed.
Corlett,J.; Atkinson,D.; De Santis,S.; Hartman, N.; Kennedy, K.; Li, D.; Marks, S.; Minamihara, Y.; Nishimura, H.; Pivi, M.; Reavill, D.; Rimmer, R.; Schlueter, R.; Wolski, A.; Anderson,S.; McKee,B.; Raubenheimer, T.; Ross, M.; Sheppard, J.C.
Symmetrical modified dual tree complex wavelet transform for processing quadrature Doppler ultrasound signals.
Dual-tree complex wavelet transform (DTCWT), which is a shift invariant transform with limited redundancy, is an improved version of discrete wavelet transform. Complex quadrature signals are dual channel signals obtained from the systems employing quadrature demodulation. An example of such signals is quadrature Doppler signal obtained from blood flow analysis systems. Prior to processing Doppler signals using the DTCWT, directional flow signals must be obtained and then two separate DTCWT applied, increasing the computational complexity. In this study, in order to decrease computational complexity, a symmetrical modified DTCWT algorithm is proposed (SMDTCWT). A comparison between the new transform and the symmetrical phasing-filter technique is presented. Additionally denoising performance of SMDTCWT is compared with the DWT and the DTCWT using simulated signals. The results show that the proposed method gives the same output as the symmetrical phasing-filter method, the computational complexity for processing quadrature signals using DTCWT is greatly reduced and finally the SMDTCWT based denoising outperforms conventional DWT with same computational complexity. PMID:22255416
Serbes, G; Aydin, N
Symmetrized complex amplitudes for He double photoionization from the time-dependent close coupling and exterior complex scaling methods
Symmetrized complex amplitudes for the double photoionization of helium are computed by the time-dependent close-coupling and exterior complex scaling methods, and it is demonstrated that both methods are capable of the direct calculation of these amplitudes. The results are found to be in excellent agreement with each other and in very good agreement with results of other ab initio methods and experiment.
Horner, D.A.; Colgan, J.; Martin, F.; McCurdy, C.W.; Pindzola, M.S.; Rescigno, T.N.
Passive control of the flow in a symmetric channel with a sudden expansion based on linear stability analysis
In the present work we investigate the stability properties of the flow in a 2D-plane channel with a symmetric sudden expansion, which is a possible schematization of a plane diffuser. The laminar flow in 2D diffusers may produce either symmetric or nonsymmetric steady solutions, depending on the value of the Reynolds number Re as compared with some critical value Rec. The stability properties of the flow are studied in the context of linear theory, characterizing the sensitivity of the instability to both a structural perturbation of the linearized flow equations and a perturbation of the base flow. The information provided by the two kinds of analysis is used to propose a passive flow control strategy, obtained by the introduction of a small cylinder in the channel, aimed at stabilizing the symmetric solution at Re>Rec. The effectiveness of this control strategy in the nonlinear case is investigated, and ultimately verified by numerical simulations of the flow in which a real control cylinder is introduced. The robustness of the control is also tested by numerical simulations in which the position of the cylinder is slightly changed with respect to the optimal one given by the sensitivity analysis.
Fani, Andrea; Camarri, Simone; Salvetti, Maria-Vittoria
Asymmetric hydrosilylation of symmetrical diketones catalyzed by a rhodium complex with trans-chelating chiral diphosphine EtTRAP
Asymmetric hydrosilylation of symmetrical diketones with diphenylsilane in the presence of catalytic amount ([substrate]\\/[catalyst] = 100) of rhodium complex coordinated with trans-chelating chiral phosphine ligand EtTRAP gave corresponding optically active symmetrical diols with high enantiomeric excesses.
Ryoichi Kuwano; Masaya Sawamura; Junya Shirai; Masatoshi Takahashi; Yoshihiko Ito
Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
In quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in some parametric regimes of scattering from a complex PT-symmetric potential. In special cases, we show that this potential can even become invisible (R=0, T=1) remarkably this time from both left and right sides. We also find that this potential in a parametric regime enjoys a pseudo-unitarity of the type: T+?{RR}=1.
Ahmed, Zafar
Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case
The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. It became necessary to linearize also around the Schwarzschild solution. The linearized equation resulting in this case is discussed using qualitative methods. The relation between the solution of the linearized and the full equation is discussed.
Schmidt, H.-J.
General theory of spherically symmetric boundary-value problems of the linear transport theory.
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Kanal, M.
Slice-selective J-coupled coherence transfer using symmetric linear phase pulses: applications to localized GABA spectroscopy
Symmetric, linear phase, slice-selective RF pulses were analyzed theoretically for performing slice-selective coherence transfer. It was shown using numerical simulations of product operators that, when a prefocusing gradient of the same area as that of the refocusing gradient is added, these pulses become slice-selective universal rotator pulses, therefore, capable of performing slice-selective coherence transfer. As an example, a slice-selective universal rotator pulse based on a seven-lobe hamming-filtered sinc pulse was applied to in vivo single-shot simultaneous spectral editing and spatial localization of neurotransmitter GABA in the human brain.
Shen, Jun
Structural tailoring effects on the magnetic behavior of symmetric and asymmetric cubane-type Ni complexes.
Using two kinds of carboxylate ligands with small but significant differences in steric size, symmetric and asymmetric Fe(II) and Ni(II) cubanes have been synthesized in a controlled fashion. Fast sweeping pulsed field measurements showed magnetization hysteresis loops for two cubane-type molecular complexes, [Ni4(?-OMe)4(O2CAr(4F-Ph))4(HOMe)8] and [Ni4(?-OMe)4(O2CAr(Tol))4(HOMe)6], thus suggesting single-molecule magnet behavior. To differentiate the magnetic properties between the symmetric and asymmetric cubanes, detailed electron paramagnetic resonance (EPR) measurements were performed. From the EPR data, taken at various frequencies and temperatures, zero-field splitting parameters D, E, and other higher-order parameters for both cubane samples were extracted. Compared to the symmetric Ni-cubane, the asymmetric one shows an increase in the D and E values by about 20%, thereby suggesting structural engineering effects on the magnetic properties. By using the magnetic parameters determined by EPR, a static magnetization curve at 2?K and a temperature dependence of the magnetic susceptibility were simulated. A good agreement between theoretical and experimental data confirms the validity of the values obtained from EPR measurements. PMID:23509044
Ponomaryov, Alexey N; Kim, Namseok; Hwang, Jaewon; Nojiri, Hiroyuki; van Tol, Johan; Ozarowski, Andrew; Park, Jena; Jang, Zeehoon; Suh, Byoungjin; Yoon, Sungho; Choi, Kwang-Yong
Global sensitivity analysis using complex linear models
A global sensitivity analysis of complex computer codes is usually performed by calculating the Sobol indices. The indices\\u000a are estimated using Monte Carlo methods. The Monte Carlo simulations are time-consuming even if the computer response is replaced\\u000a by a metamodel. This paper proposes a new method for calculating sensitivity indices that overcomes the Monte Carlo estimation.\\u000a The method assumes a
Astrid Jourdan
Isomorphic Hilbert spaces associated with different complex contours of the PT-symmetric (-x4) theory
In this work, we stress the existence of isomorphisms which map complex contours from the upper half to contours in the lower half of the complex plane. The metric operator is found to depend on the chosen contour but the maps connecting different contours are norm-preserving. To elucidate these features, we parametrized the contour z = -2i? {1+ix} considered in Phys. Rev. D 73, 085002 (2006) for the study of wrong sign x4 theory. For the parametrized contour of the form z = a? {b+icx}, we found that there exists an equivalent Hermitian Hamiltonian provided that a2c is taken to be real. The equivalent Hamiltonian is b-independent but the metric operator is found to depend on all the parameters a, b and c. Different values of these parameters generate different metric operators which define different Hilbert spaces. All these Hilbert spaces are isomorphic to each other even for the parameter values that define contours with ends in two adjacent wedges. As an example, we showed that the transition amplitudes associated with the contour z = -2i? {1+ix} are exactly the same as those calculated using the contour z = ? {1+ix}, which is not PT-symmetric and has ends in two adjacent wedges in the complex plane.
Shalaby, Abouzeid M.
Extending the eigCG algorithm to non-symmetric linear systems with multiple right-hand sides
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the Conjugate-Gradient (CG) algorithm, however, it uses only a window of the vectors generated by the CG algorithm to compute approximate eigenvalues. The number and accuracy of the eigenvectors can be increased by solving more right-hand sides. For Hermitian systems with multiple right-hand sides, the computed eigenvectors can be used to speed up the solution of subsequent systems. The algorithm was tested on Lattice QCD problems by solving the normal equations and was shown to give large speed up factors and to remove the critical slowing down as we approach light quark masses. Here, an extension to the non-symmetric case based on the two-sided Lanczos algorithm is given. The new algorithm is tested on Lattice QCD problems and is shown to give promising results. We also study the removal of the critical slowing down and compare results with those of the eigCG algorithm. We also discuss the case when the system is gamma5-Hermitian.
Abdou Abdel-Rehim, Kostas Orginos, Andreas Stathopoulos
Out-of-Core Solutions of Complex Sparse Linear Equations
ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.
Yip, E. L.
CMISTARK: Python package for the Stark-effect calculation and symmetry classification of linear, symmetric and asymmetric top wavefunctions in dc electric fields
The Controlled Molecule Imaging group (CMI) at the Center for Free Electron Laser Science (CFEL) has developed the CMISTARK software to calculate, view, and analyze the energy levels of adiabatic Stark energy curves of linear, symmetric top and asymmetric top molecules. The program exploits the symmetry of the Hamiltonian to generate fully labeled adiabatic Stark energy curves.
Chang, Yuan-Pin; Filsinger, Frank; Sartakov, Boris G.; K�pper, Jochen
Metal Complexes of Non-Symmetric Tetradentate Schiff Bases Derived from N-(1-hydroxy-2-acetonaphthone)-1-amino-2-phenyleneimine
Novel non-symmetrical tetradentate Schiff base complexes with N2O2 and N3O donor sites have been obtained using the half-unit N-(l-hydroxy-2-acetonaphthone)-l-amino-2-phenyleneimine (HL). Two reaction pathways have been used (i) preparation of the free ligand which is then reacted with the desired metal salt, and (ii) template synthesis without isolation of the free ligand. The prepared nickel and copper complexes have been characterized
Davar M. Boghaei; Maryam Lashanizadegan
Charge-transfer complexes of some linear conjugated polyenes.
On adsorption of some electron-acceptor molecules on the solid films of all-trans-beta-carotene, beta-apo-8'-carotenal, astacene and methylbixin a new absorption band appears on the longer-wavelength side of the spectrum in addition to the original bands. The position of this new band is dependent on the electron affinity (EA) of the acceptor molecules, and the intensity of this band increases with the amount of adsorbed acceptor molecules. A linear relationship between the vmax. of the new band and EA was observed. The value of the ionization potential of the polyenes estimated from such linear relationship agrees satisfactorily with the value obtained by other methods. It has been concluded that the polyenes behave as electron donor and first form molecular charge-transfer complexes (of type [polyene . I2] with iodine) with electron acceptors, these finally dissociating to yield ionic complexes (of type [polyene . I+] with iodine).
Mallik, B; Jain, K M; Misra, T N
Electrostatic complexation of linear polyelectrolytes with soft spherical nanoparticles
We use Langevin molecular dynamics simulations to study the complexation of a linear polyelectrolyte (LPE) chain with an oppositely charged soft nanoparticle, modeled by a spherical polyelectrolyte brush (SPB). By changing core radius of the SPB and length of polyelectrolyte (GPE) chains grafted at it, a structural transition from a charged, LPE-covered sphere via a softer nanobrush toward a star-like polyelectrolyte is identified. As a result, the LPE chain develops various wrapping conformations around the SPB. Our systematic analysis reveals all relevant conformational binding modes for the polyelectrolyte-nanoparticle complex.
Cao, Qianqian; Bachmann, Michael
Near consensus complex linear and nonlinear social networks
Some of the nodes of complex social networks may support for a given proposal, while the rest of the nodes may be against the given proposal. Even though all the nodes support for or are against the given proposal, the decision certitudes of individual nodes may be different. In this case, the steady state values of the decision certitudes of the majority of the nodes are either higher than or lower than a threshold value. Deriving the near consensus property is a key to the analysis of the behaviors of complex social networks. So far, no result on the behaviors of the complex social networks satisfying the near consensus property has been reported. Hence, it is useful to extend the definition of the exact consensus property to that of a near consensus property and investigate the behaviors of the complex social networks satisfying the near consensus property. This paper extends the definition of exact consensus complex social networks to that of near consensus complex social networks. For complex linear social networks, this paper investigates the relationships among the vectors representing the steady state values of the decision certitudes of the nodes, the influence weight matrix and the set of vectors representing the initial state values of the decision certitudes of the nodes under a given near consensus specification. The above analysis is based on the Eigen theory. For complex nonlinear social networks with certain types of nonlinearities, the relationship between the influence weight matrix and the vectors representing the steady state values of the decision certitudes of the nodes is studied. When a complex nonlinear social network does not achieve the exact consensus property, the optimal near consensus condition that the complex social network can achieve is derived. This problem is formulated as an optimization problem. The total number of nodes that the decision certitudes of the nodes are either higher than or lower than a threshold value is maximized subject to the corresponding near consensus specification. The optimization problem is a nonsmooth optimization problem. The nonsmooth constraints are first approximated by smooth constraints. Then, the approximated optimization problem is solved via a conventional smooth optimization approach. Computer numerical simulation results as well as the comparisons of the behaviors of complex nonlinear social networks to those of the complex linear social networks are presented. The obtained results demonstrate that some complex social networks can satisfy the near consensus property but not the exact consensus property. Also, the conditions for the near consensus property are dependent on the types of nonlinearities, the influence weight matrix and the vectors representing the initial state values of the decision certitudes of the nodes.
Ling, Bingo Wing-Kuen; Ho, Charlotte Yuk-Fan; Wang, Lidong; Teo, Kok-Lay; Tse, Chi K.; Dai, Qingyun
The integration host factor-DNA complex upstream of the early promoter of bacteriophage Mu is functionally symmetric.
Inversion of the ihf site in the promoter region of the early promoter of bacteriophage Mu did not influence the integration host factor (IHF)-mediated functions. IHF bound to this inverted site could counteract H-NS-mediated repression, directly activate transcription, and support lytic growth of bacteriophage Mu. This implies that the IHF heterodimer and its asymmetrical binding site form a functionally symmetrical complex. PMID:9139933
van Ulsen, P; Hillebrand, M; Zulianello, L; van de Putte, P; Goosen, N
Trellis complexity bounds for decoding linear block codes
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: If a trellis is optimum with respect to this partial ordering, if has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.
Kiely, A. B.; Dolinar, S.; Ekroot, L.; Mceliece, R. J.; Lin, W.
Branched-linear polyion complexes investigated by Monte Carlo simulations.
Complexes formed by one charged and branched copolymer with an oppositely charged and linear polyion have been investigated by Monte Carlo simulations. A coarse-grained description has been used, in which the main chain of the branched polyion and the linear polyion possess the same absolute charge and charge density. The spatial extension and other structural properties, such as bond-angle orientational correlation function, asphericity, and scaling analysis of formed complexes, at varying branching density and side-chain length of the branched polyion, have been explored. In particular, the balance between cohesive Coulomb attraction and side-chain repulsions resulted in two main structures of a polyion complex. These structures are (i) a globular polyion core surrounded by side chains appearing at low branching density and (ii) an extended polyion core with side chains still being expelled at high branching density. The globule-to-extended transition occurred at a crossover branching density being practically independent of the side chain length. PMID:24999910
Angelescu, Daniel G; Linse, Per
Metal-metal multiple bonding in C3-symmetric bimetallic complexes of the first row transition metals.
Metal-metal multiple bonds have been an intense area of focus in inorganic chemistry for many decades as a result of their fundamentally interesting bonding properties, as well as their potential applications in multielectron transfer and small molecule activation processes. Much of what is known in this field revolves around 2nd and 3rd row transition metals, with fundamental knowledge lacking in the area of bonds between elements of the first transition series. The smaller size and tendency of first row ions to adopt high-spin electron configurations weaken metal-metal interactions and serve to complicate the interpretation of the electronic structure and bonding in bimetallic species containing first row transition metals. Furthermore, traditional tetragonal "paddlewheel" complexes dominate the metal-metal multiple bond literature, and only recently have researchers begun to take advantage of the weaker ligand field in three-fold symmetric bimetallic complexes to encourage more favourable metal-metal bonding interactions. In the past 5 years, several research groups have exploited three-fold symmetric frameworks to investigate new trends in metal-metal bonding involving the first row transition metals. This feature article serves to highlight recent achievements in this area and to use C3-symmetric systems as a model to better understand the fundamental aspects of multiple bonds featuring first row transition metals. PMID:24413088
Krogman, Jeremy P; Thomas, Christine M
Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations
S. Ali; F. M. Mahomed; Asghar Qadir
Flexible, linear, tetranuclear palladium complexes supported by tetraphosphine ligands with electron-withdrawing groups.
A linearly ordered tetraphosphine containing electron-withdrawing substituent groups on the outer phosphorus atoms, meso-bis[{di(3,5-difluorophenyl)phosphinomethyl}phenylphosphino]methane (dpmppmF2), was prepared and reacted with [Pd2(RNC)6](PF6)2 and Pd(dba)2 to afford tetranuclear palladium complexes, [Pd4(?-dpmppmF2)2(RNC)3](PF6)2 (R = 2,6-xylyl (Xyl) (1), 2,4,6-mesityl (2), 2,6-diisopropylphenyl (3) and tert-butyl (4)), which involve an asymmetric {(RNC)Pd4(CNR)2}(2+) core supported by two dpmppmF2 ligands in anti-arrangement. Each terminal of the Pd4 chain was capped by terminal isocyanide and a semi-bridging RNC is introduced into one terminal Pd site. Mechanistic investigation suggested that the dipalladium(I) complex, [Pd2(?-dpmppmF2)2(RNC)2](PF6)2 (R = Xyl (6)), was a key intermediate to trap Pd(0) species by the uncoordinated outer phosphine pendants with electron-withdrawing groups. Variable-temperature UV-vis and (31)P{(1)H}, (1)H NMR spectroscopic studies demonstrated that the tetrapalladium complexes are quite fluxional in the solution state at high temperature (>20 �C) relating to a symmetric structure of [Pd4(?-dpmppmF2)2(RNC)2](PF6)2, and the asymmetric solid state structures are retained even in the solution at low temperature (<-60 �C). Theoretical calculations with DFT methods on the asymmetric (R = Xyl (1)) and symmetric (R = Xyl (1')) structures suggested that contribution of Pd(0)?Pd(I)-Pd(0)-Pd(I) with 60 cluster valence electrons (CVEs) would be dominant in 1, while the symmetric structure of 1' can be recognized as Pd(I)-Pd(0)-Pd(0)-Pd(I) with 58 CVEs. The new tetraphosphine dpmppmF2 was proven very effective in organizing dynamically flexible tetrapalladium chains. PMID:23880773
Tanase, Tomoaki; Hatada, Satoko; Mochizuki, Ayaka; Nakamae, Kanako; Kure, Bunsho; Nakajima, Takayuki
Simple Linear Inverse for Complex Sources in Early Warning
In this project we aim to determine a foreshock/mainshock pair in real time. That is, we are trying to determine the timing and amplitudes of events in a complex sequence (e.g. foreshock/mainshock pair) in an ongoing earthquake. We are assuming random phase in seismograms so that energy envelopes add linearly which provides the opportunity to pose the problem as a linear least squares inverse problem. We are working on a methodology to solve the least squares problem in real time. The advantage is that the inverse problem can be regularized (unlike traditional deconvolution). We parameterize earthquakes as moments in time windows. Then the problem becomes linear as the determination of the amplitude of the moment in each time window. We first construct the Green's functions for the energy envelopes derived from the predicted envelopes of channels of ground motion of the Virtual Seismologist (VS) (Cua, G. and Heaton, T. 2007). Then, these Green's functions are deconvolved (in a generalized way) from the energy envelopes of seismic records using a damped least-squares inversion in order to determine the amplitude of the moment in each time window. There is a positivity constraint that the amplitude of the moments be positive everywhere. Because the VS predicted envelopes are defined for earthquakes of magnitude 6.5 and below, this technique is not used for very large events.
Karakus, G.; Heaton, T. H.
On complexity of trellis structure of linear block codes
The trellis structure of linear block codes (LBCs) is discussed. The state and branch complexities of a trellis diagram (TD) for a LBC is investigated. The TD with the minimum number of states is said to be minimal. The branch complexity of a minimal TD for a LBC is expressed in terms of the dimensions of specific subcodes of the given code. Then upper and lower bounds are derived on the number of states of a minimal TD for a LBC, and it is shown that a cyclic (or shortened cyclic) code is the worst in terms of the state complexity among the LBCs of the same length and dimension. Furthermore, it is shown that the structural complexity of a minimal TD for a LBC depends on the order of its bit positions. This fact suggests that an appropriate permutation of the bit positions of a code may result in an equivalent code with a much simpler minimal TD. Boolean polynomial representation of codewords of a LBC is also considered. This representation helps in study of the trellis structure of the code. Boolean polynomial representation of a code is applied to construct its minimal TD. Particularly, the construction of minimal trellises for Reed-Muller codes and the extended and permuted binary primitive BCH codes which contain Reed-Muller as subcodes is emphasized. Finally, the structural complexity of minimal trellises for the extended and permuted, and double-error-correcting BCH codes is analyzed and presented. It is shown that these codes have relatively simple trellis structure and hence can be decoded with the Viterbi decoding algorithm.
Lin, Shu
A C2-symmetric, basic Fe(III) carboxylate complex derived from a novel triptycene-based chelating carboxylate ligand.
A triptycene-based bis(benzoxazole) diacid ligand H(2)L2(Ph4) bearing sterically encumbering groups was synthesized. Treatment of H(2)L2(Ph4) with Fe(OTf)(3) afforded a C(2)-symmetric trinuclear iron(III) complex, [NaFe(3)(L2(Ph4))(2)(?(3)-O)(?-O(2)CCPh(3))(2)(H(2)O)(3)](OTf)(2) (8). The triiron core of this complex adopts the well known "basic iron acetate" structure where the heteroleptic carboxylates, comprising two Ph(3)CCO(2)(-) and two (L2(Ph4))(2-) ligands, donate the six carboxylate bridges. The (L2(Ph4))(2-) ligand undergoes only minor conformational changes upon formation of the complex. PMID:22751622
Li, Yang; Wilson, Justin J; Do, Loi H; Apfel, Ulf-Peter; Lippard, Stephen J
Linear Viscoelasticity and Swelling of Polyelectrolyte Complex Coacervates
The addition of near equimolar amounts of poly(diallyldimethylammonium chloride) to poly(isobutylene-alt-maleate sodium), results in formation of a polyelectrolyte complex coacervate. Zeta-potential titrations conclude that these PE-complexes are nearly charge-neutral. Swelling and rheological properties are studied at different salt concentrations in the surrounding solution. The enhanced swelling observed at high salt concentration suggests the system behaves like a polyampholyte gel, and weaker swelling at very low salt concentrations implies polyelectrolyte gel behavior. Linear viscoelastic oscillatory shear measurements indicate that the coacervates are viscoelastic liquids and that increasing ionic strength of the medium weakens the electrostatic interactions between charged units, lowering the relaxation time and viscosity. We use the time-salt superposition idea recently proposed by Spruijt, et al., allowing us to construct master curves for these soft materials. Similar swelling properties observed when varying molecular weights. Rheological measurements reveal that PE-complexes with increasing molecular weight polyelectrolytes form a network with higher crosslink density, suggesting time-molecular weight superposition idea.
Hamad, Fawzi; Colby, Ralph
Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations
FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.
Dunham, R. S.
Data bank homology search algorithm with linear computation complexity.
A new algorithm for data bank homology search is proposed. The principal advantages of the new algorithm are: (i) linear computation complexity; (ii) low memory requirements; and (iii) high sensitivity to the presence of local region homology. The algorithm first calculates indicative matrices of k-tuple 'realization' in the query sequence and then searches for an appropriate number of matching k-tuples within a narrow range in database sequences. It does not require k-tuple coordinates tabulation and in-memory placement for database sequences. The algorithm is implemented in a program for execution on PC-compatible computers and tested on PIR and GenBank databases with good results. A few modifications designed to improve the selectivity are also discussed. As an application example, the search for homology of the mouse homeotic protein HOX 3.1 is given. PMID:7922689
Strelets, V B; Ptitsyn, A A; Milanesi, L; Lim, H A
Non-centro-symmetric electron diffraction pattern of icosahedral quasicrystal induced by combination of linear phason strain and curvature of Ewald sphere.
Non-centro-symmetric characteristics are observed in the experimental electron diffraction patterns (EDPs) from the icosahedral quasicrystalline precipitates in ZrAlNiCuNb alloys. Different from the well-known breaking of the Friedel's law, where a strong dynamical effect will reveal in EDPs the concealed non-centro-symmetry originated from the crystal structures themselves, the current results can be interpreted in terms of changes in deviation parameters due to a delicate combination of the linear phason strain characteristic of quasicrystals and the curvature of Ewald sphere. After taking this effect into consideration, the corresponding simulated EDPs fit quite well to the experimental data. PMID:24041584
Xiong, Dongxia; Lu, Lu; Wang, Jianbo; Zhao, Dongshan; Sun, Yufeng
Synthesis and spectroscopic investigations of iron(III) complexes with chlorides and dianionic, symmetrically halogen substituted phthalocyanines as ligands
The synthesis of iron(III) complexes of general formula FeCl(R-pc), where R-pc are dianionic, symmetrically halogen substituted phthalocyanines at the positions 2,9,16,23 or 1,8,15,22, from the corresponding amino substituted derivatives is described (R=Cl, Br, I). The complexes are characterized by UV-visible and infrared spectra, powder X-ray diffraction and magnetic susceptibility measurements. The effect of substituents at the periphery and the basicity of the solvents used on the electronic spectra are discussed. The Q band of the electronic spectra for symmetrically halogen substituted derivatives are redshifted and the substituents at 2,9,16,23- positions are more effective in redshifting the Q bands than those at 1,8,15,22-positions. Depending upon the basicity of the solvents, the ligand-to-metal charge transfer (LMCT) transitions on Q band envelop shift to the higher energy region in the order of pyridine>DMF>DMSO. The infrared absorption signals for C?H and metal-ligand vibrations appear to be sharper for 1,8,15,22 substituted derivatives than for 2,9,16,23 substituted ones.
Somashekarappa, M. P.; Keshavayya, J.; Sherigara, B. S.
The TGGCA-binding protein: a eukaryotic nuclear protein recognizing a symmetrical sequence on double-stranded linear DNA.
Low salt extracts of chicken oviduct nuclei contain a DNA binding protein with high affinity for specific DNA sequences in the flanking regions of the chicken lysozyme gene. Two of the three binding sites found within a total of 11 kb upstream from the promoter are located only 92 bp apart from each other. Upon comparison of the DNA binding sites, the symmetrical consensus sequence 5'- TGGCANNNTGCCA -3' can be deduced as the protein recognition site. This sequence is the central part of 23 to 25 base pairs protected by the DNA binding protein from DNAase I digestion. A homologous binding activity can be detected in nuclei from several chicken tissues and from mouse liver. Images
Borgmeyer, U; Nowock, J; Sippel, A E
Development of virus-like particle technology from small highly symmetric to large complex virus-like particle structures.
Virus-like particle (VLP) technology is a promising approach for the construction of novel vaccines, diagnostic tools, and gene therapy vectors. Initially, VLPs were primarily derived from non-enveloped icosahedral or helical viruses and proved to be viable vaccine candidates due to their effective presentation of epitopes in a native conformation. VLP technology has also been used to prepare chimeric VLPs decorated with genetically fused or chemically coupled epitope stretches selected from immunologically defined target proteins. However, structural constraints associated with the rigid geometrical architecture of icosahedral or helical VLPs pose challenges for the expression and presentation of large epitopes. Complex VLPs derived from non-symmetric enveloped viruses are increasingly being used to incorporate large epitopes and even full-length foreign proteins. Pleomorphic VLPs derived from influenza or other enveloped viruses can accommodate multiple full-length and/or chimeric proteins that can be rationally designed for multifunctional purposes, including multivalent vaccines. Therefore, a second generation of VLP carriers is represented by complex particles reconstructed from natural or chimeric structural proteins derived from complex enveloped viruses. Further development of safe and efficient VLP nanotechnology may require a rational combination of both approaches. PMID:23594863
Pushko, Peter; Pumpens, Paul; Grens, Elmars
Mechanistic Investigation into the Cleavage of a Phosphomonoester Mediated by a Symmetrical Oxyimine-Based Macrocyclic Zinc(II) Complex.
Density functional calculations are utilized to explore the hydrolysis mechanisms of the phosphomonoester 4-nitrophenyl phosphate catalyzed by a symmetrical zinc(II) complex. The formation process and properties of the active catalyst are verified. Eight plausible mechanisms are proposed and categorized into three groups. All of the proposed mechanisms, except for Mechanism 7 (see text), are SN 2-type addition-substitution reaction pathways. Nucleophilic attack at the ortho position occurs in Mechanism 7 with a relatively high reaction barrier. Mechanisms 1 and 2 in the monocatalyst model, Mechanisms 5 to 7 in the sandwich-dual-catalyst model, as well as the nucleophilic addition-substitution step in Mechanism 8 are concerted reaction pathways, whereas the rest appear to occur in a stepwise manner. Meanwhile, the explicit solvent model is utilized to consider direct hydrogen bonds and solvation interactions and these results indicate that the added water molecule is involved in the hydrolysis process, but does not change the mechanisms significantly. Mechanism 8, with the lowest reaction barrier, is the most favored reaction pathway of the eight proposed mechanisms, although Mechanisms 1, 4, and 6 are in competition with Mechanism 8. In consideration of the zinc(II) complex concentration, Mechanism 1 is only the predominant reaction pathway at a low zinc(II) complex concentration; Mechanisms 4 and 6 tend to be more competitive with increasing concentration of the zinc(II) complexes, and Mechanism 8 is favored at high zinc(II) complex concentrations. Our calculated results are consistent with, and can be used to systematically interpret, experimental observations. More importantly, insightful suggestions are made regarding the catalyst design and selection of the reaction environment. PMID:24692392
Zhang, Xuepeng; Xu, Xianyan; Xu, Huiying; Zhang, Xiting; Phillips, David Lee; Zhao, Cunyuan
Radical localization in a series of symmetric Ni(II) complexes with oxidized salen ligands.
Square-planar nickel(II) complexes of salen ligands, N,N'-bis(3-tert-butyl-(5R)-salicylidene)-1,2-cyclohexanediamine), in which R=tert-butyl (1), OMe (2), and NMe(2) (3), were prepared and the electronic structure of the one-electron-oxidized species [1-3](+�) was investigated in solution. Cyclic voltammograms of [1-3] showed two quasi-reversible redox waves that were assigned to the oxidation of the phenolate moieties to phenoxyl radicals. From the difference between the first and second redox potentials, the trend of electronic delocalization 1(+�) >2(+�) >3(+�) was obtained. The cations [1-3](+�) exhibited isotropic g tensors of 2.045, 2.023, and 2.005, respectively, reflecting a lower metal character of the singly occupied molecular orbital (SOMO) for systems that involve strongly electron-donating substituents. Pulsed-EPR spectroscopy showed a single population of equivalent imino nitrogen atoms for 1(+�), whereas two distinct populations were observed for 2(+�). The resonance Raman spectra of 2(+�) and 3(+�) displayed the ?(8a) band of the phenoxyl radicals at 1612 cm(-1), as well as the ?(8a) bands of the phenolates. In contrast, the Raman spectrum of 1(+�) exhibited the ?(8a) band at 1602 cm(-1), without any evidence of the phenolate peak. Previous work showed an intense near-infrared (NIR) electronic transition for 1(+�) (??(1/2) =660 cm(-1), ?=21,700 M(-1) cm(-1)), indicating that the electron hole is fully delocalized over the ligand. The broader and moderately intense NIR transition of 2(+�) (??(1/2) =1250 cm(-1) , ?=12,800 M(-1) cm(-1)) suggests a certain degree of ligand-radical localization, whereas the very broad NIR transition of 3(+�) (??(1/2) =8630 cm(-1), ?=2550 M(-1) cm(-1)) indicates significant localization of the ligand radical on a single ring. Therefore, 1(+�) is a Class III mixed-valence complex, 2(+�) is Class II/III borderline complex, and 3(+�) is a Class II complex according to the Robin-Day classification method. By employing the Coulomb-attenuated method (CAM-B3LYP) we were able to predict the electron-hole localization and NIR transitions in the series, and show that the energy match between the redox-active ligand and the metal d orbitals is crucial for delocalization of the radical SOMO. PMID:22997000
Chiang, Linus; Kochem, Am�lie; Jarjayes, Olivier; Dunn, Tim J; Vezin, Herv�; Sakaguchi, Miyuki; Ogura, Takashi; Orio, Maylis; Shimazaki, Yuichi; Thomas, Fabrice; Storr, Tim
Linear Transceiver Design for Interference Alignment: Complexity and Computation.
Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work 1) suggests th...
M. Razaviyayn M. S. Boroujeni Z. Luo
Complex response of a food-web module to symmetric and asymmetric migration between several patches.
We investigate the stability of a diamond food-web module on two patches coupled by migration in terms of robustness, which is the proportion of surviving species in the system. The parameters are chosen such that the dynamics on an isolated patch have a periodic attractor with all four species present as well as an attractor where the prey that is preferred by the top predator dies out. The migration rate and the migration bias between the two patches are varied, resulting in a surprisingly complex relation between migration rate and robustness. In particular, while the degree of synchronization usually increases with increasing migration rate, robustness can increase as well as decrease. We find that the main results also hold when the number of patches is larger. Different types of connectivity patterns between patches can lead to different extent of migration bias if the migration rate out of each patch is the same. PMID:24641820
Ristl, Konstantin; Plitzko, Sebastian J; Drossel, Barbara
Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - I: Ordinary Differential Equations
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of two real ordinary differential equations. The transformations that map a system of two nonlinear ordinary differential equations into systems of linear ordinary differential equations are obtained from complex transformations.
Glyphosate and ATP binding by mononuclear Zn(II) complexes with non-symmetric ditopic polyamine ligands.
Binding of Zn(II) by the ditopic ligands L1py, L2py and L1para, composed of a cyclam unit linked to the linear polyamines 1,4,8,11-tetraazaundecane (L1py and L2para) and 1,4,7-triazaheptane (L2py) via a 2,6-dimethylpyridinyl (L1py and L2py) or a 1,4-dimethylbenzyl spacer (L2para), has been analyzed by means of potentiometric and (1)H and (13)C NMR measurements. All ligands form stable mononuclear Zn(II) complexes in a wide pH range, featuring the metal ion bound to the macrocyclic unit. The open-chain polyamine unit can easily bind several protons in aqueous solution affording protonated metal complexes at neutral and acidic pH values. These complexes behave as bifunctional receptors for the anionic substrates N-(phosphonomethyl)glycine (glyphosate or PMG) and ATP. Potentiometric, (1)H and (31)P NMR measurements show that the Zn(II) complex with L1py is the better receptor for both substrates, thanks to the simultaneous presence of a pyridine linker functionalized at its 2,6 positions and of a flexible linear tetraamine chain. In fact, these structural features allow a stronger interaction of PMG and ATP with both the protonated tetraamine moiety and the Zn(II)-cyclam core. PMID:22785253
Pouessel, Jacky; Le Bris, Nathalie; Bencini, Andrea; Giorgi, Claudia; Valtancoli, Barbara; Tripier, Rapha�l
A generalized weighted linear predictor frequency estimation approach for a complex sinusoid
Based on linear prediction and weighted least squares, three simple iterative algorithms for frequency estima- tion of a complex sinusoid in additive white noise are devised. The proposed approach, which utilizes the first-order as well as higher order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor
Hing-cheung So; Frankie K. W. Chan
Noncommutative Symmetric Functions Vi: Free Quasi-Symmetric Functions and Related Algebras
This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: per- mutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions). Free quasi- symmetric functions provide a kind of noncommutative Frobenius characteristic for a certain category of
G�rard Duchamp; Florent Hivert; Jean-yves Thibon
Stability and complexity of small random linear systems
We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.
Hastings, Harold
Magnetic blocking in a linear iron(I) complex.
Single-molecule magnets that contain one spin centre may represent the smallest possible unit for spin-based computational devices. Such applications, however, require the realization of molecules with a substantial energy barrier for spin inversion, achieved through a large axial magnetic anisotropy. Recently, significant progress has been made in this regard by using lanthanide centres such as terbium(III) and dysprosium(III), whose anisotropy can lead to extremely high relaxation barriers. We contend that similar effects should be achievable with transition metals by maintaining a low coordination number to restrict the magnitude of the d-orbital ligand-field splitting energy (which tends to hinder the development of large anisotropies). Herein we report the first two-coordinate complex of iron(I), [Fe(C(SiMe3)3)2](-), for which alternating current magnetic susceptibility measurements reveal slow magnetic relaxation below 29�K in a zero applied direct-current field. This S�=� complex exhibits an effective spin-reversal barrier of Ueff�=�226(4)�cm(-1), the largest yet observed for a single-molecule magnet based on a transition metal, and displays magnetic blocking below 4.5�K. PMID:23787747
Zadrozny, Joseph M; Xiao, Dianne J; Atanasov, Mihail; Long, Gary J; Grandjean, Fernande; Neese, Frank; Long, Jeffrey R
Applications of the Category of Linear Complexes of Tilting Modules Associated with the Category
We use the category of linear complexes of tilting modules for the BGG category , associated with a semi-simple complex finite-dimensional Lie algebra , to reprove in purely algebraic way several known results about obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category\\u000a .
Volodymyr Mazorchuk
Symmetric textures
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ramond, P. (Florida Univ., Gainesville, FL (United States). Dept. of Physics)
Ramond, P. [Florida Univ., Gainesville, FL (United States). Dept. of Physics
Isotope effects in linear dihydrogen bonded complexes containing LiH
An ab initio study of linear dihydrogen-bonded complexes containing LiH (acting as a proton acceptor) was undertaken. The complexes studied were LiH...HF, LiH...HCN, and LiH...HCCH. Equilibrium geometries and harmonic vibrational frequencies were computed at various levels of theory using a 6-31++G(d,p) basis set. It was found that the LiH...HF complex was not stable at all levels of theory. The relative
Sean A. C. McDowell; Toni S. Forde
A far-infrared study and investigation of the difference between the asymmetric and symmetric POO stretching frequencies in metal diphosphonate complexes.
Lanthanide complexes of P,P'-di(2-ethylhexyl) methanediphosphonic acid, H2DEH[MDP], were prepared and investigated by infrared spectroscopy. Qualitative information about the nature of the phosphonate binding in the complexes was obtained by measuring the asymmetric and symmetric POO- stretching frequencies of the ligand. These vibrational modes appear at lower energy in the complexes than in the sodium salt. This indicates symmetrical coordination of the phosphonate groups through chelate and/or bridging interactions. The frequency difference between the POO- stretching bands {Delta}{nu} becomes smaller as the ionic potential e/r of the metal ion increases. The correlation is valid when both oxygen atoms are involved in the bonding and no other absorption bands interfere with the POO- vibrations. The origin of this empirical correlation is the change in the P---O bond order which arises from a change in the strength of the metal-diphosphonate interaction. The far-infrared spectra of the lanthanide complexes, an 54Fe-labelled compound, and the sodium salt of H2DEH[MDP] were measured to provide insight into the nature of the metal-ligand interaction. The appearance of metal-oxygen stretching bands in the iron compound indicates that the iron-diphosphonate interaction has a substantial covalent component whereas the absence of metal-oxygen stretching bands in the lanthanide complexes indicates the binding is predominantly ionic.
Herlinger, A. W.; Ferraro, J. R.; Garcia, J. A.; Chiarizia, R.; Chemistry; Loyola Univ.
Complexity Reduction and Fast Algorithm for 2-D Integer Discrete Wavelet Transform Using Symmetric Mask-Based Scheme
Wavelet coding has been shown to be better than discrete cosine transform (DCT) in image\\/video processing. Moreover, it has the feature of scalability, which is involved in modern video standards. This work presents novel algorithms, namely 2-D symmetric mask-based discrete wavelet transform (SMDWT), to improve the critical issue of the 2-D lifting-based discrete wavelet transform (LDWT), and then obtains the
Chih-Hsien Hsia; Jing-Ming Guo; Jen-Shiun Chiang
Second-order non-linear optical properties of Fe(SALEN) complexes
The second-order non-linear (NLO) properties of the set of compounds iron (III),[N,N?-ethylenebis(salicylaldiminato)(pyridyl)(X), [Fe(SALEN)(pyridyl)X], where X = F?, Cl?, Br?, I, N3?, NCS? were examined. Complexes where X is a halide or thiocyanate exhibited weak SHG intensities (0.05�0.2 � urea). Considerable enhancement of SHG intensity was demonstrated by the azide complex (X = N3?), which has a powder SHG efficiency twice
William Chiang; Donna Vanengen; Mark E. Thompson
Nonlocal \\cal{PT} -symmetric potentials
The factorization approach for complex Hamiltonians has been used to obtain the exactly solvable nonlocal variant of \\cal {PT} -symmetric local potentials. The formalism is used to obtain exact eigenvalues and eigenfunctions of the nonlocal \\cal {PT} -symmetric Scarf potential.
Roy, B.; Roychoudhury, R.
Synthesis, spectral characterization, DNA binding ability and antibacterial screening of copper(II) complexes of symmetrical NOON tetradentate Schiff bases bearing different bridges
A novel series of four copper(II) complexes were synthesized by thermal reaction of copper acetate salt with symmetrical tetradentate Schiff bases, N,N'bis(o-vanillin)4,5-dimethyl-l,2-phenylenediamine (H2L1), N,N'bis(salicylaldehyde)4,5-dimethyl-1,2-phenylenediamine (H2L2), N,N'bis(o-vanillin)4,5-dichloro-1,2-phenylenediamine (H2L3) and N,N'bis(salicylaldehyde)4,5-dichloro-1,2-phenylenediamine (H2L4), respectively. All the new synthesized complexes were characterized by using of microanalysis, FT-IR, UV-Vis, magnetic measurements, ESR, and conductance measurements, respectively. The data revealed that all the Schiff bases (H2L1-4) coordinate in their deprotonated forms and behave as tetradentate NOON coordinated ligands. Moreover, their copper(II) complexes have square planar geometry with general formula [CuL1-4]. The binding of the complexes with calf thymus DNA (CT-DNA) was investigated by UV-Vis spectrophotometry, fluorescence quenching and viscosity measurements. The results indicated that the complexes bind to CT-DNA through an intercalative mode. From the biological activity view, the copper(II) complexes and their parent ligands were screened for their in vitro antibacterial activity against the bacterial species Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli and Pseudomonas aeruginosai by well diffusion method. The complexes showed an increased activity in comparison to some standard drugs.
Bahaffi, Saleh O.; Abdel Aziz, Ayman A.; El-Naggar, Maher M.
On the Diversity of Non-Linear Transient Dynamics in Several Types of Complex Networks
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient dynamics obtained in undirected and unweighted complex networks as a consequence of self-avoiding random walks. The diversity of walks starting at a specific node $i$ is quantified in
Luciano da Fontoura Costa
Synchronization of Non-Linear Random Walk Dynamics in Complex Network
This work addresses synchronization in transient, non-linear stochastic dynamics corresponding to accesses performed by self-avoiding walks originating at each node of a complex network. More specifically, the synchronizability of accesses incoming from other nodes has been considered and quantified in terms of the entropy of the mean periods of access, being closely associated to the efficiency of access delivery to
On a refinement of the regularity theorem for solutions to the characteristic initial boundary value problem for linear symmetric hyperbolic systems
We study the initial boundary value problem for symmetric hyperbolic\\u000asystems with characteristic boundary. The regularity of solutions\\u000ais shown in a refined form, taking into account of the break\\u000adown of the full regularity.
Yasushi Shizuta; Yumi Tanaka
An ab initio study of linear dihydrogen-bonded complexes containing LiH (acting as a proton acceptor) was undertaken. The complexes studied were LiH&cellip;HF, LiH&cellip;HCN, and LiH&cellip;HCCH. Equilibrium geometries and harmonic vibrational frequencies were computed at various levels of theory using a 6-31++G(d,p) basis set. It was found that the LiH&cellip;HF complex was not stable at all levels of theory. The relative
Observation of defect states in PT-symmetric optical lattices.
We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics. PMID:23767725
Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; N�ger, Jakob; Onishchukov, Georgy; Christodoulides, Demetrios N; Peschel, Ulf
Symmetrical P4 cleavage at cobalt half sandwich complexes [(?5-C5H5)Co(L)] (L = CO, NHC)--a computational case study on the mechanism of symmetrical P4 degradation to P2 ligands.
A full theoretical mechanistic investigation on the symmetrical cleavage of P4 at the active complex fragments [(?(5)-C5H5)Co(L)] (L = CO, (i)Pr2Im; (i)Pr2Im = 1,3-di-iso-propylimidazolin-2-ylidene), which results in the formation of the complex [{(?(5)-C5H5)Co}2(?,?(2:2)-P2)2] 9, is presented. The overall reaction mechanism is a complex, multistep process. Rate-determining steps of the reaction sequence are two consecutive dissociations of the co-ligands L, which induce the decisive structural rearrangements of the P4 unit. The choice of the co-ligand L ( = CO, (i)Pr2Im) influences the kinetic barrier as well as the energy balance of the overall reaction path significantly. The calculations further reveal a strong influence of the entropic effect on the overall reaction. As a consequence, the energy balance of the overall formation of 9 starting from [(?(5)-C5H5)Co(CO)] precursors is almost thermoneutral and has to overcome high kinetic barriers, whereas the reaction starting from [(?(5)-C5H5)Co((i)Pr2Im)] precursors is exothermic, featuring lower transition barriers with stabilized intermediates. From the direct comparison of both reaction coordinates it seems that the entropic effect of the co-ligands is even stronger than their electronic influence, as for both investigated systems the reactions' energy profiles are almost identical up to intermediate [{(?(5)-C5H5)Co(L)}2(?,?(2:2)-P4)] 5 (L = CO, (i)Pr2Im). After the formation of 5, the first CO dissociation step renders the reaction endothermic for L = CO, whereas in the case of (i)Pr2Im dissociation the reaction progresses exothermically. Energy decomposition analysis and fragment analysis provide a picture of the bonding mechanisms between the metal complex fragments and P4 in the case of the most significant intermediates and the final product. PMID:23515870
Zarzycki, Bartosz; Bickelhaupt, F Matthias; Radius, Udo
An enzyme-centric approach for modelling non-linear biological complexity
Background The current challenge of Systems Biology is to integrate high throughput data sets for simulating the complexity of biological networks, exploit the evolution of nature-designed networks that maintain the robustness of a biological system, and thereby generate novel, experimentally testable hypotheses. In order to simulate non-linear biological complexities, we have previously developed an Enzyme-Centric mechanistic modeling approach and validated it using metabolic network in E. coli. The idea is to use prior knowledge of catalytic and regulatory mechanisms of each enzyme within the metabolic network to build a dynamic model for investigating the network level regulation and thus understand the nature design principle behind the network. Results In this paper, we further demonstrate the application of complex enzyme catalytic and regulatory modules to simulate nonlinear network regulatory patterns vs. simple linear conversion model. We learned and validated that it is essential to incorporate prior knowledge from the literature to simulate non-linear biological complexities. The network expandability is demonstrated and validated with the complex amino acid biosynthetic network with multi-regulations. Also, we demonstrated the compatibility of mechanistic models within close species. Furthermore, the eukaryotic protein factory model for insuring steady mRNA production is simulated and the coupling of RNA transcription and splicing is validated by both mathematical simulation and experimental analysis. Conclusion We demonstrated the importance of modeling complex enzyme catalytic and regulatory mechanisms to further understand nonlinear network regulatory patterns. The simulations presented in this paper reveal how a living system maintains homeostasis and its robustness to continue functioning while facing environmental stresses or genetic mutations.
A self-consistent three-wave coupling model with complex linear frequencies
A three-wave coupling model with complex linear frequencies is investigated for the nonlinear interaction in a triad that has linearly unstable and stable modes. Time scales associated with linear and nonlinear physics are identified and compared with features of the frequency spectrum. From appropriate time scales, the frequency spectra are well characterized even in the transition to the steady state. The nonlinear time scales that best match spectral features are the nonlinear frequency of the fixed point and a frequency that depends on the amplitude displacement from the fixed point through the large-amplitude Jacobian elliptic solution. Two limited efforts to model the effect of other triads suggest robustness in the single triad results.
Kim, J.-H.; Terry, P. W. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
Multi-cavity complex controller with vector simulator for TESLA technology linear accelerator
A digital control, as the main part of the Low Level RF system, for superconducting cavities of a linear accelerator is presented. The FPGA based controller, supported by MATLAB system, was developed to investigate a novel firmware implementation. The complex control algorithm based on the non-linear system identification is the proposal verified by the preliminary experimental results. The general idea is implemented as the Multi-Cavity Complex Controller (MCC) and is still under development. The FPGA based controller executes procedure according to the prearranged control tables: Feed-Forward, Set-Point and Corrector unit, to fulfill the required cavity performance: driving in the resonance during filling and field stabilization for the flattop range. Adaptive control algorithm is applied for the feed-forward and feedback modes. The vector Simulator table has been introduced for an efficient verification of the FPGA controller structure. Experimental results of the internal simulation, are presented for a cavity representative condition.
Czarski, Tomasz; Pozniak, Krzysztof T.; Romaniuk, Ryszard S.; Szewinski, Jaroslaw
Bayesian model selection in complex linear systems, as illustrated in genetic association studies.
Motivated by examples from genetic association studies, this article considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent a priori information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems. PMID:24350677
Wen, Xiaoquan
Dynamic systems characterized by diversified evolutions are not only more\\u000aflexible, but also more resilient to attacks, failures and changing conditions.\\u000aThis article addresses the quantification of the diversity of non-linear\\u000atransient dynamics obtained in undirected and unweighted complex networks as a\\u000aconsequence of self-avoiding random walks. The diversity of walks starting at a\\u000aspecific node $i$ is quantified in
This work addresses synchronization in transient, non-linear stochastic\\u000adynamics corresponding to accesses performed by self-avoiding walks originating\\u000aat each node of a complex network. More specifically, the synchronizability of\\u000aaccesses incoming from other nodes has been considered and quantified in terms\\u000aof the entropy of the mean periods of access, being closely associated to the\\u000aefficiency of access delivery to
Low-power complex polynomial predistorter circuit in CMOS for RF power amplifier linearization
A chip that implements an analog 5th order complex polynomial for linearization of RF power amplifiers is presented. The chip has been designed in a 0.35�m CMOS process and operates at an IF of 200MHz with signal bandwidths of several MHz. The predistorter core consumes 2mA from a 2.7V supply and 11.5mA including the input and output buffers. Experimental results
Eric Westesson; Lars Sundstr�m
The linear ubiquitin assembly complex (LUBAC) is essential for NLRP3 inflammasome activation.
Linear ubiquitination is a newly discovered posttranslational modification that is currently restricted to a small number of known protein substrates. The linear ubiquitination assembly complex (LUBAC), consisting of HOIL-1L, HOIP, and Sharpin, has been reported to activate NF-?B-mediated transcription in response to receptor signaling by ligating linear ubiquitin chains to Nemo and Rip1. Despite recent advances, the detailed roles of LUBAC in immune cells remain elusive. We demonstrate a novel HOIL-1L function as an essential regulator of the activation of the NLRP3/ASC inflammasome in primary bone marrow-derived macrophages (BMDMs) independently of NF-?B activation. Mechanistically, HOIL-1L is required for assembly of the NLRP3/ASC inflammasome and the linear ubiquitination of ASC, which we identify as a novel LUBAC substrate. Consequently, we find that HOIL-1L(-/-) mice have reduced IL-1? secretion in response to in vivo NLRP3 stimulation and survive lethal challenge with LPS. Together, these data demonstrate that linear ubiquitination is required for NLRP3 inflammasome activation, defining the molecular events of NLRP3 inflammasome activation and expanding the role of LUBAC as an innate immune regulator. Furthermore, our observation is clinically relevant because patients lacking HOIL-1L expression suffer from pyogenic bacterial immunodeficiency, providing a potential new therapeutic target for enhancing inflammation in immunodeficient patients. PMID:24958845
Rodgers, Mary A; Bowman, James W; Fujita, Hiroaki; Orazio, Nicole; Shi, Mude; Liang, Qiming; Amatya, Rina; Kelly, Thomas J; Iwai, Kazuhiro; Ting, Jenny; Jung, Jae U
1. Mono([8]annulene)Uranium(4) half-sandwich complexes, 2. Novel syntheses of symmetrically substituted cyclooctatetetraenes
A reproducible, high-yield synthesis of mono([8]annulene)uranium(4)dichloride (1) is reported, along with the X-ray crystal structural of the bis(pyridine) adduct. Metathesis reactions of the half-sandwich complex 1 with a variety of simple alkyl and alkoxy reagents failed to generate any isolable mono-ring complexes. Reactions of 1 with polydentate, delocalized anions did produce stable derivatives, including mono([8]annulene)uranium(4)bis(acetylacetonate) (4). An X-ray crystal structure of 4 is reported.
Boussie, T.R.
Surface chemistry of the linear chromium chain complex on GaN(0001)
Better understanding about the chemistry of the organometallic chain complexes reacting on the solid surface can foster concepts of nanowire fabrication which are central to the continued advance of the electronic and optoelectronic industries. In this study, the adsorption and thermal reactivity of a trinuclear chromium chain complex, tetrakis (2,2{sup '}-dipyridylamino)chromium(VI) chloride, on the GaN(0001) surface were investigated using x-ray photoelectron spectroscopy, temperature-programmed desorption, and static secondary ion mass spectrometry in order to obtain some insight into the bonding changes involved in the reaction of the linear metal chain complex on the compound semiconductor surface. One of the two terminal Cr-Cl bonds of the complex may be cleaved upon adsorption at 110 K, leading to the formation of the Ga-Cl bonds on the surface, although some complexes remained intact upon adsorption and bonded strongly to the surface. No ligand was dissociated from the chromium chain complex during the adsorption. The Cl-cleaved complex residue preserved its original chemical configuration. Both the Cl-cleaved and the intact complexes in the first layer were stable on the surface in the substrate temperature range between 110 and 260 K. A partial decomposition in which some ligands were dissociated from the adsorbed complex took place before the substrate temperature reaching 400 K. Additional Cr-Cl bonds were disrupted, resulting in a larger population of Ga-Cl bonds on the surface. Further thermal reaction at higher temperatures led to the dominance of the Ga-Cl bonding for the Cl presence on the surface. Surface etching of Ga by the dissociated Cl atoms started at a substrate temperature of {approx}525 K and the etching rate reached its maximum at {approx}590 K.
Lung, C.-H.; Peng, S.-M.; Chang, C.-C. [Department of Chemistry, National Taiwan University, Taipei, Taiwan 10617 (China)
Interactions of an asymmetric amine with a non-C2 symmetric Cu-salen complex: an EPR/ENDOR and HYSCORE investigation.
Single enantiomers of R-/S-methylbenzylamine (MBA) were found to selectively form adducts with the chiral non-C(2) symmetric Cu-salen complex N-(3,5-di-tert-butylsalicylidene)-N'-(salicylidene)-cyclohexane-1,2-diamine copper(II), hereafter labelled [Cu(3)]. The g/A spin Hamiltonian parameters of this Cu(II) complex showed a decrease in symmetry from axial to rhombic upon formation of the [Cu(3)] + MBA adducts. The selectivity in enantiomeric discrimination was found to be only 59 � 5% in favour of the heterochiral R,R'-[Cu(3)] + S-MBA and S,S'-[Cu(3)] + R-MBA adducts. This was directly evidenced by W-band EPR spectroscopy. The observed low selectivity for enantiomer discrimination is primarily attributed to the loss of the bulky tert-butyl groups from the 3,5 positions of [Cu(3)] compared to the parent N,N'-bis(3,5-di-tert-butylsalicylidene)-cyclohexane-1,2-diamine copper(II) ligand (labelled [Cu(1)]). The structure of the [Cu(3)] complex in the presence and absence of coordinating amine was further investigated by analysis of the ligand hyperfine interactions, as revealed through Q-band CW-ENDOR, X-band Davies ENDOR and HYSCORE. (1)H couplings from the -NH(2) group of the amine, observed by ENDOR and HYSCORE, provided direct evidence of amine coordination. PMID:21993696
Caretti, Ignacio; Carter, Emma; Fallis, Ian A; Murphy, Damien M; Van Doorslaer, Sabine
SHARPIN forms a linear ubiquitin ligase complex regulating NF-?B activity and apoptosis
SHARPIN is a ubiquitin-binding and ubiquitin-like domain-containing protein which, when mutated in mice, results in immune system disorders and multiorgan inflammation1,2. Here we report that SHARPIN functions as a novel component of the Linear Ubiquitin Chain Assembly Complex (LUBAC) and that the absence of SHARPIN causes disregulation of NF-?B and apoptotic signalling pathways, explaining the severe phenotypes displayed by chronic proliferative dermatitis in SHARPIN deficient mice. Upon binding to the LUBAC subunit HOIP, SHARPIN stimulates the formation of linear ubiquitin chains in vitro and in vivo. Co-expression of SHARPIN and HOIP promotes linear ubiquitylation of NEMO, an adaptor of the I?B kinases (IKKs) and subsequent activation of NF-?B signalling, while SHARPIN deficiency in mice causes an impaired activation of the IKK complex and NF-?B in B cells, macrophages, and mouse embryonic fibroblasts (MEFs). This effect is further enhanced upon concurrent downregulation of HOIL-1L, another HOIP-binding component of LUBAC. In addition, SHARPIN deficiency leads to rapid cell death upon TNF? stimulation via FADD- and Caspase-8-dependent pathways. SHARPIN thus activates NF-?B and inhibits apoptosis via distinct pathways in vivo.
Ikeda, Fumiyo; Deribe, Yonathan Lissanu; Skanland, Sigrid S.; Stieglitz, Benjamin; Grabbe, Caroline; Franz-Wachtel, Mirita; van Wijk, Sjoerd J. L.; Goswami, Panchali; Nagy, Vanja; Terzic, Janos; Tokunaga, Fuminori; Androulidaki, Ariadne; Nakagawa, Tomoko; Pasparakis, Manolis; Iwai, Kazuhiro; Sundberg, John P.; Schaefer, Liliana; Rittinger, Katrin; Macek, Boris; Dikic, Ivan
Linear complexity integral-equation based methods for large-scale electromagnetic analysis
In general, to solve problems with N parameters, the optimal computational complexity is linear complexity O( N). However, for most computational electromagnetic methods, the complexity is higher than O(N). In this work, we introduced and further developed the H - and H2 -matrix based mathematical framework to break the computational barrier of existing integral-equation (IE)-based methods for large-scale electromagnetic analysis. Our significant contributions include the first-time dense matrix inversion and LU factorization of O(N) complexity for large-scale 3-D circuit extraction and a fast direct integral equation solver that outperforms existing direct solvers for large-scale electrodynamic analysis having millions of unknowns and �100 wavelengths. The major contributions of this work are: (1) Direct Matrix Solution of Linear Complexity for 3-D Integrated Circuit (IC) and Package Extraction � O(N) complexity dense matrix inversion and LU factorization algorithms and their applications to capacitance extraction and impedance extraction of large-scale 3-D circuits � O(N) direct matrix solution of highly irregular matrices consisting of both dense and sparse matrix blocks arising from full-wave analysis of general 3-D circuits with lossy conductors in multiple dielectrics. (2) Fast H - and H2 -Based IE Solvers for Large-Scale Electrodynamic Analysis � theoretical proof on the error bounded low-rank representation of electrodynamic integral operators � fast H2 -based iterative solver with O(N) computational cost and controlled accuracy from small to tens of wavelengths � fast H -based direct solver with computational cost minimized based on accuracy � Findings on how to reduce the complexity of H - and H2 -based methods for electrodynamic analysis, which are also applicable to many other fast IE solvers. (3) Fast Algorithms for Accelerating H - and H2 -Based Iterative and Direct Solvers � Optimal H -based representation and its applications from circuits to electrically large problems � Optimal H2 -based representation for dense matrices arising from IE-based analysis � Iterative as well as direct solvers significantly accelerated by optimal H - and H2 -based representations. (4) Advanced Mathematical Computing � The construction of a simple H2 -representation with Csp = 1 � Linear-time matrix-matrix multiplication with controlled accuracy. The proposed methods have successfully solved large-scale electromagnetic scattering problems having 100 wavelengths and integrated circuit problems involving millions of unknowns in fast CPU time, modest memory consumption, and without sacrificing accuracy. Comparisons with state-of-the-art solvers have demonstrated the clear advantages of the proposed methods. The proposed methods have important applications in a wide range of areas such as electromagnetics, optics, acoustics, plasmonics, etc.
Chai, Wenwen
High bandwidth linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations
We present a new optical method to measure the linear viscoelastic properties of materials, ranging from complex fluids to soft solids, within a large frequency range (about 0.1--10^4 Hz). The surface fluctuation specular reflection technique is based on the measurement of the thermal fluctuations of the free surfaces of materials at which a laser beam is specularly reflected. The propagation of the thermal surface waves depends on the surface tension, density, and complex viscoelastic modulus of the material. For known surface tension and density, we show that the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. Using a viscoelastic solid (a cross-linked PDMS), which linear viscoelastic properties are known in a large frequency range from rheometric measurements and the time--temperature superposition principle, we show that there is a good agreement between the rheological characterization provided by rheometric and fluctuation measurements. We also present measurements conducted with complex fluids that are supramolecular polymer solutions. The agreement with other low frequency and high frequency rheological measurements is again very good, and we discuss the sensitivity of the technique to surface viscoelasticity.
Pottier, Basile; Talini, Laurence; Fr�tigny, Christian
Metal-metal interactions in linear tri-, penta-, hepta-, and nona-nuclear ruthenium string complexes.
Density functional theory (DFT) methodology was used to examine the structural properties of linear metal string complexes: [Ru(3)(dpa)(4)X(2)] (X = Cl(-), CN(-), NCS(-), dpa = dipyridylamine(-)), [Ru(5)(tpda)(4)Cl(2)], and hypothetical, not yet synthesized complexes [Ru(7)(tpta)(4)Cl(2)] and [Ru(9)(ppta)(4)Cl(2)] (tpda = tri-?-pyridyldiamine(2-), tpta = tetra-?-pyridyltriamine(3-), ppta = penta-?-pyridyltetraamine(4-)). Our specific focus was on the two longest structures and on comparison of the string complexes and unsupported ruthenium backboned chain complexes, which have weaker ruthenium-ruthenium interactions. The electronic structures were studied with the aid of visualized frontier molecular orbitals, and Bader's quantum theory of atoms in molecules (QTAIM) was used to study the interactions between ruthenium atoms. The electron density was found to be highest and distributed most evenly between the ruthenium atoms in the hypothetical [Ru(7)(tpta)(4)Cl(2)] and [Ru(9)(ppta)(4)Cl(2)] string complexes. PMID:21870194
Niskanen, Mika; Hirva, Pipsa; Haukka, Matti
A complex linear least-squares method to derive relative and absolute orientations of seismic sensors
Determining the relative orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations or ocean bottom seismometers deployed at the seafloor. To solve this problem we propose a new inversion method based on a complex linear algebra approach. Relative orientation angles are retrieved by minimizing, in a least-squares sense, the l2-norm between the complex traces (hodograms) of adjacent pairs of sensors. This methodology can be applied without restrictions only if the wavefield recorded by each pair of sensors is very similar. In most cases, it is possible to satisfy this condition by low-pass filtering the recorded waveforms. The main advantage of our methodology is that, in the complex domain, the relative orientations of seismic sensors can be viewed as a linear inverse problem, which ensures that the preferred solution corresponds to the global minimum of a misfit function. It is also possible to use simultaneously more than one independent data set (other seismic events) to better constrain the solution of the inverse problem. Furthermore, by a computational point of view, our method results faster than the relative orientation methods based on waveform cross-correlation. After several tests on synthetic data sets we applied successfully our methodology to different types of real data. These applications include the alignment of borehole sensors relative to a Vertical Seismic Profiling (VSP) acquisition and the orientation of Ocean Bottom Seismometers (OBS) relative to a neighbouring land station of known orientation. Using land stations, the absolute orientation of OBS can be retrieved. Finally, as a last application, we checked the correct orientation for land stations of a seismological array in Germany.
Grigoli, Francesco; Cesca, Simone; Dahm, Torsten; Krieger, Lars
Simply Symmetric
ERIC Educational Resources Information Center
Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and�
de Villiers, Michael
Linear Superposition and Prediction of Bacterial Promoter Activity Dynamics in Complex Conditions
Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments.
Rothschild, Daphna; Dekel, Erez; Hausser, Jean; Bren, Anat; Aidelberg, Guy; Szekely, Pablo; Alon, Uri
Efficient Digital Compensation Technique for Path Imbalances in LINC Transmitters Using Complex Gain and Linear Model
In this paper, a simple and efficient design scheme for digital compensation of path imbalances in linear amplification with nonlinear component (LINC) transmitters is proposed to reduce signal distortion. For the LINC transmitters including path imbalances, an error vector magnitude (EVM) is analyzed and an optimal complex gain that minimizes the EVM is extracted. In addition, a straight-forward compensation scheme for the path imbalances is proposed using a least square method for complex gains of each radio frequency path. The effectiveness of the proposed method is compared with the other digital compensation methods. A LINC transmitter with multi-level quadrature amplitude modulation input signals is experimented to verify the performance of the suggested scheme. The proposed compensator can reduce the EVM and the adjacent channel power ratio of the output signals less than 2% and 45dBc, respectively.
Ku, Hyunchul
A non-canonical UBA-UBL interaction forms the linear-ubiquitin-chain assembly complex
HOIL-1L and its binding partner HOIP are essential components of the E3-ligase complex that generates linear ubiquitin (Ub) chains, which are critical regulators of NF-?B activation. Using crystallographic and mutational approaches, we characterize the unexpected structural basis for the specific interaction between the Ub-like domain (UBL) of HOIL-1L and the Ub-associated domain (UBA) of HOIP. Our data indicate the functional significance of this non-canonical mode of UBA�UBL interaction in E3 complex formation and subsequent NF-?B activation. This study highlights the versatility and specificity of protein�protein interactions involving Ub/UBLs and their cognate proteins.
Yagi, Hirokazu; Ishimoto, Kazuhiro; Hiromoto, Takeshi; Fujita, Hiroaki; Mizushima, Tsunehiro; Uekusa, Yoshinori; Yagi-Utsumi, Maho; Kurimoto, Eiji; Noda, Masanori; Uchiyama, Susumu; Tokunaga, Fuminori; Iwai, Kazuhiro; Kato, Koichi
Spin depolarizing effect in collisions with neutral hydrogen. II. Application to simple/complex ions in spherically symmetric states
Aims: We develop an accurate and general semi-classical formalism that deals with the definition and the calculation of the collisional depolarizing constants of the levels of simple and complex singly-ionized atoms in arbitrary s-states perturbed by collisions with hydrogen atoms. The case of ions with hyperfine structure is investigated fully. Methods: We obtain potential energy curves based on the MSMA exchange perturbation theory by employing the Uns�ld approximation. These potentials enter the Schr�dinger equation to determine the collisional T-matrix elements in a semi-classical description. We use the T-matrix elements for the calculation of the collisional depolarization rates of simple atoms. Then, we use these rates to calculate the collisional coefficients in cases of ions with hyperfine structure. Results: We evaluate the collisional depolarization and polarization transfer rates of the ground levels of the ionized alkaline earth metals Be II, Mg II, Ca II, Sr II, and Ba II. We study the variation of the collisional rates with effective principal quantum number n* characterizing an arbitrary s-state of a perturbed simple ion. We find that the collisional rates for simple ions obey simple power laws as a function of n^*. We present direct and indirect formulations of the problem of the calculation of the depolarization and polarization transfer rates of levels of complex atoms and hyperfine levels from those for simple atoms. In particular, the indirect method allows a quick and simple calculation with its simple power-law relations. For the state 4s ^2S{1/2} of Ca II, our computed rate of the destruction of orientation differs from existing quantum chemistry calculations by only 4% at T=5000 K.
Derouich, M.; Barklem, P. S.
Schwarz Methods: To Symmetrize or not to Symmetrize
A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. This paper illustrates why symmetrizing may be a bad idea for linear methods. Numerical examples are presented for a test problem.
Holst, Michael; Vandewalle, Stefan
Synthesis and characterization of a series of transition metal complexes with a new symmetrical polyoxaaza macroacyclic Schiff base ligand: X-ray crystal structure of cobalt(II) and nickel(II) complexes and their antibacterial properties.
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]�2H2O and [CoLCl2]CH3OH�0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base. PMID:23099161
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
Synthesis and characterization of a series of transition metal complexes with a new symmetrical polyoxaaza macroacyclic Schiff base ligand: X-ray crystal structure of cobalt(II) and nickel(II) complexes and their antibacterial properties
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]�2H2O and [CoLCl2]CH3OH�0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
FORTRAN subroutines for out-of-core solutions of large complex linear systems
The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.
Halide and hydroxide linearly bridged bimetallic copper(II) complexes: trends in strong antiferromagnetic superexchange interactions.
Centrosymmetric [Cu(2)(?-X)(?-L(m)*)(2)](ClO(4))(3) (X = F(-), Cl(-), Br(-), OH(-), L(m)* = m-bis[bis(3,5-dimethyl-1-pyrazolyl)methyl]benzene)], the first example of a series of bimetallic copper(II) complexes linked by a linearly bridging mononuclear anion, have been prepared and structurally characterized. Very strong antiferromagnetic exchange coupling between the copper(II) ions increases along the series F(-) < Cl(-) < OH(-) < Br(-), where -J = 340, 720, 808, and 945 cm(-1). DFT calculations explain this trend by an increase in the energy along this series of the antibonding antisymmetric combination of the p orbital of the bridging anion interacting with the copper(II) d(z(2)) orbital. PMID:22834975
Reger, Daniel L; Pascui, Andrea E; Smith, Mark D; Jezierska, Julia; Ozarowski, Andrew
Complex scattering lengths for ultracold He collisions with rotationally excited linear and nonlinear molecules
The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H2, HD, CO, O2, and CO2) and nonlinear (H2O and NH3) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component ? to the real component ? of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, ? becomes significantly smaller than ? as the energy gap for rotational transitions increases. In all cases, ? decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H2 and HD appear to be collisionally stable due to the very low values of ?/?. Rotationally excited H2O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of ?.
Yang, Benhui; Forrey, R. C.; Stancil, P. C.; Balakrishnan, N.
Neutrophil chemotaxis in linear and complex gradients of interleukin-8 formed in a microfabricated device.
Although a wealth of knowledge about chemotaxis has accumulated in the past 40 years, these studies have been hampered by the inability of researchers to generate simple linear gradients instantaneously and to maintain them at steady state. Here we describe a device microfabricated by soft lithography and consisting of a network of microfluidic channels that can generate spatially and temporally controlled gradients of chemotactic factors. When human neutrophils are positioned within a microchannel, their migration in simple and complex interleukin-8 (IL-8) gradients can be tested. The cells exhibit strong directional migration toward increasing concentrations of IL-8 in linear gradients. Neutrophil migration halts abruptly when cells encounter a sudden drop in the chemoattractant concentration to zero ("cliff" gradient). When neutrophils are challenged with a gradual increase and decrease in chemoattractant ("hill" gradient), however, the cells traverse the crest of maximum concentration and migrate further before reversing direction. The technique described in this paper provides a robust method to investigate migratory cells under a variety of conditions not accessible to study by earlier techniques. PMID:12091913
Li Jeon, Noo; Baskaran, Harihara; Dertinger, Stephan K W; Whitesides, George M; Van de Water, Livingston; Toner, Mehmet
Morphology and phase diagram of complex block copolymers: ABC linear triblock copolymers.
Using a real space implementation of the self-consistent field theory for the polymeric system, we explore microphases of ABC linear triblock copolymers. For the sake of numerical tractability, the calculation is carried out in a two-dimensional (2D) space. Seven microphases are found to be stable for the ABC triblock copolymer in 2D, which include lamellae, hexagonal lattice, core-shell hexagonal lattice, tetragonal lattice, lamellae with beads inside, lamellae with beads at the interface, and hexagonal phase with beads at the interface. By systematically varying the composition, triangle phase diagrams are constructed for four classes of typical triblock polymers in terms of the relative strengths of the interaction energies between different species. In general, when both volume fractions and interaction energies of the three species are comparable, lamellar phases are found to be the most stable. While one of the volume fractions is large, core-shell hexagonal or tetragonal phases can be formed, depending on which of the blocks dominates. Furthermore, more complex morphologies, such as lamellae with beads inside, lamellae with beads at the interface, and hexagonal phases with beads at the interface compete for stability with lamellae structures, as the interaction energies between distinct blocks become asymmetric. Our study provides guidance for the design of microstructures in complex block copolymers. PMID:15089315
Tang, Ping; Qiu, Feng; Zhang, Hongdong; Yang, Yuliang
Linear dichroism studies of binding site structures in solution. Complexes between DNA and basic arylmethane dyes.
The interaction between B-form DNA and twelve cationic triaryl-methane dyes was studied with respect to optical properties and stabilities, using linear dichroism (LD) and aqueous two-phase partition techniques. Monovalent dyes derived from crystal violet as a rule form a single strong complex (K1 ca 10(5) M-1; site density per nucleotide base n1 ca 0.1 at 0.1M ionic strength) in which the plane of the dye is at an angle of less than 50 degrees to the local DNA helix axis. The complex with fuchsin is weaker (10(4) M-1) but can be explained by a similar orientation. For some of the dyes (those with pseudo-C2v symmetry) the angular orientations of two molecule-fixed axes can be obtained. For the divalent methyl green a second complex appears to be formed at low ionic strength. Methyl green (and to some extent 2-thiophene green and malachite green) show exciton splitting in the LD spectrum and circular dichroism assignable to exciton coupling between transition dipoles roughly parallel to the helical strands, indicating a dye-dye interaction. The optical data, supported by fitting experiments with space-filling models, suggests a general structure for the binding site. The dye is not intercalated but is bound to exposed hydrophobic regions in the major groove. The ligand is in part (the charged amino groups) in contact with the phosphoribose chain but its main surface lies against the hydrophobic base-pair stack. For a diphenylmethane dye, Michler's hydro blue, a perpendicular orientation was observed, possibly due to intercalation. PMID:647099
Nord�n, B; Tjerneld, F; Palm, E
Two dimensional symmetric correlation functions of the hat S operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the hat S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Ma, Q.; Boulet, C.; Tipping, R. H.
Two dimensional symmetric correlation functions of the ? operator and two dimensional Fourier transforms: considering the line coupling for P and R lines of linear molecules.
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ? operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements. PMID:24628166
Ma, Q; Boulet, C; Tipping, R H
Two C3 -Symmetric Dy3 (III) Complexes with Triple Di-?-methoxo-?-phenoxo Bridges, Magnetic Ground State, and Single-Molecule Magnetic Behavior.
Two series of isostructural C3 -symmetric Ln3 complexes Ln3 ?[BPh4 ] and Ln3 ?0.33[Ln(NO3 )6 ] (in which Ln(III) =Gd and Dy) have been prepared from an amino-bis(phenol) ligand. X-ray studies reveal that Ln(III) ions are connected by one ?2 -phenoxo and two ?3 -methoxo bridges, thus leading to a hexagonal bipyramidal Ln3 O5 bridging core in which Ln(III) ions exhibit a biaugmented trigonal-prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self-consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy(III) ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy?O distance, the local magnetic moments are oriented almost perpendicular to the Dy3 plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy(III) ions are separated by approximately 150 and 177?cm(-1) , for Dy3 ?[BPh4 ] and Dy3 ?0.33[Dy(NO3 )6 ], respectively. As expected for these large energy gaps, Dy3 ?[BPh4 ] and Dy3 ?0.33[Dy(NO3 )6 ] exhibit, under zero direct-current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied Hdc field of 1000?Oe, Dy3 ?[BPh4 ] exhibits two thermally activated processes with Ueff values of 34.7 and 19.5?cm(-1) , whereas Dy3 ?0.33[Dy(NO3 )6 ] shows only one activated process with Ueff =19.5?cm(-1) . PMID:24890335
H�nninen, Mikko M; Mota, Antonio J; Aravena, Daniel; Ruiz, Eliseo; Sillanp��, Reijo; Cam�n, Agust�n; Evangelisti, Marco; Colacio, Enrique
Theoretical investigation on switchable second-order nonlinear optical (NLO) properties of novel cyclopentadienylcobalt linear [4]phenylene complexes.
As a kind of novel organometallic complexes, the cyclopentadienylcobalt (CpCo) linear [4]phenylene complexes (4 = number of benzene rings) display efficient switchable nonlinear optical (NLO) response when CpCo reversibly migrates along the linear [4]phenylene triggered by heating or lighting. In this paper, the second-order NLO properties for CpCo linear [4]phenylene complexes were calculated by using the density functional theory (DFT) methods with four functionals. All of the functionals yield the same order of ? tot values: 1<2<4<3. The effect of solvent on second-order NLO properties has been studied using polarized continuum model (PCM) in the tetrahydrofuran (THF) solution. The solvent leads to a slight enhancement of the NLO responses for the studied complexes relevant to their NLO responses in vacuo. The electronic absorption spectra were investigated by the TDDFT methods. The TDDFT calculations indicate that the maximum absorption peaks of complexes 2-4 in the near-infrared spectrum area show the bathochromic shift together with a decreasing intensity compared to complex 1. We have also found that the cobalt (Co) atom acts as a donor in all the organometallic complexes and the d ? ?* and ? ? ?* charge transfer (CT) transitions contribute to the enhancement of second-order NLO response. Furthermore, two experimentally existing complexes 1 and 3 are found to have a large difference in ? tot values. It is our expectation that this difference may stimulate the search for a new type of switchable NLO material based on CpCo linear [4]phenylene complexes. PMID:23306734
Wang, Wen-Yong; Du, Xiao-Feng; Ma, Na-Na; Sun, Shi-Ling; Qiu, Yong-Qing
T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols
We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.
Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.
Complex-omega approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres
Propagation characteristics of surface plasmon-polaritons (SPPs) in linear chains of metallic nanospheres (LCMNs) can be found from a dispersion equation, by assuming that either frequency or wave number of a SPP is real. In this paper, we present a comparative study of SPP modes corresponding to the two types of complex solutions for an infinitely long LCMN embedded in a
Indika B. Udagedara; Ivan D. Rukhlenko; Malin Premaratne
Modifications to Axially Symmetric Simulations Using New DSMC (2007) Algorithms
Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.
Liechty, Derek S.
EPA Science Inventory
A General Linear Model (GLM) was used to evaluate the deviation of predicted values from expected values for a complex environmental model. For this demonstration, we used the default level interface of the Regional Mercury Cycling Model (R-MCM) to simulate epilimnetic total mer...
Complex sequences over GF(pM) with a two-level autocorrelation function and a large linear span
New complex sequences with elements are proposed that have constant absolute values of 1. The periodic autocorrelation functions of these sequences are shown to be two-level. The sequences are generated by three consecutive mapping processes. The number of sequences of fixed length is determined, which is larger than the number of binary sequences. For cryptographical reasons, the large linear span
Markus Antweiler; Leopold B�mer
Calibration of a Linear Free Energy Estimation Approach for Estimating Stability Constants for Metal-Bacterial Surface Complexes
In this study, we use the measured extent of metal adsorption onto bacterial cells to constrain a linear free energy relationship that allows estimation of unknown stability constants for metal-bacterial surface complexes based on the value of corresponding aqueous metal-acetate stability constants. A previous study (Fein et al., 2001) used metal adsorption experiments to constrain a similar relationship, but the
Brian R. Ginn; Jennifer E. S. Szymanowski; Jeremy B. Fein
Two C2-symmetric chelating P2-bisphosphazene superbases connected via a binaphthyl backbone - synthesis, structural features and preparation of a cationic alkyl aluminum complex.
Two P2-phosphazenyl groups were linked via a C2-symmetric binaphthyl backbone resulting in two novel chiral superbases with dimethylamino and pyrrolidino substituents. We investigated their basic properties and coordination chemistry towards a cationic alkyl aluminum fragment. The outstanding basicity of the chiral tetrasphosphazenes presented herein leads to interesting perspectives for application in asymmetric Br�nsted base catalysis. PMID:24637672
K�gel, Julius F; Kneusels, Nis-Julian; Sundermeyer, J�rg
Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions
We present a scheme whereby a static non-linear, non-invertible transmission function performed by the electro-optic Mach-Zehnder modulator produces highly complex optical chaos. The scheme allows the deterministic transformation of low-dimensional band-limited chaotic signals into much higher-dimensional structures with broadband spectra and without using any delay elements or feedback. Standard benchmark tests show that all the considered complexity indices are highly increased due to this transformation in a controlled fashion. This mechanism allows the design of simple optoelectronic delayed oscillators with extremely complex chaotic output.
Su�rez-Vargas, Jos� J.; M�rquez, Bicky A.; Gonz�lez, Jorge A.
Prediction of Complex Human Traits Using the Genomic Best Linear Unbiased Predictor
Despite important advances from Genome Wide Association Studies (GWAS), for most complex human traits and diseases, a sizable proportion of genetic variance remains unexplained and prediction accuracy (PA) is usually low. Evidence suggests that PA can be improved using Whole-Genome Regression (WGR) models where phenotypes are regressed on hundreds of thousands of variants simultaneously. The Genomic Best Linear Unbiased Prediction (G-BLUP, a ridge-regression type method) is a commonly used WGR method and has shown good predictive performance when applied to plant and animal breeding populations. However, breeding and human populations differ greatly in a number of factors that can affect the predictive performance of G-BLUP. Using theory, simulations, and real data analysis, we study the performance of G-BLUP when applied to data from related and unrelated human subjects. Under perfect linkage disequilibrium (LD) between markers and QTL, the prediction R-squared (R2) of G-BLUP reaches trait-heritability, asymptotically. However, under imperfect LD between markers and QTL, prediction R2 based on G-BLUP has a much lower upper bound. We show that the minimum decrease in prediction accuracy caused by imperfect LD between markers and QTL is given by (1?b)2, where b is the regression of marker-derived genomic relationships on those realized at causal loci. For pairs of related individuals, due to within-family disequilibrium, the patterns of realized genomic similarity are similar across the genome; therefore b is close to one inducing small decrease in R2. However, with distantly related individuals b reaches very low values imposing a very low upper bound on prediction R2. Our simulations suggest that for the analysis of data from unrelated individuals, the asymptotic upper bound on R2 may be of the order of 20% of the trait heritability. We show how PA can be enhanced with use of variable selection or differential shrinkage of estimates of marker effects.
de los Campos, Gustavo; Vazquez, Ana I.; Fernando, Rohan; Klimentidis, Yann C.; Sorensen, Daniel
Differential Dynamic Engagement within 24 SH3 Domain: Peptide Complexes Revealed by Co-Linear Chemical Shift Perturbation Analysis
There is increasing evidence for the functional importance of multiple dynamically populated states within single proteins. However, peptide binding by protein-protein interaction domains, such as the SH3 domain, has generally been considered to involve the full engagement of peptide to the binding surface with minimal dynamics and simple methods to determine dynamics at the binding surface for multiple related complexes have not been described. We have used NMR spectroscopy combined with isothermal titration calorimetry to comprehensively examine the extent of engagement to the yeast Abp1p SH3 domain for 24 different peptides. Over one quarter of the domain residues display co-linear chemical shift perturbation (CCSP) behavior, in which the position of a given chemical shift in a complex is co-linear with the same chemical shift in the other complexes, providing evidence that each complex exists as a unique dynamic rapidly inter-converting ensemble. The extent the specificity determining sub-surface of AbpSH3 is engaged as judged by CCSP analysis correlates with structural and thermodynamic measurements as well as with functional data, revealing the basis for significant structural and functional diversity amongst the related complexes. Thus, CCSP analysis can distinguish peptide complexes that may appear identical in terms of general structure and percent peptide occupancy but have significant local binding differences across the interface, affecting their ability to transmit conformational change across the domain and resulting in functional differences.
Stollar, Elliott J.; Lin, Hong; Davidson, Alan R.; Forman-Kay, Julie D.
Improved Low-Complexity Algorithm for 2-D Integer Lifting-Based Discrete Wavelet Transform Using Symmetric Mask-Based Scheme
Wavelet coding performs better than discrete cosine transform in visual processing. Moreover, it is scalable, which is important for modern video standards. The transpose memory requirement and operation speed are the two major concerns in 2-D lifting-based discrete wavelet transform (LDWT) implementation. This letter presents a novel algorithm, called 2-D symmetric mask-based discrete wavelet transform (SMDWT), to improve the critical
Complex mission optimization for Multiple-UAVs using Linear Temporal Logic
This paper discusses a class of mission planning problems in which mission objectives and relative timing constraints are specified using the linear temporal logic language LTL-x. Among all mission plans that satisfy the LTL-x specifications, it is desired to find those minimizing a given cost functional. We show that such an optimization problem can be formulated as a mixed-integer linear
Sertac Karaman; Emilio Frazzoli
Bis(arene) Actinide Sandwich Complexes, (eta6-C6H3R3)2An: Linear or bent?
The syntheses of the sandwich complexes ferrocene, (n5-C5H5)2-Fe, in 1951 and uranocene, (n8-C8H8)2U, in 1968 ushered in the modern eras of organotransition metal and organoactinide chemistry, respectively. Ferrocene and uranocene are examples of linear sandwich complexes, that is, those in which the (ring centroid)-M-(ring centroid) angle (denoted 0) is 180 degrees. In the case of (n5-C5H5)2M chemistry, a number of bent (0 < 180 degrees) complexes are known when M is a main-group or rare-earth element. The explanation for the bent structures of these complexes has been the subject of some debate concerning the relative importance of covalent, electrostatic, and steric interactions.
Li, Jun (Ohio State University) [Ohio State University; Bursten, Bruce E.(Ohio State University) [Ohio State University
Synthesis, crystal structure and magnetism of centrosymmetric linear trinuclear copper(II) complex of pyridine nitronyl nitroxide derivative
Novel stable dark-green solid adducts (2) were isolated from the reaction of 2-(4,4,5,5-tetramethyl-3-oxylimidazoline-1-oxide)-5-bromopyridine (1) with copper(II)-hexafluoroacetylacetonate hydrate (Cu(hfac)2�xH2O), namely [12�{Cu(hfac)2}3]. The X-ray structure revealed that, the complex is linear and centrosymmetric in the triclinic P1? space group. The striking feature of the complex is, the presence of two types of copper coordination geometries with the radical 1, a distorted octahedron
Chandrasekar Rajadurai; Sergei Ostrovsky; Karsten Falk; Volker Enkelmann; Wolfgang Haase; Martin Baumgarten
Conformally symmetric traversable wormholes
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N. [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG (United Kingdom); Department of Physics and Center for Theoretical and Computational Physics, University of Hong Kong, Pok Fu Lam Road, Hong Kong (China); Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG, United Kingdom and Centro de Astronomia e Astrofisica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisbon (Portugal)
Order Selection of the Linear Mixing Model for Complex-Valued FMRI Data
Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use\\u000a of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and\\u000a dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA).\\u000a In this work, we develop a complex-valued order selection
Wei Xiong; Yi-Ou Li; Nicolle Correa; Xi-Lin Li; Vince D. Calhoun; T�lay Adal?
Deviation Theorems For Solutions Of Linear Ordinary Differential Equations And Applications To Parallel Complexity Of Sigmoids
. By a sigmoid with a depth d we mean a computational circuit with d layers in which rationaloperations are admitted at each layer, and to jump to the next layer the substitution of a functioncomputed at the previous layer into an arbitrary real solution of a linear ordinary differential equation withthe polynomial coefficients is admitted. Sigmoids appear as a
D. Yu. Grigoriev
Neutrophil chemotaxis in linear and complex gradients of interleukin-8 formed in a microfabricated device
Although a wealth of knowledge about chemotaxis has accumulated in the past 40 years, these studies have been hampered by the inability of researchers to generate simple linear gradients instantaneously and to maintain them at steady state. Here we describe a device microfabricated by soft lithography and consisting of a network of microfluidic channels that can generate spatially and temporally
Noo Li Jeon; Harihara Baskaran; Stephan K. W. Dertinger; George M. Whitesides; Livingston Van De Water; Mehmet Toner
Organometallic complexes for nonlinear optics. 30.1 electrochromic linear and nonlinear optical properties of alkynylbis(diphosphine)ruthenium complexes.
A combination of cyclic voltammetry, UV-vis-NIR spectroelectrochemistry, time-dependent density functional theory (TD-DFT), and Z-scan measurements employing a modified optically transparent thin-layer electrochemical (OTTLE) cell has been used to identify and assign intense transitions of metal alkynyl complexes at technologically important wavelengths in the oxidized state and to utilize these transitions to demonstrate a facile electrochromic switching of optical nonlinearity. Cyclic voltammetric data for the ruthenium(II) complexes trans-[RuXY(dppe)(2)] [dppe = 1,2-bis(diphenylphosphino)ethane, X = Cl, Y = Cl (1), Ctbd1;CPh (2), 4-Ctbd1;CC(6)H(4)Ctbd1;CPh (3); X = Ctbd1;CPh, Y = Ctbd1;CPh (4), 4-Ctbd1;CC(6)H(4)Ctbd1;CPh (5)] show a quasi-reversible oxidation at 0.50-0.60 V (with respect to ferrocene/ferrocenium 0.56 V), which is assigned to the Ru(II/III) couple. The ruthenium(III) complex cations trans-[RuXY(dppe)(2)](+) were obtained by the in situ oxidation of complexes 1-5 using an OTTLE cell. The UV-vis-NIR optical spectra of 1(+)-5(+) contain a low-energy band in the near-IR region ( approximately 8000-16 000 cm(-)(1)), in contrast to 1-5, which are optically transparent at wavelengths < 22 000 cm(-)(1). TD-DFT calculations have been applied to model systems trans-[RuXY(PH(3))(4)] [X = Cl, Y = Cl, Ctbd1;CPh, or 4-Ctbd1;CC(6)H(4)Ctbd1;CPh; X = Ctbd1;CPh, Y = Ctbd1;CPh or 4-Ctbd1;CC(6)H(4)Ctbd1;CPh] to rationalize the optical spectra of 1-5 and 1(+)-5(+). The important low-energy bands in the electronic spectra of 1(+)-5(+) are assigned to the promotion of an electron from either a chloride p orbital or an ethynyl p orbital to the partially occupied HOMO. These absorption bands have been utilized to demonstrate a facile switching of cubic nonlinear optical (NLO) properties at 12 500 cm(-)(1) (corresponding to the wavelength of maximum transmission in biological materials such as tissue) using the OTTLE cell, the first electrochromic switching of molecular nonlinear refraction and absorption, and the first switching of optical nonlinearity using an electrochemical cell. PMID:12517178
Powell, Clem E; Cifuentes, Marie P; Morrall, Joseph P; Stranger, Robert; Humphrey, Mark G; Samoc, Marek; Luther-Davies, Barry; Heath, Graham A
Solution NMR characterization of an unusual distal H-bond network in the active site of the cyanide-inhibited, human heme oxygenase complex of the symmetric substrate, 2,4-dimethyldeuterohemin.
The presence of variable static hemin orientational disorder about the alpha-gamma-meso axis in the substrate complexes of mammalian heme oxygenase, together with the incomplete averaging of a second, dynamic disorder, for each hemin orientation, has led to NMR spectra with severe spectral overlap and loss of key two-dimensional correlations that seriously interfere with structural characterization in solution. We demonstrate that the symmetric substrate, 2,4-dimethyldeuterohemin, yields a single solution species for which the dynamic disorder is sufficiently rapid to allow effective and informative (1)H NMR structural characterization. A much more extensive, effective, and definitive NMR characterization of the cyanide-inhibited, symmetric heme complex of human heme oxygenase shows that the active site structure, with some minor differences, is essentially the same as that for the native protohemin in solution and crystal. A unique distal network that involves particularly strong hydrogen bonds, as well as inter-aromatic contacts, is described that is proposed to stabilize the position of the catalytically critical distal helix Asp-140 carboxylate (Liu, Y., Koenigs Lightning, L., Huang, H., Mo�nne-Loccoz, P., Schuller, D. J., Poulos, T. L., Loehr, T. M., and Ortiz de Montellano, P. R. (2000) J. Biol. Chem. 275, 34501-34507). The potential role of this network in placing a water molecule to stabilize the hydroperoxy species and as a template for the condensation of the distal helix upon substrate binding are discussed. PMID:12070167
Li, Yiming; Syvitski, Ray T; Auclair, Karine; Wilks, Angela; Ortiz De Montellano, Paul R; La Mar, Gerd N
BiCGstab(ell) for Linear Equations involving Unsymmetric Matrices with Complex Spectrum
. For a number of linear systems of equations arising from realistic problems, using theBi-CGSTAB algorithm of van der Vorst [17] to solve these equations is very attractive. Unfortunately,for a large class of equations, where, for instance, Bi-CG performs well, the convergence of BiCGSTABstagnates. This was observed specifically in case of discretized advection dominated PDE's.The stagnation is due to the
Gerard Sleijpen; Diederik Fokkema
Linear and cyclic tetranuclear copper(I) complexes containing anions of N,N'-bis(pyrimidine-2-yl)formamidine.
The reaction of Kpmf (pmf = anion of N,N[prime or minute]-bis(pyrimidyl-2-yl)formamidine, Hpmf) with CuSCN afforded the complexes K[Cu4(pmF)3(SCN)2], 1, and Cu(4)(pmf)4, 2. Reaction of 1 with [(n-Bu)4N]PF6 in THF gave the complex [(n-Bu)4N][Cu4(pmf)3(SCN)2], 3. Their structures were characterized by X-ray crystallography. Complexes 1 and 3 are the first linear tetranuclear complexes containing only Cu(I) atoms, while complex 2 is cyclic. The four Cu(I) atoms of complexes 1 and 3 are helically bridged by three tetradentate pmf- ligands. The [Cu4(pmf)3(SCN)2]- anions of 1 show weak interactions with adjacent [K(THF)5]+ cations through the sulfur atoms, forming infinite chains which are subjected to a series of intermolecular pi-pi interactions. In complex 2, the pmf- ligands are coordinated to the copper atoms in bidentate fashion through the two central amine nitrogen atoms, leaving the pyrimidine nitrogen atoms uncoordinated. Unexpected fluxional behaviors were observed for complexes 1 and 3 in solution. By the DNMR analysis, the free energy of activation (DeltaGc(not equal)) for the exchange is 12.8 kcal mol(-1) at 278 K (T(c)), and the rate constant of exchange (K(c)) is 470 s(-1) for 1. The DeltaGc(not equal) and Kc are 12.6 kcal mol(-1) at 273 K and 433 s(-1), respectively, for 3. PMID:15726154
Chan, Zhi-Kai; Wu, Ying-Yann; Chen, Jhy-Der; Yeh, Chen-Yu; Wang, Chih-Chieh; Tsai, Yi-Fang; Wang, Ju-Chun
Direct synthesis of linear trinuclear M2IIMn complexes with acetate and NN donor ligands
Two novel heterometallic complexes with general formula [M2Mn(OAc)6L2], where M = Cd (1), Cu (2) and L = 2,2'-bipyridyl (bpy) for (1), 1,10-phenanthroline (phen) for (2), were obtained using "direct synthesis" approach. Trinuclear molecular structure of the complexes was determined by single crystal X-ray analysis. EPR studies of 2 indicate that the coordination environment in Cu(II) equatorial plane remains unchanged in solution as compared to the initial compound. Due to low volatility of phen the products of its decomposition probably remain on the surface of metal oxides and, therefore, in contrary to previously studied bpy-containing complexes, the compounds with phen are not suitable precursors for binary oxides preparation.
Nahorna, Oksana V.; Makhankova, Valeria G.; Kokozay, Vladimir N.; Omelchenko, Iryna V.; Dyakonenko, Viktoriya V.; Shishkin, Oleg V.; Jezierska, Julia
Computational study of the linear proton bound ion-molecule complexes of HCNH+ with HCN and HNC
This work reports the results of a high level ab initio study of the linear proton bound ion-molecule complex of HCNH+ with HCN and its isomer HNC. The energetics, equilibrium geometries, and predicted equilibrium rotational constants of three strongly interacting ion-molecule complexes are reported from calculations performed at the coupled-cluster calculations including singles, doubles, and perturbative triple excitations (CCSD(T))/aug-cc-pVnZ (n = 2-5) level of theory. Harmonic vibrational frequencies from calculations performed at the CCSD(T)/aug-cc-pVnZ (n = 2-4) level of theory are presented. Additional calculations are performed at the CCSD(T)-F12b/VnZ-F12 level of theory, and the associated energetics, equilibrium geometries, and equilibrium spectroscopic properties are reported. Anharmonicity is treated with the vibrational configuration interaction method, and the predicted anharmonic vibrational frequencies are reported. The results of these calculations show that of the four possible linear interactions of HCNH+ with HCN and HNC, there are three strongly interacting proton bound complexes. Further, the study presents results that the fourth possible interaction provides the basis for a novel HNC to HCN isomerization pathway in the interstellar medium.
Eric Cotton, C.; Francisco, Joseph S.; Klemperer, William
Infrared linear dichroism of oriented DNA-ligand complexes prepared with the wet-spinning method.
Oriented DNA films prepared by the wet-spinning technique have been complexed with several ligands: the anthracycline antibiotic violamycin BI, the dipeptide L-carnosine, and the oligopeptide antibiotic netropsin. The formation of the DNA-ligand complexes is accompanied by dramatic changes of the conformational flexibility of DNA. The B-A transition which occurs usually between 80% and 70% relative humidity (RH) is more or less suppressed by the ligands. Violamycin BI at a total ligand per DNA base pair ratio, rt, of approximately 0.03 and L-carnosine at rt approximately 1.5 inhibit the B-A transition of approximately 18 and approximately 0.25 base pairs per ligand molecule, respectively. Netropsin at rt = 0.2 induces a very stable B-DNA even at rather low RH (23%). The total hydration of this complex is significantly higher than for a drug-free DNA film. Netropsin-DNA complexes at rt of 0.02 and 0.01 result in an inhibition of approximately 45 base pairs per drug molecule with respect to the B-A transition.
Fritzsche, H; Rupprecht, A; Richter, M
On the complexity of ml lattice decoders for decoding linear full rate space-time codes
We present a study and a comparison in terms of complexity of two ML-lattice decoders, the Sphere-Decoder (SD) and the Schnorr-Euchner de- coder (SE), when used to decode multi-antenna trans- mission schemes, using full rate space-time codes, over a Rayleigh fading channel.
Ghaya Rekaya; Jean-Claude Belfiore
Projective normality of complete symmetric varieties
We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety $X=\\\\bar{G\\/H}$ is a surjective map. As a consequence the cone defined by a complete linear system over $X$, or over a closed $G$ stable subvariety of $X$ is normal. This gives an affirmative answer to a question raised by Faltings. A
Rocco Chirivi; Andrea Maffei
Synthesis, spectroscopic, antimicrobial, DNA binding and cleavage studies of some metal complexes involving symmetrical bidentate N, N donor Schiff base ligand
The Schiff base ligand, N, N'-bis-(4-isopropylbenzaldimine)-1,2-diaminoethane (L), obtained by the condensation of 4-isopropylbenzaldehyde and 1,2-diaminoethane, has been used to synthesize the complexes of the type [ML 2X 2] [M = Co(II), Ni(II) and Zn(II); X = Cl and OAc]. The newly synthesized ligand (L) and its complexes have been characterized on the basis of elemental analyses, mass, 1H and 13C-NMR, molar conductance, IR, UV-vis, magnetic moment, CV and thermal analyses, powder XRD and SEM. IR spectral data show that the ligand is coordinated to the metal ions in a bidentate manner. The geometrical structures of these complexes are found to be octahedral. Interestingly, reaction with Cu(II) ion with this ligand undergoes hydrolytic cleavage to form ethylenediamine copper(II) complex and the corresponding aldehyde. The antimicrobial results indicate that the chloro complexes exhibit more activity than the acetato complexes. The complexes bind to CT-DNA by intercalation modes. Novel chloroform soluble ZnL 2Cl 2 complex exhibits tremendous antimicrobial, DNA binding and cleaving properties.
Arish, D.; Nair, M. Sivasankaran
Synthesis, spectroscopic, antimicrobial, DNA binding and cleavage studies of some metal complexes involving symmetrical bidentate N, N donor Schiff base ligand.
The Schiff base ligand, N,N'-bis-(4-isopropylbenzaldimine)-1,2-diaminoethane (L), obtained by the condensation of 4-isopropylbenzaldehyde and 1,2-diaminoethane, has been used to synthesize the complexes of the type [ML(2)X(2)] [M = Co(II), Ni(II) and Zn(II); X = Cl and OAc]. The newly synthesized ligand (L) and its complexes have been characterized on the basis of elemental analyses, mass, (1)H and (13)C-NMR, molar conductance, IR, UV-vis, magnetic moment, CV and thermal analyses, powder XRD and SEM. IR spectral data show that the ligand is coordinated to the metal ions in a bidentate manner. The geometrical structures of these complexes are found to be octahedral. Interestingly, reaction with Cu(II) ion with this ligand undergoes hydrolytic cleavage to form ethylenediamine copper(II) complex and the corresponding aldehyde. The antimicrobial results indicate that the chloro complexes exhibit more activity than the acetato complexes. The complexes bind to CT-DNA by intercalation modes. Novel chloroform soluble ZnL(2)Cl(2) complex exhibits tremendous antimicrobial, DNA binding and cleaving properties. PMID:21855399
Arish, D; Nair, M Sivasankaran
Parametrical optical effects in the 1:1 complex of resorcinol and urea�a non linear optical crystal
Good quality single crystals of a complex between urea and resorcinol (UR-C 6H 5O 2-:(NH 2)CO(NH 3) +) in the ratio (1:1) have been grown by low temperature solution growth technique using acetone and a mixture of acetone and water (1:1). The solubility studies have been carried out in both the solvents at various temperatures. The X-ray diffraction studies show that the complex crystallized in orthorhombic space group P2 12 12 1. The linear electro optical, piezooptical and second harmonic generation measurements were performed. The results obtained in these studies were discussed in detail. The optical transparency window observed in the visible and near IR regions recommends the crystal for nonlinear optical applications. Dependence of the effective second order optical susceptibility on time of simultaneously applied dc-electric field and UV-treatment were performed and discussed.
Krishnakumar, V.; Nagalakshmi, R.; Manohar, S.; Piasecki, M.; Kityk, I. V.; Bragiel, P.
Creating a Symmetrical Design
NSDL National Science Digital Library
This unit teaches students the meaning of symmetry by having them manipulate a variety of objects. Using this knowledge, they will create a symmetrical design and write an informative paragraph about the quilt design and the importance of symmetry.
Service, National S.
PT-Symmetric Quantum Field Theory
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)
Noncommutative spherically symmetric spaces
We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.
Murray, Sean; Govaerts, Jan [Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium); Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium) and International Chair in Mathematical Physics and Applications, University of Abomey-Calavi, 072 B. P. 50, Cotonou (Benin)
PT-symmetric Talbot effects.
We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern has to respect specific periodicities dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter, thus allowing one to control the imaging process. PMID:22861852
Ramezani, Hamidreza; Christodoulides, D N; Kovanis, V; Vitebskiy, I; Kottos, Tsampikos
Controlled loading of cryoprotectants (CPAs) to oocyte with linear and complex CPA profiles on a microfluidic platform�
Oocyte cryopreservation has become an essential tool in the treatment of infertility by preserving oocytes for women undergoing chemotherapy. However, despite recent advances, pregnancy rates from all cryopreserved oocytes remain low. The inevitable use of the cryoprotectants (CPAs) during preservation affects the viability of the preserved oocytes and pregnancy rates either through CPA toxicity or osmotic injury. Current protocols attempt to reduce CPA toxicity by minimizing CPA concentrations, or by minimizing the volume changes via the step-wise addition of CPAs to the cells. Although the step-wise addition decreases osmotic shock to oocytes, it unfortunately increases toxic injuries due to the long exposure times to CPAs. To address limitations of current protocols and to rationally design protocols that minimize the exposure to CPAs, we developed a microfluidic device for the quantitative measurements of oocyte volume during various CPA loading protocols. We spatially secured a single oocyte on the microfluidic device, created precisely controlled continuous CPA profiles (step-wise, linear and complex) for the addition of CPAs to the oocyte and measured the oocyte volumetric response to each profile. With both linear and complex profiles, we were able to load 1.5 M propanediol to oocytes in less than 15 min and with a volumetric change of less than 10%. Thus, we believe this single oocyte analysis technology will eventually help future advances in assisted reproductive technologies and fertility preservation.
Heo, Yun Seok; Lee, Ho-Joon; Hassell, Bryan A.; Irimia, Daniel; Toth, Thomas L.; Elmoazzen, Heidi; Toner, Mehmet
Controlled loading of cryoprotectants (CPAs) to oocyte with linear and complex CPA profiles on a microfluidic platform.
Oocyte cryopreservation has become an essential tool in the treatment of infertility by preserving oocytes for women undergoing chemotherapy. However, despite recent advances, pregnancy rates from all cryopreserved oocytes remain low. The inevitable use of the cryoprotectants (CPAs) during preservation affects the viability of the preserved oocytes and pregnancy rates either through CPA toxicity or osmotic injury. Current protocols attempt to reduce CPA toxicity by minimizing CPA concentrations, or by minimizing the volume changes via the step-wise addition of CPAs to the cells. Although the step-wise addition decreases osmotic shock to oocytes, it unfortunately increases toxic injuries due to the long exposure times to CPAs. To address limitations of current protocols and to rationally design protocols that minimize the exposure to CPAs, we developed a microfluidic device for the quantitative measurements of oocyte volume during various CPA loading protocols. We spatially secured a single oocyte on the microfluidic device, created precisely controlled continuous CPA profiles (step-wise, linear and complex) for the addition of CPAs to the oocyte and measured the oocyte volumetric response to each profile. With both linear and complex profiles, we were able to load 1.5 M propanediol to oocytes in less than 15 min and with a volumetric change of less than 10%. Thus, we believe this single oocyte analysis technology will eventually help future advances in assisted reproductive technologies and fertility preservation. PMID:21887438
Heo, Yun Seok; Lee, Ho-Joon; Hassell, Bryan A; Irimia, Daniel; Toth, Thomas L; Elmoazzen, Heidi; Toner, Mehmet
Copper(II) complexes of symmetrical and unsymmetrical tetradentate Schiff base ligands incorporating 1-benzoylacetone: Synthesis, crystal structures and electrochemical behavior
Three new copper(II) complexes [CuL1]2(ClO4)2 (1), [CuL2]ClO4 (2) and [CuL3] (3) with three Schiff base ligands [HL1=1-phenyl-3-{3-[(pyridin-2-ylmethylene)-amino]-propylimino}-butan-1-one, HL2=1-phenyl-3-[3-(1-pyridin-2-yl-ethylideneamino)-propylimino]-butan-1-one and H2L3=3-[3-(1-methyl-3-oxo-3-phenyl-propylideneamino)-propylimino]-1-phenyl-butan-1-one] have been synthesized and structurally characterized by X-ray crystallography. The mono-negative tetradentate asymmetric Schiff base ligands (L1)? and (L2)? are chelated in complexes 1 and 2 to form square planar copper(II) complexes. In complex 1, the two units are associated
Biswarup Sarkar; Gabriele Bocelli; Andrea Cantoni; Ashutosh Ghosh
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Glaister, P.
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
We present a new HLL-type approximate Riemann solver that aims at capturing any isolated discontinuity without necessitating extensive characteristic analysis of governing partial differential equations. This property is especially attractive for complex hyperbolic systems with more than two equations. Following Linde's (2002) approach [6], we introduce a generic middle wave into the classical two-state HLL solver. The property of this third wave is typified by the way of a "strength indicator" that is derived from polynomial considerations. The polynomial that constitutes the basis of the procedure is made non-oscillatory by an adapted fourth-order WENO algorithm (CWENO4). This algorithm makes it possible to derive an expression for the strength indicator. According to the size of this latter parameter, the resulting solver (HLL-RH), either computes the multi-dimensional Rankine-Hugoniot equations if an isolated discontinuity appears in the Riemann fan, or asymptotically tends towards the two-state HLL solver if the solution is locally smooth. The asymptotic version of the HLL-RH solver is demonstrated to be positively conservative and entropy satisfying in its first-order multi-dimensional form provided that a relevant and not too restrictive CFL condition is considered; specific limitations of the conservative increments of the numerical solution and a suited entropy condition enable to maintain these properties in its high-order version. With a monotonicity-preserving algorithm for the time integration, the numerical method so generated, is third order in time and fourth-order accurate in space for the smooth part of the solution; moreover, the scheme is stable and accurate when capturing a shock wave, whatever the complexity of the underlying differential system. Extensive numerical tests for the one- and two-dimensional Euler equation of gas dynamics and comparisons with classical Godunov-type methods help to point out the potentialities and insufficiencies of the method.
Guy, Capdeville
Synthesis and mesomorphic properties of symmetric tetradentate Schiff bases based on azo-containing salicylaldimines and their copper(II) complexes
Two new tetradentate Schiff bases, in which two identical aromatic bent core mesogenic units containing phenylazo are connected via a 1,2-phenylene spacer, N,N?-di-(5-(4-alkoxyphenyl)azo)-salicylidene-1,2-phenylene diimine (alkoxy?=?decyloxy, dodecyloxy), and their copper(II) complexes were synthesized and studied for their mesomorphic character. The ligands were prepared by the condensation of 5-((4-alkoxyphenyl)azo)salicylaldehydes with 1,2-phenylene diamine. The ligands and their copper complexes have been characterized by
Kamellia Nejati; Zolfaghar Rezvani; Eslam Alizadeh; Razie Sammimi
Linear oxygen-sensing response from a rhenium complex induced by heavy atom: Synthesis, characterization, photophysical study and sensing performance
In this paper, we synthesized a Br-containing ligand of 2-(4-bromophenyl)-5-(pyridin-2-yl)-1,3,4-oxadiazole and its corresponding Re(I) complex. Their synthesis, characterization, single crystal structure, electronic transitions and photophysical property were presented and discussed in detail. This Re(I) complex was found to be a yellow emitter with slim ? ? ?* radiative decay contribution, and its emission was also found to be sensitive towards O2. By doping this Re(I) complex into a polymer matrix, the oxygen-sensing performance of the resulted composite nanofibers was also investigated. Owing to the porous structure of the supporting matrix, the optimal sample gave the highest sensitivity of 3.91 with short response time of only 9 s. In addition, the linearity of the Stern-Volmer plots was greatly improved due to the highly pure emissive center triggered by heavy-atom turbulence effect from Br atom, as indicted by theoretical calculation result.
Pu, Wan; Lun, Zhao; Lisha, Wang; Guangyang, Xu
Linear free energy relationships for metal-ligand complexation: Bidentate binding to negatively-charged oxygen donor atoms
Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = ?OO( ?O log KHL,1 + ?O log KHL,2) where KML is the metal-ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton-ligand stability constants (the ligand p Ka values), and ?O is the Irving-Rossotti slope. The parameter ?OO is metal specific and has slightly different values for five and six membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, ?-hydroxycarboxylic acids, and ?-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of ?OO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu-NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems.
Carbonaro, Richard F.; Atalay, Yasemin B.; Di Toro, Dominic M.
Complexation of Mercury(II) in Soil Organic Matter: EXAFS Evidence for Linear Two-Coordination with Reduced Sulfur Groups
The chemical speciation of inorganic mercury (Hg) is to a great extent controlling biologically mediated processes, such as mercury methylation, in soils, sediments, and surface waters. Of utmost importance are complexation reactions with functional groups of natural organic matter (NOM), indirectly determining concentrations of bioavailable, inorganic Hg species. Two previous extended X-ray absorption fine structure (EXAFS) spectroscopic studies have revealed that reduced organic sulfur (S) and oxygen/nitrogen (O/N) groups are involved in the complexation of Hg(II) to humic substances extracted from organic soils. In this work, covering intact organic soils and extending to much lower concentrations of Hg than before, we show that Hg is complexed by two reduced organic S groups (likely thiols) at a distance of 2.33 Angstroms in a linear configuration. Furthermore, a third reduced S (likely an organic sulfide) was indicated to contribute with a weaker second shell attraction at a distance of 2.92-3.08 Angstroms. When all high-affinity S sites, corresponding to 20-30% of total reduced organic S, were saturated, a structure involving one carbonyl-O or amino-N at 2.07 Angstroms and one carboxyl-O at 2.84 Angstroms in the first shell, and two second shell C atoms at an average distance of 3.14 Angstroms, gave the best fit to data. Similar results were obtained for humic acid extracted from an organic wetland soil. We conclude that models that are in current use to describe the biogeochemistry of mercury and to calculate thermodynamic processes need to include a two-coordinated complexation of Hg(II) to reduced organic sulfur groups in NOM in soils and waters.
Skyllberg,U.; Bloom, P.; Qian, J.; Lin, C.; Bleam, W.
Symmetrical Reproductive Compatibility of Two Species in the Ciona intestinalis (Ascidiacea) Species Complex, a Model for Marine Genomics and Developmental Biology.
The sea squirt Ciona intestinalis species complex is a widely used model system for genomics and developmental biology, as well as ecology. Contrary to previous reports, here we show no difference in the success of development and hatching between hybrid and conspecific crosses between the two species within this complex known as types A and B, from a region in the English Channel where they are sympatric. We grew laboratory hybrids in the field for three months, and successfully obtained reproductive adults. In back-crosses of F1 laboratory hybrids to parental types, normal larvae were obtained. We conclude that hybrid crosses generate viable offspring and the resulting hybrids are interfertile with types A and B. However we also show that introgression in the natural sympatric population remains low. We discuss possible pre-zygotic and post-zygotic mechanisms which reproductively isolate these species. PMID:24882097
Sato, Atsuko; Shimeld, Sebastian M; Bishop, John D D
From symmetrical to asymmetrical nitrido phosphino-thiol complexes: a new class of neutral mixed-ligand (99m)Tc compounds as potential brain imaging agents.
A general procedure is presented for the preparation of a new class of nitrido asymmetrical Tc-99m complexes containing two different bidentate ligands bound to the same [Tc(N)]2+ core that could be used to design either essential or target specific imaging agents. This procedure is based on the chemical properties of a new monosubstituted [Tc(N)(R2PS)Cl(PPh3)] species composed of a TcN multiple bond and an ancillary phosphine thiol ligand (R2PSH). This intermediate readily reacts with bidentate mononegative ligands (S--Y) containing soft pi-donor coordinating atoms to give neutral pentacoordinate asymmetrical complexes of the type [Tc(N)(R2PS)(S--Y)]. The ability of several bidentate ligands containing different combination of heteroatoms (S, N, O) to form complexes with the [Tc(N)(R2PS)]+ building block was investigated. It was found that mononegative dithiocarbamate (DTC) or cysteine carboxyl derivate ligands promptly react with the monosubstituted species to form the final mixed compound in high yield. Preliminary biodistribution data in rats of some representative [Tc(N)(R2PS)(DTC)] compounds revealed an interesting initial brain uptake (in the range 0.20 +/- 0.01% ID/g and 0.91 +/- 0.06% ID/g), indicating their ability to cross in and out of the intact BBB. In these complexes the dithiocarbamate, or more generally the bidentate ligand (S--Y), can be designed to carry a functional group or a bioactive molecule, which could be involved in a trapping mechanism to increase brain retention for longer time intervals. These results could be conveniently utilized to devise a new procedure for the production of a novel class of brain perfusion and/or brain receptor imaging agents. PMID:16536474
Bolzati, Cristina; Benini, Elisa; Cavazza-Ceccato, Mario; Cazzola, Emiliano; Malago, Erica; Agostini, Stefania; Tisato, Francesco; Refosco, Fiorenzo; Bandoli, Giuliano
Technetium and rhenium in five-coordinate symmetrical and dissymmetrical nitrido complexes with alkyl phosphino-thiol ligands. Synthesis and structural characterization.
The reactivity of bulky alkylphosphino-thiol ligands (PSH) toward nitride-M(V, VI) (M = Tc/Re) precursors was investigated. Neutral five-coordinate monosubstituted complexes of the type [M(N)(PS)Cl(PPh(3))] (Tc1-4, Re1-2) were prepared in moderate to high yields. It was found that these [M(N)(PS)Cl(PPh(3))] species underwent ligand-exchange reactions under mild conditions when reacted with bidentate mononegative ligands having soft donor atoms such as dithiocarbamates (NaL(n)) to afford stable dissymmetrical mixed-substituted complexes of the type [M(N)(PS)(L(n))] (Tc5,8-10, Re5-9) containing two different bidentate chelating ligands bound to the [M[triple bond]N](2+) moiety. In these reactions, the dithiocarbamate replaced the two labile monodentate ligands (Cl and PPh(3)) leaving the [M(N)(PS)](+) building block intact. In the above reactions, technetium and rhenium were found to behave in a similar way. Instead, under more drastic conditions, reactions of PSH with [M(N)Cl(2)(PPh(3))(2)] gave a mixture of monosubstituted [M(N)(PS)Cl(PPh(3))] and bis-substituted species [M(N)(PS)(2)] (Tc11-14) in the case of technetium, whereas only monosubstituted [M(N)(PS)Cl(PPh(3))] complexes were recovered for rhenium. All isolated products were characterized by elemental analysis, IR and multinuclear ((1)H, (13)C, and (31)P) NMR spectroscopies, ESI MS spectrometry, and X-ray crystal structure determination of the representative monosubstituted [Tc(N)(PStbu)Cl(PPh(3))] (Tc4) and mixed-substituted [Re(N)(PScy)(L(3))] (Re7) and [Re(N)(PSiso)(L(4))] (Re9) complexes. The latter rhenium complexes represent the first example of a square-pyramidal nitrido Re species with the basal plane defined by a PS(3) donor set. Monosubstituted [M(N)(PS)Cl(PPh(3))] species bearing the substitution-inert [M(N)(PS)](+) moieties act as suitable building blocks proposed for the construction of new classes of dissymmetrical nitrido compounds with potential application in the development of essential and target specific (99m)Tc and (188)Re radiopharmaceuticals for imaging and therapy, respectively. PMID:19007158
Bolzati, Cristina; Cavazza-Ceccato, Mario; Agostini, Stefania; Tisato, Francesco; Bandoli, Giuliano
Resonances for Symmetric Two-Barrier Potentials
We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the�
Fernandez, Francisco M.
A Concrete Security Treatment of Symmetric Encryption
We study notions and schemes for symmetric (ie. private key) encryption in a concrete security framework. We give four different notions of security against chosen plaintext attack and analyze the concrete complexity of reductions among them, providing both upper and lower bounds, and obtaining tight relations. In this way we classify notions (even though polynomially reducible to each other) as
Mihir Bellare; Anand Desai; E. Jokipii; Phillip Rogaway
Symmetrized curve-straightening
The �traditional� curve-straightening flow is based on one of the standard Sobolev inner products and it is known to break certain symmetries of reflection. The purpose of this paper is to show that there are alternative Riemannian structures on the space of curves that yield flows that preserve symmetries. This feature comes at a price. In one symmetrizing metric the
Anders Linn�r
Yangian symmetric correlators
Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan-Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are obtained and relations are formulated. In this way basic notions of the Quantum inverse scattering method provide a convenient formulation for high symmetry and integrability not only in lower dimensions.
Chicherin, D.; Kirschner, R.
Multistrip multigap symmetric RPC
The characteristics of a symmetric multigap resistive plate chamber with multistrip readout electrode, recently developed by us, continued to be investigated. Studies of the time resolution, efficiency, average charge and dark rate as a function of applied voltage and the influence of the angle of incidence of the detected particle on these observables have been performed. Different type of discriminators have been tested.
Petrovici, M.; Herrmann, N.; Hildenbrand, K. D.; Augustinski, G.; Ciobanu, M.; Cruceru, I.; Duma, M.; Hartmann, O.; Koczon, P.; Kress, T.; Marquardt, M.; Moisa, D.; Petri?, M.; Schroeder, C.; Simion, V.; Stoicea, G.; Weinert, J.
The characteristics of a symmetric multigap resistive plate chamber with multistrip readout electrode, recently developed by us, continued to be investigated. Studies of the time resolution, efficiency, average charge and dark rate as a function of applied voltage and the influence of the angle of incidence of the detected particle on these observables have been performed. Different type of discriminators
M. Petrovici; N. Herrmann; K. D. Hildenbrand; G. Augustinski; M. Ciobanu; I. Cruceru; M. Duma; O. Hartmann; P. Koczon; T. Kress; M. Marquardt; D. Moisa; M. Petris; C. Schroeder; V. Simion; G. Stoicea; J. Weinert
Reactive desorption electrospray ionization linear ion trap mass spectrometry of latest-generation counterfeit antimalarials via noncovalent complex formation.
Desorption electrospray ionization mass spectrometry (DESI MS) is rapidly becoming accepted as a powerful surface characterization tool for a wide variety of samples in the open air. Besides its well-established high-throughput capabilities, a unique feature of DESI is that chemical reactions between the charged spray microdroplets and surface molecules can be exploited to enhance ionization. Here, we present a rapid screening assay for artesunate antimalarials based on reactive DESI. Artesunate is a vital therapy for Plasmodium falciparum malaria, but artesunate tablets have been counterfeited on a very large scale in SE Asia, and more recently in Africa. For this reason, faster and more sensitive screening tests are urgently needed. The proposed DESI assay is based on the formation of stable noncovalent complexes between linear alkylamines dissolved in the DESI spray solution and artesunate molecules exposed on the tablet surface. We found that, depending on amine type and concentration, a sensitivity gain of up to 170x can be obtained, in comparison to reagent-less DESI. Hexylamine (Hex), dodecylamine (DDA), and octadecylamine (ODA) produced proton-bound noncovalent complexes with gas-phase stabilities, increasing in the order [M + Hex + H]+ < [M + DDA + H]+ < [M + ODA + H]+. Tandem MS experiments revealed that complex formation occurred by hydrogen bonding between the amine nitrogen and the ether-like moieties within the artesunate lactone ring. After the reactive DESI assay was fully characterized, it was applied to a set of recently collected suspicious artesunate tablets purchased in shops and pharmacies in SE Asia. Not only did we find that these samples were counterfeits, but we also detected the presence of several wrong active ingredients. Of particular concern was the positive detection of artesunate traces in the surface of one of the samples, which we quantified with standard chromatographic techniques. PMID:17269655
Nyadong, Leonard; Green, Michael D; De Jesus, Victor R; Newton, Paul N; Fern�ndez, Facundo M
Synthesis, characterization and electrochemical behaviour of some copper(II) complexes with linear and tripodal tetradentate ligands derived from Schiff bases
New copper(II) complexes [Cu(H2L)(H2O)n]Cl2�xH2O (n = 0 or 2) with linear and tripodal tetradentate ligands have been synthesized and characterized using elemental analysis, molar conductance, IR spectra, magnetic measurements, electronic and ESR spectra. The spectral studies support the binding of linear ligands with two N and two O donor sites to copper(II) ion, providing a square planar geometry and show
S. Djebbar-Sid; O. Benali-Baitich; J. P. Deloume
Symmetric modular torsatron
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Rome, J.A.; Harris, J.H.
Theoretical prediction of the linear isomers for rare gas-carbon disulfide complexes: He-CS2, Ne-CS2, and Ar-CS2
Theoretical studies of the potential energy surfaces (PESs) and bound states are performed for rare gas-carbon disulfide complexes, He-CS2, Ne-CS2, and Ar-CS2. Three two-dimensional intermolecular PESs are constructed from ab initio data points which are calculated at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. We find that the three PESs have very similar features and each PES can be characterized by a global T-shaped minimum, two equivalent local linear minima, and the saddle points between them. The T-shaped isomer is energetically more stable than the linear isomer for each complex. The linear isomers, which have not been observed in experiment so far, are predicted from our PESs and further identified by bound state calculations. Moreover, we assign several intermolecular vibrational states for both the T-shaped and linear isomers of the three complexes via the analysis of wavefunctions. The corresponding vibrational frequencies are calculated from the bound state energies for these assigned states. These frequencies could be helpful for further experimental studies, especially for the linear isomers. We also calculate the rovibrational transition frequencies for the three T-shaped isomers and the pure rotational transition frequencies for the linear isomers, respectively. The accuracy of the PESs is validated by the good agreement between theoretical and experimental results for the rovibrational transition frequencies and spectroscopic parameters.
Zang, Limin; Dai, Wei; Zheng, Limin; Duan, Chuanxi; Lu, Yunpeng; Yang, Minghui
Ejs Symmetric Top Model
The Ejs Symmetric Top model displays the motion of a top, in both the space frame and body frame, with no net toque applied. The top has an initial angular speed in the x, y, and z directions. The moments of inertia in each direction, and the initial angular positions and angular speeds can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting �Open Ejs Model� from the pop-up menu item. Ejs Symmetric Top model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_rigid_bodies_symmetric.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for rigid body dynamics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.
Aguirregabiria, Juan
Complex-? approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres
Propagation characteristics of surface plasmon-polaritons (SPPs) in linear chains of metallic nanospheres (LCMNs) can be found from a dispersion equation, by assuming that either frequency or wave number of a SPP is real. In this paper, we present a comparative study of SPP modes corresponding to the two types of complex solutions for an infinitely long LCMN embedded in a gain medium. We show that even though gain predominantly affects the SPP dispersion obtained with real frequency, both solutions result in the same dispersion and attenuation of SPP modes, when Ohmic losses are almost compensated by gain. In this regime, an analytic expression for the propagation length of SPPs exists, and the SPPs� dispersion is determined by a real equation. We also demonstrate that for a given amount of gain (below the amplification limit of ~1000 cm-1), transversely polarized SPPs attenuate slower than longitudinally polarized SPPs and are, therefore, preferable for the purpose of energy transfer in gain-supplied LCMNs. The transmission windows for SPP modes of different polarizations do not overlap each other, which facilitates realization of LCMN-based plasmonic filters. Our results may prove useful in design optimization of all-optical chips for power-efficient optical supercomputers.
Udagedara, Indika B.; Rukhlenko, Ivan D.; Premaratne, Malin
Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements
Generalized quantum measurements [also known as positive operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric informationally complete (SIC) POVM, is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.
Medendorp, Z. E. D.; Shalm, L. K.; Steinberg, A. M. [Centre for Quantum Information and Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7 (Canada); Torres-Ruiz, F. A. [Center for Optics and Photonics, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Departamento de Ciencias Fisicas, Universidad de La Frontera, Temuco, Casilla 54-D (Chile); Tabia, G. N. M.; Fuchs, C. A. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 (Canada)
Construction of dynamics and time-ordered exponential for unbounded non-symmetric Hamiltonians
We prove under certain assumptions that there exists a solution of the Schr�dinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not normal. We also prove that, under the same assumptions, there exists a time evolution operator in the interaction picture and that the evolution operator enjoys a useful series expansion formula. This expansion is considered to be one of the mathematically rigorous realizations of so-called "time-ordered exponential," which is familiar in the physics literature. We apply the general theory to prove the existence of dynamics for the mathematical model of Quantum Electrodynamics quantized in the Lorenz gauge, the interaction Hamiltonian of which is not even symmetric or normal.
Futakuchi, Shinichiro; Usui, Kouta
Polarization aberrations. 1. Rotationally symmetric optical systems.
The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed. PMID:20935891
McGuire, J P; Chipman, R A
Complexes Formed in Solution Between Vanadium(IV)/(V) and the Cyclic Dihydroxamic Acid Putrebactin or Linear Suberodihydroxamic Acid
An aerobic solution prepared from V(IV) and the cyclic dihydroxamic acid putrebactin (pbH2) in 1:1 H2O/CH3OH at pH = 2 turned from blue to orange and gave a signal in the positive ion electrospray ionization mass spectrometry (ESI-MS) at m/zobs 437.0 attributed to the monooxoV(V) species [VVO(pb)]+ ([C16H26N4O7V]+, m/zcalc 437.3). A solution prepared as above gave a signal in the 51V NMR spectrum at ?V = ?443.3 ppm (VOCl3, ?V = 0 ppm) and was electron paramagnetic resonance silent, consistent with the presence of [VVO(pb)]+. The formation of [VVO(pb)]+ was invariant of [V(IV)]:[pbH2] and of pH values over pH = 2�7. In contrast, an aerobic solution prepared from V(IV) and the linear dihydroxamic acid suberodihydroxamic acid (sbhaH4) in 1:1 H2O/CH3OH at pH values of 2, 5, or 7 gave multiple signals in the positive and negative ion ESI-MS, which were assigned to monomeric or dimeric V(V)� or V(IV)�sbhaH4 complexes or mixed-valence V(V)/(IV)�sbhaH4 complexes. The complexity of the V-sbhaH4 system has been attributed to dimerization (2[VVO(sbhaH2)]+ ? [(VVO)2(sbhaH2)2]2+), deprotonation ([VVO(sbhaH2)]+ � H+ ? [VVO(sbhaH)]0), and oxidation ([VIVO(sbhaH2)]0 �e� ? [VVO(sbhaH2)]+) phenomena and could be described as the sum of two pH-dependent vectors, the first comprising the deprotonation of hydroxamate (low pH) to hydroximate (high pH) and the second comprising the oxidation of V(IV) (low pH) to V(V) (high pH). Macrocyclic pbH2 was preorganized to form [VVO(pb)]+, which would provide an entropy-based increase in its thermodynamic stability compared to V(V)�sbhaH4 complexes. The half-wave potentials from solutions of [V(IV)]:[pbH2] (1:1) or [V(IV)]:[sbhaH4] (1:2) at pH = 2 were E1/2 ?335 or ?352 mV, respectively, which differed from the expected trend (E1/2 [VO(pb)]+/0 < VV/IV�sbhaH4). The complex solution speciation of the V(V)/(IV)�sbhaH4 system prevented the determination of half-wave potentials for single species. The characterization of [VVO(pb)]+ expands the small family of documented V�siderophore complexes relevant to understanding V transport and assimilation in the biosphere.
An application of the complex general linear model to analysis of fMRI single subjects multiple stimuli input data
The general linear model (GLM) has been extensively applied to fMRI data in the time domain. However, traditionally time series data can be analyzed in the Fourier domain where the assumptions made as to the noise in the signal can be less restrictive and statistical tests are mathematically more rigorous. A complex form of the GLM in the Fourier domain has been applied to the analysis of fMRI (BOLD) data. This methodology has a number of advantages over temporal methods: 1. Noise in the fMRI data is modeled more generally and closer to that actually seen in the data. 2. Any input function is allowed regardless of the timing. 3. Non-parametric estimation of the transfer functions at each voxel are possible. 4. Rigorous statistical inference of single subjects is possible. This is demonstrated in the analysis of an experimental design with random exponentially distributed stimulus inputs (a two way ANOVA design with input stimuli images of alcohol, non-alcohol beverage and positive or negative images) sampled at 400 milliseconds. This methodology applied to a pair of subjects showed precise and interesting results (e.g. alcoholic beverage images attenuate the response of negative images in an alcoholic as compared to a control subject).
Rio, Daniel; Rawlings, Robert; Woltz, Lawrence; Gilman, Jodi; Hommer, Daniel
Polynuclear complexes: two amino-phenol macrocycles spaced by several linear polyamines; synthesis, binding properties, and crystal structure.
The synthesis and characterization of the new polytopic ligands 1,14-bis(3,6,9-triaza-15-hydroxybicyclo[9.3.1]pentadeca-11,13,1(15)-trien-6-yl)-3,6,9,12-tetraazatetradecane L1, 1,15-bis(3,6,9-triaza-15-hydroxybicyclo[9.3.1]pentadeca-11,13,1(15)-trien-6-yl)-3,6,10,13-tetraazapentadecane L2, and 1,16-bis(3,6,9-triaza-15-hydroxybicyclo[9.3.1]pentadeca-11,13,1(15)-trien-6-yl)-3,7,10,14-tetraazahexadecane L3, containing two equal amino-phenol macrocycles spaced by several linear tetraamines, are reported. The basicity and coordination behavior toward the Cu(II) ion were potentiometrically determined in aqueous solution at 298.1 K. All the ligands show similar acid-base properties behaving as octaprotic bases in the examined pH range (pH = 2-12). The acid protons of L1-L3 cannot be removed under the experimental conditions used; thus, the main deprotonated species obtainable in aqueous solution are the neutral ligands, having amphionic character as demonstrated by UV-vis experiments. These species are able to form mono-, di-, and trinuclear Cu(II) complexes having stoichiometry [CuL](2+), [Cu(2)L](4+), and [Cu(3)L](6+), respectively, that can lose one or two protons giving rise to [CuH(-1)L](+), [Cu(2)H(-2)L](2+), and [Cu(3)H(-2)L](4+). Depending on the used ligand to metal molar ratio, the mono-, di-, or trinuclear species prevail over the others in solution. Both di- and trinuclear complexes are able to add secondary ligands (such as OH(-)), and in some cases two Cu(II) can cooperate to stabilize them by coordinating the guest in a bridged conformation. The structure of the [Cu(2)L3](4+) cation was resolved by X-ray analysis of the {[Cu(2)L3](ClO(4))(4) x 3 H(2)O}(2) x H(2)O crystalline complex. It shows that each Cu(II) is penta-coordinated by one phenolate oxygen, two amine functions, belonging to one macrocyclic unit, and two amine functions of the spacer; in this species the distance between the two Cu(II) is about 5.3 A. PMID:19856893
Ambrosi, Gianluca; Formica, Mauro; Fusi, Vieri; Giorgi, Luca; Macedi, Eleonora; Micheloni, Mauro; Paoli, Paola; Rossi, Patrizia
Linear optimal control of tokamak fusion devices
The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
Kessel, C.E.; Firestone, M.A.; Conn, R.W.
Symmetrical peripheral gangrene.
Two cases of symmetrical peripheral gangrene associated with intracardiac lesions are described. One had a secondary deposit from a uterine leiomyosarcoma in the wall of the right ventricle, the other had a free ball thrombus in the right atrium; there were no valvular lesions in either case. The published reports of this type of gangrene indicate that it may result from (1) va sospastic conditions, (2) small vessel obstruction, or (3) conditions producing a very low cardiac output. The two patients reported are unusual examples of the last. Images
McGouran, R C; Emmerson, G A
Linear-dendritic supramolecular complexes as nanoscale reaction vessels for "green" chemistry. Diels-Alder reactions between fullerene C60 and polycyclic aromatic hydrocarbons in aqueous medium.
This study describes the first Diels-Alder (DA) reaction performed in aqueous medium with highly hydrophobic compounds-fullerene (C 60) as the dienophile and anthracene (An) or tetracene (Tet) as the dienes, respectively. The reactions are performed in nanocontainers, constructed by self-assembly of linear-dendritic amphiphilic copolymers with poly(ethylene glycol), PEG or poly(ethylene oxide), PEO as the hydrophilic blocks and poly(benzyl ether) monodendrons as the hydrophobic fragments: G3PEO13k, dG3 and dG2. Comparative studies under identical conditions are carried out with an amphiphilic linear-linear copolymer, poly(styrene)1800- block-PEO2100, PSt-PEO, and the nonionic surfactant Igepal CO-720, IP720. The binding affinity of supermolecules built of these amphiphiles toward the DA reagents decreases in the following order: G3PEO13k > dG3 > PSt-PEO > dG2 > IP720. The kinetic constant of binding is evaluated for tetracene and decreases in a similar fashion: 5 x 10 (-7) M/min (G3PEO13k), through 4 x 10 (-7) M/min (PSt-PEO) down to 1.5 x 10 (-7) M/min for IP720. The mobility of substrates encapsulated in the micellar core, estimated by pyrene fluorescence decay, is 95-121 ns for the micelles of the linear-dendritic copolymers and notably higher for PSt-PEO (152 ns), revealing the much denser interior of the linear analogue. The apparent kinetic constant for the DA reaction of C 60 and Tet within the G3PEO13k supermolecule in aqueous medium is markedly higher than in organic solvent (toluene), 208 vs 1.82 M /min. With G3PEO13k the conversions reach 49% for the DA reaction between C 60 and An, and 55% for C 60 and Tet. Besides the monoadduct (26.5% yield) the reaction with An produces exclusively increasing amounts of D 2 h -symmetric antipodal bis-adduct, whose yield reaches up to 22.5% after 48 h. In addition to the environmentally friendly conditions notable advantages of the synthetic strategy described are the extended stability of the linear-dendritic nanovessels, the easy collection of the products formed, and the recovery and reuse of unreacted reagents and linear-dendritic copolymers. PMID:18781794
Simonyan, Arsen; Gitsov, Ivan
Complex dynamics and targeted energy transfer in linear oscillatorscoupled to multi-degree-of-freedom essentially nonlinear attachments
We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable)\\u000a stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the\\u000a linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted\\u000a energy transfer from the linear to the
Stylianos Tsakirtzis; Panagiotis N. Panagopoulos; Gaetan Kerschen; Oleg Gendelman; Alexander F. Vakakis; Lawrence A. Bergman
Symmetrization for redundant channels
A plurality of redundant channels in a system each contain a global image of all the configuration data bases in each of the channels in the system. Each global image is updated periodically from each of the other channels via cross channel data links. The global images of the local configuration data bases in each channel are separately symmetrized using a voting process to generate a system signal configuration data base which is not written into by any other routine and is available for indicating the status of the system within each channel. Equalization may be imposed on a suspect signal and a number of chances for that signal to heal itself are provided before excluding it from future votes. Reconfiguration is accomplished upon detecting a channel which is deemed invalid. A reset function is provided which permits an externally generated reset signal to permit a previously excluded channel to be reincluded within the system. The updating of global images and/or the symmetrization process may be accomplished at substantially the same time within a synchronized time frame common to all channels.
Tulplue, Bhalchandra R. (Inventor); Collins, Robert E. (Inventor)
Poly(ethylene glycol)-block-poly(L-lysine) dendrimer: novel linear polymer/dendrimer block copolymer forming a spherical water-soluble polyionic complex with DNA.
Methoxypoly(ethylene glycol)-block-poly(L-lysine) dendrimer was designed to form a water-soluble complex with plasmid DNA. The copolymer was synthesized by the liquid-phase peptide synthesis method. It was characterized by 1H NMR and matrix-assisted laser desorption ionization-time-of-flight (MALDI-TOF) mass spectrum. Agarose gel electrophoresis and DNase I protection assay proved that this linear polymer/dendrimer block copolymer assembled spontaneously with plasmid DNA, forming a water-soluble complex which increased the stability of the complexed DNA. Atomic force microscopy of the complex was evaluated at various charge ratios showing that the copolymer/DNA complex was like a globular shape. PMID:9893965
Choi, J S; Lee, E J; Choi, Y H; Jeong, Y J; Park, J S
Novel binding regioselectivity in the interpenetration of a non-symmetric axle into a non-symmetric pillar[5]arene wheel.
We describe the regioselective complexation of a non-symmetric 5-bromovaleronitrile axle by a non-symmetric pillar[5]arene bearing different alkyl (methyl and pentyl) rims, forming an oriented interpenetrated complex with the directionality of CN@methyl rim and Br@pentyl rim. PMID:24681988
Shu, Xiaoyan; Chen, Wei; Hou, Dabin; Meng, Qingbin; Zheng, Renlin; Li, Chunju
Optical realization of optimal symmetric real state quantum cloning machine
We present an experimentally uniform linear optical scheme to implement the optimal 1?2 symmetric and optimal 1?3 symmetric economical real state quantum cloning machine of the polarization state of the single photon. This scheme requires single-photon sources and two-photon polarization entangled state as input states. It also involves linear optical elements and three-photon coincidence. Then we consider the realistic realization of the scheme by using the parametric down-conversion as photon resources. It is shown that under certain condition, the scheme is feasible by current experimental technology.
Hu, Gui-Yu; Zhang, Wen-Hai; Ye, Liu
We prove that in characteristic zero the multiplication of\\u000asections of line bundles generated by global sections on a\\u000acomplete symmetric variety X=\\\\overline{G\\/H}\\u000ais a surjective map.\\u000aAs a consequence, the cone defined by a complete linear system\\u000aover $X$ or over a closed $G$ -stable subvariety of $X$ is normal.\\u000aThis gives an affirmative answer to a question raised
Andrea Maffei
Symmetric multilayer megampere X-pinch
Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of �1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.
Shelkovenko, T. A.; Pikuz, S. A.; McBride, R. D.; Knapp, P. F.; Wilhelm, G.; Sinars, D. B.; Hammer, D. A.; Orlov, N. Yu.
Chirally symmetric but confining dense, cold matter
The folklore tradition about the QCD phase diagram is that at the chiral restoration phase transition at finite density hadrons are deconfined and there appears the quark matter. We address this question within the only known exactly solvable confining and chirally symmetric model. It is postulated within this model that there exists linear Coulomb-like confining interaction. The chiral symmetry breaking and the quark Green function are obtained from the Schwinger-Dyson (gap) equation while the color-singlet meson spectrum results from the Bethe-Salpeter equation. We solve this model at T=0 and finite chemical potential {mu} and obtain a clear chiral restoration phase transition at the critical value {mu}{sub cr}. Below this value the spectrum is similar to the previously obtained one at {mu}=0. At {mu}>{mu}{sub cr} the quarks are still confined and the physical spectrum consists of bound states which are arranged into a complete set of exact chiral multiplets. This explicitly demonstrates that a chirally symmetric matter consisting of confined but chirally symmetric hadrons at finite chemical potential is also possible in QCD. If so, there must be nontrivial implications for astrophysics.
Glozman, L. Ya.; Wagenbrunn, R. F. [Institute for Physics, Theoretical Physics Branch, University of Graz, Universitaetsplatz 5, A-8010 Graz (Austria)
Elucidation of structure-function relationships in photosynthetic light-harvesting antenna complexes by non-linear polarization spectroscopy in the frequency domain (NLPF).
Photosynthetically active pigments are usually organized into pigment-protein complexes. These include light-harvesting antenna complexes (LHCs) and reaction centers. Site energies of the bound pigments are determined by interactions with their environment, i.e., by pigment-protein as well as pigment-pigment interactions. Thus, resolution of spectral substructures of the pigment-protein complexes may provide valuable insight into structure-function relationships. By means of conventional (linear) and time-resolved spectroscopic techniques, however, it is often difficult to resolve the spectral substructures of complex pigment-protein assemblies. Nonlinear polarization spectroscopy in the frequency domain (NLPF) is shown to be a valuable technique in this regard. Based on initial experimental work with purple bacterial antenna complexes as well as model systems NLPF has been extended to analyse the substructure(s) of very complex spectra, including analyses of interactions between chlorophylls and "optically dark" states of carotenoids in LHCs. The paper reviews previous work and outlines perspectives regarding the application of NLPF spectroscopy to disentangle structure-function relationships in pigment-protein complexes. PMID:21316796
Lokstein, Heiko; Krikunova, Maria; Teuchner, Klaus; Voigt, Bernd
Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima-Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435-457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249-275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler-Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375-413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647-667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001-1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima-Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.
Ueda, Yoshihiro; Duan, Renjun; Kawashima, Shuichi
Laplace And Segal-Bargmann Transforms On Hermitian Symmetric Spaces And Orthogonal Polynomials
Abstract: Let D = G=K be a complex bounded symmetric domain of tube type in a complexJordan algebra V and let DR= J \\\\ D D be its real form in a formally real Euclidean Jordanalgebra J V ; DR= H=L is a bounded realization of the symmetric cone in J . We considerrepresentations of H that are gotten by
Mark Davidson; Gestur �lafsson; Genkai Zhang
The connection between symmetric method and symplectic method.
Symmetric methods are described in a certain sense as symplectic methods for integrating linear conservative dynamical systems. They are applicable to nonlinear Hamiltonian systems. However, the authors have found that they are not suitable for the systems that depend on velocity explicitly.
Huang, Tianyi; Wang, Changbin; Zhao, Zhangyin
Diagonalization and simultaneous symmetrization of the gas-dynamic matrices
The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.
Warming, R. F.; Beam, R. M.; Hyett, B. J.
Application of Kalman filtering for online estimation of symmetrical components for power system protection
This paper presents a new model that enables linear Kalman filtering (KF) to be applied for the direct estimation of symmetrical components in unbalanced three-phase systems. Computational experiments implementing KF using both synthetic and actual data sets are reported. It is shown that Kalman filtering models are well suited for symmetrical component estimation online. The effects of sampling rate, data
S. A. Soliman; M. E. El-Hawary
Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method
This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.
Yu, XiaoChun; Bai, YuGuang; Cui, Miao; Gao, XiaoWei
Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems
This article presents a method for complexity reduction in reachability analysis and safety-preserving controller synthesis via Schur-based decomposition. The decomposition results in either decoupled or weakly-coupled (lower dimensional) subsystems. Reachable sets, computed independently for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Moreover, applying this technique to a class of unstable LTI systems,
Shahab Kaynama; Meeko Oishi
Ring-opening reactions induced by gold(I) of five- and four-coordinate palladium(II) and platinum(II) complexes containing tripodal or linear polyphosphines.
The tripodal ligands NP(3)(tris[2-(diphenylphosphino)ethyl]amine) and PP(3)(tris[2-(diphenylphosphino)ethyl]phosphine), form five-coordinate [Pd(NP(3))X]X [X = Cl (1), Br (2)], [M(PP(3))X]X [M = Pd: X = Cl (4), Br (5), I (6); M = Pt, X = Cl (7), Br (8), I (9)] and four-coordinate[Pd(NP(3))I]I (3) complexes containing three fused rings around the metal. The interaction between Au(tdg)X (tdg = thiodiglycol; X = Cl, Br) or AuI and the respective ionic halo complexes 1-9 in a 1:1 stoichiometric ratio occurs via a ring-opening reaction with formation of the heterobimetallic systems PdAu(NP(3))X(3)[X = Cl (11), Br (12), I (13)], [MAu(PP(3))X(2)]X [M = Pd: X = Cl (14), Br (15), I (16); M = Pt: X = Cl (17), Br (18), I (19)]. The cations of complexes 17 and 18 were shown, by X-ray diffraction, to contain a distorted square-planar Pt(II) arrangement (Pt(P(2)P)X) where PP(3) is acting as tridentate chelating ligand and an almost linear PAuX moiety bearing the dangling phosphorus formed in the ring-opening process. PPh(3) coordinates to Au(I) and not to M(II) when added in excess to 14 and 17. Complexes 14-17 and [Pt(P(4))](BPh(4))(2) (10) (P4=linear tetraphosphine) also react with A(I), via chelate ring-openings to give MAu(2)(PP(3))X(4) [M = Pd: X = Cl (20), Br (21), I (22); M = Pt: X = Cl (23)] and [Pt(2)Au(2)(mu-Cl)(2)(mu-P(4))(2)](BPh(4))(4) (24), respectively. PMID:15303168
Fern�ndez, Dami�n; Garc�a-Seijo, Mar�a I; Casti�eiras, Alfonso; Garc�a-Fern�ndez, Mar�a E
Thin-shell wormholes: Linearization stability
The class of spherically symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat. {copyright} 1995 The American Physical Society.
Poisson, E.; Visser, M. [Physics Department, Washington University, St. Louis, Missouri 63130-4899 (United States)] [Physics Department, Washington University, St. Louis, Missouri 63130-4899 (United States)
Inertial effects in anomalous dielectric relaxation of symmetrical top molecules.
The linear dielectric response of an assembly of noninteracting symmetrical top molecules (each of which is free to rotate in space) is evaluated in the context of fractional dynamics. The infinite hierarchy of differential-recurrence relations for the relaxation functions appropriate to the dielectric response is derived by using the underlying inertial fractional Klein-Kramers equation. On solving this hierarchy in terms of matrix continued fractions (as in the normal rotational diffusion), the complex dynamic susceptibility is obtained and is calculated for typical values of the model parameters. For the limiting case of spherical top molecules, the solution is obtained in terms of an ordinary continued fraction. It is shown that the model can reproduce nonexponential anomalous dielectric relaxation behavior at low frequencies (omegatau
Titov, Sergey V; Kalmykov, Yuri P; Coffey, William T
Titov, Sergey V; Kalmykov, Yuri P; Coffey, William T
Reversible Switching between Nonquenched and Quenched States in Nanoscale Linear Arrays of Plant Light-Harvesting Antenna Complexes
A simple and robust nanolithographic method that allows sub-100 nm chemical patterning on a range of oxide surfaces was developed in order to fabricate nanoarrays of plant light-harvesting LHCII complexes. The site-specific immobilization and the preserved functionality of the LHCII complexes were confirmed by fluorescence emission spectroscopy. Nanopatterned LHCII trimers could be reversibly switched between fluorescent and quenched states by controlling the detergent concentration in the imaging buffer. A 3-fold quenching of the average fluorescence intensity was accompanied by a decrease in the average (amplitude-weighted) fluorescence lifetime from approximately 2.24 ns to approximately 0.4 ns, attributed to the intrinsic ability of LHCII to switch between fluorescent and quenched states upon changes in its conformational state. The nanopatterning methodology was extended by immobilizing a second protein, the enhanced green fluorescent protein (EGFP), onto LHCII-free areas of the chemically patterned surfaces. This very simple surface chemistry, which allows simultaneous selective immobilization and therefore sorting of the two types of protein molecules on the surface, is a key underpinning step toward the integration of LHCII into switchable biohybrid antenna constructs.
Reversible Switching between Nonquenched and Quenched States in Nanoscale Linear Arrays of Plant Light-Harvesting Antenna Complexes.
A simple and robust nanolithographic method that allows sub-100 nm chemical patterning on a range of oxide surfaces was developed in order to fabricate nanoarrays of plant light-harvesting LHCII complexes. The site-specific immobilization and the preserved functionality of the LHCII complexes were confirmed by fluorescence emission spectroscopy. Nanopatterned LHCII trimers could be reversibly switched between fluorescent and quenched states by controlling the detergent concentration in the imaging buffer. A 3-fold quenching of the average fluorescence intensity was accompanied by a decrease in the average (amplitude-weighted) fluorescence lifetime from approximately 2.24 ns to approximately 0.4 ns, attributed to the intrinsic ability of LHCII to switch between fluorescent and quenched states upon changes in its conformational state. The nanopatterning methodology was extended by immobilizing a second protein, the enhanced green fluorescent protein (EGFP), onto LHCII-free areas of the chemically patterned surfaces. This very simple surface chemistry, which allows simultaneous selective immobilization and therefore sorting of the two types of protein molecules on the surface, is a key underpinning step toward the integration of LHCII into switchable biohybrid antenna constructs. PMID:24988144
Vasilev, Cvetelin; Johnson, Matthew P; Gonzales, Edward; Wang, Lin; Ruban, Alexander V; Montano, Gabriel; Cadby, Ashley J; Hunter, C Neil
Plane symmetric thin-shell wormholes: Solutions and stability
Using the cut-and-paste procedure, we construct static and dynamic, plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes can be interpreted as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin-shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin-shell wormholes made of phantom energy are unstable.
Lemos, Jose P. S.; Lobo, Francisco S. N. [Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Institute of Gravitation and Cosmology, University of Portsmouth, Portsmouth PO1 2EG, United Kingdom and Centro de Astronomia e Astrofisica da Universidade de Lisboa, Campo Grande, Edificio C8, 1749-016 Lisboa (Portugal)
An unprecedented "linear-bent" isomerism in tri-nuclear Cu2(II)Zn(II) complexes with a salen type di-Schiff base ligand.
Two new trinuclear hetero-metallic copper(II)-zinc(II) complexes [(CuL)(2)Zn(N(3))(2)] (1A and 1B) have been synthesized using [CuL] as a so-called "metalloligand" (where H(2)L = N,N'-bis(salicylidene)-1,3-propanediamine) and structurally characterized. Complexes 1A and 1B have the same molecular formula but crystallize in different crystal systems (triclinic for 1A and monoclinic for 1B) with space group P1 for 1A and P2(1)/c for 1B. 1A is an angular trinuclear species, in which two terminal four-coordinate square planar "metalloligand" [CuL] are coordinated to a central Zn(II) through double phenoxido bridges. The Zn(II) is in a six-coordinate distorted octahedral environment being bonded additionally to two mutually cis nitrogen atoms of terminal azide ions. In complex 1B, in addition to the double phenoxido bridge, the two terminal Cu(II) ions are linked to the central Zn(II) via a ?(-l,l) azido bridge giving rise to a square pyramidal environment around the Cu(II) ions and consequently the structure becomes linear. These two species can be considered as "linear-bent" isomers. EPR spectra and ESI mass spectra show that the two isomers are identical in solution. The DFT calculation reveals that the energy of 1A is 7.06 kcal mol(-1) higher than that of 1B. The existence of both isomers in the solid state suggests that crystal packing interactions in are more efficient and probably compensate for the difference in energy. PMID:22858718
Das, Lakshmi Kanta; Park, Sung-Woo; Cho, Seung Joo; Ghosh, Ashutosh
Bis(arene) actinide sandwich complexes, ({eta}{sup 6}-C{sub 6}H{sub 3}R{sub 3}){sub 2}An: Linear or bent?
The syntheses of the sandwich complexes ferrocene, ({eta}{sup 5}-C{sub 5}H{sub 5}){sub 2}-Fe, in 1951 and uranocene, ({eta}{sup 8}-C{sub 8}H{sub 8}){sub 2}U, in 1968 ushered in the modern eras of organotransition metal and organoactinide chemistry, respectively. Ferrocene and uranocene are examples of linear sandwich complexes, that is, those in which the (ring centroid)-M-(ring centroid) angle (denoted {theta}) is 180{degree}. In the case of ({eta}{sup 5}-C{sub 5}H{sub 5}){sub 2}M chemistry, a number of bent ({theta} < 180{degree}) complexes are known when M is a main-group or rare-earth element. The explanation for the bent structures of these complexes has been the subject of some debate concerning the relative importance of covalent, electrostatic, and steric interactions. The authors report optimized geometries of Bz{sub 2}An (An = Th-Am) and ({eta}{sup 6}-C{sub 6}H{sub 3}R{sub 3}){sub 2}An (An = Th, U, Pu; R = Me, {sup t}Bu) obtained by using local density approximation (LDA) and Perdew-Wang (PW91) gradient-corrected relativistic density functional theory (DFT) methods. These DFT methods are found to be able to reproduce the experimental geometries and vibrational frequencies of organoactinide complexes with satisfactory accuracy. The (TTB){sub 2}An calculations that are reported here are, to date, the largest full geometry optimizations to be carried out on an actinide system.
Li, J.; Bursten, B.E.
Linear {Ni(II) -Ln(III) -Ni(II) } Complexes Containing Twisted Planar Ni(?-phenolate)2 Ln Fragments: Synthesis, Structure, and Magnetothermal Properties.
Sequential reaction of a multisite LH4 ligand {2-[2-hydroxy-3-(hydroxymethyl)-5-methylbenzylideneamino]-2-methylpropane-1,3-diol} with appropriate lanthanide salts followed by the addition of Ni(NO3 )2 ?6?H2 O in a 4:1:2 stoichiometric ratio in the presence of triethylamine afforded four heterobimetallic trinuclear complexes [Ni2 Gd(LH3 )4 ]?3?NO3 ?3?MeOH?H2 O ?CH3 CN (1), [Ni2 Tb(LH3 )4 ]?3?NO3 ?3?MeOH?CH3 CN (2), [Ni2 Dy(LH3 )4 ] ?3?NO3 ?3?MeOH?H2 O?CH3 CN (3), and [Ni2 Ho(LH3 )4 ]?3?NO3 ?3?MeOH?H2 O ?CH3 CN (4). Complexes 1-4 possess linear trimetallic cores with a central lanthanide ion. Magnetic studies revealed a predominant ferromagnetic interaction between the Ni and Ln centers. Alternating current susceptibility measurements of complex 3 showed a small frequency dependence of the out-of-phase signal, ?''M , under zero direct current field, but without achieving a net maximum above 2?K. Magnetic studies on 1 revealed that it has a significant magnetocaloric effect. PMID:24817615
Das, Sourav; Dey, Atanu; Kundu, Subrata; Biswas, Sourav; Mota, A J; Colacio, Enrique; Chandrasekhar, Vadapalli
Symmetrizations for clustering directed graphs
Graph clustering has generally concerned itself with clustering undirected graphs; however the graphs from a number of important domains are essentially directed, e.g. networks of web pages, research papers and Twitter users. This paper investigates various ways of symmetrizing a directed graph into an undirected graph so that previous work on clustering undirected graphs may subsequently be leveraged. Recent work
Venu Satuluri; Srinivasan Parthasarathy
Symmetrized Bregman Divergences and Metrics
While JB divergences are non-negative, symmetric, and zero only when x = y, they are not squares of metrics in general. We show that square root of JB divergences give a metric only when the associated convex functions have a certain conditional positive definiteness (CPD) structure. Using results from harmonic analysis of infinitely divisible distributions (6), we show that the
Arindam Banerjee; Daniel Boley; Sreangsu Acharyya
DEC OSF\\/1 Symmetric Multiprocessing
The primary goal for an operating system in a symmetric multiprocessing (SMP) implementation is to convert the additional computing power provided to the system, as processors are added, into improved system performance without compromising system quality. The DEC OSF\\/1 version 3.0 operating system uses a number of techniques to achieve this goal. The techniques include algorithmic enhancements to improve parallelism
Jeffrey M. Denham; Paula Long; James A. Woodward
Simulation of Symmetrical Induction Machinery
The effectiveness of an analog computer in studying the performance of induction machinery is demonstrated with computer results which show the dynamic behavior of 2-phase and 3-phase machines during balanced and unbalanced operation. The computer simulation for these various modes of operation is conveniently obtained from the equations which describe the symmetrical induction machine in an arbitrary reference frame. Of
P. C. Krause; C. H. Thomas
On Symmetrical Multilevel Diversity Coding
Symmetrical multilevel diversity coding with independent data streams has been studied by Roche et al. (1992), and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their
Raymond W. Yeung; Zhen Zhang
Spreads and the symmetric topos
We introduce a new intrinsic notion of spread for toposes and geometric morphisms, and use it to give a �topological� characterization of Lawvere distributions on a topos. In the process, we relate spreads to zero-dimensional locales, and establish two new pure\\/spread factorizations for geometric morphisms. Our results are then applied to the study of the symmetric topos as a generalized
M. Bunge; J. Funk
Method of Multiple Reference Frames Applied to the Analysis of Symmetrical Induction Machinery
A method of analyzing the constant-speed performance of a symmetrical induction machine with applied stator phase voltages of any periodic form is presented. Symmetrical components are not used in this analysis. Instead, it is shown that by employing a series of reference frames, dc circuit theory may be used to determine the performance of induction machines. Since phasor and complex
Linear electric field mass spectrometry
A mass spectrometer and methods for mass spectrometry are described. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field. 8 figs.
McComas, D.J.; Nordholt, J.E.
A mass spectrometer and methods for mass spectrometry. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field.
McComas, David J. (Los Alamos, NM); Nordholt, Jane E. (Los Alamos, NM)
A new axis-symmetric, multigrid based Stokes solver for compressible flow
Mantle convection is governed by the conservation of momentum and mass, yielding the Stokes equations, and the conservation of energy. We solve these equations for a compressible Newtonian fluid with infinite Prandtl number, using finite elements on a 2d annulus. A Conjugate Gradient method together with a Multigrid solver is used to solve the resulting linear system of equations. Parallelization for symmetric multiprocessing architectures enables fast calculations at the resolutions necessary to resolve convection patterns at earth-like Rayleigh numbers. Mathematical formulations that are similar to those of the 3d mantle convection code TERRA together with a modular design enable us to use the code as a framework to test various discretization approaches. Also, different Multigrid designs can be selected, yielding distinctive cycling patterns and smoothers. These can be applied to several levels of complexity in the original problem, currently ranging from the Poisson equation to compressible Stokes flow.
Weism�ller, J.; Mohr, M.; Bunge, H.-P.
Homogeneous solvation controlled photoreduction of cobalt(III) complexes in aqueous 2-methyl-2-propanol solutions. Linear solvation energy relationship and cyclic voltammetric analyses
The effect of solvent participation on the ligand-to-metal charge transfer (LMCT, L ? Co III) reduction of the of Co III(en) 2Br(RC 6H 4NH 2) 2+ where R = m-OCH 3, p-F, H, m-CH 3, p-CH 3,p-OC 2H 5 and p-OCH 3 were examined in aqueous 2-methyl-2-propanol (Bu tOH) solutions. The change in the reduction behavior of Co III centre was also examined through cyclic voltammetric studies. The observed reduction in quantum yield due to LMCT excitation can mainly be accounted using linear solvation energy relationship (LSER) comprising model correlation equations. These consist of empirical parameters such as Grunwald-Winstein's solvent ionizing power, Y, Dimroth-Richardt's solvent micro-polarity parameter, ETN, Gutmann's donor number, DN N, along with Kamlet-Taft's solvatochromic parameters (hydrogen bond acceptor acidity/basicity ?/ ? and solvent dipolarity/polarizability, ?*). The origin of solvent effect is found to be due to microscopic interaction between the solvent donor and the nitrogen-bound hydrogen of the ligand. Cyclic voltammograms show an irreversible reduction of Co III in DMF using Glassy Carbon Electrode, GCE, the redox peaks for the aniline complexes appear at -0.20 and 0.525 V. Irradiation of the complexes with UV light ( ? = 254 nm) in binary mixtures produce Co IIaq and the concentration of this species are highly dependent on xalc ( xalc = mole fraction of alcohol). The observed quantum yield (log ?Co(II)) is found to be linearly related to mole fraction of organic co-solvent added in the mixture, therefore, log ?Co(II) = 26.41 � 10 -2 when x2 = 0.0094 and 43.75 � 10 -2 when x2 = 0.076 for a typical complex Co III(en) 2Br( p-OCH 3C 6H 4NH 2) 2+ in aqueous 2-methyl-2-propanol at 300 K. Cyclic voltammetry and LSER analyses illustrate the variation of reduction property of Co(III) by the aryl ligand and homogeneous solvation of the excited state of the complex Co III(en) 2Br(RC 6H 4NH 2) 2+ in H 2O/Bu tOH mixtures.
Anbalagan, K.; Lydia, I. Sharmila
A New Smoothing Newton Method for Symmetric Cone Complementarity Problems
\\u000a Based on a new smoothing function, a smoothing Newton-type method is proposed for the solution of symmetric cone complementarity\\u000a problems (SCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each\\u000a iteration. Moreover, it does neither have restrictions on its starting point nor need additional computation which keep the\\u000a iteration sequence staying
Lixia Liu; Sanyang Liu
Symmetric eigenfilters for partial shortening in ADSL DMT transceivers
A partial shortening method of equalization for xDSL is presented. The novel method is suitable for FDD systems, shortening the effective channel impulse response and, additionally, achieving out-of-band noise reduction. A family of solutions based on linear phase FIR equalizers is described. The mathematical framework for all symmetric filters is developed. Channel shortening and bit rate simulation results for several
Carlos Ribeiro; Paulo S. R. Diniz
Observational Tests of Baryon Symmetric Cosmology.
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiat...
F. W. Stecker
Bregman sided and symmetrized centroids
We generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Because Bregman divergences are typically asymmetric, we consider both the left-sided and right-sided centroids and the symmetrized centroids, and prove that all three are unique. We give closed-form solutions for the sided centroids that are generalized means, and design a provably
Frank Nielsen; Richard Nock
Symmetric informationally complete quantum measurements
We consider the existence in arbitrary finite dimensions d of a positive operator valued measure (POVM) comprised of d2 rank-one operators all of whose operator inner products are equal. Such a set is called a �symmetric, informationally complete� POVM (SIC�POVM) and is equivalent to a set of d2 equiangular lines in Cd. SIC�POVMs are relevant for quantum state tomography, quantum
Joseph M. Renes; Robin Blume-Kohout; A. J. Scott; Carlton M. Caves
Spherically symmetric quantum geometry: Hamiltonian constraint
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric
Martin Bojowald; Rafal Swiderski
A Hopf laboratory for symmetric functions
An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focused on Laplace pairing, Sweedler cohomology for 1- and 2-cochains and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown
Bertfried Fauser; P. D. Jarvis
The theory of domains of positivity or symmetric cones is closely tied to that of Euclidean Jordan algebras and plays an important role in various branches of analysis and geometry. The goal of this paper is to provide a self-contained description of Riemannian and Finsler geometries of symmetric cones and their applications. 1. Symmetric cones and Euclidean Jordan algebras An
Symmetric functions and P-recursiveness
Many enumeration problems, such as that of counting nonnegative integer matrices with given row and column sums, have solutions which can be expressed as coefficients of symmetric functions. We show here how useful formulas can be obtained from these symmetric function generating functions. In some cases, the symmetric functions yield reasonably simple explicit formulas or generating functions for the coefficients.
Ira M. Gessel
Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices
We introduce a discrete lossy system, into which a double "hot spot" (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic waveguides, with a pair of amplified nonlinear cores embedded into it. We focus on the case of self-defocusing nonlinearity and cubic losses acting at the HSs. Symmetric localized modes pinned to the double HS are constructed in an implicit analytical form, which is done separately for the cases of odd and even numbers of intermediate sites between the HSs. In the former case, some stationary solutions feature a W-like shape, with a low peak at the central site, added to tall peaks at the positions of the embedded HSs. The special case of two adjacent HSs is considered too. Stability of the solution families against small perturbations is investigated in a numerical form, which reveals stable and unstable subfamilies. The instability generated by an isolated positive eigenvalue leads to a spontaneous transformation into a co-existing stable antisymmetric mode, while a pair of complex-conjugate eigenvalues gives rise to persistent breathers. This article is a contribution to the volume dedicated to Professor Helmut Brand on the occasion of his 60th birhday.
Chow, K. W.; Ding, Edwin; Malomed, B. A.; Tang, A. Y. S.
A PT-symmetric QES partner to the Khare�Mandal potential with real eigenvalues
We consider a PT-symmetric partner to Khare�Mandal's recently proposed non-Hermitian potential with complex eigenvalues. Our potential, which is quasi-exactly solvable, is shown to possess only real eigenvalues.
B. Bagchi; S. Mallik; C. Quesne; R. Roychoudhury
On the Closure Problem in the Reduction of Complex Atmospheric Models by PIPs and EOFs: A Comparison for the Case of a Two-Layer Model with Zonally Symmetric Forcing
The reduction of complex systems to their essential degrees of freedom (e.g., patterns spanning that part of state space that the system's trajectory passes in time) and development of reduced models based on these might be one tool for improving basic understanding of simulation results obtained from current, increasingly more complex, meteorological circulation models. Some successful work on the reduction
U. Achatz; G. Schmitz
Laplace and Segal�Bargmann transforms on Hermitian symmetric spaces and orthogonal polynomials
Let D=G\\/K be a complex bounded symmetric domain of tube type in a complex Jordan algebra V and let DR=J?D?D be its real form in a formally real Euclidean Jordan algebra J?V; DR=H\\/L is a bounded realization of the symmetric cone in J. We consider representations of H that are gotten by the generalized Segal�Bargmann transform from a unitary G-space
Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge
The in-plane vibration of a complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of the cables and transverse vibrations of segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge are determined, and orthogonality relations of the mode shapes are established. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for various symmetrical and non-symmetrical bridge cases with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies when the bridge model is symmetrical and/or partially symmetrical, and the mode shapes tend to be more localized when the bridge model is less symmetrical. The relationships between the natural frequencies and mode shapes of the cable-stayed bridge and those of a single fixed-fixed cable and the single simply-supported deck beam are analyzed. The results, which are validated by commercial finite element software, demonstrate some complex classical resonance behavior of the cable-stayed bridge.
Cao, D. Q.; Song, M. T.; Zhu, W. D.; Tucker, R. W.; Wang, C. H.-T.
Modeling Symmetric Macromolecular Structures in Rosetta3
Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems.
DiMaio, Frank; Leaver-Fay, Andrew; Bradley, Phil; Baker, David; Andre, Ingemar
Quadratic convergence of a smoothing Newton method for symmetric cone programming without strict complementarity
This paper deals with symmetric cone programming (SCP), which includes the linear programming (LP), the second-order cone\\u000a programming (SOCP), the semidefinite programming (SDP) as special cases. Based on the Chen�Mangasarian smoothing function\\u000a of the projection operator onto symmetric cones, we establish a smoothing Newton method for SCP. Global and quadratic convergence\\u000a of the proposed algorithm is established under the primal
Lingchen Kong
Magnetic evidence of a crustal fault affecting a linear laccolith: The Guadiana Fault and the Monchique Alkaline Complex (SW Iberian Peninsula)
Magnetic anomalies can help reveal the structure of the upper crust in regions with intermediate or basic igneous rocks, and their continuity is essential to determine the position of crustal faults. The southwestern Iberian Peninsula constitutes the foreland of the Betic Cordillera and is characterized by an elongated E-W dipole extending 200 km toward its external zones. The anomaly is related to the outcropping Monchique Alkaline Complex, characterized by rocks of moderate magnetic susceptibility (0.029 SI) intruding into the metapelitic host rock of the South Portuguese Zone. Analysis of aeromagnetic and field magnetic anomalies serves to constrain the geometry of this laccolith. Toward the east, the magnetic dipole has a 60 km long N-S sharp boundary that coincides with the southern part of the Guadiana River. Field magnetic and gravity anomalies confirm the presence of this structure. It is produced by a sharp step in the elongated anomalous body, with an E downthrown block, interpreted as the offset produced by a deep N-S crustal fault-the Guadiana Fault. Therefore, the Guadiana River has three long linear segments near its mouth, locally coinciding with a N-S trending joint set, that support the presence of this major fault. To date, no evidence of this tectonic discontinuity, coinciding with the Spanish-Portuguese border, has been reported. Magnetic research is essential for understanding the structure of wide regions intruded by intermediate and/or basic igneous rocks.
Gonz�lez-Castillo, Lourdes; Galindo-Zald�var, Jes�s; Ruiz-Const�n, Ana; Pedrera, Antonio
Coacervation in Symmetric Mixtures of Oppositely Charged Rodlike Polyelectrolytes
Phase separation in the salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the symmetric mixtures are carried out. It is shown that electrostatics favor nematic ordering. Also, the coexistence curves for the symmetric mixtures are computed, and the effects of the linear charge density and the electrostatic interaction strength on the phase boundaries are studied. It is found that the counterions are uniformly distributed in the coexisting phases for low electrostatic interaction strengths characterized by the linear charge density of the polyelectrolytes and the Bjerrum's length. However, the counterions also phase separate along with the rodlike polyelectrolytes with an increase in the electrostatic interaction strength. It is shown that the number density of the counterions is higher in the concentrated (or coacervate) phase than in the dilute (or supernatant) phase. In contrast to the rodlike mixtures, flexible polyelectrolyte mixtures can undergo only isotropic-isotropic phase separation. A comparison of the coexistence curves for the weakly charged rodlike with the flexible polyelectrolyte mixtures reveals that the electrostatic driving force for the isotropic-isotropic phase separation is stronger in the flexible mixtures.
Kumar, Rajeev; Fredrickson, Glenn
Integrability properties of symmetric-space fields reduced from axially symmetric Einstein and Yang-Mills equations
A gauge-covariant symmetric-space formulation and integrability properties are given for symmetric-space fields reduced from the stationary axially symmetric Einstein equation and static axially symmetric self-dual Yang-Mills equations.
Chau, L.; Chou, K.; Hou, B.; Song, X.
Linear lattice gauge theory
Linear lattice gauge theory is based on link variables that are arbitrary complex or real N�N matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space both formulations belong to the same universality class, such that the continuum limits of linear and non-linear lattice gauge theory are identical. We explore if the linear formulation can help to find a non-perturbative continuum limit formulated in terms of continuum fields. Linear lattice gauge theory exhibits excitations beyond the gauge fields. In the linear formulation the running gauge coupling corresponds to the flow of the minimum of a "link potential". This minimum occurs for a nonzero value of the link variable l0 in the perturbative regime, while l0 vanishes in the confinement regime. We discuss a flow equation for the scale-dependent location of the minimum l0(k).
Wetterich, C.
Nonlinear modes in finite-dimensional PT-symmetric systems.
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schr�dinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra does not imply similarity of the structure or stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. In addition, the stability is not directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use a graph representation of PT-symmetric networks allowing for a simple illustration of linearly equivalent networks and indicating their possible experimental design. PMID:23003257
Zezyulin, D A; Konotop, V V
A C(3)-symmetric chiroptical molecular propeller based on hexakis(phenylethynyl)benzene with a threefold terephthalamide: stereospecific propeller generation through the cooperative transmission of point chiralities on the host and guest upon complexation.
Propeller-shaped dynamic helicity was generated in a hexakis(phenylethynyl)benzene framework that preferred a particular sense to afford a strong CD signal, which was realized by the cooperative transmission of point chiralities upon complexation with a chiral guest through a threefold binding site presented by a syn-formed terephthalamide. PMID:23801052
Katoono, Ryo; Kawai, Hidetoshi; Ohkita, Masakazu; Fujiwara, Kenshu; Suzuki, Takanori
Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method
The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schr�dinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schr�dinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly,
Ramiro Acevedo; Richard Lombardini; Matthew A. Turner; James L. Kinsey; Bruce R. Johnson
The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schro�dinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schro�dinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly,
The Generalized Sidelobe Canceller Based on Quaternion Widely Linear Processing
We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC.
Tao, Jian-wu; Chang, Wen-xiu
New Technologies of Symmetric-Wave Multicolor Thermometry and Their Metrological Characteristics
The influence of the optical characteristics of multicolor thermometry on its methodical and instrumental errors was investigated and, on the basis of the investigations performed, a new direction of symmetric-wave multicolor pyrometry of radiation, including linear and universal thermometric technologies, has been developed. It is shown that, in the case where the spectral distribution of the radiating capacity of a body is linear, the methodical error in determining its temperature by the method of linear symmetric-wave pyrometry of radiation is close to zero and is practically determined by the discreteness of the selection of temperatures of this body. The errors in measuring the temperature of the majority of materials, e.g., tungsten, by the method of linear symmetric-wave thermometry are 9.1-25.0, 5.9-6.8, and 2.4-3.3 times smaller than those given by classical energy, spectral-ratio and polychromatic pyrometries of radiation. The universal thermometry method proposed allows one to eliminate the methodical error, predominating in optical thermometry, in determining the temperatures of bodies with different linear and nonlinear spectral distributions of their radiating capacity. The residual instrumental error given by linear and universal symmetric-wave pyrometries of radiation of a body does not exceed the error in measuring its initial monochromatic radiation temperatures, i.e., 0.2-0.5%.
Zhukov, L. F.; Kornienko, A. L.
Monolithic symmetric ion trap for quantum simulation
We describe the novel design of a monolithic two-level ion trap that combines the flexibility and scalability of VLSI silicon microfabrication with the superior trapping characteristics of multi-level traps. Electrostatic simulations demonstrate that the trap has a deep trapping potential (1 eV for Yb+ ion) and radially symmetric RF confinement field. The trap has an angled through-chip slot which allows backside ion loading and through laser access while avoiding surface light scattering and dielectric charging. The geometrical trap features and dimensions are optimized for investigating ion chains with equal ion spacing. Control potentials have been derived to produce linear equally-spaced ion chains of up to 50 ions that can be used to perform simulations of quantum magnets. The potentials are optimized to give ion separations of 5 to 10 microns, micromotion compensation, and constant motional mode axes and frequencies along the chain. The trap is in fabrication at Georgia Tech using techniques similar to those developed for the planar ion traps.
Drift waves in helically symmetric stellarators
The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is bad and magnitude of the local magnetic shear and magnetic field is minimum. Modes are found more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of ?i is found to be 2/3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear and the compression of flux surfaces in the bad curvature region. In most of these studies, a simplified adiabatic electrons response is used. Progress on a more rigorous treatment of the electrons will be reported that accounts for toroidally and helically trapped particles and landau resonances in stellarator geometry.
Rafiq, Tariq
The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to be more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of ?i is found to be 2/3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear, and the compression of flux surfaces in the unfavorable curvature region.
Rafiq, T.; Hegna, C. C.
Artificial Second Order Non-Linearity in Photonic Crystals.
We describe a technique for obtaining effective second order non- linearity X(sup 2) in non-centro-symmetric Photonic Crystal made from centro- symmetric materials (e.g., glass, Ge or Si). The effect is based on the electric quadrupole transition, strong ...
A. Feigel B. Sfez Z. Kotler
Symmetrical mixtures in external fields.
We have studied the behavior of symmetrical binary mixtures of Lennard-Jones particles in contact with strongly adsorbing walls using Monte Carlo simulation methods in the grand canonical and semi-grand canonical ensembles. Two types of the surface potential have been applied. The first depends on the distance from the surface only, while the second involves periodic modulations in the directions parallel to the wall. In the latter case, it has been assumed that the solid substrate is a fcc crystal with the surface being the (100) face. We have considered the systems in which the surface potential is strong enough to induce the layer-by-layer adsorption at low temperatures and discussed the interplay between the demixing transition and the structure of thin films for several systems characterized by different parameters describing the interactions in the system. PMID:23822318
Materniak, S; Patrykiejew, A
Variational Iterative Methods for Nonsymmetric Systems of Linear Equations.
We consider a class of interative algorithms for solving systems of linear equations where the coefficient matrix is nonsymmetric with positive-definite symmetric part. The algorithms are modelled after the conjugate gradient method, and are well-suited f...
S. C. Eisenstat H. C. Elman M. H. Schultz
On H?-control for symmetric systems
Results regarding H? control for symmetric systems are introduced. It is shown that in order to find the compensator, only one nonlinear matrix equation has to be solved, instead of two Riccati equations as in the general case. A numerically robust algorithm for the solution of the equation introduced is presented. The compensator obtained is also shown to be symmetric.
L. Fortuna; G. Muscato; G. Nunnari
Continuity and Separation in Symmetric Topologies
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Harris, J.; Lynch, M.
Symmetric drawings of triconnected planar graphs
Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we need two steps. The first step is to find appropriate automorphisms. The second step is to draw the graph to display the automorphisms. Our aim in this paper is to construct maximally symmetric straight-line drawings of
Seok-Hee Hong; Brendan D. McKay; Peter Eades
On the Symmetric Space ?-MODEL Kinematics
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.
Yilmaz, Nejat T.
Angular Motion of Spinning Almost Symmetric Missiles.
An almost symmetric missile is a missile whose zero-spin pitch and yaw frequencies are 'nearly' equal. The angular motion of a spinning almost symmetric missile can be described by five rotating modal vectors. Two of these vectors vanish when the frequenc...
C. H. Murphy
Symmetric Distributed Source Coding using LDPC Code
Distributed source coding is a promising enabling technology for sensor network applications. Symmetric distributed source coding can achieve the entire Slepian-Wolf rate region and offer sensor network applications a wide range of options to compress and transmit data. In this paper, we design a new symmetric distributed coding scheme that realize the benefits of both simplified code construction and bit
Baochun Bai; Yang Yang; Pierre Boulanger; Janelle J. Harms
Higher Dimensional Spherically Symmetric Expanding Wormholes in Einstein's Gravity
We present ( n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein's framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.
Ebrahimi, Esmaeil
We present (n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein's framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.
Geometrodynamics in a spherically symmetric, static crossflow of null dust
The spherically symmetric, static space-time generated by a crossflow of noninteracting radiation streams, treated in the geometrical optics limit (null dust), is equivalent to an anisotropic fluid forming a radiation atmosphere of a star. This reference fluid provides a preferred/internal time, which is employed as a canonical coordinate. Among the advantages we encounter a new Hamiltonian constraint, which becomes linear in the momentum conjugate to the internal time (therefore yielding a functional Schroedinger equation after quantization), and a strongly commuting algebra of the new constraints.
Horvath, Zsolt; Kovacs, Zoltan; Gergely, Laszlo A. [Departments of Theoretical and Experimental Physics, University of Szeged, Szeged 6720, Dom ter 9 (Hungary)
BDDC for nonsymmetric positive definite and symmetric indefinite problems
The balancing domain decomposition methods by constraints are extended to solving both nonsymmetric, positive definite and symmetric, indefinite linear systems. In both cases, certain nonstandard primal constraints are included in the coarse problems of BDDC algorithms to accelerate the convergence. Under the assumption that the subdomain size is small enough, a convergence rate estimate for the GMRES iteration is established that the rate is independent of the number of subdomains and depends only slightly on the subdomain problem size. Numerical experiments for several two-dimensional examples illustrate the fast convergence of the proposed algorithms.
Tu, Xuemin; Li, Jing
Light induced Josephson like current between two coupled nonlinear cavities coupled with a symmetrically positioned photonic crystal waveguide.
We consider light transmission in a photonic crystal waveguide coupled with two identical nonlinear cavities positioned symmetrically beside the waveguide and coupled with each other. Using Green function theory we show three scenarios for the transmission. The first one inherits the linear case in which the light transmission preserves the symmetry. In the second scenario the symmetry is broken by the light intensities at the cavities. In the third scenario the intensities are equal but the phases of the complex amplitudes are different at the cavities. This results in a Josephson like current between the cavities. The model consideration agrees well with computations of the Poynting current in a photonic crystal waveguide coupled with two optical cavities filled with a Kerr material. PMID:21406925
Bulgakov, Evgeny; Pichugin, Konstantin; Sadreev, Almas
Light induced Josephson like current between two coupled nonlinear cavities coupled with a symmetrically positioned photonic crystal waveguide
We consider light transmission in a photonic crystal waveguide coupled with two identical nonlinear cavities positioned symmetrically beside the waveguide and coupled with each other. Using Green function theory we show three scenarios for the transmission. The first one inherits the linear case in which the light transmission preserves the symmetry. In the second scenario the symmetry is broken by the light intensities at the cavities. In the third scenario the intensities are equal but the phases of the complex amplitudes are different at the cavities. This results in a Josephson like current between the cavities. The model consideration agrees well with computations of the Poynting current in a photonic crystal waveguide coupled with two optical cavities filled with a Kerr material.
Inverse eigenproblem for R-symmetric matrices and their approximation
Let be a nontrivial involution, i.e., R=R-1[not equal to]�In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n�n matrix , find such that , where is the solution set of IEP and ||[dot operator]|| is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition.
Yuan, Yongxin
Entropic gravity versus gravitational pseudotensors in static spherically symmetric spacetimes
We present some well-known energy-momentum complexes and evaluate the gravitational energy associated with static spherically symmetric spacetimes. In fact, the energy distribution of the aforementioned gravitational background that is contained in a two-sphere of radius r shows that a test particle situated at a finite distance r experiences the gravitational field of the effective gravitational mass. In addition, we apply Verlinde's entropic gravity to find the emergent gravitational energy on static spherically symmetric screens. In this setup, we find that the energy distribution in the prescription of M�ller is similar to the energy derived from the emergent gravity, while other prescriptions give the different results. This result may confirm the argument of Lessner who argues that M�ller's definition of energy is a powerful concept of energy in General Relativity.
Mehdipour, S. Hamid
Maximum-confidence discrimination among symmetric qudit states
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of sequential maximum-confidence (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.
Jimenez, O. [Departamento de Fisica, Facultad de Ciencias Basicas, Universidad de Antofagasta, Casilla 170, Antofagasta (Chile); Center for Optics and Photonics, Universidad de Concepcion, Casilla 4016, Concepcion (Chile); Solis-Prosser, M. A.; Delgado, A.; Neves, L. [Center for Optics and Photonics, Universidad de Concepcion, Casilla 4016, Concepcion (Chile); MSI-Nucleus on Advanced Optics, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)
Optimally smooth symmetric quadrature mirror filters for image coding
Symmetric quadrature mirror filters (QMFs) offer several advantages for wavelet-based image coding. Symmetry and odd-length contribute to efficient boundary handling and preservation of edge detail. Symmetric QMFs can be obtained by mildly relaxing the filter bank orthogonality conditions. We describe a computational algorithm for these filter banks which is also symmetric in the sense that the analysis and synthesis operations have identical implementations, up to a delay. The essence of a wavelet transform is its multiresolution decomposition, obtained by iterating the lowpass filter. This allows one to introduce a new design criterion, smoothness (good behavior) of the lowpass filter under iteration. This design constraint can be expressed solely in terms of the lowpass filter tap values (via the eigenvalue decomposition of a certain finite-dimensional matrix). Our innovation is to design near- orthogonal QMFs with linear-phase symmetry which are optimized for smoothness under iteration, not for stopband rejection. The new class of optimally smooth QMF filter banks yields high performance in a practical image compression system.
Heller, Peter N.; Shapiro, Jerome M.; Wells, Raymond O., Jr.
PT-symmetric laser absorber
In a recent work, Y. D. Chong [Phys. Rev. Lett.0031-900710.1103/PhysRevLett.105.053901 105, 053901 (2010)] proposed the idea of a coherent perfect absorber (CPA) as the time-reversed counterpart of a laser, in which a purely incoming radiation pattern is completely absorbed by a lossy medium. The optical medium that realizes CPA is obtained by reversing the gain with absorption, and thus it generally differs from the lasing medium. Here it is shown that a laser with an optical medium that satisfies the parity-time (PT) symmetry condition ?(-r)=?*(r) for the dielectric constant behaves simultaneously as a laser oscillator (i.e., it can emit outgoing coherent waves) and as a CPA (i.e., it can fully absorb incoming coherent waves with appropriate amplitudes and phases). Such a device can thus be referred to as a PT-symmetric CPA laser. The general amplification or absorption features of the PT CPA laser below lasing threshold driven by two fields are determined.
Introduction to Linear Dynamical Systems
Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.Topics include: Least-squares approximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.Prerequisites: Exposure to linear algebra and matrices. You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.
Boyd, Stephen
Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial
We demonstrate the coexistence of two tunable symmetric and asymmetric resonances in a metamaterial composed of asymmetrical split-rings (ASRs) patterned on a dielectric layer numerically and experimentally. The full-wave simulation and measurement results demonstrate that the metamaterial reveals a symmetric cross-polarization transmission band with a ripple-free peak and asymmetric co-polarization transmission bands characterized by trapped-mode resonances. Both symmetric and asymmetric resonances can be easily tuned via the incident angle of electromagnetic waves. The resonant excitation and coupling of the electric and magnetic dipole moments contribute to the conversion of two orthogonal linear polarizations. The ASR metamaterial shows a directionally asymmetric transmission for both linearly and circularly polarized waves for large angles of incidence. The proposed ASR metamaterial is of importance to develop novel metamaterial-based devices.
Shi, J. H.; Zhu, Z.; Ma, H. F.; Jiang, W. X.; Cui, T. J.
Chiral-symmetric technicolor with standard model Higgs boson
Most of the traditional technicolor-based models are known to be in a strong tension with the electroweak precision tests. We show that this serious issue is naturally cured in strongly coupled sectors with chiral-symmetric vectorlike gauge interactions in the framework of the gauged linear ? model. We discuss possible phenomenological implications of such a nonstandard chiral-symmetric technicolor scenario in its simplest formulation preserving the standard model (SM) Higgs mechanism. For this purpose, we assume the existence of an extra technifermion sector confined under extra SU(3)TC at the energy scales reachable at the LHC, ?TC�0.1-1TeV and interacting with the SM gauge bosons in a chiral-symmetric (vectorlike) way. In the framework of this scenario, the SM Higgs vacuum expectation value acquires a natural interpretation in terms of the condensate of technifermions in confinement in the nearly conformal limit. We study the influence of the lowest-lying composite physical states, namely, technipions, technisigma, and constituent technifermions, on the Higgs sector properties in the SM and other observables at the LHC. We find that the predicted Higgs boson signal strengths in ??, vector-boson VV*, and fermion ff� decay channels can be sensitive to the new strongly coupled dynamics and are consistent with the current SM-like Higgs boson observations in the limit of relatively small Higgs-technisigma mixing. At the same time, the chiral-symmetric technicolor provides us with rich technipion phenomenology at the LHC, and its major implications are discussed in detail.
Pasechnik, Roman; Beylin, Vitaly; Kuksa, Vladimir; Vereshkov, Grigory
Symmetric Monotone Venn Diagrams with Seven Curves
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2 n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A k-region in a diagram is a region that is in the interior of precisely k curves. A n-Venn diagram is symmetric if it has a point of rotation about which rotations of the plane by 2?/n radians leaves the diagram fixed; it is polar symmetric if it is symmetric and its stereographic projection about the infinite outer face is isomorphic to the projection about the innermost face. A Venn diagram is monotone if every k-region is adjacent to both some (k - 1)-region (if k > 0) and also to some k + 1 region (if k < n). A Venn diagram is simple if at most two curves intersect at any point. We prove that the "Gr�nbaum" encoding uniquely identifies monotone simple symmetric n-Venn diagrams and describe an algorithm that produces an exhaustive list of all of the monotone simple symmetric n-Venn diagrams. There are exactly 23 simple monotone symmetric 7-Venn diagrams, of which 6 are polar symmetric.
Cao, Tao; Mamakani, Khalegh; Ruskey, Frank
Supersymmetric harmonic maps into symmetric spaces
We study supersymmetric harmonic maps from the point of view of integrable systems. We show that the superharmonic maps from R into a symmetric space are solutions of an integrable system and that we have a Weierstrass-type representation in terms of holomorphic potentials (as well as of meromorphic potentials). At the end of the paper we show that superprimitive maps from R into a 4-symmetric space give us, by restriction to R2, solutions of the second elliptic system associated with the previous 4-symmetric space.
Khemar, Idrisse
A two-step design method for high compact rotationally symmetric optical system for LED surface light source.
A two-step optimization method is proposed to design a compact single-surface far-field illumination system, satisfying the requirements of illuminance uniformity and light control efficiency with h/D less than 3:1. In the first step, the conventional tailored edge-ray design (TED) method is employed to generate prescribed illumination distribution for the rotationally symmetric optical system, and an optimization process is added to reach a balance between illuminance uniformity and light control efficiency. Based on the improved TED method, we can construct an initial optical system more accurate than that obtained by point source assumption. In the second step, an iterative feedback modification process is employed to optimize the initial optical system, so that the degradation of performance due to insufficient control of skew rays is mitigated. Because the initial optical system constructed in the first step is accurate enough, the second-step feedback modification can converge to a satisfactory result within several iterations. As an example, a free-form rotationally symmetric lens with the height of h = 25 mm is designed for a discoidal LED source with the diameter of D = 10 mm. Both high illuminance uniformity of 0.75 and high light control efficiency of 0.86 are obtained simultaneously. The method can be further used to achieve more complex non-uniform illumination distributions. The design of an optical system with h/D = 2.5:1 and a circular linear illumination distribution is demonstrated. PMID:24922232
Mao, Xianglong; Li, Hongtao; Han, Yanjun; Luo, Yi
The free-electron laser in a symmetrical confocal resonator
A tapered wiggler is used in a FEL oscillator to improve the saturation efficiency. During signal buildup the tapered wiggler does not provide optimum phase synchronism between the electron beam and the electromagnetic wave, resulting in an appreciable loss in small-signal gain. This problem can be ameliorated by using a multicomponent wiggler, which is a combination of a uniform wiggler and a tapered section. During buildup, gain is primarily contributed by the linear element, and at high power levels the gain and efficiency are enhanced by the taper. Ideally, one would like to have the optical waist location near the linear section at small-signal levels and at near the tapered section at high power levels. Placing the FEL in a symmetrical confocal resonator approaches this desired effect automatically since it has the unique characteristic that a stable mode exists for all locations of the waist of a Gaussian beam along the axis of the interferometer.
Ozcan, Meric; Pantell, Richard H.
An application of eigenspace methods to symmetric flutter suppression
An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Results indicate that the methods provide feedback control laws that make stability of the nominal closed loop systems insensitive to changes in dynamic pressure.
Fennell, Robert E.
Transitions between symmetric and asymmetric solitons in dual-core systems with cubic-quintic nonlinearity
It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition into an asymmetric soliton via a subcritical bifurcation. A similar phenomenon was found in a dual-core system with quadratic nonlinearity, and in linearly coupled fiber Bragg gratings, with a difference
Lior Albuch; Boris A. Malomed
Diffraction Fields in the Focal Space of Symmetrical Hyperbolic Focusing Lens
The fields refracted by circular symmetric hyperbolic lens illuminated by a linearly polarized plane wave are calculated from the induced surface currents. It is shown that the fields in the axial region approximate to the fields in the aperture of corrugated horn under balanced hybrid condition. The image structures for different focal ratio are compared with the classical Airy pattern,
W. B. Dou; Z. L. Sun; X. Q. Tan
Generalized quantum measurements [also known as positive operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric informationally complete (SIC) POVM, is the most
Z. E. D. Medendorp; L. K. Shalm; A. M. Steinberg; F. A. Torres-Ruiz; G. N. M. Tabia; C. A. Fuchs
Block-Diagonalization of the Symmetric First-Order Coupled-Mode System
We consider the Hamiltonian coupled-mode system that occur in nonlinear optics, photonics, and atomic physics. Spectral stability of gap solitons is determined by eigenvalues of the linearized coupled-mode system, which is equivalent to a four-by-four Dirac system with sign-indefinite metric. In the special class of symmetric nonlinear potentials, we construct a block-diagonal representation of the linearized equations, when the spectral
Marina Chugunova; Dmitry Pelinovsky
Dual linearized gravity in arbitrary dimensions
We construct a dual formulation of linearized gravity in a first-order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field \\Phi_{[\
Ajith, K. M.; Harikumar, E.; Sivakumar, M.
On the pseudo-norm and admissible solutions of the {\\cal PT} -symmetric Scarf I potential
The physically admissible solutions of the {\\cal PT} -symmetric Scarf I potential are identified in the domain of real and complex energies. It is found that generally there are no admissible complex-energy solutions, and there is one with real energy. In a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi-parity q = �; however, the two sets are not {\\cal PT} -orthogonal in the domain of real energies. The sign of the pseudo-norm of states with real energy is found to oscillate as (-1)n, in accordance with the example of other {\\cal PT} -symmetric potentials possessing an infinite number of discrete levels. It is argued that the spontaneous breakdown of {\\cal PT} -symmetry cannot be defined for the Scarf I potential. A comparison with some {\\cal PT} -symmetric extensions of the infinite square well is presented.
L�vai, G.
PT-symmetric quantum mechanics
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H�=H on the Hamiltonian, where � represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement
Carl M. Bender; Stefan Boettcher; Peter N. Meisinger
Nonlocality and entanglement for symmetric states
In this paper, building on some recent progress combined with numerical techniques, we shed some light on how the nonlocality of symmetric states is related to their entanglement properties and on their potential usefulness in quantum information processing. We use semidefinite programming techniques to devise a device-independent classification of three 4-qubit states into two classes inequivalent under local unitaries and permutation of systems. We study nonlocal properties when the number of parties grows large for two important classes of symmetric states: W states and GHZ states, showing that they behave differently under the inequalities we consider. We also discuss the monogamy arising from the nonlocal correlations of symmetric states. We show that although monogamy in a strict sense is not guaranteed for all symmetric states, strict monogamy is achievable for all Dicke states when the number of parties goes to infinity.
Wang, Zizhu; Markham, Damian
Postpartum Peripheral Symmetrical Gangrene: A Case Report
Background Symmetrical peripheral gangrene is usually associated with underlying medical problems and it is seldom seen in pregnancy. Sepsis though common in a setting of delivery by unskilled midwife is rarely accompanied by symmetrical gangrene. Case Presentation We report a case of symmetrical peripheral gangrene which occurred in the winter, triggered possibly by sepsis and a single dose of ergot. A high index of suspicion, early diagnosis and intervention with appropriate measures will result in favorable outcome in such cases. Conclusion Although postpartum period is of high risk for sepsis and use of ergot alkaloids is common in labor but occurrence of peripheral symmetrical gangrene is rare. A high index of suspicion for the diagnosis and timely intervention will prevent irreparable damage and loss of limb.
Sharma, Lipi; Mehta, Sumita; Rajaram, Shalini; Aggarwal, Rachna; Gupta, Sanjay; Goel, Neerja
Symmetric Space ?-MODEL Dynamics:. Current Formalism
After explicitly constructing the symmetric space sigma model Lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism, we derive the field equations of the theory.
Multiple symmetric lipomatosis: a diagnostic dilemma.
Introduction. Multiple symmetric lipomatosis, or Madelung's disease, is a rare condition which is characterized with large symmetrical accumulation of noncapsulated fat tissue in upper arms, neck, and shoulder areas. The disease etiology is unknown, with the highest incidence in the Mediterranean region. Case Presentation. Here, we present the case of Madelung's disease with symmetric fat distribution throughout the neck and history of alcoholism. The patient was treated from several diseases associated with alcoholism and hospitalized several times, but the diagnosis of Madelung's disease was omitted. The thyroid gland disease was excluded, while enlargement of the neck adipose tissue was attributed to obesity. Conclusions. This study points out possible diagnostic mistakes when a physician is not aware of a differentiation diagnosis of symmetrically enlarged neck masses, especially in geographic regions with high incidence of this disease. PMID:23983713
Mimica, Mladen; Pravdic, Danijel; Nakas-Icindic, Emina; Karin, Maja; Babic, Emil; Tomic, Monika; Bevanda, Milenko
VLSI implementation of a reduced symmetric fuzzy singleton set
A fuzzy logic controller (FLC) has been proposed and implemented in many control systems to deliver smooth and more reliable outputs than the traditional control systems. In most of the existing VLSI FLC chips, the architectures are based on general purpose microcontroller structure tailored to fuzzy logic implementation. The drawbacks in these types of FLC VLSI chips are low speed, high cost, and long design time. Moreover, an expensive development system is also needed to program a general purpose microcontroller for a specific fuzzy logic control system. In order to alleviate the drawbacks in existing VLSI fuzzy logic circuits, a reduced symmetric fuzzy singleton set (RSFSS) is proposed in this paper. The proposed RSFSS system can handle three input variables, nine rules for each input variable, and produces two output values. Each rule is based on a symmetric triangular membership function. The triangular membership functions of each state variable are defined symmetrically with respect to the centroid of the universe of discourse. Since the hardware complexity is greatly reduced, the entire FLC based on the RSFS structure can be implemented on a VLSI chip with a dimension of 2.22 mm X 2.22 mm.
Chang, Yi-Chieh; Wu, Kung C.
Symmetric splitting of very light systems
Inclusive and coincidence measurements have been performed to study symmetric products from the reactions 74-186 MeV 12C+40Ca, 141 MeV 9Be+40Ca, and 153 MeV 6Li+40Ca. The binary decay of the composite system has been verified. Energy spectra, angular distributions, and fragment correlations are presented. The total kinetic energies for the symmetric products from these very light composite systems are compared to
K. Grotowski; Z. Majka; R. Planeta; M. Szczodrak; Y. Chan; G. Guarino; L. G. Moretto; D. J. Morrissey; L. G. Sobotka; R. G. Stokstad; I. Tserruya; S. Wald; G. J. Wozniak
Symmetric informationally complete measurements of arbitrary rank
There has been much interest in so-called SIC-POVMs, i.e., rank 1 symmetric informationally complete positive operator valued\\u000a measures. In this paper we discuss the larger class of POVMs that are symmetric and informationally complete, but not necessarily\\u000a rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM that is closely related to the
D. M. Appleby
Parameter Estimates for Symmetric Stable Distributions
Building on results of an earlier article [6], estimators are suggested for the scale parameter and characteristic exponent of symmetric stable distributions, and Monte Carlo studies of these estimators are reported. The powers of various goodness-of-fit tests of a Gaussian null hypothesis against non-Gaussian stable alternatives are also investigated. Finally, a test of the stability property of symmetric stable variables
Eugene F. Fama; Richard Roll
Properties of internal solitary waves in a symmetric three-layer fluid
Though all the natural media have smooth density stratifications (with the exception of special cases such as sea surface, inversion layer in the atmosphere), the scales of density variations can be different, and some of them can be considered as very sharp. Therefore for the description of internal wave propagation and interaction in the ocean and atmosphere the n-layer models are often used. In these models density profile is usually approximated by a piecewise-constant function. The advantage of the layered models is the finite number of parameters and relatively simple solutions of linear and weakly nonlinear problems. Layered models are also very popular in the laboratory experiments with stratified fluid. In this study we consider symmetric, continuously stratified, smoothed three-layer fluid bounded by rigid horizontal surface and bottom. Three-layer stratification is proved to be a proper approximation of sea water density profile in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because in the symmetric case it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, that are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. The goal of our study is to determine the properties of localized stationary internal gravity waveforms (solitary waves) in this symmetric three-layer fluid. The investigation is carried out in the framework of improved mathematical model describing the transformation of internal wave fields generated by an initial disturbance. The model is based on the program complex for the numerical simulation of the two-dimensional (vertical plane) fully nonlinear Euler equations for incompressible stratified fluid under the Boussinesq approximation. Initial disturbances of both polarities evolve into stationary, solitary-like waves of corresponding polarity, for which we found the amplitude-width, amplitude-velocity, mass-amplitude, and energy-amplitude relations. Small-amplitude impulses to a good approximation can be described by the modified Korteweg-de Vries equation, but larger waves tend to become wide, and absolute value of their amplitude is bounded by the upper limit. Authors thank prof. K.G. Lamb for the opportunity to use the program code for numerical simulations of Euler equations. The research was supported by RFBR (09-05-00447, 09-05-00204) and by President of RF (MD-3024.2008.5 for young doctors of science).
Vladykina, E. A.; Polukhina, O. E.; Kurkin, A. A.
The Topology of Three-Dimensional Symmetric Tensor Fields
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
Vibration reduction of beams under successive traveling loads by means of linear and nonlinear dynamic absorbers
The goal of the present work is to assess the performances of dynamic vibration absorbers (DVA) in suppressing the vibrations of a simply supported beam subjected to an infinite sequence of regularly spaced concentrated moving loads. In particular, several types of DVA are considered: linear, cubic, higher odd-order monomials and piecewise linear stiffness; linear, cubic and linear-quadratic viscous damping. The purpose is to clarify if nonlinear DVAs show improvements with respect to the classical linear devices. The dynamic scenario is deeply investigated in a wide range of operating conditions, spanning the parameter space of the DVA (damping, stiffness). Nonlinear stiffness can lead to complex dynamics such as quasi-periodic, chaotic and sub-harmonic responses; moreover, acting on the stiffness nonlinearity no improvement is found with respect to the linear DVA. A nonlinear non-symmetric dissipation in the DVA leads to a great reduction of the beam response, the reduction is larger with respect to the linear DVA.
Samani, Farhad S.; Pellicano, Francesco
Invariant hyperkaehler structures on the cotangent bundles of Hermitian symmetric spaces
Let G/K be an irreducible Hermitian symmetric space of compact type with standard homogeneous complex structure. Then the real symplectic manifold (T*(G/K),{omega}) has the natural complex structure J{sup -}. All G-invariant Kehler structures (J,{omega}) on G-invariant subdomains of T*(G/K) anticommuting with J{sup -} are constructed. Each hypercomplex structure of this kind, equipped with a suitable metric, defines a hyperkehler structure. As an application, a new proof of the theorem of Harish-Chandra and Moore for Hermitian symmetric spaces is obtained.
Mykytyuk, I V [National University 'Lvivska Polytechnica', Lvov (Ukraine)
Elementary Linear Algebra
This online textbook, Elementary Linear Algebra, is made available by Keith Matthews of the Department of Mathematics at the University of Queensland. Sections are organized into chapters such as Linear Equations, Matrices, Subspaces, Determinants, Complex Numbers, Eigenvalues and Eigenvectors, Identifying Second Degree Equations, and Three-dimensional Geometry. Each chapter features problems with the solutions available on-site. This is an excellent companion guide for college students taking linear algebra. In addition, the site includes an exact arithmetic matrix program, CMAT, that "performs exact calculations on matrices whose elements are rational numbers, complex rational numbers or numbers from a finite field of p (prime) elements." This program makes it easier to calculate problems such as the reduced row echelon form, the determinant, and the characteristic polynomial of a matrix.
Matthews, Keith R.
Linear Functions
In this tutorial, "Linear functions of the form f(x) = ax + b and the properties of their graphs are explored interactively using an applet." The applet allows students to manipulate variables to discover the changes in intercepts and slope of the graphed line. There are six questions for students to answer, exploring the applet and observing changes. The questions' answers are included on this site. Additionally, a tutorial for graphing linear functions by hand is included.
Linear Inequalities
In this activity, students graph up to four linear inequalities on the same graph. Students can also graph individual points to see if they satisfy the conditions of the inequalities they graphed. This activity allows students to explore linear inequalities and examine the region that will satisfy multiple inequalities at once. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
A Low Complexity Equalization Method for Cooperative Communication Systems Based on Distributed Frequency-Domain Linear Convolutive Space-Frequency Codes
In this paper, we consider the cooperative communi- cation system based on distributed frequency-domain linear con- volutive space-frequency codes (FLC-SFC) with multiple carrier frequency offsets (CFOs) when the channels from relay nodes to destination node are flat fading. Through the mathematical derivation, the cooperative system model is simplified. Then, the equivalent banded system model is obtained and the related analysis
Jun Xiao; Yanxiang Jiang; Xiaohu You
A QMR-based interior-point algorithm for solving linear programs
A new approach for the implementation of interior-point methods for solving linear programs is proposed. Its main feature\\u000a is the iterative solution of the symmetric, but highly indefinite 2�2-block systems of linear equations that arise within\\u000a the interior-point algorithm. These linear systems are solved by a symmetric variant of the quasi-minimal residual (QMR) algorithm,\\u000a which is an iterative solver for
Roland W. Freund; Florian Jarre
Computational power of symmetric Hamiltonians
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still bounded error, quantum polynomial time complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a universal quantum interface, a device which enables control of an arbitrary computation through the control of a fixed number of spins, and using it as a building block to entirely remove the need for control, except in the system initialization. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a Quantum-Merlin-Arthur-complete problem.
Kay, Alastair
Galois Groups of Second and Third Order Linear Differential Equations
this paper we show howfactorization properties of these symmetric powers can be used to determine structuralproperties of the galois groups of second and third order linear differential equation. Thisin turn will allow us to give necessary and sufficient conditions for these linear differentialequations to have liouvillian solutions. For example we show (Corollary 4.4):
Michael F. Singer; Felix Ulmer
Eigenvalue structure of a Bose-Einstein condensate in a {PT}-symmetric double well
We study a Bose-Einstein condensate in a {PT}-symmetric double-well potential where particles are coherently injected in one well and removed from the other well. In mean-field approximation the condensate is described by the Gross-Pitaevskii equation thus falling into the category of nonlinear non-Hermitian quantum systems. After extending the concept of {PT} symmetry to such systems, we apply an analytic continuation to the Gross-Pitaevskii equation from complex to bicomplex numbers and show a thorough numerical investigation of the four-dimensional bicomplex eigenvalue spectrum. The continuation introduces additional symmetries to the system which are confirmed by the numerical calculations and furthermore allows us to analyse the bifurcation scenarios and exceptional points of the system. We present a linear matrix model and show the excellent agreement with our numerical results. The matrix model includes both exceptional points found in the double-well potential, namely an EP2 at the tangent bifurcation and an EP3 at the pitchfork bifurcation. When the two bifurcation points coincide the matrix model possesses four degenerate eigenvectors. Close to that point we observe the characteristic features of four interacting modes in both the matrix model and the numerical calculations, which provides clear evidence for the existence of an EP4.
Dast, Dennis; Haag, Daniel; Cartarius, Holger; Main, J�rg; Wunner, G�nter
Upon completing this lesson, student should be able to use the addition, subtraction, multiplication, and division properties of inequalities to solve linear inequalities; write the answer to an inequality using interval notation; and draw a graph to give a visual answer to an inequality problem. The lesson begins with explanations of inequality signs and interval notation and then moves on to demonstrate addition/subtraction and multiplication/division properties in inequalities. The site demonstrates a strategy for solving linear inequalities and presents three problems for students to practice what they have learned. There is also a link to a previous tutorial which covers solving linear equations of one variable for students who need the review.
Seward, Kim; Puckett, Jennifer
Linear Algebra
A mathematics professor from Saint Michael's College is the author of this free online textbook about linear algebra. Being just shy of 450 pages, the book is very comprehensive and of high quality. It gives an excellent introduction into topics such as vector spaces, linear systems, and determinants, and the author is quite good at defining a consistent notation throughout the book. Each chapter has several examples that demonstrate the concepts, concluding with exercises to be solved by the reader. Solutions to the exercises are given in a separate file. [CL
Hefferon, Jim.
Permutation inference for the general linear model.
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the glm. PMID:24530839
Winkler, Anderson M; Ridgway, Gerard R; Webster, Matthew A; Smith, Stephen M; Nichols, Thomas E
Permutation inference for the general linear model
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm � the �randomise� algorithm � for permutation inference with the glm.
Winkler, Anderson M.; Ridgway, Gerard R.; Webster, Matthew A.; Smith, Stephen M.; Nichols, Thomas E.
Turbulent Parameter Evolution in Madison Symmetric Torus RFP Plasmas
Using Fourier analysis and chaos theory, the turbulent parameters have been used to characterize turbulence in many different plasma systems. The Fourier components measure the characteristic frequency that is associated with instabilities that drive turbulence, the amount of energy associated with turbulence and the rate at which that energy moves between scales. The chaos components measure the complexity and volatility of the fluctuations. The Madison Symmetric Torus provides a plethora of plasma regimes to study turbulence and its associated transitions. Magnetic field fluctuations measurements have been made during the ramp-up, sawtooth crash, and equilibrium phases of a standard discharge, along with the increased confinement period during poloidal pulse current drive (PPCD). While the Fourier components of the turbulent parameters are independent of plasma current, the chaotic components show that the complexity and volatility are dependent on both plasma current and density.
Titus, J. B.; Mezonlin, E. D.; Alexander, A. B.; Johnson, J. A., III
Asymmetric Flow in Symmetric Branched Structures
We investigate the fluid flow through a cascade of bifurcations by direct simulation of the 2D Navier-Stokes equations. We show that, for a fully symmetric tree with n generations ( n>=3\\), the flow distribution becomes significantly heterogeneous at an increased Reynolds number. We develop a binary tree model and find that the distribution of flow at the outlet branches can be described by a self-affine landscape, with a self-affine exponent ? = 0.9 for the human lung. We suggest that the asymmetric flow occurring in symmetric branched structures may be important both for the morphogenesis of the bronchial tree, and for its functioning during inspiration.
Andrade, J. S., Jr.; Alencar, A. M.; Almeida, M. P.; Mendes Filho, J.; Buldyrev, S. V.; Zapperi, S.; Stanley, H. E.; Suki, B.
Inclusive and coincidence measurements have been performed to study symmetric products from the reactions 74--186 MeV /sup 12/C+ /sup 40/Ca, 141 MeV /sup 9/Be+ /sup 40/Ca, and 153 MeV /sup 6/Li+ /sup 40/Ca. The binary decay of the composite system has been verified. Energy spectra, angular distributions, and fragment correlations are presented. The total kinetic energies for the symmetric products from these very light composite systems are compared to liquid drop model calculations and fission systematics.
Grotowski, K.; Majka, Z.; Planeta, R.; Szczodrak, M.; Chan, Y.; Guarino, G.; Moretto, L.G.; Morrissey, D.J.; Sobotka, L.G.; Stokstad, R.G.; Tserruya, I.; Wald, S.; Wozniak, G.J.
Symmetric integrator for nonintegrable Hamiltonian relativistic systems
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for long-term numerical integrations of geodesic orbits in spacetime backgrounds, whose corresponding Hamiltonian system is nonintegrable, and, in general, for any nonintegrable Hamiltonian system whose kinetic part depends on the position variables. We show by numerical examples that the new integrator is faster and more accurate (i) than the standard symplectic integration schemes with or without standard adaptive step size controllers and (ii) than an adaptive step Runge-Kutta scheme.
Seyrich, Jonathan; Lukes-Gerakopoulos, Georgios
Quantum Secret Sharing Using Symmetric W State
Quantum secret sharing (QSS) is an important branch of quantum cryptography, but the existing literature contains no mention of a QSS scheme that applies in the symmetric W states. Here, we demonstrate a multipartite QSS protocol that is encoded into these quantum states with unitary operation pairs. This paper proposes a new method of constructing a QSS protocol for the symmetric W state. This scheme is more efficient than other existing QSS schemes because our proposed protocol uses only a single photon measurement and XOR to recover the secret KEY of Alice.
Liu, Lin-Lin; Tsai, Chia-Wei; Hwang, Tzonelih
Observational tests of Baryon symmetric cosmology
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of pi(0)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the amma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurement of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed.
Stecker, F. W.
All-optical symmetric ternary logic gate
Symmetric ternary number (radix=3) has three logical states (1�, 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript.
Chattopadhyay, Tanay
The Axially Symmetric One-Monopole
We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this solution with theta-winding number m = 1 and phi-winding number n = 1 is an axially symmetric generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solutions of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing. This solution is a non-BPS solution.
Wong, K.-M.; Teh, Rosy [School of Physics, Universiti Sains Malaysia, 11800 USM Penang (Malaysia)
Stabilization and rovibronic spectra of the T-shaped and linear ground-state conformers of a weakly bound rare-gas-homonuclear dihalogen complex: He...Br2
Laser-induced fluorescence spectra of Br2 entrained in a He supersonic expansion have been recorded in the Br2 B-X, 8-0, 12-0, and 21-0 spectral regions at varying downstream distances, and thus different temperature regimes. Features associated with transitions of the T-shaped and linear He...Br2(X,?''=0) complexes are identified. The changes in the relative intensities of the T-shaped and linear features with cooling in the expansion indicate that the linear conformer is energetically more stable than the T-shaped conformer. A He+Br2(X,?''=0) ab initio potential-energy surface, computed at the coupled cluster level of theory with a large, flexible basis set, is used to calculate the binding energies of the two conformers, 15.8 and 16.5 cm-1 for the T-shaped and linear complexes, respectively. This potential and an excited-state potential [M. P. de Lara-Castells, A. A. Buchachenko, G. Delgado-Barrio, and P. Villareal, J. Chem. Phys. 120, 2182 (2004)] are used to calculate the excitation spectra of He...79Br2(X,?''=0) in the Br2 B-X, 12-0 region. The calculated spectra are used to make spectral assignments and to determine the energies of the excited-state intermolecular vibrational levels accessed in the observed transitions. Temperature-dependent laser-induced fluorescence spectra and a simple thermodynamic model [D. S. Boucher, J. P. Darr, M. D. Bradke, R. A. Loomis, and A. B. McCoy, Phys. Chem. Chem. Phys. 6, 5275 (2004)] are used to estimate that the linear conformer is 0.4(2) cm-1 more strongly bound than the T-shaped conformer. Two-laser action spectroscopy experiments reveal that the binding energy of the linear He...79Br2(X,?''=0) conformer is 17.0(8) cm-1, and that of the T-shaped He...79Br2(X,?''=0) conformer is then 16.6(8) cm-1, in good agreement with the calculated values.
Boucher, David S.; Strasfeld, David B.; Loomis, Richard A.; Herbert, John M.; Ray, Sara E.; McCoy, Anne B.
Symmetric mode resonance of bubbles attached to a rigid boundary
Experimental results are compared with a theoretical analysis concerning wall effects on the symmetric mode resonance frequency of millimeter-sized air bubbles in water. An analytical model based on a linear coupled-oscillator approximation is used to describe the oscillations of the bubbles, while the method of images is used to model the effect of the wall. Three situations are considered: a single bubble, a group of two bubbles, and a group of three bubbles. The results show that bubbles attached to a rigid boundary have lower resonance frequencies compared to when they are in an infinite uniform liquid domain (referred to as free space). Both the experimental data and theoretical analysis show that the symmetric mode resonance frequency decreases with the number of bubbles but increases as the bubbles are moved apart. Discrepancies between theory and experiment can be explained by the fact that distortion effects due to buoyancy forces and surface tension were ignored. The data presented here are intended to guide future investigations into the resonances of larger arrays of bubbles on rigid surfaces, which may assist in surface sonochemistry, sonic cleaning, and micro-mixing applications.
Payne, Edward M. B.; Illesinghe, Suhith J.; Ooi, Andrew; Manasseh, Richard
This is a basic course, produced by Gilbert Strang of the Massachusetts Institute of Technology, on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Strang, Gilbert
Linear Equations
This narrated demonstration introduces students to linear equations with one variable, their visual representation, and how to solve them. After the clear instructions, students are allowed to test what they've learned by solving two equations on their own. The lesson is concluded with a review of the objective and summary of the key points.
Linear Filters
Created by Joshua Holden for the Connected Curriculum Project, the purpose of this module is to explore a common application of difference equations and linear algebra in electrical engineering and signal processing. The is part of a larger collection of modules hosted by Duke University.
Holden, Joshua
Linear Regression
This site, created by Michelle Lacey of Yale University, gives an explanation, a definition and an example of linear regression. Topics include: least-squares, residuals, extrapolation, outliers, and influential observations. Lacey's presentation is thoughtful in its layout. The author intertwines useful graphs within her textual explanations, this makes it accessible for almost any mathematics audience. Overall, this is a useful resource.
Lacey, Michelle
Single subject image analysis using the complex general linear model--an application to functional magnetic resonance imaging with multiple inputs.
A linear time invariant model is applied to functional fMRI blood flow data. Based on traditional time series analysis, this model assumes that the fMRI stochastic output sequence can be determined by a constant plus a linear filter (hemodynamic response function) of several fixed deterministic inputs and an error term assumed stationary with zero mean. The input function consists of multiple exponential distributed (time delay between images) visual stimuli consisting of negative and erotic images. No a priori assumptions are made about the hemodynamic response function that, in essence, is calculated at each spatial position from the data. The sampling rate for the experiment is 400 ms in order to allow for filtering out higher frequencies associated with the cardiac rate. Since the statistical analysis is carried out in the Fourier domain, temporal correlation problems associated with inference in the time domain are avoided. This formal model easily lends itself to further development based on previously developed statistical techniques. PMID:16530880
Rio, Daniel E; Rawlings, Robert R; Woltz, Lawrence A; Salloum, Jasmin B; Hommer, Daniel W
Molecular structure and tautomerization of the 1:1 complex of luteoskyrin and rugulosin
A novel 1:1 natural product complex ( 1) containing luteoskyrin ( 2) and rugulosin ( 3) was isolated from the acetone extract of culture broth of Myrothecium sp. In DMSO solution, the 1H and 13C NMR spectra showed only half proton and carbon signals indicating that both compounds exist as a symmetric enol-enol form. In contrast, in the solid state, X-ray analysis revealed that 2 bound 3 with high specificity through intermolecular hydrogen bonds and ?-? interactions, and both 2 and 3 tautomerized to a non-symmetric enol-ketone form due to the strong linear hydrogen bonding between the ketone group and the alcoholic hydroxyl group. In addition, complex 1 showed potent cytotoxic activity against cell lines KB (human epidermoid carcinoma cell), HT-29 (human colon cancer cell) and 3T3 (mouse embryonic fibroblast cell) with IC 50 values of 0.57, 3.11 and 5.83 ?M, respectively.
Zhou, Guang-Xiong; Mo, Shun-Yan; He, Hui-Xiao; Shi, Jian-Gong; Ye, Wen-Cai; Liu, Zhong; Jiang, Ren-Wang
Clay content analysis across landscape by means of linear and non-linear empirical models
In soil science literature there exist many applications that deals with the spatial prediction of soil features by means of a set of statistical techniques. In this work the amount of clay content at level of soil horizon was put in a spatial framework and analyzed using four alternative models for describing its variability in a geopedological complex landscape such as Telese valley (Campania, South Italy) study area. Three statistical models were involved, that is (i) the multiple linear regression (MLR), (ii) the multicollocated ordinary cokriging (MOCOK), and (iii) a two-layers FFBP (FeedForward Back-Propagation) neural network with topology 6 : 1 (ANN). Apart from these technologies (neurocomputing, and multivariate regression and geostatistics) a polygonal soil map (UDP) was also used for the sake of comparing complex and sometimes cumbersome models with the standard approach of representing the soil spatial distribution. Clay data was splitted in calibration/validation subsets in order to unbiasedly compare the four models (in order of complexity UDP, MLR, MOCOK, ANN). Comparison was based on multi-criteria assessment using six measures of performance: RMSE (root mean square error), MBE (mean bias error), Pearson's correlation (r), an efficiency index (eff), SMAPE (symmetrical mean absolute percent error), and Wilmott's agreement index (D). Generally all indicators seem to demonstrate that the more complex (from UDP to ANN) the models the better their performance in representing the spatial variability of some pedological parameters. Despite such statement much endeavour should be spent in model comparison by considering also the cost/profit trade off incorporating a cost function.
Langella, G.; Minieri, L.; Terribile, F.
Maximizing the area of an axially-symmetric polygon inscribed by a simple polygon
Abstract In this paper we solve the following optimization problem: Given a simple polygon P , what is the maximum-area polygon that is axially symmetric and is contained by P ?W e propose an algorithm for solving this problem, analyze its complexity, and describe our implementation of it (for the case of a convex polygon). The algorithm is based on
V. Rogol
Maximizing the area of an axially symmetric polygon inscribed in a simple polygon
In this paper we resolve the following problem: Given a sim- ple polygon , what is the maximum-area polygon that is axially symmetric and is contained by ? We propose an al- gorithm for answering this question, analyze the algorithm's complexity, and describe our implementation of it (for con- vex polygons). The algorithm is based on building and in- vestigating
Gill Barequet; Vadim Rogol
Exocyclic coordination and translocation of metal ions in laterally non-symmetric aza cryptands
Laterally non-symmetric aza cryptands incorporating N atoms in the three bridges, readily make inclusion complexes with a number of transition as well as main- group metal ions. The donor ability of the N a toms in the bridges can be modulated through attachment of electron-withdrawing groups. In this modified cryp- tand, a metal ion can be translocated from inside the
Bamaprasad Bag; Pritam Mukhopadhyay; Parimal K. Bharadwaj
On the Decay of Correlations in Non-Analytic SO(n)Symmetric Models
:�� We extend the method of complex translations which was originally employed by McBryan-Spencer [2] to obtain a decay rate\\u000a for the two point function in two-dimensional SO(n)-symmetric models with non-analytic Hamiltonians for .
Ali Naddaf
Synthesis, crystal structure and magnetic properties of quasi-linear tetranuclear copper(II) Schiff base complexes formed by covalent linkage of asymmetrically dibridged dicopper(II) units
Alkoxo-phenoxo bridged tetranuclear copper(II) complexes [Cu4L2(O2CC6H4-p-OH)2] (1) and [Cu4L2(O2CC6H4-o-OH)2] (2) containing pentadentate Schiff base ligand N,N?-(2-hydroxypropane-1,3-diyl)bis(salicylaldimine) (H3L) are prepared and structurally characterized. Crystal structures of the complexes show the covalent linkage between two {Cu2L(O2CR)}(R = C6H4-p-OH, C6H4-o-OH) units through the phenoxo atoms of the Schiff base ligand showing axial\\/equatorial bonding modes. The Cu(1)�O(2)�Cu(2) alkoxo bridge angle is 131� in 1
Arindam Mukherjee; Manas K. Saha; Indranil Rudra; Suryanarayanasastry Ramasesha; Munirathinam Nethaji; Akhil R. Chakravarty
Luminescence and non-linear optical properties of erbium-tetraphenylprophyrin complexes incorporated within a silica matrix by a sol-gel process
A simplified method of synthesis and purification of Erbium-Tetraphenylporphyrin (ErTpp) complexes, and their incorporation within a silica gel by the sol-gel process, is presented. On the basis of optical spectroscopic measurements in the UV-VIS range it was found that in ErTpp complexes the tetraphenylporphyrin molecule served as a protective screen for erbium ions. The half-width of the erbium ion luminescence band for the 4S 3/2 ? 4I 15/2 transition was narrower by a factor of 5-6 in the new material than the corresponding value in erbium doped glasses or glass ceramics. It was shown that the value of the nonlinear refraction coefficient in ErTpp gels could considerably exceed that of silica glasses.
Clark, A.; Terpugov, V.; Medrano, F.; Cervantes, M.; Soto, D.
Third-order optical non-linearity in Zn(II) complexes of 5,10,15,20-tetraarylethynyl-substituted porphyrins
Third-order optical nonlinearity ?(3) of complexes in 5,10,15,20-tetraarylethynyl-substituted porphyrins has been measured using the Z-scan technique. The real and imaginary parts of ?(3) were measured at three different wavelengths and found to be in the region 1.05 � 10 -12 esu and 5.2 � 10 -12 esu, respectively. Experimental characterisation shows a saturation absorption at wavelengths close to resonance and reverse saturation absorption at off-resonance wavelengths.
Henari, Fryad Z.; Blau, Werner J.; Milgrom, Lionel R.; Yahioglu, Gokhan; Phillips, David; Lacey, Jackie A.
Two loop QCD vertices at the symmetric point
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MS� scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MS� are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the ? function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.
Gracey, J. A.
Parity-time-symmetric whispering-gallery microcavities
Optical systems combining balanced loss and gain provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time (PT)-symmetric Hamiltonians. Such systems can be used to create synthetic materials with properties that cannot be attained in materials having only loss or only gain. Here we report PT-symmetry breaking in coupled optical resonators. We observed non-reciprocity in the PT-symmetry-breaking phase due to strong field localization, which significantly enhances nonlinearity. In the linear regime, light transmission is reciprocal regardless of whether the symmetry is broken or unbroken. We show that in one direction there is a complete absence of resonance peaks whereas in the other direction the transmission is resonantly enhanced, a feature directly associated with the use of resonant structures. Our results could lead to a new generation of synthetic optical systems enabling on-chip manipulation and control of light propagation.
Peng, Bo; �zdemir, ?ahin Kaya; Lei, Fuchuan; Monifi, Faraz; Gianfreda, Mariagiovanna; Long, Gui Lu; Fan, Shanhui; Nori, Franco; Bender, Carl M.; Yang, Lan
Symmetric nonnegative matrix factorization: algorithms and applications to probabilistic clustering.
Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: ?-SNMF and ? -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression. PMID:22042156
He, Zhaoshui; Xie, Shengli; Zdunek, Rafal; Zhou, Guoxu; Cichocki, Andrzej
Linearity asymmetry in FET resistive mixers
This paper investigates up/down conversion asymmetry in intermodulation distortion observed in measurements of resistive FET mixers. Symmetric behaviour is intuitively expected of such a topology, so a first principle analysis is carried out to determine the responsible mechanism. Previous analysis of up/down conversion asymmetry has focused on conversion gain in diode based mixers, whereas the effects investigated in this paper are for mixers with symmetry in this aspect. The aim is to fully understand the intermodulation mechanism, so that performance can be enhanced. The approach taken is to consider the mixer as a two-port nonlinear element driven by multiple frequency sources. Mixing performance then becomes a function of the relative frequencies and amplitudes, which is related to the mode of operation as an up or down converter. This investigation is performed with FET models of increasing complexity and physical accuracy. In this manner the effect on intermodulation and other mixer performance parameters can be isolated to those differences introduced with each model change such as the effect of adding higher order even/odd terms to the drain or gate non-linear model independently. The result is an understanding into the FET properties that contribute to intermodulation distortion. This knowledge is useful to designers as it allows educated modifications to mixer topology to obtain improved linearity. Results also give the ability to minimize the asymmetry, reducing the design cost involved in producing a separate solution for each mode. These results can also be used to guide modification of the physical structure of a FET for mixer applications.
Powles, Lindsay; Parker, Anthony E.; Mahon, Simon J.
Local conservation laws in nonlinear sigma models based on symmetric spaces
The formalism of a class of two-dimensional field theories known as nonlinear sigma models based on a symmetric space is reviewed, and the projective representation of such a symmetric space is used to find a natural geometric interpretation for the Riccati-like equations, and the consequent infinity of local conservation laws, for these models. The inverse scattering method, which has been used to great effect in the search for exact solutions to certain nonlinear partial differential equations in two variables is reviewed. These general methods are illustrated by applying them to the Korteweg-de Vries equation. After a short mathematical digression on symmetric spaces, the inverse scattering formalism is developed for nonlinear sigma models in which the fundamental field takes values in a symmetric space G/H, where G is the global invariance group of the model, and H is a subset of G is the hidden local invariance group. The isospectral pair of the inverse scattering method is interpreted as expressing the infinitesimal linear action of the group G on itself. On the other hand, the group G can be taken to act nonlinear on one of its associated symmetric spaces G/H. This nonlinear action is taken to be infinitesimal. A pair of Riccati-like equations is found. A natural geometric interpretation for the Riccati equations which in the literature appear ex nihilo is found.
Snyder, M.A.
-symmetric nonlinear metamaterials and zero-dimensional systems
A one dimensional, parity-time ()-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken -phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern ( dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the interelement coupling. In the presence of nonlinearity, the dimer chain configuration with balanced gain and loss supports nonlinear localized modes in the form of a novel type of discrete breathers below the lower branch of the linear spectrum. These breathers that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamental gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behavior is similar to a transition from the exact to the broken phase in higher-dimensional -symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of a piece-wise constant gain/loss function that allows the construction of a phase diagram with alternating stable and unstable regions.
Tsironis, G. P.; Lazarides, N.
Generation arbitrary permutation symmetric state with projection
We proposed a scheme to generate arbitrary permutation symmetric multi-partite state. The system contains N equally single quantum particles (We use atoms for these particles) which may interact with single photon to generate entanglement between them. This entanglement can be obtained by the transition from three-level lambda atom's exited state to different low levels and emitting corresponding polarized photon, or
Fangwen Sun; Chee Wei Wong
Rounding in Symmetric Matrices and Undirected Graphs
We consider the problem of rounding the entries of a matrix without distorting the row, column, and grand totals. This problem arises in controlling statistical disclosure, in data analysis, and elsewhere. There are algorithms in the literature which produce roundings that are �tight� in the sense of distorting the totals very little. We concentrate on the case of symmetric matrices.
Pavol Hell; David G. Kirkpatrick; Brenda Li
Unidirectional nonlinear PT-symmetric optical structures
We show that nonlinear optical structures involving a balanced gain-loss profile can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T), with optical nonlinear effects. This unidirectional dynamics is specifically demonstrated for the case of an integrable PT-symmetric nonlinear system.
Ramezani, Hamidreza [Department of Physics, Wesleyan University, Middletown, Connecticut 06459 (United States); Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, Connecticut 06459 (United States); Max-Planck-Institute for Dynamics and Self-Organization, D-37073 Goettingen (Germany); El-Ganainy, Ramy; Christodoulides, Demetrios N. [College of Optics and Photonics-CREOL, University of Central Florida, Orlando, Florida 32816 (United States)
Iris Recognition Using Circular Symmetric Filters
This paper proposes a new method for personal identification based on iris recognition. The method consists of three major components: image preprocessing, feature extraction and classifier design. A bank of circular symmetric filters is used to capture local iris characteristics to form a fixed length feature vector. In iris matching, an efficient approach called nearest feature line (NFL) is used.
Li Ma; Yunhong Wang; Tieniu Tan
Stability Analysis of a Symmetrical Induction Machine
A stability study of an induction machine is performed by applying the root-locus criterion to the equations which describe the behavior of the machine during small displacements about a steady-state operating point. This investigation reveals that a symmetrical induction machine may become unstable at low speeds (low frequencies) even though balanced, constant amplitude, sinusoidal voltages are applied to the stator
The Low Pressure Plane Symmetric Discharge
It is shown that the low pressure plane symmetric plasma equation, using the collision-free model of Tonks and Langmuir, can be solved analytically. Simple expressions are obtained for the mean velocity and the mean square velocity of the ions, and for the wall potential with respect to the plasma. The conditions for the formation of a stable plasma-sheath boundary are
E. R. Harrison; W. B. Thompson
Bruhat Order in Full Symmetric Toda System
In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the full symmetric Toda system in dimensions n = 3, 4 coincides with the Hasse diagram of the Bruhat order of symmetric groups S 3 and S 4. The method we use is based on the existence of a vast collection of invariant subvarieties of the Toda flow in orthogonal groups. We show how one can extend it to the case of general n. The resulting theorem identifies the set of singular points of dim = n Toda flow with the elements of the permutation group S n , so that points will be connected by a trajectory, if and only if the corresponding elements are Bruhat comparable. We also show that the dimension of the submanifolds, spanned by the trajectories connecting two singular points, is equal to the length of the corresponding segment in the Hasse diagram. This is equivalent to the fact that the full symmetric Toda system is in fact a Morse-Smale system.
Chernyakov, Yu. B.; Sharygin, G. I.; Sorin, A. S.
The deuterium puzzle in the symmetric universe
An attempt was made to use deuterium abundance in the symmetric universe to prove that no nucleosynthesis takes place during annihilation and therefore neutrons were loss before nucleosynthesis. Data cover nucleosynthesis during the radiative era, cross section estimates, maximum abundance of He-4 at the end of nucleosynthesis area, and loss rate.
Leroy, B.; Nicolle, J. P.; Schatzman, E.
Models of helically symmetric binary systems
Results from helically symmetric scalar-field models and first results from a convergent helically symmetric binary neutron-star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity ?. In the scalar-field models and the neutron-star code, helical symmetry leads to a system of mixed elliptic hyperbolic character. The scalar-field models involve nonlinear terms of the form ?3, (??)2 and ?squ? that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used, and it improves with an outer boundary in the near zone. In the neutron-star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than ~1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves, and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.
Yoshida, Shin'ichirou; Bromley, Benjamin C.; Read, Jocelyn S.; Uryu, Koji; Friedman, John L.
Phenomenology of quark-lepton symmetric models.
Quark-lepton symmetric models are a new class of gauge theories which unify the quarks and leptons. In these models the gauge group of the standard model is extended to include a color group for the leptons, and consequently the quarks and leptons can the...
R. Foot H. Lew Volkas
This course, presented by MIT and taught by Professor Gilbert Strang, provides undergraduate level algebra instruction. The materials cover matrix theory and linear algebra including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. The course includes video lectures, assignments and exams (with solutions) and lecture notes. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.
Linear Models
This site uses linear models to demonstrate the change in bird populations on a barren island over time, supply and demand, and the natural cleaning of a polluted lake by fresh water over time. The problems are laid out and turned into both graphic and equation form in order to understand the rate of change happening in each scenario. There are also links to previously covered materials that can help student review material from past math lessons.
Wattenberg, Frank
Symmetric vs asymmetric PCR and molecular beacon probe in the detection of a target gene of adenovirus.
A DNA fragment (307 bp) from the conserved region of an adenovirus gene (hexon) was amplified by symmetric and by asymmetric polymerase chain reaction (PCR). Two amplifications, one in the absence other in the presence of a molecular beacon probe were conducted by both symmetric and asymmetric PCR. The probe sequence was complementary to an internal segment of the amplified fragment. The product amplified in the absence and presence of the probe was detected by agarose gel and fluorescence analysis, respectively. A symmetric PCR results in exponentially grown double stranded DNA. An asymmetric PCR generates one of the strands by linear ampIlification and a fraction of its total product as double-stranded DNA limited by the concentration ratio of the primers used. Thus asymmetric PCR provided lower intensity signal hence less sensitivity than symmetric PCR by agarose gel analysis as expected. However, signal from a beacon probe based PCR assay is generated only from the probe fraction that hybridizes successfully competing against the strand complementary to the target strand of the product generated by PCR. The symmetric PCR has so far been used for the molecular beacon based fluorescent signal detection. The present study compared the level of fluorescent signal detectable from a symmetric PCR with that from an asymmetric PCR. The fluorescent data analysis demonstrated that a significant higher level of fluorescent signal hence higher sensitivity of detection is obtainable using asymmetric PCR than symmetric PCR performed in presence of the molecular beacon probe. PMID:10722789
Poddar, S K
Anion dependent self-assembly of a linear hexanuclear Yb(III) salen complex with enhanced near-infrared (NIR) luminescence properties.
Reactions of H2salen (H2L, N,N'-ethylene bis(salicylideneimine)) with Yb(CF3SO3)3, Yb(OAc)34H2O and Yb(NO3)36H2O in MeOH�EtOH under reflux gave NIR luminescent complexes [Yb6L9(H2L)2] (1), [Yb3L3(HL)(OH)2] (2) and [Yb2L2(H2L)2(NO3)(MeOH)2]NO3 (3), respectively. PMID:24019025
Yang, Xiaoping; Oye, Michael M; Jones, Richard A; Huang, Shaoming
IR linear dichroic study of high-symmetry molecules dissolved in a liquid crystal solvent. II. Metal hexacarbonyl complexes M(CO) 6 (M = Mo, Cr)
The presence of weak specific solvent�solute interactions is proved by studying the splitting of the ? 3(F 1u) band of M(CO) 6 (M = Mo, Cr) in some isotropic electron donor solvents. A similar spectral effect is observed in the smectic, nematic and isotropic phases of the liquid crystal ZLI 1167 (Merck) and is explained by similar interactions. The complex (bisignate) shape of the IR-LD spectra of M(CO) 6 in the anisotropic solvent is considered to be a manifestation of the same solvent effect.
Rogojerov, Marin I.; Arnaudov, Michail G.
Application of asymptotic iteration method to the Khare-Mandal and its PT -symmetric QES partner potential
We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although\\u000a the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for\\u000a certain values of potential parameters, its PT-symmetric partner exhibits real
Okan �zer; Vedat Aslan
MIC linearizer for satellite communications
MIC implementation of a predistortion-type nonlinearity compensating circuit or linearizer (LRZ) using FETAs in a distortion generator was studied and a compact, lightweight MIC-LRZ using tip devices was developed. The LRZ circuit has a symmetric construction which enables it to have a wideband characteristic, and its nonlinearities can be adjusted electrically. The LRZ can compensate nonlinearity up to saturation of the traveling wave tube amplifier (TWTA) and can provide large performance improvement using a TWTA with backoff operation. The TWTA with the soft-limiter LRZ (SL-LRZ) exhibits soft-limiter transfer characteristics in which the input-output amplitude response is linear up to saturation and phase nonlinearity is negligible. The MIC-LRZ and SL-LRZ are compact, lightweight, and effective for use with earth stations HPAs and satellite TWTAs.
Sato, G.
Characterization of Randomly Time-Variant Linear Channels
This paper is concerned with various aspects of the characterization of randomly time-variant linear channels. At the outset it is demonstrated that time-varying linear channels (or filters) may be characterized in an interesting symmetrical manner in time and frequency variables by arranging system functions in (timefrequency) dual pairs. Following this a statistical characterization of randomly time-variant linear channels is carried
P. Bello
Linear Projective Program Syntax
Based on an extremely simple program notation more advanced program features can be developed\\u000ain linear projective program syntax such as conditional statements, while loops, recursion, use of an\\u000aevaluation stack, object classes, method calls etc. Taking care of a cumulative and bottom up introduction of\\u000asuch complex features while providing appropriate projections into the lower levels of language development
J. A. Bergstra; I. Bethke
Linear Plasmids and Phytopathogenicity
The occurrence of plasmids is typically correlated with the acquisition of specialized traits that\\u000a can be very diverse. Production of secondary metabolites, achievement of complex catabolic reactions, and\\u000a adaptation to particular habitats are just a�few examples of functions that are often encoded by circular\\u000a or linear extrachromosomal replicons. Although virulence is another classical characteristic that is frequently\\u000a associated with the
Isolde Francis; Dirk Gevers; Mansour Karimi; Marcelle Holsters; Danny Vereecke
Segal-Bargmann transform on Hermitian symmetric spaces and Orthogonal Polynomials
Let $\\\\mathcal{D}=G\\/K$ be a complex bounded symmetric domain of tube type in a complex Jordan algebra $V$ and let $\\\\mathcal{D}_{\\\\mathbb{R}}=H\\/L\\\\subset \\\\mathcal{D}$ be its real form in a formally real Euclidean Jordan algebra $J\\\\subset V$. We consider representations of $H$ that are gotten by the generalized Segal-Bargmann transform from a unitary $G$-space of holomorphic functions on $\\\\mathcal{D}$ to an $L^2$-space on
Mark Davidson; Gestur Olafsson; Genkai Zhang
Ferromagnetic behavior in linear charge-transfer complexes. Structural and magnetic characterization of octamethylferrocene salts: (Fe(C sub 5 Me sub 4 H) sub 2 ) sup sm bullet + (A) sup sm bullet minus (A = TCNE, TCNQ)
The reaction of Fe{sup II}({eta}{sup 5}-C{sub 5}Me{sub 4}H){sub 2} with cyano acceptors A (A = TCNE (tetracyanoethylene), TCNQ (7,7,8,8-tetracyano-p-quanodimethane), n-C{sub 4}(CN){sub 6} (n-hexacyanobutadiene), C{sub 6}(CN){sub 6} (tris(dicyanomethylene)cyclopropane), DDQ (2,3-dichloro-5,6-dicyanobenzoquinone), TCNQF{sub 4} (perfluoro-7,7,8,8-tetracyano-p-quinodimethane) results in formation of 1:1 charge-transfer salts of (Fe{sup III})(C{sub 5}Me{sub 4}H){sub 2}){sup {sm bullet}+}(A){sup {sm bullet}{minus}} composition. The TCNE and TCNQ complexes have been structurally characterized. The high-temperature magnetic susceptibility for polycrystalline samples of these complexes can be fit by the Curie-Qeiss law, {chi} = C(T-{theta}){sup {minus}1}, with {theta} = +0.5 {plus minus} 2.2 K, and {mu}{sub eff} ranges from 2.71 to 3.97 {mu}{sub B}, suggesting that the polycrystalline samples measured had varying degrees of orientation. The 7.0 K EPR spectrum of the radical cation exhibits an axially symmetric powder pattern with g{sub {parallel}} = 4.11 and g{sub {perpendicular}} = 1.42, and the EPR parameters are essentially identical with those reported for ferrocenium and decamethylferrocenium. No EPR spectrum is observed at 78 K. Akin to the (Fe(C{sub 5}Me{sub 5}){sub 2}){sup {sm bullet}+} salts, these salts have {sup 57}Fe Moessbauer spectra consistent with complete charge transfer; however, unlike the case for the former complexes, quadrupole splittings of 0.30 and 0.220 mm/s are observed at 4.8 and 298 K, respectively. The absence of strong interionic magnetic coupling for the (Fe(C{sub 5}Me{sub 4}H){sub 2}){sup {sm bullet}+} salts contrasts with the behavior of the (Fe(C{sub 5}Me{sub 5}){sub 2}){sup {sm bullet}+} salts. 26 refs., 13 figs., 8 tabs.
Miller, J.S.; Glatzhofer, D.T.; O'Hare, D.M. (E.I. de Pont de Nemours and Co., Inc., Wilmington, DE (USA)); Reiff, W.M. (Northeastern Univ., Boston, MA (USA)); Chakraborty, A.; Epstein, A.J. (Ohio Sate Univ., Columbus (USA))
Symmetric Key Structural Residues in Symmetric Proteins with Beta-Trefoil Fold
To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric.
Huang, Yanzhao; Xiao, Yi
Development of the Complex General Linear Model in the Fourier Domain: Application to fMRI Multiple Input-Output Evoked Responses for Single Subjects
A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.
Rio, Daniel E.; Rawlings, Robert R.; Woltz, Lawrence A.; Gilman, Jodi; Hommer, Daniel W.
Development of the complex general linear model in the Fourier domain: application to fMRI multiple input-output evoked responses for single subjects.
A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function. PMID:23840281
Rio, Daniel E; Rawlings, Robert R; Woltz, Lawrence A; Gilman, Jodi; Hommer, Daniel W
Bifurcations of symmetrical caustics: the creation-annihilation of two symmetric butterflies
The problem of the bifurcations of symmetrical singularities is attacked in the case of the most simple symmetry. We show that the Lagrangian singularities invariant through the mirror symmetry may undergo two types of bifurcations involving butterflies. In both cases, a pair of symmetric butterflies is created or disappears. In addition, we give a concrete application of our results in the domain of geometrical optics.
Joets, A.; Ribotta, R.
Ionization in symmetric and nearly symmetric low energy ion�surface collisions
Multiply charged ions are emitted following bombardment of Al(100) and Si(111) by low energy Si+ and P+ ions. The ion formation is attributed to inner-shell electron promotion during a hard collision between symmetric or nearly symmetric atomic species, followed by Auger decay outside the surface. The relative yield of triply charged Si ions for Si+?Si(111) is much smaller than that
X. Chen; Z. Sroubek; J. A. Yarmoff
Geometrical Transformation of Linear Diode-Laser Arrays for Longitudinal Pumping of Solid-State Lasers.
A 200-stripe linear diode-laser array is geometrically transformed into a two-dimensional, symmetric virtual source with symmetric divergence to end-pump a Nd:YAG laser. The geometrical transformation is performed by two planes of diffractive optical elem...
J. R. Leger W. C. Goltsos
On static spherical symmetric solutions of the Bach-Einstein gravitational field equations
The fourth-order field equations based on a Lagrangian which is a linear combination of the Einstein-Hilbert Ricci-scalar Lagrangian and the Bach (1921) Weyl-scalar Lagrangian are investigated analytically, combining the local expansions of Stelle (1978) and Fiedler and Schimming (1983). The equations are rewritten in equivalent but different versions; linearizations are derived; and nonstandard analysis is applied to demonstrate that no static spherically symmetric solutions exist in a defined vicinity of Minkowski space. The results are discussed in the light of the particle program of Einstein and Pauli (1943), and it is found that a particle corresponding to any nontrivial static spherically symmetric asymptotically flat singularity-free solution of the equations must be very massive, with a phenomenological energy density at least 40 orders of magnitude greater than that of a neutron star.
Linear stability analysis of dynamical quadratic gravity
We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even-parity sector, exemplified by Einstein-Dilaton-Gauss-Bonnet gravity, and the odd-parity sector, exemplified by dynamical Chern-Simons modified gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on spherically symmetric and axially symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Ayzenberg, Dimitry; Yagi, Kent; Yunes, Nicol�s
Channel entrance flow and its linear stability
In this work, we present a temporal linear stability analysis of developing channel flow. For the main flow, the considered solution is analytic. It is based on the hypothesis of small disturbances from fully developed flow and it is valid for intermediate Reynolds numbers. The disturbances are separated into symmetric and anti-symmetric eigenmodes of the velocity. We deal subsequently with the linear stability of this main flow, taking into account the nearly parallel flow assumption. The stability problem formulation leads to the Orr-Sommerfeld equation. This equation is then resolved using the Chebyshev spectral collocation method. The stability results depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry.
Hifdi, Ahmed; Ouazzani Touhami, Mohammed; Khalid Naciri, Ja�far
It is well known that a symmetric soliton in coupled nonlinear Schroedinger\\u000a(NLS) equations with the cubic nonlinearity loses its stability with the\\u000aincrease of its energy, featuring a transition into an asymmetric soliton via a\\u000asubcritical bifurcation. A similar phenomenon was found in a dual-core system\\u000awith quadratic nonlinearity, and in linearly coupled fiber Bragg gratings, with\\u000aa difference
Symmetric instability in two-layer rotating shallow water model and its nonlinear evolution
We study symmetric instability in 2-layer rotating shallow water model. We consider a barotropic localized jet on the f-plane and on the equatorial-beta plane, and use the collocation method to obtain the structure of linearly unstable modes. We then simulate the nonlinear evolution of the flow disturbed by thus obtained most unstable mode, with the help of a high-resolution finite-volume
F. Bouchut; E. Scherer; V. Zeitlin
A regularized smoothing Newton method for solving the symmetric cone complementarity problem
The symmetric cone complementarity problem (denoted by SCCP) is a class of equilibrium optimization problems, and it contains the standard linear\\/nonlinear complementarity problem (LCP\\/NCP), the second-order cone complementarity problem (SOCCP) and the semidefinite complementarity problem (SDCP) as special cases. In this paper, we present a regularized smoothing Newton algorithm for SCCP by making use of Euclidean Jordan algebraic technique. Under
Changfeng Ma
(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively mathcal{PT} -Symmetric
The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the �quasi-parity� on the Dirac particles� spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S( z)= S( x- ib) (an inversely linear plus linear, leading to a mathcal{PT-} symmetric oscillator model), and S( x)= S r ( x)+ iS i ( x) (a mathcal{PT} -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an ?-weak-pseudo-Hermiticity generator are presented and a complexified mathcal{PT} -symmetric periodic-type model is used as an illustrative example.
Mustafa, Omar; Mazharimousavi, S. Habib
Conformal Operators from Spinor Fields - I: Symmetric Tensor Case.
The full system of conformal symmetric traceless tensor operators with minimal twist constructed from generalized free massless spinor fields is given. A series of symmetric tensor operators with higher twist and the simplest antisymmetric tensor operator...
V. K. Dobrev A. C. Ganchev O. I. Yordanov
First stable reduced form of [Co(5)](+10): fine tuning of linear pentacobalt(ii) complexes containing delocalized metal-metal bonds through ligand modification.
Pentacobalt EMACs [Co(5)(mu(5)-dpzpda)(4)X(2)] (X = Cl(-) (), NCS(-) ()) with fine-tuning of the supporting ligand based on the tripyridyldiamine ligand, N,N'-di(pyrazin-2-yl)pyridine-2,6-diamine (H(2)dpzpda), and their reduced form (Ph(4)P)[Co(5)(mu(5)-dpzpda)(4)X(2)] (X = Cl(-) (), NCS(-) ()) were first synthesized and structurally characterized. The structures of showed direct Co-Co bonds with Co-Co distances in the range 2.2385(7)-2.2888(15) A, and valence electrons delocalized through the whole metal chain with distances of longer than 9.06 A. The distances of the inner Co-Co bonds and the Co-axial ligands became longer after reduction, whereas no significant change was observed in the distances of the outer Co-Co bonds and Co-N (supporting ligand) bonds, which was consistent with the MO analysis. Electrochemical studies on both and showed one reversible oxidation and one reversible reduction at E(1/2) = +0.82 and -0.05 V for , and at E(1/2) = +0.89 and +0.02 V for , respectively. The redox reactions of the thiocyanate complex happened at higher potentials than the chloride complex . A magnetism study of revealed anomalous magnetic behaviour similar to that of heptacobalt EMACs, and a deviation from the Curie-Weiss law was observed. The chi(M)T value at 300 K is 0.84 and 1.16 emu K mol(-1) for and , respectively, suggesting spin-equilibrium or a spin-admixture between doublet and quartet states arising from the Boltzmann distribution over different energy levels. Similar results were obtained for and , showing intermediate chi(M)T values between a diamagnetic and a triplet state of 0.15-0.96 emu K mol(-1) in the temperature range 5-300 K. The structural and magnetic results were interpreted through an EHMO study. PMID:19153628
Wang, Wen-Zhen; Ismayilov, Rayyat Huseyn; Wang, Rui-Ren; Huang, Yi-Lin; Yeh, Chen-Yu; Lee, Gene-Hsiang; Peng, Shie-Ming
Compressive sensing with dispersion compensation on non-linear wavenumber sampled spectral domain optical coherence tomography
We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.
Xu, Daguang; Huang, Yong; Kang, Jin U.
Parity-time-symmetric plasmonic metamaterials
We theoretically investigate the optical properties of parity-time (PT)-symmetric three-dimensional metamaterials composed of strongly coupled planar plasmonic waveguides. By tuning the loss-gain balance, we show how the initially isotropic material becomes both asymmetric and unidirectional. Investigation of the band structure near the material's exceptional point reveals several interesting optical properties, including double negative refraction, Bloch power oscillations, unidirectional invisibility, and reflection and transmission coefficients that are simultaneously equal to or greater than unity. The highly tunable optical dispersion of PT-symmetric metamaterials provides a foundation for designing an unconventional class of three-dimensional bulk synthetic media, with applications ranging from lossless subdiffraction-limited optical lenses to nonreciprocal nanophotonic devices.
Alaeian, Hadiseh; Dionne, Jennifer A.
Binary switching in a 'symmetric' potential landscape
A binary switch is the basic building block for information processing. The potential energy profile of a bistable binary switch is a �symmetric' double well. The traditional method of switching it from one state (one well) to the other is to tilt the profile towards the desired state. Here, we present a case, where no such tilting is necessary to switch successfully, even in the presence of thermal noise. This happens because of the built-in dynamics inside the switch itself. It differs from the general perception on binary switching that in a �symmetric' potential landscape, the switching probability is 50% in the presence of thermal noise. Our results, considering the complete three-dimensional potential landscape, demonstrate intriguing phenomena on binary switching mechanism. With experimentally feasible parameters, we theoretically demonstrate such intriguing possibility in electric field induced magnetization switching of a shape-anisotropic single-domain magnetostrictive nanomagnet with two stable states at room-temperature.
Roy, Kuntal; Bandyopadhyay, Supriyo; Atulasimha, Jayasimha
Binary switching in a 'symmetric' potential landscape.
A binary switch is the basic building block for information processing. The potential energy profile of a bistable binary switch is a 'symmetric' double well. The traditional method of switching it from one state (one well) to the other is to tilt the profile towards the desired state. Here, we present a case, where no such tilting is necessary to switch successfully, even in the presence of thermal noise. This happens because of the built-in dynamics inside the switch itself. It differs from the general perception on binary switching that in a 'symmetric' potential landscape, the switching probability is 50% in the presence of thermal noise. Our results, considering the complete three-dimensional potential landscape, demonstrate intriguing phenomena on binary switching mechanism. With experimentally feasible parameters, we theoretically demonstrate such intriguing possibility in electric field induced magnetization switching of a shape-anisotropic single-domain magnetostrictive nanomagnet with two stable states at room-temperature. PMID:24154561
Observational tests of baryon symmetric cosmology
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of Pi(O)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the gamma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurements of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed. Previously announced in STAR as N83-10996
High energy concentration by symmetric shock focusing
High-energy concentrations in gas are achieved experimentally in a specially constructed shock tube facility at KTH Mechanics. The high-energy concentration is manifested by a formation of a hot, light-emitting gas core. Experimental, numerical and theoretical investigations show that the shape of the imploding shock is of pivotal importance for the final energy concentration. Cylindrical shocks are unstable. Symmetric polygonal shocks are shown to be dynamically stable and are produced by various methods, e.g. thin wing profiles placed radially in the test section. Such symmetric polygonal shocks are able to produce extremely high energy levels at the focal point. Spectral data from 60 nanosecond short intervals of 8 microsecond light pulse give temperatures in the range of 6,000 K.
Apazidis, N.; Kjellander, M.; Tillmark, N.
Stereoisomers of compounds with symmetric constitutions.
Chiral organic compounds with unsymmetric constitutions can lead to N(r) = 2(n) stereoisomers. By contrast, if a chiral compound has a symmetric constitution, then the number of stereoisomers is reduced. In this publication, we wish to present an algorithm to calculate the number of stereoisomers of chiral organic compounds of the latter type (e. g. sugar acids). The first step is the development of two different functions for unbranched compounds where the number of repeating units is even or uneven. Other stereogenic units like double bonds, chiral axes or planes are not discussed. The results are then checked against the actual isomers. The next step leads to a unified equation to predict the precise number of stereoisomers that can exist. Thus, the relationship between chirality and symmetry is shown in detail. Additionally, the algorithm is applied to some drug molecules with symmetric constitutions. PMID:16281306
Siebert, Carsten D; Tampe, Niels
PT-symmetric representations of fermionic algebras
A recent paper by Jones-Smith and Mathur, Phys. Rev. A 82, 042101 (2010) extends PT-symmetric quantum mechanics from bosonic systems (systems for which T{sup 2}=1) to fermionic systems (systems for which T{sup 2}=-1). The current paper shows how the formalism developed by Jones-Smith and Mathur can be used to construct PT-symmetric matrix representations for operator algebras of the form {eta}{sup 2}=0, {eta}{sup 2}=0, {eta}{eta}+{eta}{eta}={alpha}1, where {eta}={eta}{sup PT}=PT{eta}T{sup -1}P{sup -1}. It is easy to construct matrix representations for the Grassmann algebra ({alpha}=0). However, one can only construct matrix representations for the fermionic operator algebra ({alpha}{ne}0) if {alpha}=-1; a matrix representation does not exist for the conventional value {alpha}=1.
Bender, Carl M. [Physics Department, Washington University, St. Louis, Missouri 63130 (United States); Klevansky, S. P. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany)
Compactly Supported Orthogonal Symmetric Scaling Functions
Daubechies (1988, Comm. Pure Appl. Math.41, 909�996) showed that, except for the Haar function, there exist no compactly supported orthogonal symmetric scaling functions for the dilation q = 2. Nevertheless, such scaling functions do exist for dilations q>2 (as evidenced by Chui and Lian's construction (1995, Appl. Comput. Harmon. Anal.2, 68�84) for q = 3); these functions are the main
Eugene Belogay; Yang Wang
Symmetrically reduced Galileon equations and solutions
The maximally complicated arbitrary-dimensional �maximal� Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional (Monge-Ampere) equation, axial symmetry to its cubic extension, etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.
Deser, S.; Franklin, J.
Noncommutative analogues of classical operations on symmetric functions are investigated,and applied to the description of idempotents and nilpotents in descent algebras.Its is shown that any sequence of Lie idempotents (one in each descent algebra) givesrise to a complete set of indecomposable orthogonal idempotents of each descent algebra,and various deformations of the classical sequences of Lie idempotents are obtained. Inparticular, we
D. Krob; B. Leclerc; Y. Thibon
Symmetrical Core Improves Micro-Fluxgate Sensors
Microfluxgate sensor with flat coil and double-sided symmetrical core has significantlyimproved parameters over the original asymmetric single-sided core design. The magneticcircuit of the new sensor is more closed and so the core is deeper saturated. The sensorhysteresis was decreased from 30 T to 2.5 T (for full range). Noise level was decreasedfrom 242 nT to 27 nT rms (0.1 mHz
A. Tipek; M. Ishida; S. Kawahito
Symmetrical core improves micro-fluxgate sensors
New micro-fluxgate sensor with flat excitation and sensing coils and double-sided symmetrical core has significantly improved parameters over the original asymmetric single-sided core design. The main advantage of the new design is that the demagnetization with respect to the excitation field is much lower than demagnetization with respect to the external measured field. The magnetic circuit of the new sensor
P. Ripka; S. O. Choi; A. Tipek; S. Kawahito; M. Ishida
Scattering from a PT symmetric standing wave
We study the Kapitza-Dirac diffraction of a free beam particle in the presence of a PT symmetric standing wave. We discuss that the momentum and total probability are not conserved in the non-Hermitian scattering process. We show that the average momentum gain/loss does not vanish over a period even if the non-Hermitian optical potential changes periodically in time. We give the resonance conditions at which large momentum transfer is produced.
Yuce, C.
[Surgical reduction in benign symmetrical lipomatosis].
We report on a 50-year-old female patient suffering from benign symmetric lipomatosis of her upper arms, shoulders, neck, back, abdomen, and thighs. Concomitantly, we found hypertension, hyperuricemia, and hypertriglyceridemia. Since the patient complained of occasional pain in her upper arms and shoulders induced by work or pressure and suffered psychically from her deformity, we decided to reduce the fatty tissue of the upper arms surgically--with good cosmetic and functional results. PMID:2264376
Pfannschmidt, N; J�ger, K
Static axially symmetric solutions in Nordtvedt's theory
Static axially symmetric solutions in vacuum are obtained in the general scalar-tensor theory proposed by Nordtvedt. The solutions are asymptotically flat and under certain conditions give very large red shift. The asymptotic behavior and singularity are studied and a comparison is made with a corresponding solution with spherical symmetry. It is also observed that with a conformal transformation the Nordtvedt metric appears to reduce to the Brans-Dicke one.
Chatterjee, S.
Active tokamak limiters; symmetrizing the edge plasma
The surface layers of tokamak plasmas are strongly unstable to low frequency oscillations. The limiter, by imposing a non-axisymmetric state in the plasma scrape-off layer, may be the source of the free energy driving the instabilities. An active, two-faced sandwich limiter is proposed to symmetrize the scrape-off layer, thereby minimizing the mismatch between the inner and outer tokamak states.
Motley, R.W.
High energy density dielectrics for symmetric Blumleins
Multilayer, tape cast ceramics are being developed for use in large area, high voltage devices in order to achieve high specific energy densities (>106 J\\/m3) and physical size reduction. In particular, symmetric Blumleins are desired with the following properties: High voltage hold off (⩾300 kV); High, nondispersive permittivity: ≈100 to 900; Ability to be fabricated into various shapes and sizes;
W. Huebner; S. C. Zhang
Cuspidality of symmetric powers with applications
The purpose of this paper is to prove that the symmetric fourth\\u000apower of a cusp form on ${\\\\rm GL}(2)$, whose existence was proved\\u000aearlier by the first author, is cuspidal unless the corresponding\\u000aautomorphic representation is of dihedral, tetrahedral, or octahedral\\u000atype. As a consequence, we prove a number of results toward the\\u000aRamanujan-Petersson and Sato-Tate conjectures. In particular,
Henry H. Kim; Freydoon Shahidi
Highly symmetric travelling waves in pipe flow
The recent theoretical discovery of finite-amplitude travelling waves in pipe flow has re-ignited interest in the transitional phenomena that Osborne Reynolds studied 125 years ago. Despite all being unstable, these waves are providing fresh insight into the flow dynamics. Here we describe two new classes of highly-symmetric travelling waves (possessing rotational, shift-&-reflect and mirror symmetries) and report a new family
Chris C. T. Pringle; Yohann Duguet; Rich R. Kerswell
Binding in Charged Spherically Symmetric Objects
We consider the subject of self-binding in static, spherically symmetric objects consisting of a charged fluid. We have shown\\u000a previously that in the case of a perfect fluid, only the localized part of the mass contributes to gravitational self-binding\\u000a of such objects and that in the limiting case of objects comprised purely of electromagnetic mass, there is no gravitational\\u000a binding.
Matthew Corne; Arkady Kheyfets; Jennifer Piasio; Chad Voegele
Optical isolation via -symmetric nonlinear Fano resonances.
We show that Fano resonances created by two -symmetric nonlinear micro-resonators coupled to a waveguide, have line-shape and resonance position that depends on the direction of the incident light. We utilize these features in order to induce asymmetric transport, up to 47 dBs, in the optical C-window. Our theoretical proposal requires low input power and does not compromise the power or frequency characteristics of the output signal. PMID:24787845
Nazari, F; Bender, N; Ramezani, H; Moravvej-Farshi, M K; Christodoulides, D N; Kottos, T
The Limit of Applicability of Linear Wave Refraction Theory in a Convergence Zone.
Reported is an experimental investigation to assess the limits of applicability of linear wave refraction theory in a convergence zone. One bottom topography with parallel circular contours symmetric about the center of the tank was used and three wave pe...
R. W. Whalin
An interior-point method for generalized linear-fractional programming
We develop an interior-point polynomial-time algorithm for a generalized linear-fractional problem. The latter problem can be regarded as a nonpolyhedral extension of the usual linear-fractional programming; typical example (which is of interest for control theory) is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables.
Yurii Nesterov; A. S. Nemirovskii
Macromolecular symmetric assembly prediction using swarm intelligence dynamic modeling.
Proteins often assemble in multimeric complexes to perform a specific biologic function. However, trapping these high-order conformations is difficult experimentally. Therefore, predicting how proteins assemble using in silico techniques can be of great help. The size of the associated conformational space and the fact that proteins are intrinsically flexible structures make this optimization problem extremely challenging. Nonetheless, known experimental spatial restraints can guide the search process, contributing to model biologically relevant states. We present here a swarm intelligence optimization protocol able to predict the arrangement of protein symmetric assemblies by exploiting a limited amount of experimental restraints and steric interactions. Importantly, within this scheme the native flexibility of each protein subunit is taken into account as extracted from molecular dynamics (MD) simulations. We show that this is a key ingredient for the prediction of biologically functional assemblies when, upon oligomerization, subunits explore activated states undergoing significant conformational changes. PMID:23810695
Degiacomi, Matteo T; Dal Peraro, Matteo
Elliptical symmetric distribution based maximal margin classification for hyperspectral imagery
It has been verified that hyperspectral data is statistically characterized by elliptical symmetric distribution. Accordingly, we introduce the ellipsoidal discriminant boundaries and present an elliptical symmetric distribution based maximal margin (ESD-MM) classifier for hypespectral classification. In this method, the characteristic of elliptical symmetric distribution (ESD) of hyperspectral data is combined with the maximal margin rule. This strategy enables the ESD-MM
Lin He; Zhuliang Yu; Zhenghui Gu; Yuanqing Li
General theory for multiple input-output perturbations in complex molecular systems. 1. Linear QSPR electronegativity models in physical, organic, and medicinal chemistry.
In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturbations. The perturbations refers to changes in initial temperature, solvent, salt, salt concentration, solvent, and/or structure of the anion or cation of more than 150 different drugs and surfactants. QSPR-Perturbation Theory models may be useful for multi-objective optimization of organic synthesis, physicochemical properties, biological activity, metabolism, and distribution profiles towards the design of new drugs, surfactants, asymmetric ligands for catalysts, and other materials. PMID:23889050
Gonz�lez-D�az, Humberto; Arrasate, Sonia; G�mez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M
High-efficiency Fresnel lens fabricated by axially symmetric photoalignment method.
In this study, a Fresnel lens with radial and azimuthal liquid crystal (LC) alignments in the odd and even zones was fabricated using the photoalignment technique based on an azo dye doped in LC cells. The lens has approximately 35% focusing efficiency as determined using a linearly polarized probe beam. In addition, the lens converts the input linear polarization into axially symmetrical polarization at the focal plane. The fabricated Fresnel lens is polarization-independent and has electrically controllable focusing efficiency. Moreover, the far-field pattern of a probe beam through the device placed between the polarizers agrees with the pattern obtained from the simulation. PMID:23142883
Huang, Yao-Han; Ko, Shih-Wei; Chu, Shu-Chun; Fuh, Andy Ying-Guey
Spatial-frequency Fourier polarimetry of the complex degree of mutual anisotropy of linear and circular birefringence in the diagnostics of oncological changes in morphological structure of biological tissues
Theory of polarisation-correlation analysis of laser images of histological sections of biopsy material from cervix tissue based on spatial frequency selection of linear and circular birefringence mechanisms is formulated. Comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy (CDMA), produced by fibrillar networks formed by myosin and collagen fibres of cervix tissue in different pathological conditions, namely, pre-cancer (dysplasia) and cancer (adenocarcinoma), are presented. The values and variation ranges of statistical (moments of the first - fourth order), correlation (excess-autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of the CDMA coordinate distributions are studied. Objective criteria for pathology diagnostics and differentiation of its severity degree are determined. (image processing)
Ushenko, Yu A; Gorskii, M P; Dubolazov, A V; Motrich, A V; Ushenko, V A; Sidor, M I [Yuriy Fedkovych Chernivtsi National University, Chernivtsi (Ukraine)
Substrate protein switches GroE chaperonins from asymmetric to symmetric cycling by catalyzing nucleotide exchange
The complex kinetics of Pi and ADP release by the chaperonin GroEL/GroES is influenced by the presence of unfolded substrate protein (SP). Without SP, the kinetics of Pi release are described by four phases: a �lag,� a �burst� of ATP hydrolysis by the nascent cis ring, a �delay� caused by ADP release from the nascent trans ring, and steady-state ATP hydrolysis. The release of Pi precedes the release of ADP. The rate-determining step of the asymmetric cycle is the release of ADP from the trans ring of the GroEL-GroES1 �bullet� complex that is, consequently, the predominant species. In the asymmetric cycle, the two rings of GroEL function alternately, 180� out of phase. In the presence of SP, a change in the kinetic mechanism occurs. With SP present, the kinetics of ADP release are also described by four phases: a lag, a �surge� of ADP release attributable to SP-induced ADP/ATP exchange, and a �pause� during which symmetrical �football� particles are formed, followed by steady-state ATP hydrolysis. SP catalyzes ADP/ATP exchange on the trans ring. Now ADP release precedes the release of Pi, and the rate-determining step of the symmetric cycle becomes the hydrolysis of ATP by the symmetric GroEL-GroES2 football complex that is, consequently, the predominant species. A FRET-based analysis confirms that asymmetric GroEL-GroES1 bullets predominate in the absence of SP, whereas symmetric GroEL-GroES2 footballs predominate in the presence of SP. This evidence suggests that symmetrical football particles are the folding functional form of the chaperonin machine in vivo.
Ye, Xiang; Lorimer, George H.
Sorting linearly polarized photons with a single scatterer.
Intuitively, light impinging on a spatially mirror-symmetric object will be scattered equally into mirror-symmetric directions. This intuition can fail at the nanoscale if the polarization of the incoming light is properly tailored, as long as mirror symmetry is broken in the axes perpendicular to both the incident wave vector and the remaining mirror-symmetric direction. The unidirectional excitation of plasmonic modes using circularly polarized light has been recently demonstrated. Here, we generalize this concept and show that linearly polarized photons impinging on a single spatially symmetric scatterer created in a silicon waveguide are guided into a certain direction of the waveguide depending exclusively on their polarization angle and the structure asymmetry. Our work broadens the scope of polarization-induced directionality beyond plasmonics, with applications in polarization (de)multiplexing, unidirectional coupling, directional switching, radiation polarization control, and polarization-encoded quantum information processing in photonic integrated circuits. PMID:24690796
Rodr�guez-Fortu�o, Francisco J; Puerto, Daniel; Griol, Amadeu; Bellieres, Laurent; Mart�, Javier; Mart�nez, Alejandro
The Caenorhabditis elegans septin complex is nonpolar
Septins are conserved GTPases that form heteromultimeric complexes and assemble into filaments that play a critical role in cell division and polarity. Results from budding and fission yeast indicate that septin complexes form around a tetrameric core. However, the molecular structure of the core and its influence on the polarity of septin complexes and filaments is poorly defined. The septin complex of the nematode Caenorhabditis elegans is formed entirely by the core septins UNC-59 and UNC-61. We show that UNC-59 and UNC-61 form a dimer of coiled-coil-mediated heterodimers. By electron microscopy, this heterotetramer appears as a linear arrangement of four densities representing the four septin subunits. Fusion of GFP to the N termini of UNC-59 and UNC-61 and subsequent electron microscopic visualization suggests that the sequence of septin subunits is UNC-59/UNC-61/UNC-61/UNC-59. Visualization of GFP extensions fused to the extremity of the C-terminal coiled coils indicates that these extend laterally from the heterotetrameric core. Together, our study establishes that the septin core complex is symmetric, and suggests that septins form nonpolar filaments.
John, Corinne M; Hite, Richard K; Weirich, Christine S; Fitzgerald, Daniel J; Jawhari, Hatim; Faty, Mahamadou; Schlapfer, Dominik; Kroschewski, Ruth; Winkler, Fritz K; Walz, Tom; Barral, Yves; Steinmetz, Michel O
Experimental Study of the Vibrational Behaviour of a Coupled Non-Linear Mechanical System
The article describes an experimental analysis devised to determine the responses of a multi-degree-of-freedom non-linear mechanical system to various types and degrees of excitation. Such a system was designed and built to permit analysis in the time, frequency and phase-space domains. The system consisted of six planar pendulums that were coupled by springs having non-linear non-symmetric elastic force characteristics. The free responses showed several internal resonances and thus confirmed the expected behaviour of the system. The embedding procedure was adopted in order to reconstruct the abstract phase space from a single time history. As the main intention of the work is to assess the qualitative difference between linear and non-linear behaviour of a given mechanical system under external harmonic excitation, the increase in the complexity of the system's responses with increasing amplitude of excitation is shown using time-history plots, power spectra, bicoherences, delay-time maps, integrals of correlation dimension and greatest Lyapunov exponents. The bicoherence analysis showed the effect of periodicity on the linear behaviour of the system. By estimating bicoherence it was possible to detect the effect of quadratic phase coupling on non-linear behaviour. The effects of different windows and variations in the number of segments in the averaging process are also shown. Convergence was found in correlation dimension estimates with an increasing embedding dimension when the excitation was harmonic. The correlation dimension was found to increase with an increase of the driving force, thus confirming on increased complexity of the system's responses. The estimated greatest Lyapunov exponents showed the non-chaotic character of dynamics.
Bolte� Ar, M.; Hammond, J. K.
Partially PT symmetric optical potentials with all-real spectra and soliton families in multidimensions.
Multidimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial directions. However, we show that if the potential is only partially PT symmetric, i.e., it is invariant under complex conjugation and reflection in a single spatial direction, then it can also possess all-real spectra and continuous families of solitons. These results are established analytically and corroborated numerically. PMID:24690689
Yang, Jianke
An Approximate Solution and Master Curves for Buckling of Symmetrically Laminated Composite Cylinders
Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of buckling-design technology.
Expanding symmetric multiprocessor capability through gang scheduling
Symmetric Multiprocessor (SMP) systems normally provide both space- sharing and time-sharing to insure high system utilization and good responsiveness. However the prevailing lack of concurrent scheduling for parallel programs precludes SMP use in addressing many large-scale problems. Tightly synchronized communications are impractical and normal time-sharing reduces the benefit of cache memory. Evidence gathered at Lawrence Livermore National Laboratory (LLNL) indicates that gang scheduling can increase the capability of SMP systems and parallel program performance without adverse impact upon system utilization or responsiveness.
Jette, M.A.
Bilateral symmetric stress fractures in a toddler.
Stress fractures are a common injury among adolescent athletes and military recruits. The increase in child participation in organized sport activities has contributed to the inclusion of the skeletally immature age group among those who may suffer from this problem. Bilateral simultaneous symmetric tibial stress fractures that are infrequent in older children are even more rare in toddlers. This entity may cause a diagnostic problem as it must be differentiated from infectious disease, acute trauma or even from the result of a battered child. PMID:11269816
Keret, D; Segev, E; Hayek, S; Lokiec, F; Wientroub, S
Design of spherical symmetric gradient index lenses
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Mi�ano, Juan C.; Grabovi?ki?, Dejan; Ben�tez, Pablo; Gonz�lez, Juan C.; Santamar�a, Asunci�n
Scattering in PT-symmetric quantum mechanics
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.
Cannata, Francesco [Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica dell' Universita, Via Irnerio 46, I 40126 Bologna (Italy)]. E-mail: email@example.com; Dedonder, Jean-Pierre [GMPIB Universite Paris 7 - Denis-Diderot, 2 Place Jussieu, F-75251, Paris Cedex 05 (France)]. E-mail: firstname.lastname@example.com; Ventura, Alberto [Ente Nuove Tecnologie, Energia e Ambiente, Bologna and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (Italy)]. E-mail: email@example.com
Time-symmetric quantum theory of smoothing.
Smoothing is an estimation technique that takes into account both past and future observations and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism, thereby generalizing prior work on classical and quantum filtering, retrodiction, and smoothing. The proposed theory solves the important problem of optimally estimating classical Markov processes coupled to a quantum system under continuous measurements, and is thus expected to find major applications in future quantum sensing systems, such as gravitational wave detectors and atomic magnetometers. PMID:19659059
Tsang, Mankei
Hoop conjecture in spherically symmetric spacetimes
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is, they do not require any auxiliary assumptions such as maximality, time symmetry, or special extrinsic foliations, and most importantly they can easily be generalized to the nonspherical case once an existence theory for a modified version of the Jang equation is developed. Moreover, our methods also yield positivity and monotonicity properties of the Misner-Sharp energy.
Khuri, Marcus A. [Department of Mathematics, Stony Brook University, Stony Brook, New York 11794 (United States)
Linear trimer analogues of calixarene as chiral coordinating ligands: X-ray crystallographic and NMR spectroscopic characterization of chiral and achiral trisphenolates complexed to titanium(IV) and aluminum(III).
Achiral and chiral linear trisphenol analogues of calixarene (HOArCH(2)Ar'(OH)C(R)HArOH, Ar = 4,6-di-tert-butylphenyl; Ar' = 4-tert-butylphenyl; R = H (achiral), Me (chiral)) were prepared in anticipation of their adoption of a chiral conformation upon coordination to Lewis acidic metal centers. The trisphenols react with 1 equiv of Ti(OR')(4) (R' = i-Pr or t-Bu) to yield complexes with molecular formula Ti(2)(OArCH(2)Ar'(O)C(R)HArO)(2)(OR')(2) (R = H, Me; R' = i-Pr or t-Bu). An X-ray crystal structure of the titanium complex of the achiral trisphenol (R = H; R' = t-Bu) reveals that the trisphenolate ligand adopts an unsymmetrical (and therefore chiral) conformation, with eta(2)-coordination to one metal center and eta(1)-coordination to the second metal center. The chiral trisphenol, which contains a stereogenic center (indicated as C in the shorthand notation used above), coordinates titanium in an analogous fashion to produce only one diastereomer (out of four possible); therefore, the configuration of the stereogenic center controls the conformation adopted by the bound ligand. The reaction of achiral trisphenol with AlMe(3) produces a compound with molecular formula Al(2)(OArCH(2)Ar'(O)CH(2)ArO)(2). (1)H NMR spectroscopy and X-ray crystallography reveal that the trisphenolate ligand adopts an asymmetric, C(2) conformation in this complex, where the central phenolate oxygen bridges the aluminum centers and the terminal phenolate oxygens each coordinate a separate aluminum center. Because these trisphenolate ligands adopt chiral conformations when coordinated to metal centers, they may be useful for developing diastereo- or enantioselective catalysts and reagents. PMID:12099869
Appiah, William O; DeGreeff, Angela D; Razidlo, Gina L; Spessard, Sarah J; Pink, Maren; Young, Victor G; Hofmeister, Gretchen E
Three-Dimensional Solutions for Contact Area in Laminated Composite Pinned Joints with Symmetric and Non-Symmetric Stacking Sequences
The aim of this study is computing and evaluating the behavior of the laminated composite plate at the contact area in single lap, mechanically fastened joints. The analyses involve three dimensional finite element models performed by ABAQUS 6.4-PR11 code to evaluate the stress distribution in contact surface, separation angle, the magnitude and location of maximum radial stress. Results are determined for composite laminates with different layer configurations and attempts are made to validate the models with previous works. For cross ply and angle ply configurations only symmetric stacking sequences are used while for quasi-isotropic laminate both symmetric and non-symmetric models are generated. In cross-ply laminate symmetric separation about bearing plane could be found while in quasi-isotropic and angle-ply laminates non-symmetric separation occurs. Also, the separation angle is less than 90� in symmetric laminates and greater than 90� in some plies of non-symmetric laminates.
Javadi, H.; Rajabi, I.; Yavari, V.; Kadivar, M. H.
Partial symmetrization of the photosynthetic reaction center
The bacterial photosynthetic reaction center (RC) is a pigmented intrinsic membrane protein that performs the primary charge separation event of photosynthesis, thereby converting light to chemical energy. The RC pigments are bound primarily by two homologous peptides, the L and M subunits, each containing five transmembrane helices. These {alpha} helices and pigments are arranged in an approximate C{sub 2} symmetry and form two possible electron transfer pathways. Only one of these pathways is actually used. In an attempt to identify nonhomologous residues that are responsible for functional differences between the two branches, homologous helical regions that interact extensively with the pigments were genetically symmetrized (that is, exchanged). For example, replacement of the fourth transmembrane helix (D helix) in the M subunit with the homologous helix from the L subunit yields photosynthetically inactive RCs lacking a critical photoactive pigment. Photosynthetic revertants have been isolated in which single amino acid substitutions (intragenic suppressors) compensate for this partial symmetrization. 20 refs., 3 figs., 1 tab.
Robles, S.J.; Youvan, D.C. (Massachusetts Institute of Technology, Cambridge (USA)); Breton, J. (CEN Saclay, Gif-sur-Yvette (France))
Group Lifting Structures For Multirate Filter Banks, II: Linear Phase Filter Banks
The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole-and half-sample symmetric classes. Group lifting structures defined for the reversible and irreversible classes of whole-and half-sample symmetric filter banks are shown to satisfy the hypotheses of the uniqueness theorem for group lifting structures. It follows that linear phase lifting factorizations of whole-and half-sample symmetric filter banks are therefore independent of the factorization methods used to compute them. These results cover the specification of user-defined whole-sample symmetric filter banks in Part 2 of the ISO JPEG 2000 standard.
Brislawn, Christopher M [Los Alamos National Laboratory
The Tile Complexity of Linear Assemblies
Self-assembly is fundamental to both biological processes and nanoscience. Key features of self-assembly are its probabilistic nature and local programmability. These features can be leveraged to design better self-assembled systems. The conventional Tile Assembly Model (TAM) developed by Winfree using Wang tiles is a powerful, Turing-universal theoretical framework which models varied self-assembly processes. A particular challenge in DNA nanoscience is
Harish Chandran; Nikhil Gopalkrishnan; John H. Reif
Tunneling control using classical non-linear oscillator
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
Kar, Susmita; Bhattacharyya, S. P.
Helical [110] Gold Nanowires Make Longer Linear Atomic Chains
Quantum mechanical molecular dynamics shows that gold nanowires formed along the [110] direction reconstruct upon stress to form helical nanowires. The mechanism for this formation is discussed. These helical nanowires evolve on stretching to form linear atomic chains. Because helical nanowires do not form symmetrical tips, a requirement to stop the growth of atomic chains, these nanowires produce longer atomic
E. P. M. Amorim; E. Z. da Silva
Linearly Bounded Liars, Adaptive Covering Codes, and Deterministic Random Walks
We analyze a deterministic form of the random walk on the integer line called the {\\\\em liar machine}, similar to the rotor-router model, finding asymptotically tight pointwise and interval discrepancy bounds versus random walk. This provides an improvement in the best-known winning strategies in the binary symmetric pathological liar game with a linear fraction of responses allowed to be lies.
Joshua N. Cooper; Robert B. Ellis
A generalized linear Hubble law for an inhomogeneous barotropic universe
In this work, I present a generalized linear Hubble law for a barotropic spherically symmetric inhomogeneous spacetime, which is in principle compatible with the acceleration of the cosmic expansion obtained as a result of high redshift supernovae data. The new Hubble function, defined by this law, has two additional terms besides an expansion term, similar to the usual volume expansion
J.-F. Pascual-S�nchez
Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite
Angelos Barmpoutis; Bing Jian; Baba C. Vemuri; Timothy M. Shepherd
Interactions Between a Symmetrical Minor Groove Binding Compound and DNA Oligonucleotides: H and F NMR Studies
High-resolution NMR techniques (proton and F) have been used to study the interactions between several DNA oligonucleotides with varying length of AT base pairs and the synthetic pyrrole-containing compound (P1-F4S-P1), which has properties similar to the DNA minor groove binding drug distamycin A When this two-fold symmetrical DNA binding molecule is added to the self-complementary DNA oligomers, the resulting complex
Andrew H.-J. Wang; Sylvain Cottens; Peter B. Dervan; James P. Yesinowski; Gijs A. van der Marel; Jacques H. van Boom
AFM observation of surface acoustic waves emitted from single symmetric SAW transducers.
We report the first experimental observation of surface acoustic waves (SAWs) launched from a single symmetric SAW transducer, employing scanning acoustic force microscopy (SAFM). SAFM is a simple technique for the imaging of complex interdigital transducer (IDT) radiation patterns with nanometer lateral resolution. We demonstrate submicron lateral resolution and high sensitivity by investigating a single excitation element on a weakly coupling substrate (GaAs), visualizing the launched wave and second-order effects. PMID:11381686
Hesjedal, T; Behme, G
Solvable simulation of a double-well problem in PT-symmetric quantum mechanics
Within the framework of Script PScript T-symmetric quantum mechanics of bound states (which works with parity-pseudo-Hermitian Hamiltonians H = Script PHdaggerScript P and real spectra) we mimic some effects of the double-well structure of potentials by a pair of delta functions with mutually complex conjugate strengths. The model is solvable by the standard matching technique and exhibits several interesting features.
Miloslav Znojil
A permanent magnet tubular linear generator for wave energy conversion
A novel three-phase permanent magnet tubular linear generator (PMTLG) with Halbach array is proposed for the sea wave energy conversion. Non-linear axi-symmetrical finite element method (FEM) is implemented to calculate the magnetic fields along air-gap for different Halbach arrays of PMTLGs. The PMTLG characteristics are analyzed and the simulation results are validated by the experiment. An assistant tooth is implemented to greatly minimize the end and cogging effects which cause the oscillatory detent force.
Yu, Haitao; Liu, Chunyuan; Yuan, Bang; Hu, Minqiang; Huang, Lei; Zhou, Shigui
BioClips of symmetric and asymmetric cell division.
Animations have long been used as tools to illustrate complex processes in such diverse fields as mechanical engineering, astronomy, bacteriology and physics. Animations in biology hold particular educational promise for depicting complex dynamic processes, such as photosynthesis, motility, viral replication and cellular respiration, which cannot be easily explained using static two-dimensional images. However, these animations have often been restrictive in scope, having been created for a specific classroom or research audience. In recent years, a new type of animation has emerged called the BioClip (http://www.bioclips.com) that strives to present science in an interactive multimedia format, which is, at once, informative and entertaining, by combining animations, text descriptions and music in one portable cross-platform document. In the present article, we illustrate the educational value of this new electronic resource by reviewing in depth two BioClips our group has created which describe the processes of symmetric and asymmetric cell division (http://www.wormclassroom.org/cb/bioclip). PMID:17437407
Lu, Fong-Mei; Eliceiri, Kevin W; White, John G
Exact quantization of a PT-symmetric (reversible) Li�nard-type nonlinear oscillator
We carry out an exact quantization of a PT-symmetric (reversible) Li�nard-type one-dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time-independent classical Hamiltonian is of nonstandard type and is invariant under a combined coordinate reflection and time reversal transformation. We use the von Roos symmetric ordering procedure to write down the appropriate quantum Hamiltonian. While the quantum problem cannot be tackled in coordinate space, we show how the problem can be successfully solved in momentum space by solving the underlying Schr�dinger equation therein. We explicitly obtain the eigenvalues and eigenfunctions (in momentum space) and deduce the remarkable result that the spectrum agrees exactly with that of the linear harmonic oscillator, which is also confirmed by a semiclassical modified Bohr-Sommerfeld quantization rule, while the eigenfunctions are completely different.
Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.
Cutting Force Predication Based on Integration of Symmetric Fuzzy Number and Finite Element Method
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force.
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
Symmetric instability in the Gulf Stream
Analyses of wintertime surveys of the Gulf Stream (GS) conducted as part of the CLIvar MOde water Dynamic Experiment (CLIMODE) reveal that water with negative potential vorticity (PV) is commonly found within the surface boundary layer (SBL) of the current. The lowest values of PV are found within the North Wall of the GS on the isopycnal layer occupied by Eighteen Degree Water, suggesting that processes within the GS may contribute to the formation of this low-PV water mass. In spite of large heat loss, the generation of negative PV was primarily attributable to cross-front advection of dense water over light by Ekman flow driven by winds with a down-front component. Beneath a critical depth, the SBL was stably stratified yet the PV remained negative due to the strong baroclinicity of the current, suggesting that the flow was symmetrically unstable. A large eddy simulation configured with forcing and flow parameters based on the observations confirms that the observed structure of the SBL is consistent with the dynamics of symmetric instability (SI) forced by wind and surface cooling. The simulation shows that both strong turbulence and vertical gradients in density, momentum, and tracers coexist in the SBL of symmetrically unstable fronts. SI is a shear instability that draws its energy from geostrophic flows. A parameterization for the rate of kinetic energy (KE) extraction by SI applied to the observations suggests that SI could result in a net dissipation of 33 mW m-2 and 1 mW m-2 for surveys with strong and weak fronts, respectively. The surveys also showed signs of baroclinic instability (BCI) in the SBL, namely thermally direct vertical circulations that advect biomass and PV. The vertical circulation was inferred using the omega equation and used to estimate the rate of release of available potential energy (APE) by BCI. The rate of APE release was found to be comparable in magnitude to the net dissipation associated with SI. This result points to an energy pathway where the GS's reservoir of APE is drained by BCI, converted to KE, and then dissipated by SI and its secondary instabilities. Similar dynamics are likely to be found at other strong fronts forced by winds and/or cooling and could play an important role in the energy balance of the ocean circulation.
Thomas, Leif N.; Taylor, John R.; Ferrari, Raffaele; Joyce, Terrence M.
Eigenvalue similarity rules for symmetric cross-ply laminated plates
Symmetric cross-ply laminated plates are analyzed by employing a previously presented affine stretching process, some material constant definitions from Tsai (1964), and by gneralizing existing similarity rules. As examples, similarity rules are employed to find the frequency spectrum of a cross-ply symmetric plate from the corresponding isotropic solution, and a similarity solution is presented for the vibration of an axially loaded, simply supported cross-ply symmetric plate. Buckling similarity rules are also presented.
Brunelle, E. J.
On the Method of N-Body Hyperspherical Basis Symmetrization
Parentage Scheme of Summarization (PSS) to the N-body symmetrized basis construction necessary for the description of the structural characteristics and decay reactions of the hypernuclear and nuclear systems with arbitrary amount of particles is introduced. Proposed method allows to construct N-particle symmetrized hyperspherical functions on the bases of N-particle hyperspherical functions symmetrized with respect to N�1-particles by the use of
Lia Leon Margolin
Various scattering properties of a new PT-symmetric non-Hermitian potential
We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}?(tanh[(x??d)/d]+tanh(?)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (?,d) becomes imaginary. For the case of ??i?, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d?id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: �Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. �Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. �Co-existence of MSS with deep energy minima of transitivity is obtained. �Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. �Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.
Ghatak, Ananya, E-mail: email@example.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)] [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Raka Dona Ray, E-mail: email@example.com [Department of Physics, Rajghat Besant School, Varanasi-221001 (India); Mandal, Bhabani Prasad, E-mail: email@example.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)
Hermitian four-well potential as a realization of a PT-symmetric system
A PT-symmetric Bose-Einstein condensate can be theoretically described using a complex optical potential; however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents of a two-well system are implemented by coupling two additional wells to the system, which act as particle reservoirs. In terms of a simple four-mode model we derive conditions under which the two middle wells of the Hermitian four-well system behave exactly as the two wells of the PT-symmetric system. We apply these conditions to calculate stationary solutions and oscillatory dynamics. By means of frozen Gaussian wave packets we relate the Gross-Pitaevskii equation to the four-mode model and give parameters required for the external potential, which provides approximate conditions for a realistic experimental setup.
Kreibich, Manuel; Main, J�rg; Cartarius, Holger; Wunner, G�nter
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.
M�ller, Ingo