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| Semiclassical Limits of Eigenfunctions on Flat $n$-Dimensional Tori
Aïssiou, Tayeb
We provide a proof of a conjecture by Jakobson, Nadirashvili, and Toth stating that on an $n$-dimensional flat torus $\mathbb T^{n}$, and the Fourier transform of squares of the eigenfunctions $|\varphi_\lambda|^2$ of the Laplacian have uniform $l^n$ bounds that do not depend on the eigenvalue $\lambda$. The proof is a generalization of an argument by Jakobson, et al. for the lower dimensional cases. These results imply uniform bounds for semiclassical limits on $\mathbb T^{n+2}$. We also prove a geometric lemma that bounds the number of codimension-one simplices satisfying a certain restriction on an $n$-dimensional sphere $S^n(\lambda)$ of radius $\sqrt{\lambda}$, and we use it in the proof.
| Ordering the Representations of $S_n$ Using the Interchange Process
Alon, Gil; Kozma, Gady
Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett, and Richthammer, we define an associated order $\prec$ on the irreducible representations of $S_n$. Aldous' conjecture is equivalent to certain representations being comparable in this order, and hence determining the ``Aldous order'' completely is a generalized question. We show a few additional entries for this order.
| Derivations and Valuation Rings
Ayuso, Fortuny P.
A complete characterization of valuation rings closed for a holomorphic derivation is given, following an idea of Seidenberg, in dimension $2$.
| Comparison Theorem for Conjugate Points of a Fourth-order Linear Differential Equation
Ben Amara, Jamel
In 1961, J. Barrett showed that if the first conjugate point $\eta_1(a)$ exists for the differential equation $(r(x)y'')''= p(x)y,$ where $r(x)\gt 0$ and $p(x)\gt 0$, then so does the first systems-conjugate point $\widehat\eta_1(a)$. The aim of this note is to extend this result to the general equation with middle term $(q(x)y')'$ without further restriction on $q(x)$, other than continuity.
| Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections
Biswas, Indranil; Dey, Arijit
We show that there is a bijective correspondence between the polystable parabolic principal $G$-bundles and solutions of the Hermitian-Einstein equation.
| Cliquishness and Quasicontinuity of Two-Variable Maps
Bouziad, A.
We study the existence of continuity points for mappings $f\colon X\times Y\to Z$ whose $x$-sections $Y\ni y\to f(x,y)\in Z$ are fragmentable and $y$-sections $X\ni x\to f(x,y)\in Z$ are quasicontinuous, where $X$ is a Baire space and $Z$ is a metric space. For the factor $Y$, we consider two infinite ``point-picking'' games $G_1(y)$ and $G_2(y)$ defined respectively for each $y\in Y$ as follows: in the $n$-th inning, Player I gives a dense set $D_n\subset Y$, respectively, a dense open set $D_n\subset Y$. Then Player II picks a point $y_n\in D_n$; II wins if $y$ is in the closure of ${\{y_n:n\in\mathbb N\}}$, otherwise I wins. It is shown that (i) $f$ is cliquish if II has a winning strategy in $G_1(y)$ for every $y\in Y$, and (ii) $ f$ is quasicontinuous if the $x$-sections of $f$ are continuous and the set of $y\in Y$ such that II has a winning strategy in $G_2(y)$ is dense in $Y$. Item (i) extends substantially a result of Debs and item (ii) indicates that the problem of Talagrand on separately continuous maps has a positive answer for a wide class of ``small'' compact spaces.
| The Uncomplemented Subspace $\mathbf K(X,Y) $
Ghenciu, Ioana
A vector measure result is used to study the complementation of the space $K(X,Y)$ of compact operators in the spaces $W(X,Y)$ of weakly compact operators, $CC(X,Y)$ of completely continuous operators, and $U(X,Y)$ of unconditionally converging operators. Results of Kalton and Emmanuele concerning the complementation of $K(X,Y)$ in $L(X,Y)$ and in $W(X,Y)$ are generalized. The containment of $c_0$ and $\ell_\infty$ in spaces of operators is also studied.
| An Asymptotic Bound on the Composition Number of Integer Sums of Squares Formulas
Hrubeš, P.; Wigderson, A.; Yehudayoff, A.
Let $\sigma_{\mathbb Z}(k)$ be the smallest $n$ such that there exists an identity \[ (x_1^2 + x_2^2 + \cdots + x_k^2) \cdot (y_1^2 + y_2^2 + \cdots + y_k^2) = f_1^2 + f_2^2 + \cdots + f_n^2, \] with $f_1,\dots,f_n$ being polynomials with integer coefficients in the variables $x_1,\dots,x_k$ and $y_1,\dots,y_k$. We prove that $\sigma_{\mathbb Z}(k) \geq \Omega(k^{6/5})$.
| Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity
Islam, Muhammad N.
In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes.
| On Perturbations of Continuous Maps
Jacob, Benoît
We give sufficient conditions for the following problem: given a topological space $X$, a metric space $Y$, a subspace $Z$ of $Y$, and a continuous map $f$ from $X$ to $Y$, is it possible, by applying to $f$ an arbitrarily small perturbation, to ensure that $f(X)$ does not meet $Z$? We also give a relative variant: if $f(X')$ does not meet $Z$ for a certain subset $X'\subset X$, then we may keep $f$ unchanged on $X'$. We also develop a variant for continuous sections of fibrations and discuss some applications to matrix perturbation theory.
| Eigenvalue Approach to Even Order System Periodic Boundary Value Problems
Kong, Qingkai; Wang, Min
We study an even order system boundary value problem with periodic boundary conditions. By establishing the existence of a positive eigenvalue of an associated linear system Sturm-Liouville problem, we obtain new conditions for the boundary value problem to have a positive solution. Our major tools are the Krein-Rutman theorem for linear spectra and the fixed point index theory for compact operators.
| Central Extensions of Loop Groups and Obstruction to Pre-Quantization
Krepski, Derek
An explicit construction of a pre-quantum line bundle for the moduli space of flat $G$-bundles over a Riemann surface is given, where $G$ is any non-simply connected compact simple Lie group. This work helps to explain a curious coincidence previously observed between Toledano Laredo's work classifying central extensions of loop groups $LG$ and the author's previous work on the obstruction to pre-quantization of the moduli space of flat $G$-bundles.
| Evolution of Eigenvalues along Rescaled Ricci Flow
Li, Junfang
In this paper, we discuss monotonicity formulae of various entropy functionals under various rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue of a family of geometric operators $-4\Delta + kR$ is monotonic along the normalized Ricci flow for all $k\ge 1$ provided the initial manifold has nonpositive total scalar curvature.
| On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type
Munteanu, Radu-Bogdan
Product type equivalence relations are hyperfinite measured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property A. This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper.
| On the Gras Conjecture for Imaginary Quadratic Fields
Oukhaba, Hassan; Viguié, Stéphane
In this paper we extend K. Rubin's methods to prove the Gras conjecture for abelian extensions of a given imaginary quadratic field $k$ and prime numbers $p$ that divide the number of roots of unity in $k$.
| An Extension of the Dirichlet Density for Sets of Gaussian Integers
Rêgo, L. C.; Cintra, R. J.
Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.
| Semi-invariant Submersions from Almost Hermitian Manifolds
Sahin, Bayram
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.
| On Some Non-Riemannian Quantities in Finsler Geometry
Shen, Zhongmin
In this paper we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we study a new non-Riemannian quantity defined by the S-curvature. We show some relationships among the flag curvature, the S-curvature, and the new non-Riemannian quantity.
| On the Smallest and Largest Zeros of Müntz-Legendre Polynomials
Stefánsson, Úlfar F.
Müntz-Legendre polynomials $L_n(\Lambda;x)$ associated with a sequence $\Lambda=\{\lambda_k\}$ are obtained by orthogonalizing the system $(x^{\lambda_0}, x^{\lambda_1}, x^{\lambda_2}, \dots)$ in $L_2[0,1]$ with respect to the Legendre weight. If the $\lambda_k$'s are distinct, it is well known that $L_n(\Lambda;x)$ has exactly $n$ zeros $l_{n,n}\lt l_{n-1,n}\lt \cdots \lt l_{2,n}\lt l_{1,n}$ on $(0,1)$. First we prove the following global bound for the smallest zero, $$ \exp\biggl(-4\sum_{j=0}^n \frac{1}{2\lambda_j+1}\biggr) \lt l_{n,n}. $$ An important consequence is that if the associated Müntz space is non-dense in $L_2[0,1]$, then $$ \inf_{n}x_{n,n}\geq \exp\biggl({-4\sum_{j=0}^{\infty} \frac{1}{2\lambda_j+1}}\biggr)\gt 0, $$ so the elements $L_n(\Lambda;x)$ have no zeros close to 0.
| Productively Lindelöf Spaces May All Be $D$
Tall, Franklin D.
We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every Lindelöf space is Lindelöf, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.
| A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible
Tausk, Daniel V.
It was claimed by Halmos in 1944 that if $G$ is a Hausdorff locally compact topological abelian group and if the character group of $G$ is torsion free, then $G$ is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of $G$ is both torsion free and divisible, it does not follow that $G$ is divisible.
| Functional Equations and Fourier Analysis
Yang, Dilian
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations - the d'Alembert equation, the Wilson equation, and the d'Alembert long equation - on compact groups.
| On the Notion of Visibility of Torsors
Agashe, Amod
Let $J$ be an abelian variety and $A$ be an abelian subvariety of $J$, both defined over $\mathbf{Q}$. Let $x$ be an element of $H^1(\mathbf{Q},A)$. Then there are at least two definitions of $x$ being visible in $J$: one asks that the torsor corresponding to $x$ be isomorphic over $\mathbf{Q}$ to a subvariety of $J$, and the other asks that $x$ be in the kernel of the natural map $H^1(\mathbf{Q},A) \to H^1(\mathbf{Q},J)$. In this article, we clarify the relation between the two definitions.
| Cesàro Operators on the Hardy Spaces of the Half-Plane
Arvanitidis, Athanasios G.; Siskakis, Aristomenis G.
In this article we study the Cesàro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also discussed.
| Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius
Betsakos, Dimitrios; Pouliasis, Stamatis
We prove variants of Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we examine when a similar monotonicity property holds for the hyperbolic metric.
| Sign Changes of the Liouville Function on Quadratics
Borwein, Peter; Choi, Stephen K. K.; Ganguli, Himadri
Let $\lambda (n)$ denote the Liouville function. Complementary to the prime number theorem, Chowla conjectured that \begin{equation*} \label{a.1} \sum_{n\le x} \lambda (f(n)) =o(x)\tag{$*$} \end{equation*} for any polynomial $f(x)$ with integer coefficients which is not of form $bg(x)^2$.
| The Smallest Pisot Element in the Field of Formal Power Series Over a Finite Field
Chandoul, A.; Jellali, M.; Mkaouar, M.
Dufresnoy and Pisot characterized the smallest Pisot number of degree $n \geq 3$ by giving explicitly its minimal polynomial. In this paper, we translate Dufresnoy and Pisot's result to the Laurent series case.
| Embedding Distributions of Generalized Fan Graphs
Chen, Yichao; Mansour, Toufik; Zou, Qian
Total embedding distributions have been known for a few classes of graphs. Chen, Gross, and Rieper computed it for necklaces, close-end ladders and cobblestone paths. Kwak and Shim computed it for bouquets of circles and dipoles. In this paper, a splitting theorem is generalized and the embedding distributions of generalized fan graphs are obtained.
| On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate
Cheng, Lixin; Luo, Zhenghua; Zhou, Yu
In this note, we first give a characterization of super weakly compact convex sets of a Banach space $X$: a closed bounded convex set $K\subset X$ is super weakly compact if and only if there exists a $w^*$ lower semicontinuous seminorm $p$ with $p\geq\sigma_K\equiv\sup_{x\in K}\langle\,\cdot\,,x\rangle$ such that $p^2$ is uniformly Fréchet differentiable on each bounded set of $X^*$. Then we present a representation theorem for the dual of the semigroup $\textrm{swcc}(X)$ consisting of all the nonempty super weakly compact convex sets of the space $X$.
| Transcendental Solutions of a Class of Minimal Functional Equations
Coons, Michael
We prove a result concerning power series $f(z)\in\mathbb{C}[\mkern-3mu[z]\mkern-3mu]$ satisfying a functional equation of the form $$ f(z^d)=\sum_{k=1}^n \frac{A_k(z)}{B_k(z)}f(z)^k, $$ where $A_k(z),B_k(z)\in \mathbb{C}[z]$. In particular, we show that if $f(z)$ satisfies a minimal functional equation of the above form with $n\geqslant 2$, then $f(z)$ is necessarily transcendental. Towards a more complete classification, the case $n=1$ is also considered.
| Quasisymmetrically Minimal Moran Sets
Dai, Mei-Feng
M. Hu and S. Wen considered quasisymmetrically minimal uniform Cantor sets of Hausdorff dimension $1$, where at the $k$-th set one removes from each interval $I$ a certain number $n_{k}$ of open subintervals of length $c_{k}|I|$, leaving $(n_{k}+1)$ closed subintervals of equal length. Quasisymmetrically Moran sets of Hausdorff dimension $1$ considered in the paper are more general than uniform Cantor sets in that neither the open subintervals nor the closed subintervals are required to be of equal length.
| Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel
Pérez, Juan de Dios; Suh, Young Jin
We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and satisfies a further condition.
| A Note on Conjectures of F. Galvin and R. Rado
Dorais, François G.
In 1968, Galvin conjectured that an uncountable poset $P$ is the union of countably many chains if and only if this is true for every subposet $Q \subseteq P$ with size $\aleph_1$. In 1981, Rado formulated a similar conjecture that an uncountable interval graph $G$ is countably chromatic if and only if this is true for every induced subgraph $H \subseteq G$ with size $\aleph_1$. Todorčević has shown that Rado's Conjecture is consistent relative to the existence of a supercompact cardinal, while the consistency of Galvin's Conjecture remains open. In this paper, we survey and collect a variety of results related to these two conjectures. We also show that the extension of Rado's conjecture to the class of all chordal graphs is relatively consistent with the existence of a supercompact cardinal.
| Restricting Fourier Transforms of Measures to Curves in $\mathbb R^2$
Erdoğan, M. Burak; Oberlin, Daniel M.
We establish estimates for restrictions to certain curves in $\mathbb R^2$ of the Fourier transforms of some fractal measures.
| Certain Properties of $K_0$-monoids Preserved by Tracial Approximation
Fan, Qingzhai
We show that the following $K_0$-monoid properties of $C^*$-algebras in the class $\Omega$ are inherited by simple unital $C^*$-algebras in the class $TA\Omega$: (1) weak comparability, (2) strictly unperforated, (3) strictly cancellative.
| Involutions and Anticommutativity in Group Rings
Goodaire, Edgar G.; Milies, César Polcino
Let $g\mapsto g^*$ denote an involution on a group $G$. For any (commutative, associative) ring $R$ (with $1$), $*$ extends linearly to an involution of the group ring $RG$. An element $\alpha\in RG$ is symmetric if $\alpha^*=\alpha$ and skew-symmetric if $\alpha^*=-\alpha$. The skew-symmetric elements are closed under the Lie bracket, $[\alpha,\beta]=\alpha\beta-\beta\alpha$. In this paper, we investigate when this set is also closed under the ring product in $RG$. The symmetric elements are closed under the Jordan product, $\alpha\circ\beta=\alpha\beta+\beta\alpha$. Here, we determine when this product is trivial. These two problems are analogues of problems about the skew-symmetric and symmetric elements in group rings that have received a lot of attention.
| The Sizes of Rearrangements of Cantor Sets
Hare, Kathryn E.; Mendivil, Franklin; Zuberman, Leandro
A linear Cantor set $C$ with zero Lebesgue measure is associated with the countable collection of the bounded complementary open intervals. A rearrangment of $C$ has the same lengths of its complementary intervals, but with different locations. We study the Hausdorff and packing $h$-measures and dimensional properties of the set of all rearrangments of some given $C$ for general dimension functions $h$. For each set of complementary lengths, we construct a Cantor set rearrangement which has the maximal Hausdorff and the minimal packing $h$-premeasure, up to a constant. We also show that if the packing measure of this Cantor set is positive, then there is a rearrangement which has infinite packing measure.
| Multiple Solutions for Nonlinear Periodic Problems
Kyritsi, Sophia Th.; Papageorgiou, Nikolaos S.
We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term $f(t,x)$ that exhibits a $(p-1)$-superlinear growth in $x \in \mathbb{R}$ near $\pm\infty$ and near zero. A special case of the differential operator is the scalar $p$-Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).
| Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases
Ma, Li; Wang, Jing
In this paper, we consider the Gross-Pitaevskii equation for the trapped dipolar quantum gases. We obtain the sharp criterion for the global existence and finite time blow up in the unstable regime by constructing a variational problem and the so-called invariant manifold of the evolution flow.
| Application of Measure of Noncompactness to Infinite Systems of Differential Equations
Mursaleen, M.
In this paper we determine the Hausdorff measure of noncompactness on the sequence space $n(\phi)$ of W. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces $n(\phi)$ and $m(\phi)$. Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.
| Coessential Abelianization Morphisms in the Category of Groups
Oancea, D.
An epimorphism $\phi\colon G\to H$ of groups, where $G$ has rank $n$, is called coessential if every (ordered) generating $n$-tuple of $H$ can be lifted along $\phi$ to a generating $n$-tuple for $G$. We discuss this property in the context of the category of groups, and establish a criterion for such a group $G$ to have the property that its abelianization epimorphism $G\to G/[G,G]$, where $[G,G]$ is the commutator subgroup, is coessential. We give an example of a family of 2-generator groups whose abelianization epimorphism is not coessential. This family also provides counterexamples to the generalized Andrews--Curtis conjecture.
| A Factorization Theorem for Multiplier Algebras of Reproducing Kernel Hilbert Spaces
Prunaru, Bebe
Let $(X,\mathcal B,\mu)$ be a $\sigma$-finite measure space and let $H\subset L^2(X,\mu)$ be a separable reproducing kernel Hilbert space on $X$. We show that the multiplier algebra of $H$ has property $(A_1(1))$.
| On Domination in Zero-Divisor Graphs
Rad, Nader Jafari; Jafari, Sayyed Heidar; Mojdeh, Doost Ali
We first determine the domination number for the zero-divisor graph of the product of two commutative rings with $1$. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a right zero-divisor.
| Structure in Sets with Logarithmic Doubling
Sanders, T.
Suppose that $G$ is an abelian group, $A \subset G$ is finite with $|A+A| \leq K|A|$ and $\eta \in (0,1]$ is a parameter. Our main result is that there is a set $\mathcal{L}$ such that \begin{equation*} |A \cap \operatorname{Span}(\mathcal{L})| \geq K^{-O_\eta(1)}|A| \quad\text{and}\quad |\mathcal{L}| = O(K^\eta\log |A|). \end{equation*} We include an application of this result to a generalisation of the Roth--Meshulam theorem due to Liu and Spencer.
| Convergent Sequences in Discrete Groups
Thom, Andreas
We prove that a finitely generated group contains a sequence of non-trivial elements that converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian. As a consequence of the methods used, we show that a finitely generated group satisfies Chu duality if and only if it is virtually abelian.
| Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces
Wnuk, Witold
Following ideas used by Drewnowski and Wilansky we prove that if $I$ is an infinite dimensional and infinite codimensional closed ideal in a complete metrizable locally solid Riesz space and $I$ does not contain any order copy of $\mathbb R^{\mathbb N}$ then there exists a closed, separable, discrete Riesz subspace $G$ such that the topology induced on $G$ is Lebesgue, $I \cap G = \{0\}$, and $I + G$ is not closed.
| Closed Left Ideal Decompositions of $U(G)$
Zelenyuk, Yevhen
Let $G$ be an infinite discrete group and let $\beta G$ be the Stone--Čech compactification of $G$. We take the points of $ėta G$ to be the ultrafilters on $G$, identifying the principal ultrafilters with the points of $G$. The set $U(G)$ of uniform ultrafilters on $G$ is a closed two-sided ideal of $\beta G$. For every $p\in U(G)$, define $I_p\subseteq\beta G$ by $I_p=\bigcap_{A\in p}\operatorname{cl} (GU(A))$, where $U(A)=\{p\in U(G):A\in p\}$. We show that if $|G|$ is a regular cardinal, then $\{I_p:p\in U(G)\}$ is the finest decomposition of $U(G)$ into closed left ideals of $\beta G$ such that the corresponding quotient space of $U(G)$ is Hausdorff.
| The $f$-Chromatic Index of a Graph Whose $f$-Core has Maximum Degree $2$
Akbari, S.; Chavooshi, M.; Ghanbari, M.; Zare, S.
Let $G$ be a graph. The minimum number of colors needed to color the edges of $G$ is called the chromatic index of $G$ and is denoted by $\chi'(G)$. It is well-known that $\Delta(G) \leq \chi'(G) \leq \Delta(G)+1$, for any graph $G$, where $\Delta(G)$ denotes the maximum degree of $G$. A graph $G$ is said to be Class $1$ if $\chi'(G) = \Delta(G)$ and Class $2$ if $\chi'(G) = \Delta(G) + 1$. Also, $G_\Delta$ is the induced subgraph on all vertices of degree $\Delta(G)$. Let $f:V(G)\rightarrow \mathbb{N}$ be a function. An $f$-coloring of a graph $G$ is a coloring of the edges of $E(G)$ such that each color appears at each vertex $v\in V(G)$ at most $f (v)$ times. The minimum number of colors needed to $f$-color $G$ is called the $f$-chromatic index of $G$ and is denoted by $\chi'_{f}(G)$. It was shown that for every graph $G$, $\Delta_{f}(G)\le \chi'_{f}(G)\le \Delta_{f}(G)+1$, where $\Delta_{f}(G)=\max_{v\in V(G)} \big\lceil \frac{d_G(v)}{f(v)}\big\rceil$. A graph $G$ is said to be $f$-Class $1$ if $\chi'_{f}(G)=\Delta_{f}(G)$, and $f$-Class $2$, otherwise. Also, $G_{\Delta_f}$ is the induced subgraph of $G$ on $\{v\in V(G):\,\frac{d_G(v)}{f(v)}=\Delta_{f}(G)\}$. Hilton and Zhao showed that if $G_{\Delta}$ has maximum degree two and $G$ is Class $2$, then $G$ is critical, $G_{\Delta}$ is a disjoint union of cycles and $\delta(G)=\Delta(G)-1$, where $\delta(G)$ denotes the minimum degree of $G$, respectively. In this paper, we generalize this theorem to $f$-coloring of graphs. Also, we determine the $f$-chromatic index of a connected graph $G$ with $|G_{\Delta_f}|\le 4$.
| On Certain Multivariable Subnormal Weighted Shifts and their Duals
Athavale, Ameer; Patil, Pramod
To every subnormal $m$-variable weighted shift $S$ (with bounded positive weights) corresponds a positive Reinhardt measure $\mu$ supported on a compact Reinhardt subset of $\mathbb C^m$. We show that, for $m \geq 2$, the dimensions of the $1$-st cohomology vector spaces associated with the Koszul complexes of $S$ and its dual ${\tilde S}$ are different if a certain radial function happens to be integrable with respect to $\mu$ (which is indeed the case with many classical examples). In particular, $S$ cannot in that case be similar to ${\tilde S}$. We next prove that, for $m \geq 2$, a Fredholm subnormal $m$-variable weighted shift $S$ cannot be similar to its dual.
| Inclusion Relations for New Function Spaces on Riemann Surfaces
Aulaskari, Rauno; Rättyä, Jouni
We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, BMOA or the recently defined $Q_p$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces.
| Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$
Ayadi, Adlene
We give a characterization of hypercyclic abelian group $\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$ is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.
| A Note on Homological Dimensions of Artinian Local Cohomology Modules
Bahmanpour, Kamal
Let $(R,{\frak m})$ be a non-zero commutative Noetherian local ring (with identity), $M$ be a non-zero finitely generated $R$-module. In this paper for any ${\frak p}\in {\rm Spec}(R)$ we show that $ \operatorname{{\rm injdim_{_{R_{\frak p}}}}} H^{i-\dim(R/{\frak p})}_{{\frak p}R_{\frak p}}(M_{\frak p})$ and ${\rm fd}_{R_{\p}} H^{i-\dim(R/{\frak p})}_{{\frak p}R_{\frak p}}(M_{\frak p})$ are bounded from above by $ \operatorname{{\rm injdim_{_{R}}}} H^i_{\frak m}(M)$ and $ {\rm fd}_R H^i_{\frak m}(M)$ respectively, for all integers $i\geq \dim(R/{\frak p})$.
| The Lang--Weil Estimate for Cubic Hypersurfaces
Browning, T. D.
An improved estimate is provided for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible, projective, cubic hypersurface that is not equal to a cone.
| Weak Sequential Completeness of $\mathcal K(X,Y)$
Bu, Qingying
For Banach spaces $X$ and $Y$, we show that if $X^\ast$ and $Y$ are weakly sequentially complete and every weakly compact operator from $X$ to $Y$ is compact then the space of all compact operators from $X$ to $Y$ is weakly sequentially complete. The converse is also true if, in addition, either $X^\ast$ or $Y$ has the bounded compact approximation property.
| Linear Forms in Monic Integer Polynomials
Dubickas, Artūras
We prove a necessary and sufficient condition on the list of nonzero integers $u_1,\dots,u_k$, $k \geq 2$, under which a monic polynomial $f \in \mathbb{Z}[x]$ is expressible by a linear form $u_1f_1+\dots+u_kf_k$ in monic polynomials $f_1,\dots,f_k \in \mathbb{Z}[x]$. This condition is independent of $f$. We also show that if this condition holds, then the monic polynomials $f_1,\dots,f_k$ can be chosen to be irreducible in $\mathbb{Z}[x]$.
| Equivariant Forms: Structure and Geometry
Elbasraoui, Abdelkrim; Sebbar, Abdellah
In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of $\operatorname{SL}_2(\mathbb{Z})$ by means of the cross-ratio, the weight 2 modular forms, the quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.
| A Cohomological Property of $\pi$-invariant Elements
Filali, M.; Monfared, M. Sangani
Let $A$ be a Banach algebra and $\pi \colon A \longrightarrow \mathscr L(H)$ be a continuous representation of $A$ on a separable Hilbert space $H$ with $\dim H =\frak m$. Let $\pi_{ij}$ be the coordinate functions of $\pi$ with respect to an orthonormal basis and suppose that for each $1\le j \le \frak m$, $C_j=\sum_{i=1}^{\frak m} \|\pi_{ij}\|_{A^*}\lt \infty$ and $\sup_j C_j\lt \infty$. Under these conditions, we call an element $\overline\Phi \in l^\infty (\frak m , A^{**})$ left $\pi$-invariant if $a\cdot \overline\Phi ={}^t\pi (a) \overline\Phi$ for all $a\in A$. In this paper we prove a link between the existence of left $\pi$-invariant elements and the vanishing of certain Hochschild cohomology groups of $A$. Our results extend an earlier result by Lau on $F$-algebras and recent results of Kaniuth-Lau-Pym and the second named author in the special case that $\pi \colon A \longrightarrow \mathbf C$ is a non-zero character on $A$.
| Universally Overconvergent Power Series via the Riemann Zeta-function
Gauthier, P. M.
The Riemann zeta-function is employed to generate universally overconvergent power series.
| Real Dimension Groups
Handelman, David
Dimension groups (not countable) that are also real ordered vector spaces can be obtained as direct limits (over directed sets) of simplicial real vector spaces (finite dimensional vector spaces with the coordinatewise ordering), but the directed set is not as interesting as one would like, i.e., it is not true that a countable-dimensional real vector space that has interpolation can be represented as such a direct limit over the a countable directed set. It turns out this is the case when the group is additionally simple, and it is shown that the latter have an ordered tensor product decomposition. In the Appendix, we provide a huge class of polynomial rings that, with a pointwise ordering, are shown to satisfy interpolation, extending a result outlined by Fuchs.
| Ziegler's Indecomposability Criterion
Herzog, Ivo
Ziegler's Indecomposability Criterion is used to prove that a totally transcendental, i.e., $\Sigma$-pure injective, indecomposable left module over a left noetherian ring is a directed union of finitely generated indecomposable modules. The same criterion is also used to give a sufficient condition for a pure injective indecomposable module ${_R}U$ to have an indecomposable local dual $U_R^{\sharp}.$
| Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups
Hoang, Giabao; Ressler, Wendell
In this paper we give a lower bound with respect to block length for the trace of non-elliptic conjugacy classes of the Hecke groups. One consequence of our bound is that there are finitely many conjugacy classes of a given trace in any Hecke group. We show that another consequence of our bound is that class numbers are finite for related hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms. We give canonical class representatives and calculate class numbers for some classes of hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms.
| On Automorphisms and Commutativity in Semiprime Rings
Liau, Pao-Kuei; Liu, Cheng-Kai
Let $R$ be a semiprime ring with center $Z(R)$. For $x,y\in R$, we denote by $[x,y]=xy-yx$ the commutator of $x$ and $y$. If $\sigma$ is a non-identity automorphism of $R$ such that $$ \Big[\big[\dots\big[[\sigma(x^{n_0}),x^{n_1}],x^{n_2}\big],\dots\big],x^{n_k}\Big]=0 $$ for all $x \in R$, where $n_{0},n_{1},n_{2},\dots,n_{k}$ are fixed positive integers, then there exists a map $\mu\colon R\rightarrow Z(R)$ such that $\sigma(x)=x+\mu(x)$ for all $x\in R$. In particular, when $R$ is a prime ring, $R$ is commutative.
| On the $p$-norm of an Integral Operator in the Half Plane
Liu, Congwen; Zhou, Lifang
We give a partial answer to a conjecture of Dostanić on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.
| Resultants of Chebyshev Polynomials: A Short Proof
Louboutin, Stéphane R.
We give a simple proof of the value of the resultant of two Chebyshev polynomials (of the first or the second kind), values lately obtained by D. P. Jacobs, M. O. Rayes and V. Trevisan.
| Characterization of Simple Highest Weight Modules
Mazorchuk, Volodymyr; Zhao, Kaiming
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
| Randers Metrics of Constant Scalar Curvature
Sevim, Esra Sengelen; Shen, Zhongmin
Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic.
| Optimal Control Strategies for Virus Spreading in Inhomogeneous Epidemic Dynamics
Shang, Yilun
In this paper, we study the spread of virus/worm in computer networks with a view to addressing cyber security problems. Epidemic models have been applied extensively to model the propagation of computer viruses, which characterize the fact that infected machines may spread malware to other hosts connected to the network. In our framework, the dynamics of hosts evolves according to a modified inhomogeneous Susceptible-Infectious-Susceptible (SIS) epidemic model with time-varying transmission rate and recovery rate. The infection of computers is subject to direct attack as well as propagation among hosts. Based on optimal control theory, optimal attack strategies are provided by minimizing the cost (equivalently maximizing the profit) of the attacker. We present a threshold function of the fraction of infectious hosts, which captures the dynamically evolving strategies of the attacker and reflects the persistence of virus spreading. Moreover, our results indicate that if the infectivity of a computer worm is low and the computers are installed with antivirus software with high reliability, the intensity of attacks incurred will likely be low. This agrees with our intuition.
| Inverse Semigroups and Sheu's Groupoid for the Odd Dimensional Quantum Spheres
Sundar, S.
In this paper, we give a different proof of the fact that the odd dimensional quantum spheres are groupoid $C^{*}$-algebras. We show that the $C^{*}$-algebra $C(S_{q}^{2\ell+1})$ is generated by an inverse semigroup $T$ of partial isometries. We show that the groupoid $\mathcal{G}_{tight}$ associated with the inverse semigroup $T$ by Exel is exactly the same as the groupoid considered by Sheu.
| Regulator Indecomposable Cycles on a Product of Elliptic Curves
Türkmen, İnan Utku
We provide a novel proof of the existence of regulator indecomposables in the cycle group $CH^2(X,1)$, where $X$ is a sufficiently general product of two elliptic curves. In particular, the nature of our proof provides an illustration of Beilinson rigidity.
| On Induced Representations Distinguished by Orthogonal Groups
Valverde, Cesar
Let $F$ be a local non-archimedean field of characteristic zero. We prove that a representation of $GL(n,F)$ obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.
| Asymptotics and Uniqueness of Travelling Waves for Non-Monotone Delayed Systems on 2D Lattices
Yu, Zhi-Xian; Mei, Ming
We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D lattice equations with non-monotone birth functions. First, with the help of Ikehara's Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier results in the literature.
| Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic
Ayadi, K.; Hbaib, M.; Mahjoub, F.
In this paper, we study rational approximations for certain algebraic power series over a finite field. We obtain results for irrational elements of strictly positive degree satisfying an equation of the type \begin{equation} \alpha=\displaystyle\frac{A\alpha^{q}+B}{C\alpha^{q}} \end{equation} where $(A, B, C)\in (\mathbb{F}_{q}[X])^{2}\times\mathbb{F}_{q}^{\star}[X]$. In particular, we will give, under some conditions on the polynomials $A$, $B$ and $C$, well approximated elements satisfying this equation.
| Envelope Dimension of Modules and the Simplified Radical Formula
Nikseresht, A.; Azizi, A.
We introduce and investigate the notion of envelope dimension of commutative rings and modules over them. In particular, we show that the envelope dimension of a ring, $R$, is equal to that of the $R$-module $R^{(\mathbb{N})}$. Also we prove that the Krull dimension of a ring is no more than its envelope dimension and characterize Noetherian rings for which these two dimensions are equal. Moreover we generalize and study the concept of simplified radical formula for modules, which we defined in an earlier paper.
| Carmichael meets Chebotarev
Banks, William D.; Güloğlu, Ahmet M.; Yeager, Aaron M.
For any finite Galois extension $K$ of $\mathbb Q$ and any conjugacy class $C$ in $\operatorname {Gal}(K/\mathbb Q)$, we show that there exist infinitely many Carmichael numbers composed solely of primes for which the associated class of Frobenius automorphisms is $C$. This result implies that for every natural number $n$ there are infinitely many Carmichael numbers of the form $a^2+nb^2$ with $a,b\in\mathbb Z $.
| Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
Bartošová, Dana
It is a well-known fact, that the greatest ambit for a topological group $G$ is the Samuel compactification of $G$ with respect to the right uniformity on $G.$ We apply the original description by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using Fraïssé theory and Ramsey theory. This work generalizes some of the known results about countable structures.
| On the Sum of Digits of Numerators of Bernoulli Numbers
Bérczes, Attila; Luca, Florian
Let $b\gt 1$ be an integer. We prove that for almost all $n$, the sum of the digits in base $b$ of the numerator of the Bernoulli number $B_{2n}$ exceeds $c\log n$, where $c:=c(b)\gt 0$ is some constant depending on $b$.
| The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames
Currey, B.; Mayeli, A.
In this work we introduce a class of discrete groups containing subgroups of abstract translations and dilations, respectively. A variety of wavelet systems can appear as $\pi(\Gamma)\psi$, where $\pi$ is a unitary representation of a wavelet group and $\Gamma$ is the abstract pseudo-lattice $\Gamma$. We prove a condition in order that a Parseval frame $\pi(\Gamma)\psi$ can be dilated to an orthonormal basis of the form $\tau(\Gamma)\Psi$ where $\tau$ is a super-representation of $\pi$. For a subclass of groups that includes the case where the translation subgroup is Heisenberg, we show that this condition always holds, and we cite familiar examples as applications.
| On the Radius of Comparison of a Commutative C*-algebra
Elliott, George A.; Niu, Zhuang
Let $X$ be a compact metric space. A lower bound for the radius of comparison of the C*-algebra $\operatorname{C}(X)$ is given in terms of $\operatorname{dim}_{\mathbb{Q}} X$, where $\operatorname{dim}_{\mathbb{Q}} X $ is the cohomological dimension with rational coefficients. If $\operatorname{dim}_{\mathbb{Q}} X =\operatorname{dim} X=d$, then the radius of comparison of the C*-algebra $\operatorname{C}(X)$ is $\max\{0, (d-1)/2-1\}$ if $d$ is odd, and must be either $d/2-1$ or $d/2-2$ if $d$ is even (the possibility of $d/2-1$ does occur, but we do not know if the possibility of $d/2-2$ also can occur).
| Dimension Functions of Self-Affine Scaling Sets
Fu, Xiaoye; Gabardo, Jean-Pierre
In this paper, the dimension function of a self-affine generalized scaling set associated with an $n\times n$ integral expansive dilation $A$ is studied. More specifically, we consider the dimension function of an $A$-dilation generalized scaling set $K$ assuming that $K$ is a self-affine tile satisfying $BK = (K+d_1) \cup (K+d_2)$, where $B=A^t$, $A$ is an $n\times n$ integral expansive matrix with $\lvert \det A\rvert=2$, and $d_1,d_2\in\mathbb{R}^n$. We show that the dimension function of $K$ must be constant if either $n=1$ or $2$ or one of the digits is $0$, and that it is bounded by $2\lvert K\rvert$ for any $n$.
| A Generalization of a Theorem of Boyd and Lawton
Issa, Zahraa; Lalín, Matilde
The Mahler measure of a nonzero $n$-variable polynomial $P$ is the integral of $\log|P|$ on the unit $n$-torus. A result of Boyd and Lawton says that the Mahler measure of a multivariate polynomial is the limit of Mahler measures of univariate polynomials. We prove the analogous result for different extensions of Mahler measure such as generalized Mahler measure (integrating the maximum of $\log|P|$ for possibly different $P$'s), multiple Mahler measure (involving products of $\log|P|$ for possibly different $P$'s), and higher Mahler measure (involving $\log^k|P|$).
| A Non-zero Value Shared by an Entire Function and its Linear Differential Polynomials
Lahiri, Indrajit; Kaish, Imrul
In this paper we study uniqueness of entire functions sharing a non-zero finite value with linear differential polynomials and address a result of W. Wang and P. Li.
| Small Prime Solutions to Cubic Diophantine Equations
Liu, Zhixin
Let $a_1, \cdots, a_9$ be non-zero integers and $n$ any integer. Suppose that $a_1+\cdots+a_9 \equiv n( \textrm{mod}\,2)$ and $(a_i, a_j)=1$ for $1 \leq i \lt j \leq 9$. In this paper we prove that (i) if $a_j$ are not all of the same sign, then the above cubic equation has prime solutions satisfying $p_j \ll |n|^{1/3}+\textrm{max}\{|a_j|\}^{14+\varepsilon};$ and (ii) if all $a_j$ are positive and $n \gg \textrm{max}\{|a_j|\}^{43+\varepsilon}$, then the cubic equation $a_1p_1^3+\cdots +a_9p_9^3=n$ is soluble in primes $p_j$. This result is the extension of the linear and quadratic relative problems.
| Upper Bounds for the Essential Dimension of $E_7$
MacDonald, Mark L.
This paper gives a new upper bound for the essential dimension and the essential 2-dimension of the split simply connected group of type $E_7$ over a field of characteristic not 2 or 3. In particular, $\operatorname{ed}(E_7) \leq 29$, and $\operatorname{ed}(E_7;2) \leq 27$.
| Estimates for Compositions of Maximal Operators with Singular Integrals
Oberlin, Richard
We prove weak-type $(1,1)$ estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator $\Delta^*\Psi$ where $\Delta^*$ is Bourgain's maximal multiplier operator and $\Psi$ is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the $L^q$ operator norm when $1 \lt q \lt 2.$ We also consider associated variation-norm estimates.
| Quantum Limits of Eisenstein Series and Scattering States
Petridis, Yiannis N.; Raulf, Nicole; Risager, Morten S.
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.
| Erratum to ``Quantum Limits of Eisenstein Series and Scattering States''
Petridis, Yiannis N.; Raulf, Nicole; Risager, Morten S.
This paper provides an erratum to Y. N. Petridis, N. Raulf, and M. S. Risager, ``Quantum Limits of Eisenstein Series and Scattering States.'' Canad. Math. Bull., published online 2012-02-03, http://dx.doi.org/10.4153/CMB-2011-200-2.
| On Mertens' Theorem for Beurling Primes
Pollack, Paul
Let $1 \lt p_1 \leq p_2 \leq p_3 \leq \dots$ be an infinite sequence $\mathcal{P}$ of real numbers for which $p_i \to \infty$, and associate to this sequence the Beurling zeta function $\zeta_{\mathcal{P}}(s):= \prod_{i=1}^{\infty}(1-p_i^{-s})^{-1}$. Suppose that for some constant $A\gt 0$, we have $\zeta_{\mathcal{P}}(s) \sim A/(s-1)$, as $s\downarrow 1$. We prove that $\mathcal{P}$ satisfies an analogue of a classical theorem of Mertens: $\prod_{p_i \leq x}(1-1/p_i)^{-1} \sim A \e^{\gamma} \log{x}$, as $x\to\infty$. Here $\e = 2.71828\ldots$ is the base of the natural logarithm and $\gamma = 0.57721\ldots$ is the usual Euler--Mascheroni constant. This strengthens a recent theorem of Olofsson.
| On the Average Number of Square-Free Values of Polynomials
Shparlinski, Igor E.
We obtain an asymptotic formula for the number of square-free integers in $N$ consecutive values of polynomials on average over integral polynomials of degree at most $k$ and of height at most $H$, where $H \ge N^{k-1+\varepsilon}$ for some fixed $\varepsilon\gt 0$. Individual results of this kind for polynomials of degree $k \gt 3$, due to A. Granville (1998), are only known under the $ABC$-conjecture.
| Left-orderability and Exceptional Dehn Surgery on Twist Knots
Teragaito, Masakazu
We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a $3$-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.
| On Countable Dense and $n$-homogeneity
van Mill, Jan
We prove that a connected, countable dense homogeneous space is $n$-homogeneous for every $n$, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers Problem 136 of Watson in the Open Problems in Topology Book in the negative.
| Note on Kasparov Product of $C^*$-algebra Extensions
Wei, Changguo
Using the Dadarlat isomorphism, we give a characterization for the Kasparov product of $C^*$-algebra extensions. A certain relation between $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ is also considered when $B$ is not stable and it is proved that $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ are not isomorphic in general.
| Free Groups Generated by Two Heisenberg Translations
Xie, BaoHua; Wang, JieYan; Jiang, YuePing
In this paper, we will discuss the groups generated by two Heisenberg translations of $\mathbf{PU}(2,1)$ and determine when they are free.


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MSI Z87M Gaming Review
MSI Z87M Gaming Introduction:
Last year when Intel launched its Fourth Generation Core series processors and supporting Z87 chipset, its partners launched a myriad of high performance motherboards. It's all so the Fourth Gen Core series processors from Intel had the best chance of success when it came to reliability and ultimately chip performance. What we saw with MSI's offering was the company moving in the right direction to capture a larger part of the lucrative gaming centric motherboard market by offering features that gamers want. Things like better onboard sound, Killer Gaming's E2200 series network hardware, easy performance improvement through OC Genie 4, one touch overclocking, and good reliability thanks to the company's Military Class IV component selection.
Priced at $159, the MSI Z87M Gaming is priced around $30 less than the full size Z87-GD65 Gaming and MSI took all that was good with the Z87-GD65 Gaming and put it into a smaller MATX form factor, giving us the Z87M Gaming. With its pedigree established, let's see if lightning can strike twice in the same product line.
MSI Z87M Gaming Closer Look:
MSI's packaging of its Gaming series products is bright and has a ton of eye appeal if you are shopping in a traditional brick and mortar retail outlet. The Dragon themed red and black imagery has taken over as the look to have for motherboards targeted at the enthusiast and gamer. The front features a tribal dragon image in silver/grey as the dominant feature of the package, while you have support for Fourth Generation Core series processors from Intel and the inclusion of a Killer Gaming E2200 series NIC. The back panel looks at some of the more specific features the MSI Z87M Gaming has to offer. Here the Killer Gaming E2205 is touted as a tool to reduce ping and latency for an improved online experience. Further mentions include Audio Boost, one second overclocking with OC Genie 4, Sound Blaster Cinema, Military Class IV component selection, and how the PS/2 Gaming port is more robust and features gold contacts. All important features that help set the MSI Gaming series apart from the crowd. You even get multi GPU capabilities with the Z87M Gaming!
Internally you have two levels to the packaging. The top layer holds the board in place securely while the bottom level holds the substantial bundle of accessories.
The accessory bundle included with the Z87M Gaming consists of the documentation and hardware needed to get the board functioning to its maximum capacity. For documentation you get the users guide, installation guide, "Do Not Disturb" door tag, and the driver/utility disc. The hardware side of the bundle includes the basics, such as the quartet of SATA 6Gbps data cables, a pair of M-Connectors, SLI Bridge connection (Crossfire Bridges are included with the video cards), a good looking case badge, and I/O shield. The case badge on its own will stand out from the crowd if you proudly display it. The I/O Shield offers three-way protection in the form of an EMI protection with an aluminum shield, in addition to the force absorbing foam inner core layer. M-Connections have been a standard on MSI boards for several years and make installing front panel connections onto the board much easier.
When I looked at the Z87-GD65 and the MPower Max boards from MSI, I found that the company had indeed turned the corner and offered a top notch product for the end user. With a list of high end features, the boards performed well right out of the gate and delivered excellent performance. The hope is that by shrinking the form factor we get the same solid performance we saw last year.

subset: commoncrawl


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Romantic relationships tend to have more holidays that require presents than other relationships, so you want to ensure that you have plenty of gift ideas for your boyfriend that will work throughout the year! He'll love whatever you give him, but personalized gifts for boyfriends are great to show him that you really care.
Figuring out gifts for your boyfriend for Valentine's Day can be tricky. On one hand, you don't want to be too mushy, but on the other hand, the holiday celebrates love and commitment, and your gift should speak to that. The quickest way to a man's heart is through his stomach, so an assortment of treats and chocolates to be shared together make good gift ideas for men during this holiday.
Like Valentine's Day, anniversaries are another day to celebrate love. Get a little personal with boyfriend anniversary gifts that show him how much you've enjoyed the journey you've been on with him. A personalized picture frame that holds your favorite photo will do just the trick. If you and your partner have travelled as many physical miles as you have metaphorical, other gifts for boyfriends could include a map that marks all of the places you've visited together or personalized luggage for your next big excursion.
Since Christmas is such a high-volume gift buying time, Christmas gifts for boyfriends can hold extra pressure when you're shopping for everyone on your list. Stuff his stockings with technology you know he'll love. Watches, phone cases, and fitness trackers make great male Christmas gifts, but could also be wonderful gifts to get your girlfriend, as well.
Boyfriend gifts don't have to be limited to a holiday: the best gift for your boyfriend can mean even more if it's given just because you love him.


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Pinkerton gives OK to technology in classroomsBy HUNTER McGEE
Union Leader Correspondent
September 17. 2013 11:24PM
DERRY — Instead of giving a lengthy answer to a student's question, some teachers at Pinkerton Academy this year might be overheard saying, "just Google it."
Under a new technological program launched this year, students can bring their smartphones, laptops and other electronic devices into the classroom, said Beverly Lannan, dean of faculty. The devices can be used for doing research on Google or to view educational videos online, Lannan said.
"We have done some training and we are hoping teachers can use the technology for instruction and students can use it as a learning tool," Lannan said.
Students will have to sign a personal device contract and their parents would have to give consent for them to participate, Lannan said. By signing the form, students will also acknowledge that they will only use the devices for educational purposes. Students whose parents don't provide consent will be allowed to use other more traditional methods of research, she added.
The program was approved just last spring by the school's Board of Trustees. In previous years, the Internet was available and students could go online at the school's media center.
"We've always had the Internet," Lannan said. "We just didn't allow all these devices in the classroom. So, we have opened it up a lot more compared to last year."
While other high schools have used similar programs in recent years, change has come more slowly to Pinkerton. Administrators wanted to get a good grasp of the program before bringing it to teachers and students, Lannan said.
Last year, teachers attended workshops so they could become more comfortable with the technology and to find ways to incorporate it in the classroom, she said. So far, Lannan said she hasn't heard any negative feedback from teachers as to how the program is faring in the classroom.
"I think as more teachers become comfortable and get more training, the more we'll see them using this technology," Lannan said.
While some parents would welcome the technology, Lannan said she understood some parents might be hesitant to allow their students to participate .
Parent Brenda Modrak, of Derry, said Tuesday she had mixed emotions about the program. While the technology might assist some students, Modrak said she was concerned other students might take advantage of the opportunity.
"I think they would be sending text messages," Modrak said. "A teacher only has two eyes and can't see everybody at the same time."
Modrak's triplets are juniors at the school. Modrak said she could see her children using the technological devices in college, but not in high school.
"We don't have smart phones for the kids, nor do we have extra laptops, so for us, it's a moot point. In college, 'yes,' but not in high school."
One of Modrak's children, Stephanie, 16, said she has seen some students using their iPhones to do research in her English class.
"I guess it's helpful as long as the kids are using it for the correct purpose," the junior said.
Education Social issues Technology Derry Top Section Stories


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Secondary Sales and An Investor Covenant You Don't Want To MissBy William Carleton // March 16, 2016 in Angels, Convertible Notes, Emerging Companies, Seed Financings
Dear Readers: This is a post I co-wrote with Joe Wallin, who has published the almost identical post here.
If you are investing in early stage companies, there are certain deal terms you want.
Most you probably know already: if it's a round of convertible notes, you want a discount and a cap; if it's a priced round, you want a liquidation preference. Etc.
But there is a new thing you need to add to your list of "must haves."
You now want your investment documents to include a Section 4(a)(7) covenant.
What the heck is Section 4(a)(7)?
Section 4(a)(7) is a new federal securities law that basically says, it's OK for you to sell your investment in a private company, as long as you don't generally advertise the securities for sale, sell to another accredited investor, and the company cooperates with certain information requirements.
The new federal law trumps state law. So state law won't hold you up.
Unlike the existing resale exemption most commonly used, there is no holding period required under this new law.
What is a Section 4(a)(7) covenant?
This new law is great—but you need the company's assistance to access it, because the law requires the company to provide certain information to the purchaser.
So, get this covenant in your investment documents, and it may be easier for you to later sell your shares.
You can find draft covenants to include in your securities purchase agreements here.
And if you're a founder or exec, don't despair: Section 4(a)(7) will work for you, too. For a longer, in depth discussion of the new law, see this article in TechCrunch.


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Braised Turkey and Homemade Potato Gnocchi
|Potatoes, Eggs, Poultry, Vegetables, Berries, Mushrooms
|Day Part
|Cuisine Type
Source: Chef Patrick Connolly Radius Restaurant, Boston, MA National Turkey Federation
Dark meat turkey takes well to braising—a long, slow cooking method that turns tougher cuts of meat and poultry meltingly tender and flavorful.
Turkey Legs
4 tbsp. extra virgin olive oil
1 large carrot, large dice
1 med. leek, large dice
1 large onion, large dice
1 pint dry white wine
2 turkey legs (about 1 lb. total)
3 qt. turkey stock
3 oz. dried mushrooms
1 tbsp. juniper berries
2 tbsp. black peppercorns
3 bay leaves
Potato Gnocchi
6 russet potatoes
2 egg yolks
1 tbsp. extra virgin olive oil
2 tbsp. kosher salt
2 cups all-purpose flour
2 tbsp. unsalted butter
1 med. shallot, minced
2 tbsp. fresh rosemary, finely chopped
2 tbsp. pink peppercorns, finely chopped
2 oz. grated Parmesan cheese
2 oz. shaved Parmesan cheese, for garnish
- Heat olive oil in a med. pot; brown diced carrot, leek and onions. Deglaze with wine.
- Lightly season turkey legs with salt and pepper. Add legs to vegetables; cover with stock; stir in dried mushrooms.
- Wrap juniper berries, black peppercorns and bay leaves in cheesecloth and tie shut. Gently hammer to break peppercorns and berries. Place in pot with meat and vegetables.
- Bring to a simmer and turn off heat. Cover pot with foil and place in 325ºF oven for about 90 min. or until turkey slides down bone about an inch. Pick turkey off bones. Strain and reserve braising liquid.
- Prepare Gnocchi: Roast potatoes on bed of salt at 350ºF for 1 hr. or until fully cooked. Peel and run through food mill.
- Mix egg yolk with olive oil; add to potatoes along with salt.
- Gently work ingredients together and slowly add flour. Avoid over-mixing. Cut small pieces from dough and roll out by-hand into ropes; keep table dusted with flour so dough doesn't stick. Using a bench knife, cut ropes into small, uniform pieces. Cook in boiling water in small batches until gnocchi float; remove with slotted spoon.
- When ready to serve, sauté shallots, some braising liquid and a little butter until shallots lose their rawness. Add some turkey meat, chopped rosemary and pink peppercorns. Add cooked gnocchi to sauté pan; toss with grated Parmesan. Use additional stock and butter as needed. Spoon into bowls and garnish with shaved Parmesan.


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Updated 11:30 a.m. RIDGEFIELD, Conn. — The lockout has been lifted at Ridgefield's public schools after a report earlier Monday of a 'suspicious person' near the Branchville train station.
Superintendent Deborah Low said schools got the all clear at 11:15 a.m.
"Branchville students are now taking buses from East Ridge back to Branchville. Schools are no longer on a modified lockdown. As planned for today, a police presence remains at each school," Low said in an alert on the district's website.
All nine public school in Ridgefield were put into lockdown Monday morning due to a "possibly suspicious person" at the Branchville train station.
"A little bit before 8 o'clock this morning we got a report of a suspicious male wearing all black, possibly carrying a weapon described to us as in a sling over his shoulder," Capt. Tom Comstock of the Ridgefield Police said at briefing Monday morning. "We have no confirmation of this."
There was one witness, who Comstock said has not changed their story regarding it being a long gun, possibly a rifle. The suspect had been described a white male and police are searching the area with dogs and by foot.
Comstock said that the suspect was reported to be walking north on Route 7.
Buses headed to Branchville Elementary Monday morning were re-routed to East Ridge Middle School. Branchville Elementary students are in the gymnasium at East Ridge.
"As planned for today, a police presence remains at each school," Low said.
Not just schools were locked down. Lolly Turner, owner of Whistle Stop Bakery at the train station, said that police came to the bakery and told them to lock down, to shut off the lights and go home.
"What we were told was that someone had called in that a person dressed in all black carrying what could possibly be a gun," said Turner. "We were told that this person was seen at the elementary school."
But the lock down at the bakery was over just as soon as it began, Turner said. She said that police — she thinks it was the state police — had come and told her and her staff that the parking lot was clear and that they could open again.
"After last Friday , everyone is so hyper-sensitive about these things," Turner said.
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Advance Your Career Today!
A graduate degree from Pace University will give you the edge you need to secure an incredible job or promotion, or perhaps change careers altogether. You can start your studies as early as January by attending one of our upcoming Accelerated Admission Days. Admission counselors will be available to review your application materials and answer any questions you may have pertaining to the admission process, financial aid, and our academic programs. Just bring an application and all supporting documents with you and we will waive the $70 application fee and provide you with an admission decision that same day.*
To take advantage of this opportunity, please be sure to bring the following items with you:
- A completed application for graduate admission. You can complete our online application ahead of time, or bring a paper application with you. Downloadable PDFs of grad applications can be found on the Forms and Brochures page.
- Official copies (in sealed envelopes) of all college transcripts.
- Two letters of recommendation
- Essay/Personal Statement
- Resume
- GMAT/GRE/TOEFL/IELTS score (if required for your program)
- MA in Media and Communication Arts applicants must submit a student portfolio. View the Dyson Graduate Application for more information.
Schedule an Appointment
To schedule an appointment for one of the Graduate Accelerated Admission Days listed below, please call or e-mail the Office of Graduate Admission on the campus you are interested in attending.
Pace University's New York City and Westchester campuses offer full and part-time programs for more than 60 graduate degrees. To explore our graduate program offerings, please visit our Graduate Academics web page.
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* A small number of applications for certain programs may require additional review and a decision will follow soon after.


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A quilt is made up of many blocks of fabric. Show us what living in Visitacion Valley means to you by creating a 10" x 10" square that will be incorporated into our community quilt.
Bring a picture of your favorite spot in Visitacion Valley and learn to make a quilt square around it using one of several quilting techniques we will be teaching. You will learn how to cut fabric and patch the pieces together on a sewing machine.
No sewing experience necessary. Children are welcome if accompanied by an adult.
Visitacion Valley Quilts is a six month long project to create a community quilt representative of this diverse San Francisco neighborhood. The program is a partnership between the San Francisco Public Library and Quiltworks, a local nonprofit quilting studio.
For more information about the project contact Shawna at firstname.lastname@example.com.


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Just a photographer and film maker. Just 21. Just got...
- by Catherine.ˣ
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- Published: 22 Apr 2014
- Updated: 25 Apr 2014
- Status: Complete
Always. It's a strong word. It can mean a lot, like how it meant to me when Niall told me he'd always love me. It can be a word that means nothing, like how it meant to Niall when he said he'd always love me. And then the next day, he left Mullingar and never came back. And I was alone. Always.
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Kendall Jenner: Last Minute Holiday Shopping
Kendall Jenner patiently waits for her car at valet after shopping at Topanga Mall on Sunday afternoon (December 23) in Canoga Park, Calif.
The 17-year-old emerging model was spotted with a bag from Louis Vuitton and Neiman Marcus.
"last minute Christmas shopping," Kendall tweeted of her excursion.
In a recent interview with Gilette, Kendall dished what she loves to do in her free time — horseback riding!
"I started horseback riding about 10 years ago," she shared. "And then my dad came to Kylie and I and said my aunt has a dude ranch in Wyoming so we go every summer to this dude ranch."
10+ pics inside…
Posted to: Kendall Jenner


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- Inside Athletics
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Face Stetson on Wednesday evening in quarterfinals
MACON, Ga. (March 6, 2013) – As ETSU head coach Karen Kemp said in her postgame press conference following the recent loss to USC Upstate, the conference tournament signifies the start of a "new season" and the No. 7 seed Lady Bucs will begin this new season in an Atlantic Sun Championship quarterfinal matchup with the No. 2 seed Stetson Hatters on Wednesday evening at 6 p.m. in Macon, Ga. inside Hawkins Arena.
A variety of events turned Saturday's loss to Upstate into a disappointing effort and was not the way the Blue and Gold wanted to end the regular season. The good news is that the Lady Bucs can put this game behind them and focus on another opportunity to revive their season. ETSU will look to do so against a team that it stacks up well against and is very beatable. Topping the Hatters will be even more of a challenge though for the Lady Bucs who will be without sophomore center Tiana Burley (Camilla, Ga.) who must sit out this contest due to the flagrant-two foul call she was issued late in the contest versus Upstate. In two meetings with Stetson this season, Burley has averaged 12 points per game, including a double-double of 20 points and 12 rebounds in the most recent matchup. In a season that has been full of adverse situations, this circumstance offers yet another opportunity for fellow Lady Bucs to step up to help supplement for this loss of production.
The matchup between the Lady Bucs and the Hatters will be the 18th all-time meeting between the two schools, a series in which ETSU leads with a 13-4 overall series advantage. ETSU and Stetson have met twice this season, with the most recent contest being a 74-65 loss on Feb. 9 in DeLand, Fla. The Lady Bucs fared well in the first half before Stetson put together a second half run that put ETSU away. The Blue and Gold got a strong contribution from Burley, but had the services of a severely-limited Destiny Mitchell (Bluffton, Ga.) who was still hobbled from an injury suffered a few games prior.
For more on Wednesday's game, read the game notes below. For more on ETSU women's basketball throughout the 2012-13 season, visit ETSUBucs.com and click on the women's hoops link.
The ETSU Department of Intercollegiate Athletics would like to ask both the print and broadcast media to honor our request to be called "ETSU" throughout the 2012-13 season ... East Tennessee State in first reference is acceptable, but subsequent references should be ETSU ... On TV graphics, please use ETSU ... Our nickname is the Lady Buccaneers, but Lady Bucs is also acceptable.
ETSU (8-17, 6-12) aimed to end the regular season with a win when they welcomed the USC Upstate Spartans to the ETSU/MSHA Athletics Center on Senior Day. The Lady Bucs started the game strong with a 10-3 spurt before the first media timeout. The Spartans did themselves no favors by going frigid from the field and by not matching ETSU's intensity on the glass. The Lady Bucs built their lead up to as many as 12 points with three minutes remaining, but a 9-2 Upstate run cut this advantage to 26-21 at the break. The Spartans carried the momentum over to the second half and scored the first five points of the period to tie the game at 26. After ETSU built up a four point lead, Upstate responded with a 12-3 streak to take a 51-46 lead with 3:47 remaining and hung on to defeat the Lady Bucs, 60-56.
Wednesday's contest inside Hawkins Arena will be the 18th all-time meeting between the two teams, a series in which ETSU holds a 13-4 overall series advantage. The Lady Bucs and the Hatters met twice this season, with the most recent matchup being on Feb. 9, when Stetson swept the regular season series with a 74-65 victory. In this meeting, ETSU faced a hot Stetson Hatters squad who raced out to an early lead, primarily off of fast break points and points off turnovers. The Lady Bucs finally were able to get something going with points in the paint and nailing a few triples. The Blue and Gold was able to tie the game with 10 minutes remaining, but Stetson stormed back with a 20-0 run over the next seven minutes and a 25-5 streak to end the half, taking a 44-24 advantage into the break. The Lady Bucs used a 9-2 run of their own over the first four minutes of the second period to inch closer. SU responded and kept ETSU at bay with a double-digit deficit for most of the half, with the closest being 10 points at the 7:29 mark. Late baskets for ETSU proved to be too little, too late as they dropped a 74-65 decision to the Hatters. The Blue and Gold received another strong performance from forward Tiana Burley who notched her third double-double in the past four games with game-highs of 20 points and 12 rebounds. The Lady Bucs had only one extra double-digit scorer with 10 points from Cara Bowling (Elizabethton, Tenn.).
After being inserted into the starting lineup for the first time this season against North Florida on Jan. 26, sophomore guard Cara Bowling has successfully responded to the promotion. Following scoring 14 points in her first game as a starter this season, Bowling has kept the momentum going with strong offensive performances since. In the Elizabethton, Tenn. native's last five games, she is averaging 11.2 points per game, including two made three-pointers per game. The sharpshooter scored a career-high 21 points, featuring an also career-high five made three-pointers, in a 65-60 win at North Florida.
The Lady Bucs have recently discovered the most offensive production through points in the paint. ETSU is currently averaging 30 points in the paint per game, including an average of 33 points in its last five. In a loss at Jacksonville, the Blue and Gold recorded 54 points in the paint, the most since scoring 50 against Jacksonville earlier this season on Jan. 28 in Johnson City.
The Blue and Gold have outrebounded the opposition in 19 of the 25 games this season and enter Saturday's game with a plus-6.0 rebounding margin (43.9-37.9), ranking first in the A-Sun … in a loss at FGCU, the Lady Bucs outrebounded the Eagles by 20, 53-33 … the Lady Bucs' plus-6.0 rebound margin currently ranks in the top 30 nationally. ETSU also outrebounds its A-Sun opponents at a plus-6.9 clip.
After being inserted into the starting lineup at the beginning of conference play, Shawn Randall (Orlando, Fla.) has answered the call and has been stellar in league play. In her first start of the season at USC Upstate, Randall tallied 16 points and was 4-of-6 from behind the arc. The junior guard followed this performance with strong showings at Lipscomb (13 points, 4 rebounds), at Northern Kentucky (9 points), at Kennesaw State (18 points), vs. KSU (10 points) and at Jacksonville (17 points). Randall is currently averaging 8.8 points per game in Atlantic Sun action.
In addition to running the team as a true freshman point guard, Brianna McQueen (Jonesboro, Ga.) has shown no fear at the free throw stripe with the game on the line. At Lipscomb and at Kennesaw State, McQueen stepped the line and buried clutch free throws down the stretch to seal the game in the Lady Bucs' favor. McQueen is currently ninth in the A-Sun in free throw shooting at 73.9 percent.
Currently the Lady Bucs are averaging 5.5 blocks per contest, good for tops in the Atlantic Sun. ETSU swatted a season-high nine shots in a loss at Stetson on Feb. 9. The Blue and Gold are led by Tosha Austin's (Chattanooga, Tenn.) 1.2 blocks per game which ranks in the top five individually in the league. Austin also currently ranks tied for 13th all-time in blocked shots in Atlantic Sun history with 128 rejections.
Destiny Mitchell has scored in double figures in 10 out of the 22 games she has played in this season and is averaging 11.0 points per contest … Mitchell scored a season-high 26 points in the opener at High Point back on Nov. 10 and added 14 points and 16 rebounds in the 10-point win vs. Memphis to close out the month of November ... Mitchell is currently 13th in the A-Sun in scoring (11.0), second in rebounding (8.1), sixth in steals (1.9) and fifth in field goal percentage (49.5).
Mitchell is well on her way to become the 21st Lady Buc to join the 1,000-point club ... Before being slowed by injury in the final third of the regular season, she was on pace to break the 1,000-point mark near the end of February as she registered 347 points as a freshman and 367 points as a sophomore for 714 total points... through ETSU's first 25 games of the 2012-13 season she has scored 241 to move her career total to 955 .. if Mitchell scores in similar fashion in the next two years as she did as a rookie and as a sophomore, she will put herself in the top-10 in Lady Buc history.
After a solid start to the season for the now eligible transfer, Serena Clark (Stone Mountain, Ga.) has really turned it on when it comes to Atlantic Sun action. Through the first 18 games of league play, Clark is averaging 8.2 points and 7.4 rebounds per game, including back-to-back double-doubles at Lipscomb and at Northern Kentucky with 10 points & 14 rebounds and 16 points, 10 rebounds & seven steals, respectively. An additional double-double was added to her total when she recorded 15 points and 11 rebounds at Jacksonville.
The Lady Bucs have been a tough team to beat when it comes to the second half of the season (games played from January-March) … since January of 2008, ETSU is 82-41 (.667) in the months of January through March, including a program-best 19-3 mark in 2009-10.
Through the duration of the season, ETSU has gotten strong contributions from its bench. On the season ETSU averages roughly 25 bench points per game, including a season-high 44 points off the bench against Memphis on Nov. 30. Key reserves Maria Bond (Macon, Ga.) (6.6 ppg) and Brianna McQueen (8.6 ppg) have been vital for the Lady Bucs.
The Lady Bucs have enjoyed a lot of success since joining the A-Sun in 2005-06 … since joining the league, the Lady Buccaneers have averaged 15 conference wins a year, including a league-best and school record 18-2 mark in 2009-10, three Atlantic Sun Tournament titles (2008-2010), and two regular season championships (2008 and 2010) …in total, ETSU is 105-45 (.700) against conference foes since moving into the A-Sun … the Lady Bucs have also won 85 of their last 120 games against conference foes (includes the 2008, 2009, 2010, and 2011 A-Sun Tournaments).
Since the 2002-03 season the Lady Bucs are 106-19 when the they hit the 75-point plateau, including 76-15 since the 2006-07 season... recently, ETSU put up 86 to defeat Lipscomb by 22 and earn the 106th such victory.
ETSU fans wanting to receive Buccaneer news, score updates, in-game promotions and much more sent to their mobile device can do so by signing up for "Buc Updates." Click here to sign up today!
For more information on Buccaneer athletics, visit ETSUBucs.com.


text: Imagine waking up one day and finding your life is dark – literally. Your vision is blurred and your eyes have difficulty adjusting to light and dark. How would you feel? How different would your life be? For many people and pets, this is how the beginning stages of blindness feels. Glaucoma is one of


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Iams Nutrition Insider: The latest insights on inflammatory bowel disease (Sponsored by Iams)
Jul 01, 2010
The role of gut bacteria
With the advantage of hindsight, we can now see that the effectiveness of metronidazole in treating IBD should have been an early clue to the potential importance of bacteria as a cause of IBD. Metronidazole has benefitted many patients diagnosed as having IBD because of what was hypothesized to be an immunomodulatory effect.6 However, current thought is that metronidazole may be beneficial in these patients because of its efficacy in killing anaerobic bacteria. Another clue has been the finding that many dogs and some cats with steroid-resistant IBD may respond better to an elimination diet trial or antimicrobial therapy than to anti-inflammatory drugs.
Dysbiosis refers to an imbalance in the commensal intestinal bacterial population such that bacterial species that tend to favor inflammation in the intestinal mucosa (e.g. Escherichia coli) are overrepresented while those species that are less likely to induce inflammation (e.g. Bifidobacterium species) are underrepresented. The result is initiation and/or perpetuation of intestinal inflammation.


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goodbye 50
It's kind of awkward that I am saying goodbye to 50-Something Moms Blog before I even turn 50, but I am. Much to the surprise of many of its 800+ (past and present) writers, The Silicon Valley Moms Group founders announced that all of its blogs, including 50-Something Moms Blog would be ending at the end of this month. The announcement did come as a huge shock to many as was evident by the email responses of many of the SV Moms Group writers but reading the email that we all received earlier this month, it was clear that this was a very emotional, very difficult and painful decision. Of course in the beginning, some of us did not accept this decision too graciously. Change, especially sudden change is hard. It's scary. It's unnerving as we wonder what else is going to happen now that this has happened? It is the rare person who openly embraces changes like this. I am definitely not one of those people and I was clearly in the majority of the writers and bloggers of SV Moms Group who struggled with the shock, surprise and disappointment of the news.
Still I couldn't help but think that as women who better to accept and embrace this change? We are genetically wired to handle nothing but change, major change practically our entire lives. As little girls our bodies morph, sometimes painfully, while the hormones rage and our emotions twist and turn and we become women. It isn't too long when we find our bodies stretching and growing in impossible ways as we house life that we help to create. What pregnant woman hasn't looked at her hugely pregnant belly and wondered if it will burst open because it sure as hell isn't going to get any bigger...is it? It does get bigger and bigger. Then our bodies continue the major upheaval as we birth those babies. During all this crazy-assed physical changing our minds change too. I swear nothing changes our thinking, our beliefs, our values more than when we give and sustain a life with our bodies. It's insane, I tell you. And while we go a little bit insane thanks to sleep deprivations, morphing post-partum bodies and those crazy, stupid hormones again, we somehow to manage and to many watching on the outside, make it all look so damn easy. Then just when we come to a place where we enjoy this life being a girl, or at least grudgingly accept it, our bodies freak out again, the hormones rage a little then rage a lot then flame out and we find ourselves looking around a little dazed and wondering WTF was that? Puberty is just a whiny toddler compared to that Menopause bitch. Again, we survive and although we may know the truth, we manage to look graceful...yeah a little sweaty thanks to hot flashes, but we still look lovely and graceful. At least I have been told that while I am weathering through this stage. We women are all about change whether we like it or not...and we seem to do it well...so say the men in our lives, and, well, they are right.
As the days have quickly passed this month, we have vented, mourned, offered virtual hugs and well wishes and have begun to figure out ways to keep in touch and keep this venture going or at least something that resembles it whether it is at new sites or our own personal blogs. SV Moms Group was abundantly endowed with talented, amazing writers so it is good to see some beginning to accept the change and go on to the next writing/blogging opportunity and adventure. My time was all too brief having only had the honor to write for them for five months but it was a great time. I loved the challenge and I can only hope that my writing has continued to grow and develop all the more because of it. To the founders and partners of the Silicon Valley Moms Blog and Silicon Valley Moms Group, I offer my best wishes for wherever the road takes you and I thank you for allowing me to be a small part of great group of witty, wise, talented, opinionated blogging women and men. I'm ready to look to the next adventure and I am sure that I will be sharing it over at Adventures In Juggling.
Original post to 50-Something Moms blog.


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Government, industry still waiting for clear policy on cybersecurity, but it's not likely to emerge soon
Cybersecurity has been a hot topic for the past couple of years. It has assumed a high profile in the Obama administration, with a cybersecurity coordinator installed in the White House. A number of bills have been introduced in the House and Senate that would lay out clearer lines of authority for information security. After years of carping about the shortcomings of the Federal Information Security Management Act, it seemed likely that Congress would pass some kind of FISMA reform.
But here we are in the closing weeks of the 111th Congress and nothing has happened. But that might not be such a bad thing — it might be better to do nothing than to pass the wrong legislation.
The issue is not quite dead. A comprehensive cybersecurity bill, S. 3480, introduced by Independent Sen. Joseph Lieberman of Connecticut and Republican Sen. Susan Collins of Maine has passed out of committee but has not been acted on by the full Senate. The sitting Congress still has time to consider the bill during the short session, which Collins urged it to do Nov. 17 during a cybersecurity hearing before the Homeland Security and Governmental Affairs Committee. "I personally think it is an ideal issue for the lame duck Congress to take up," she said.
Related coverage:
Let's kill the kill-switch debate
'One of a kind' Stuxnet worm remains a serious mystery
Lieberman expressed little hope that the bill would be passed by this Congress, however. "It's unfortunate that the clock will run out on us before we have a chance to complete negotiations with other committees and with the administration, who I regret to say did not engage as early in the process of developing this legislation as was necessary," he said.
Several companion bills already are pending on the House side, and in a last minute Hail Mary effort, Rep. Bennie G. Thompson (D-Miss.), chairman of the House Homeland Security Committee, introduced a new bill last week, the Homeland Security Cyber and Physical Infrastructure Protection Act of 2010, H.R. 6423. The bill would give the Homeland Security Department the authority to establish and enforce risk-based information security standards for government IT systems as well as for private-sector systems design as critical infrastructure.
This bill is not a companion to the Lieberman-Collins bill in the Senate, a spokeswoman for Thompson said. "It's quite different," and is not intended to facilitate last minute passage of cybersecurity legislation in both houses, she said. Thomson had been considering introducing a bill this year, and this bill puts him on record with what he is proposing while he still chairs the committee.
It is unlikely that either bill will make it through both houses during a lame-duck session that still has to do something about a federal budget and is wrestling with issues like "don't ask/don't tell."
It is impossible to say at this point what the appetite and ability of the next Congress will be to pass cybersecurity legislation. A few things clearly are needed in this area — most importantly, some clear lines of authority. DHS has been given the nominal lead for civilian government IT security, but little or no authority. By default, the Office of Management and Budget has been doing the heavy lifting through FISMA.
But securing the private-sector portion of the critical infrastructure is more problematic. Standards and help from government are needed, but mandates and regulatory enforcement could do more harm than good.
Outspoken IT consultant Tony Summerlin recently called provisions in the Lieberman-Collins bill for government oversight of private systems, "just short of insane," and said government first needs to put its own house in order.
"Before they start regulating industry, perhaps they ought to do something about the 30,000 Chinese crawling over their networks every day," Summerlin said.
About the Author
William Jackson is a Maryland-based freelance writer.
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How about a GED, college major or graduate degree with emphasis on cyberspace security that should be offered in more colleges? The generation of online social networking, particularly the young, would become aware and perhaps more discrete than they are now if they comprehend the risks. Classroom discussions on research/homework and personal experience will enhance awareness and establish best pratices. In addition, a profession on cybersecurity could be a stable IT career that will perhaps stay in the US as well as can be marketable globally.
We need one of those thousand-page comprehensive reform bills that noone has read. That way, everyone could do whatever they wanted, and it would be OK - or not, but noone would know.
Cybersecurity and whqt it is, should be, can be and/or will become is and has been an ongoing debate for many years now. The problem is that the threat's are always changing and 'one size fits all' doesn't and never has worked very well. Such an approach never will, but still folks want to know that that sort of stibility is maintained. Legislation cannot 'Fix' the problem, only good ongoing research, deployment of that research, and really good white hat hackers filling the gaps will keep public, private, and government secrets or PII data secure.
Geez, How lame is this...the damn Republicans, Democrats and Independents can't craft a basic bill that would enable basic common sense security. This is a bad joke on the tax payers. This is the same insanity that led to the bombing of the twin towers on 911. People in the government saw it coming and just couldn't get their act together. Also, there is no mention of local, county and state enterprise infrastructure; DUH! Many jurisdictions in this country are host to tens of thousands of DOD workers and other National Critical Infrastructure facilities and those governments require their enterprise networks to be secure as well, to ensure first responder supporting IT technology is available if needed. If the Federal Gov can't get a bill written and passed in 2010 at least they could allocate grants for cyber security so the more nimble local, county and state governments can begin to fund better security of their networks. OH YEAH, by the way, change the damn grant process so any local, county or state government that wins a grant must commit to funding freshmen and sustainment of the CAPX funds for at least ten years. Good Federal Government isn't rocket science...it just takes thoughtless dedication by individuals willing to work together...any qualified volunteers out there?
The end user remains one of the main threats to security. Sensitive records are dropped on a Flash Drive that gets reused and reused until it is lost. Files are e-mailed outside of the parent organization with no check of the idenity of the receipient, much less encryption of the attachment etc.
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Rahim AlemFree Agent
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|Bengals | Rahim Alem waived
Tue, 03 Aug 2010 11:38:17 -0700
The Cincinnati Bengals have waived DL Rahim Alem, reports The Cincinnati Enquirer's Joe Reedy.
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|Bengals | Seven UDFAs signed
Fri, 30 Apr 2010 06:33:24 -0700
The Cincinnati Bengals have announced they have signed undrafted free-agent DE Rahim Alem (Louisiana State), RB Cordera Eason (Mississippi), S Bryan Evans (Georgia), S Jeromy Miles (Massachusetts), LB Vincent Rey (Duke), FB Joe Tronzo (Louisville) and LS Mike Windt (Cincinnati). Terms of the contracts were not disclosed.
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|NFL | 12 from Louisiana State invited to NFL Combine
Tue, 02 Feb 2010 20:25:32 -0800
NFLCombine.net reports Louisiana State DE Rahim Alem, DT Charles Alexander, OT Ciron Black, LB Harry Coleman, CB Chris Hawkins, WR/RB Trindon Holliday, FS Chad Jones, WR Brandon Lafell, LB Perry Riley, RB Charles Scott, RB Keiland Williams and DT Al Woods have been invited to participate in the 2010 NFL Scouting Combine Feb. 24 to March 2.
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I like to put my board upwind and out toward the water so i can see if i can get it, if not i'm overpowerd and drop my kite right back down and rig down
Interesting...how far upwind? a couple of miles?
As far as landing your kite in the l/z, do it quickly if you feel you're way overpowered. I wouldn't mind if you were landing your kite on mine while I'm setting up. For 1, you are safe, and 2, you will give me a launch!


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The clients, a young couple with two children who after living in a conventional home wanted to change to one integrated to nature. The land, with upward topography, is limited to the south, north and east by high buildings. The west adjoining provides a wide view of the mountains.
The model work generated numberless changes until achieving the volume needed by the construction: the Nautilus. The metaphor was to feel like an internal inhabitant of a snail, like a mollusk moving from one chamber to another, like a symbiotic dweller of a huge fossil maternal cloister. This home social life flows inside the Nautilus without any division, a harmonic area in three dimensions where you can notice the continuous dynamic of the fourth dimension when moving in spiral over the stairs with a feeling of floating over the vegetation.
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Posted on March 6, 2017 Written by Leave a Comment
J. Kale Flagg Explains Von Vesting's Experience
Posted on November 15, 2012 Written by
Over the past decade, J. Kale Flagg and the partners of Von Vesting have purchased and sold over seventeen hundred properties. Von Vesting's partners have proven their success in navigating the distressed property market for over 12 years. As well, J. Kale Flagg notes that Von Vesting has generated substantial returns for investors. This has been done by implementing management and oversight systems and tools to remove the guesswork and has equated to consistently stellar results, says J. Kale Flagg.
J. Kale Flagg reports that Von Vesting has:
- Returned equity investors over 20% IRR in nine (9) of the past twelve (12) years and over 12% IRR in all twelve (12) of the past 12 years
- Has worked with varying degrees of capital, peaked with total debt & equity of approximately $49,000,000 (in 2008)
- Achieved approximately 54% return to equity investors (IRR)(their best to date- 2008)
- Built $6mm rental fund (purchased, improved and rented approximately fifty two (52) properties for angel investor group)—currently in its 5th year of 7-year plan— estimated 12% non-leveraged cash-on-cash return plus approximately 17% equity
Rental Funds are a business J. Kale Flagg explains that Von Vesting understands, knows, and appreciates. According to J. Kale Flagg, Rental Funds are about purchasing with an eye on sustainable and growing rents, equity appreciation, and lowest improvement and maintenance costs possible. In other words, immediate cash flow while time provides appreciation. The flipping model on the other hand, reports J. Kale Flagg, is all about purchasing & improving intelligently while accurately forecasting the sales price that the improved property will sell at quickly. In other words: velocity. J. Kale Flagg notes that Von Vesting has extensive experience and success in both models.
In Q4 2011, reports J. Kale Flagg, Von Vesting launched a new Flip Fund, the American Redevelopment Fund, LP. Since inception, the Fund has raised approximately $2 million in equity and is in current discussion with several other investors who see value in these efforts, says J. Kale Flagg. The Fund will have a minimum of $3.5 million in equity by year-end 2012; J. Kale Flagg says this is an initial goal. The Fund is seeking $10mm to leverage its equity to maximize profits for investors.
J. Kale Flagg is the COO of Von Vesting, a documented, brick & mortar, professionally managed company that has a fully integrated operation to expeditiously source, purchase, renovate, and sell single-family residences in Northern California for profit. With an investment strategy that implements a minimum 10-15% ROI for every property and stresses velocity, Von Vesting is a leader in the redevelopment industry. An average elapsed time (from purchase to close of escrow for vacant properties) of approximately 95 days, enables that 10-15% ROI for each property to replicate approximately three times per year – earning the Fund a 30-45% IRR per year, with 50% of those profits going to investors. According to J. Kale Flagg, the firm has a simple investment philosophy: steal 'em so you can give 'em away. In other words, do the hunting to buy extremely low and sell within market comps, but at low enough prices to move inventory quickly to ensure a constantly revolving line of cash and profits.
J. Kale Flagg Leading Social Networks
Posted on November 13, 2012 Written by
Connect with J. Kale Flagg on Facebook, Twitter, Google+ and Linkedin Connect with J. Kale Flagg on Facebook Join our fan page on the world's largest, fastest growing social network, and interact with other like minded folks. Plus, get … [Continue reading]
Videos of J. Kale Flagg
Posted on November 12, 2012 Written by
J. Kale Flagg on Von Vesting's Investment Strategy Von Vesting continues to wow investors. Kale Flagg explains how and why. J. Kale Flagg Q&A about Distressed Real Estate Veteran … [Continue reading]