what is the full form of n c c
National Cadet Corps
4737830
National Cadet Corps (India) The National Cadet Corps is an Indian military cadet corps with its Headquarters at New Delhi, Delhi, India. It is open to school and college students on voluntary basis. National Cadet Corps is a Tri-Services Organization, comprising the Army, Navy and Air Force, engaged in grooming the youth of the country into disciplined and patriotic citizens. The National Cadet Corps in India is a voluntary organization which recruits cadets from high schools, colleges and universities all over India. The Cadets are given basic military training in small arms and parades. The officers and cadets have no
National Cadet Corps (India)
17457929
patterns. C-term domains are grouped by sequence homology into classes I-III, with apparently no restriction on which N-term classes they can pair with to form a full VSG. To dimerize, VSG N-terminal domains form a bundle of four alpha helices directed by hydrophobic interactions, around which hang smaller structural features (five smaller helices and three beta-sheets). VSG is anchored to the cell membrane via a glycophosphatidylinositol (GPI) anchor—a noncovalent linkage from the C-terminus which directs its forward trafficking from the ER to the membrane. This GPI anchor is specifically cleaved by GPI Phospholipase C, cleaving the membrane-form VSG, and allowing
Variant surface glycoprotein
17227108
resolution; it is a homohexameric complex (approximately 360 kDa) with a double-doughnut structure and a central pore which is open at the N-terminal ends and partially sealed at the C-terminal ends due to the presence of six arginine residues. The hexamer has twelve ATP molecules between the N- (CI) and C-terminal (CII) domains, which demonstrate ATPase activity. The CI and CII domains are linked by the N-terminal region of the CII domain. The last 20 residues from the C-terminal of the CII domain protrude from the doughnut to form what is called the A-loop. Interfaces on KaiC's CII domain are
KaiC
10087626
Protein kinase C zeta type Protein kinase C, zeta (PKCζ), also known as PRKCZ, is a protein that in humans is encoded by the "PRKCZ" gene. The PRKCZ gene encodes at least two alternative transcripts, the full-length PKCζ and an N-terminal truncated form PKMζ. PKMζ is thought to be responsible for maintaining long-term memories in the brain. The importance of PKCζ in the creation and maintenance of long-term potentiation was first described by Todd Sacktor and his colleagues at the State University of New York at Brooklyn in 1993. PKC-zeta has an N-terminal regulatory domain, followed by a hinge region
Protein kinase C zeta type
6622378
"n" be the number of prime gaps of size "n" below "x". The first Hardy–Littlewood conjecture says the asymptotic density is of form where "C" is a function of "n", and formula_3 means that the quotient of two expressions tends to 1 as "x" approaches infinity. "C" is the twin prime constant where the product extends over all prime numbers "p" ≥ 3. "C" is "C" multiplied by a number which depends on the odd prime factors "q" of "n": For example, "C" = "C" and "C" = 2"C". Twin primes have the same conjectured density as cousin primes, and
Polignac's conjecture
1546228
theorem can also be extended to hypergraphs. An "m"-hypergraph is a graph whose "edges" are sets of "m" vertices – in a normal graph an edge is a set of 2 vertices. The full statement of Ramsey's theorem for hypergraphs is that for any integers "m" and "c", and any integers "n", …, "n", there is an integer "R"("n", …, "n";"c", "m") such that if the hyperedges of a complete "m"-hypergraph of order "R"("n", …, "n";"c", "m") are coloured with "c" different colours, then for some "i" between 1 and "c", the hypergraph must contain a complete sub-"m"-hypergraph of order
Ramsey's theorem
14805833
"N". The jet space can be endowed with a smooth structure (i.e. a structure as a C manifold) which make it into a topological space. This topology is used to define a topology on C("M","N"). For a fixed integer consider an open subset and denote by "S"("U") the following: The sets "S"("U") form a basis for the Whitney C-topology on C("M","N"). For each choice of , the Whitney C-topology gives a topology for C("M","N"); in other words the Whitney C-topology tells us which subsets of C("M","N") are open sets. Let us denote by W the set of open subsets of
Whitney topologies
17273631
(Gly)n containing molecule to form a fusion between the two molecules with an intervening LPXT(Gly)n motif. To achieve N-terminal labeling of a protein, the LPXTG motif is engineered to be at the C-terminus of the label. The protein is engineered to have an N-terminal (Gly)n. To achieve C-terminal labeling of the same protein, the LPXTG motif is engineered to be at the C-terminus of the protein. A (Gly)n molecule is engineered to contain the label at its C-terminus. Finally, both N and C-termini of proteins can be labeled by using Sortases of different substrate specificity. For example, Sortase A from
Sortase A
17218241
to Harish-Chandra of the space of complex symmetric "n" by "n" matrices as a dense open subset of the compact Grassmannian of Langrangian subspaces of C. Morevoer this embedding is equivariant for the action of the real symplectic group. In fact, with the standard complex inner product on C, the Grassmannian of "n"-dimensional subspaces has a continuous transitive action of SL(2"n",C) and its maximal compact subpgroup SU(2"n"). It can be identified with the space of orthogonal rank "n" projections, a compact subspace of M(C). Taking coordinates ("z"...,"z","w"...,"w") on C, the symplectic form is given by An "n"-dimensional subspace "U" is
Invariant convex cone
90266
of a C*-algebra is itself a C*-algebra. The algebra M("n", C) of "n" × "n" matrices over C becomes a C*-algebra if we consider matrices as operators on the Euclidean space, C, and use the operator norm ||.|| on matrices. The involution is given by the conjugate transpose. More generally, one can consider finite direct sums of matrix algebras. In fact, all C*-algebras that are finite dimensional as vector spaces are of this form, up to isomorphism. The self-adjoint requirement means finite-dimensional C*-algebras are semisimple, from which fact one can deduce the following theorem of Artin–Wedderburn type: Theorem. A finite-dimensional
C*-algebra
18450777
|x| = n and want to reduce it to an instance x' of a problem B with |x'| = n'. A gap-preserving reduction from A to B is a set of functions (k(n), k'(n'), c(n), c'(n')) such that For minimization problems: For maximization problems: If c' > c, then this is a "gap-amplifying reduction". This problem is a form of the Boolean satisfiability problem (SAT), where each clause contains three distinct literals and we want to maximize the number of clauses satisfied. Håstad showed that the (1/2+ε, 1-ε)-gap version of a similar problem, MAX E3-X(N)OR-SAT, is NP-hard. The MAX E3-X(N)OR-SAT
Gap reduction
13689595
than "C. n. euphemia" if anything; however, except in lightness they resemble "C. n. neogama" even more strongly, and they do not form a geographically separate and distinct population. They are thus today treated as a pale local form of the nominate subspecies, with no formal taxonomic standing. Finally, some authors include the Old Wife Underwing ("C. palaeogama") in "C. neogama". These two are recognizably distinct in appearance and widely sympatric however, and there is no good indication that they are just one species. In fact, "C. neogama" occurs at the type locality of "C. palaeogama" (the area around Baltimore,
Catocala neogama
6495007
generate work). In daily life, the vast majority of flames one encounters are those of organic compounds including wood, wax, fat, common plastics, propane, and gasoline. The constant-pressure adiabatic flame temperature of such substances in air is in a relatively narrow range around 1950 °C. This is because, in terms of stoichiometry, the combustion of an organic compound with "n" carbons involves breaking roughly 2"n" C–H bonds, "n" C–C bonds, and 1.5"n" O bonds to form roughly "n" CO molecules and "n" HO molecules. Because most combustion processes that happen naturally occur in the open air, there is nothing that
Adiabatic flame temperature
767478
case of an earlier conjecture of Bunyakovsky and remains open. Hardy and Littlewood further assert that, asymptotically, the number "P"("n") of primes of the form "ax" + "bx" + "c" and less than "n" is given by where "A" depends on "a", "b", and "c" but not on "n". By the prime number theorem, this formula with "A" set equal to one is the asymptotic number of primes less than "n" expected in a random set of numbers having the same density as the set of numbers of the form "ax" + "bx" + "c". But since "A" can take
Ulam spiral
11353792
and is mediated instead by the C terminus of the protein. This suggests that hPINX1 may have functionally separable cellular effects in which the N terminus is involved in RNA processing via the G-patch, and the C terminus is involved in telomere dynamics.” It is suggested that “PINX1 represses telomerase activity in vivo by binding to the assembled hTERT-hTR complex.” The TID domain of PINX1 is likely what binds to hTERT. In cells, full-length PINX1 is not as strong as just the TID domain at inhibiting telomerase. This may be due to full-length PINX1 being subject to “endogenous regulation such
PINX1
554172
polynomial. Another thing to notice is the sets "O"("n") and "O"("c") are very different. If "c" is greater than one, then the latter grows much faster. A function that grows faster than "n" for any "c" is called "superpolynomial". One that grows more slowly than any exponential function of the form "c" is called "subexponential". An algorithm can require time that is both superpolynomial and subexponential; examples of this include the fastest known algorithms for integer factorization and the function "n". We may ignore any powers of "n" inside of the logarithms. The set "O"(log "n") is exactly the same
Big O notation
8640011
oxidative stress. A glycosylated form of the N-terminal peptide may be associated with cachexia (muscle wasting) in cancer patients. The C-termial precursor DCD-1L is a 48 residue peptide that shows partial helicity in solution, as evidenced by the determination of its solution structure by NMR and CD-spectroscopy. The full length precursor is processed by undetermined proteases present in human sweat, to form several shorter peptides that show variable antimicrobial activity, named according to their C-terminal triplet of amino acids and their resiude length. One such active peptide is SSL25, which shows a 2-fold increase in activity against E.coli compared to
Dermcidin
9858468
XCL1 Chemokine (C motif) ligand (XCL1) is a small cytokine belonging to the C chemokine family that is also known as lymphotactin. Chemokines are known for their function in inflammatory and immunological responses. This family C chemokines differs in structure and function from most chemokines. There are only two chemokines in this family and what separated them from other chemokines is that they only have two cysteines; one N-terminal cysteine and one cysteine downstream. These both are called Lymphotactin, alpha and beta form, and claim special characteristics only found between the two. Lymphotactins can go through a reversible conformational change
XCL1
14775220
C. N. James Cabin The C. N. James Cabin is a frontier-style log cabin, originally used as both a store and home, constructed in 1868. It was later also used as a church. It stands in what is now Augusta, Kansas, United States. The builder and proprietor of the store was Chester N. James, a merchant who moved to the area to establish a trading post. James was a central figure in the organization of Augusta Township and eventually the incorporation of Augusta itself. Augusta is named for James' wife. The C. N. James Cabin was added to the National
C. N. James Cabin
19043123
"c"=8.726(2) Å, "β"=91.64(3)° and "V"=765.2(3) Å at 56 GPa and ambient temperature. The space group is "P"2/"c" and the unit cell contains 48 N molecules arranged into a layered structure. When the ζ-N phase is compressed at room temperature over 150 GPa an amorphous form is produced. This is designated as the μ-phase. It is a narrow gap semiconductor. The μ-phase has been brought to atmospheric pressure by first cooling it to 100 K. Under pressures higher than 110 GPa and temperatures around 2000 K nitrogen forms a network solid, bound by single covalent bonds in what is called a
Solid nitrogen
14738073
zero, so it is either empty or consists of a single point. So it is sufficient to show that it is not empty. Pick an element "x" of "C" for each "n". Since the diameter of "C" tends to zero and the "C" are nested, the "x" form a Cauchy sequence. Since the metric space is complete this Cauchy sequence converges to some point "x". Since each "C" is closed, and "x" is a limit of a sequence in "C", "x" must lie in "C". This is true for every "n", and therefore the intersection of the "C" must contain
Cantor's intersection theorem
12236588
carbon end and a positive one on the oxygen end, as in C≡C−C≡O, C≡C−C≡C−C≡O, and, in general, (C≡C−)C≡O. Carbon monoxide itself follows this pattern: its predominant form is believed to be C≡O. Another family of oxocarbons that has attracted special attention are the cyclic radialene-type oxocarbons CO or (CO). They can be regarded as cyclic polymers of carbon monoxide, or "n"-fold ketones of "n"-carbon cycloalkanes. Carbon monoxide itself (CO) can be regarded as the first member. Theoretical studies indicate that ethylene dione (CO or O=C=C=O) and cyclopropanetrione CO do not exist. The next three members — CO, CO, and CO
Oxocarbon
10976620
cannot execute in parallel. Estrin's scheme is one method that attempts to overcome this serialization while still being reasonably close to optimal. Estrin's scheme operates recursively, converting a degree-"n" polynomial in "x" (for "n"≥2) to a degree- polynomial in "x" using independent operations (plus one to compute "x"). Given an arbitrary polynomial "P"("x") = "C" + "C""x" + "C""x" + "C""x" + ⋯ + "Cx", one can group adjacent terms into sub-expressions of the form ("A" + "Bx") and rewrite it as a polynomial in "x": "P"("x") = ("C" + "C""x") + ("C" + "C""x")"x" + ("C" + "C""x")"x" +
Estrin's scheme
5886811
fully supported through 2008. Kodak cited poor profitability of the sector in its announcement. Kodak DCS Pro SLR/c The Kodak Professional DCS Pro SLR/c is a 13.5 megapixel digital SLR camera produced by Eastman Kodak. It is full frame—it uses an image sensor that is the full size of a 35 mm (36x24 mm) frame. It is compatible with Canon EOS (EF mount) lenses. The camera was launched on March 18, 2004 and incorporates the internal systems of the previous Nikon-compatible SLR/n in a Sigma SA9 SLR body. Both the SLR/c and the SLR/n were officially discontinued by Kodak on
Kodak DCS Pro SLR/c
5886810
Kodak DCS Pro SLR/c The Kodak Professional DCS Pro SLR/c is a 13.5 megapixel digital SLR camera produced by Eastman Kodak. It is full frame—it uses an image sensor that is the full size of a 35 mm (36x24 mm) frame. It is compatible with Canon EOS (EF mount) lenses. The camera was launched on March 18, 2004 and incorporates the internal systems of the previous Nikon-compatible SLR/n in a Sigma SA9 SLR body. Both the SLR/c and the SLR/n were officially discontinued by Kodak on May 31, 2005, although remaining stock would be sold and the cameras would be
Kodak DCS Pro SLR/c
1742629
"T", "F"), a "configuration" is a set "C" so that "C" ⊆ "P". Definition 3. An "elementary net" is a net of the form "EN" = ("N", "C") where: Definition 4. A "Petri net" is a net of the form "PN" = ("N", "M", "W"), which extends the elementary net so that: If a Petri net is equivalent to an elementary net, then "Z" can be the countable set {0,1} and those elements in "P" that map to 1 under "M" form a configuration. Similarly, if a Petri net is not an elementary net, then the multiset "M" can be
Petri net
14261641
1,3-Bis(dicyanomethylene)squarate 1,3-Bis(dicyanomethylene)squarate is a divalent anion with chemical formula or ((N≡C−)C=)(CO). It is one of the pseudo-oxocarbon anions, as it can be described as a derivative of the squarate oxocarbon anion through the replacement of two opposite oxygen atoms by dicyanomethylene groups =C(−C≡N). The anion can be obtained by reacting squaric acid with aniline to form the diester 1,3-dianiline squarate (a yellow solid), before treating the diester with malononitrile (N≡C−)CH and sodium ethoxide to give the disodium tetrahydrate salt 2Na··4HO, an orange water-soluble solid. The hydrated salt loses the water below 100 °C, but the resulting anhydrous salt is stable
1,3-Bis(dicyanomethylene)squarate
77190
the full class of context-sensitive languages. The equivalence was established by Penttonen normal form. The following grammar, with start symbol "S", generates the canonical non-context-free language { "a""b""c" : "n" ≥ 1 } : Rules 1 and 2 allow for blowing-up "S" to "a""BC"("BC"); rules 3 to 6 allow for successively exchanging each "CB" to "BC" (four rules are needed for that since a rule "CB" → "BC" wouldn't fit into the scheme α"A"β → αγβ); rules 7–10 allow replacing a non-terminals "B" and "C" with its corresponding terminals "b" and "c" respectively, provided it is in the right place.
Context-sensitive grammar
17712717
Carolina Mutual. W.E.B. Du Bois had a different approach, supporting agitation to demand full civil rights for blacks—yet he also celebrated Durham. Reflecting on his visit to Durham, he notes that the "social and economic development [of African American people in the city] is perhaps more striking than that of any similar group in the nation." He goes on to mention the actions of C. C. Spaulding, then general manager of N. C. Mutual, who took children from a school to town "to show them what colored People were doing in Durham." He saw Spaulding's action as an abnormal display
North Carolina Mutual Life Insurance Company
8789572
p21), but it also plays a very important role in regulating cell growth (upregulates ribosomal RNA and proteins), apoptosis (downregulates Bcl-2), differentiation, and stem cell self-renewal. Nucleotide metabolism genes are upregulated by Myc, which are necessary for Myc induced proliferation or cell growth. There have been several studies that have clearly indicated Myc's role in cell competition. A major effect of c-myc is B cell proliferation. c-Myc induces MTDH(AEG-1) gene expression and in turn itself requires AEG-1 oncogene for its expression. Myc-nick is a cytoplasmic form of Myc produced by a partial proteolytic cleavage of full-length c-Myc and N-Myc. Myc
Myc
4647969
not ligate C and C, leaving the full forms of C and C as they are: is an example of such a non-ligated form. The sequences ङ्क ङ्ख ङ्ग ङ्घ , in correct Devanagari handwriting, should be written as conjuncts (the virama and the top cross line of the second letter disappear, and what is left of the second letter is written under the ङ and joined to it). Virama Virama ( ्) is a generic term for the diacritic in many Brahmic scripts, ்including Devanagari and Eastern Nagari script, used to suppress the inherent vowel that otherwise occurs with
Virama
2927339
C-terminus The C-terminus (also known as the carboxyl-terminus, carboxy-terminus, C-terminal tail, C-terminal end, or COOH-terminus) is the end of an amino acid chain (protein or polypeptide), terminated by a free carboxyl group (-COOH). When the protein is translated from messenger RNA, it is created from N-terminus to C-terminus. The convention for writing peptide sequences is to put the C-terminal end on the right and write the sequence from N- to C-terminus. Each amino acid has a carboxyl group and an amine group. Amino acids link to one another to form a chain by a dehydration reaction which joins the amine
C-terminus
3971832
the loop spaces of the unitary/orthogonal group. The complex case is particularly simple: every nondegenerate quadratic form on a complex vector space is equivalent to the standard diagonal form where , so there is essentially only one Clifford algebra in each dimension. This is because the complex numbers include formula_3 by which formula_4 and so positive or negative terms are equivalent. We will denote the Clifford algebra on C with the standard quadratic form by Cℓ(C). There are two separate cases to consider, according to whether "n" is even or odd. When "n" is even the algebra Cℓ(C) is central
Classification of Clifford algebras
6097914
action of "G" on "N" we can form the semidirect product formula_2. This contains "N" as a normal subgroup, and the action of "G" on "N" is given by conjugation in the semidirect product. We can replace "N" by its complex group algebra "C"["N"], and again form a product formula_3 in a similar way; this algebra is a sum of subspaces "gC"["N"] as "g" runs through the elements of "G", and is the group algebra of formula_2. We can generalize this construction further by replacing "C"["N"] by any algebra "A" acted on by "G" to get a crossed product formula_5,
Crossed product
8849240
that had not been degraded. An exponential increase in C/N ratios is observed with increasing water depth—with C/N ratios reaching 10 at intermediate water depths of about 1000 meters, and up to 15 in the deep ocean (~ >2500 meters) . This elevated C/N signature is preserved in the sediment, until another form of diagenesis, post-depositional diagenesis, alters its C/N signature once again. Post-depositional diagenesis occurs in organic-carbon-poor marine sediments where bacteria are able to oxidize organic matter in aerobic conditions as an energy source. The oxidation reaction proceeds as follows: CHO + HO → CO + 4H + 4e,
Carbon-to-nitrogen ratio
11527789
provide strong cell adhesion. Functional αE-catenin is required for normal embryonic development, as a mutation eliminating the C-terminal 1/3 of the protein resulting in a complete loss-of-function phenotype showed disruption of the trophoblast epithelium and arrested development at the blastocyst stage. αE-catenin specifically, not β- or γ-catenin, binds F-actin and organizes and tethers the filaments at regions of cell-cell contact. Studies show that full-length αE-catenin binds and bundles F-actin in a superior fashion relative to individual N-terminal or C-terminal domains. αE-catenin, along with β-catenin and plakoglobin form distinct complexes with N-cadherin that are involved in forming cell-cell contacts and differentiation
Catenin alpha-1
16713225
given column vector with "n" components. We split the matrix A into where B and C are "n" × "n" matrices. If, for an arbitrary "n" × "n" matrix M, M has nonnegative entries, we write M ≥ 0. If M has only positive entries, we write M > 0. Similarly, if the matrix M − M has nonnegative entries, we write M ≥ M. Definition: A = B − C is a regular splitting of A if B ≥ 0 and C ≥ 0. We assume that matrix equations of the form where g is a given column vector,
Matrix splitting
11324363
HOMER1 Homer protein homolog 1 or Homer1 is a neuronal protein that in humans is encoded by the "HOMER1" gene. Other names are Vesl and PSD-Zip45. Homer1 protein has an N-terminal EVH1 domain, involved in protein interaction, and a C-terminal coiled-coil domain involved in self association. It consists of two major splice variants, short-form (Homer1a) and long-form (Homer1b and c). Homer1a has only EVH1 domain and is monomeric while Homer1b and 1c have both EVH1 and coiled-coil domains and are tetrameric. The coiled-coil can be further separated into N-terminal half and C-terminal half. The N-terminal half of the coiled-coil domain
HOMER1
8682951
and a quadratic form "Q", which maps a vector "v" to complex number "Q"("v"). The Clifford algebra "C"ℓ(C) is the ring generated by products of vectors in C subject to the relation Spinors are modules of the Clifford algebra, and so in particular there is an action of C on the space of spinors. The subset of C that annihilates a given spinor ψ is a complex subspace C. If ψ is nonzero then "m" is less than or equal to "n". If "m" is equal to "n" then ψ is said to be a "pure spinor". Every pure spinor
Pure spinor
8472396
uses a zinc cofactor in each. There are two distinct domains in each monomer: the N-terminal domain from residues 1-212 and the C-terminal domain from residues 213-313. The N-terminal domain of aspartoacylase is similar to that of zinc-dependent hydrolases such as carboxypeptidaseA. However, carboxypeptidases do not have something similar to the C-domain. In carboxypeptidase A, the active site is accessible to large substrates like the bulky C-terminal residue of polypeptides, whereas the C-domain sterically hinders access to the active site in aspartoacylase. Instead, the N-domain and C-domain of aspartoacylase form a deep narrow channel that leads to the active site.
Aspartoacylase
13270168
In the solid phase, the observed N=N and N−F bond distances in the NF cation are 1.089(9) and 1.257(8) Å respectively, among the shortest experimentally observed N−N and N−F bonds. Dinitrogen difluoride Dinitrogen difluoride is a chemical compound with the formula NF. It is a gas at room temperature, and was first identified in 1952 as the thermal decomposition product of the azide NF. It has the structure F−N=N−F and exists in both a "cis"- and "trans"-form. The "cis" configuration lies in a C symmetry and the "trans"-form has a symmetry of C. These isomers are thermally interconvertible but can
Dinitrogen difluoride
10213879
2.55 "vs" 3.44). Bond lengths for paraffinic C–O bonds are in the range of 143 pm – less than those of C–N or C–C bonds. Shortened single bonds are found with carboxylic acids (136 pm) due to partial double bond character and elongated bonds are found in epoxides (147 pm). The C–O bond strength is also larger than C–N or C–C. For example, bond strengths are /mol (at 298 K) in methanol, /mol in methylamine, and /mol in ethane. Carbon and oxygen form terminal double bonds in functional groups collectively known as carbonyl compounds to which belong such compounds as
Carbon–oxygen bond
6441909
line (say the Riemann sphere) Σ"C" can be identified with projective space of dimension "n". If "G" has genus "g" ≥ 1 then the Σ"C" are closely related to the Jacobian variety "J" of "C". More accurately for "n" taking values up to "g" they form a sequence of approximations to "J" from below: their images in "J" under addition on "J" (see theta-divisor) have dimension "n" and fill up "J", with some identifications caused by special divisors. For "g" = "n" we have Σ"C" actually birationally equivalent to "J"; the Jacobian is a blowing down of the symmetric product.
Symmetric product of an algebraic curve
8580039
spaces reduces to determining all nonequivalent sets of structure constants. This can be done, using the "tensor" properties of the quantities "C", by the following simple method (C. G. Behr, 1962). The unsymmetric "tensor" "C" can be resolved into a symmetric and an antisymmetric part. The first is denoted by "n", and the second is expressed in terms of its "[[dual vector]]" "a": Substitution of this expression in leads to the condition By means of the transformations the symmetric "tensor" "n" can be brought to diagonal form with [[eigenvalues and eigenvectors|eigenvalues]] "n", "n", "n". Equation shows that the "vector" "a"
BKL singularity
3371777
always an integer. By a theorem of Lagrange every nonnegative integer can be written as a sum of at most four squares. Thus, every nonnegative integer is the norm of some Lipschitz (or Hurwitz) quaternion. More precisely, the number "c"("n") of Hurwitz quaternions of given positive norm "n" is 24 times the sum of the odd divisors of "n". The generating function of the numbers "c"("n") is given by the level 2 weight 2 modular form where and is the weight 2 level 1 Eisenstein series (which is a quasimodular form) and σ("n") is the sum of the divisors of
Hurwitz quaternion
557266
on a complex vector space of dimension "n" is equivalent to the standard diagonal form Thus, for each dimension "n", up to isomorphism there is only one Clifford algebra of a complex vector space with a nondegenerate quadratic form. We will denote the Clifford algebra on C with the standard quadratic form by Cℓ(C). For the first few cases one finds that where denotes the algebra of matrices over C. In this section, Hamilton's quaternions are constructed as the even sub algebra of the Clifford algebra Cℓ(R). Let the vector space "V" be real three-dimensional space R, and the quadratic
Clifford algebra
10780656
"C" topology. Here "C" is the function space whose members are continuous functions with r continuous derivatives from a manifold "M" to a manifold "N". The space "C"("M", "N"), of "C" mappings between "M" and "N", is a Baire space, hence any residual set is dense. This property of the function space is what makes generic properties "typical". A property of an irreducible algebraic variety "X" is said to be true generically if it holds except on a proper Zariski-closed subset of "X", in other words, if it holds on a non-empty Zariski-open subset. This definition agrees with the topological
Generic property
5320017
was used (in place of the more common N) that a large amount of C would be generated from the nitrogen by the (n,p) reaction. As the nitrogen required for such a fuel would be so expensive it is likely that the fuel would have to be reprocessed by pyroprocessing to enable the N to be recovered. It is likely that if the fuel was processed and dissolved in nitric acid that the nitrogen enriched with N would be diluted with the common N. Much of what is known about uranium carbide is in the form of pin-type fuel elements
Nuclear fuel
9777477
first proved in 1882 what mathematicians now think of as the connection between Abel summation and (H, "n") summation; was his first example. The fact that is the (H, 2) sum of guarantees that it is the Abel sum as well; this will also be proved directly below. The other commonly formulated generalization of Cesàro summation is the sequence of (C, "n") methods. It has been proven that (C, "n") summation and (H, "n") summation always give the same results, but they have different historical backgrounds. In 1887, Cesàro came close to stating the definition of (C, "n") summation, but
1 − 2 + 3 − 4 + ⋯
138856
Michel Eugène Chevreul, though he used initially some variant terms, "graisse acide" and "acide huileux" ("acid fat" and "oily acid"). Fatty acids differ by length, often categorized as short to very long. Saturated fatty acids have no C=C double bonds. They have the same formula CH(CH)COOH, with variations in "n". An important saturated fatty acid is stearic acid (n = 16), which when neutralized with lye is the most common form of soap. Unsaturated fatty acids have one or more C=C double bonds. The C=C double bonds can give either "cis" or "trans" isomers. In most naturally occurring unsaturated fatty
Fatty acid
8197304
in enteroendocrine cells of the small intestine, where it leads to secretion and smooth muscle contraction. Neurotensin shares significant sequence similarity in its 6 C-terminal amino acids with several other neuropeptides, including neuromedin N (which is derived from the same precursor). This C-terminal region is responsible for the full biological activity, the N-terminal portion having a modulatory role. The neurotensin/neuromedin N precursor can also be processed to produce large 125–138 amino acid peptides with the neurotensin or neuromedin N sequence at their C terminus. These large peptides appear to be less potent than their smaller counterparts, but are also less
Neurotensin
18668547
Caudron C.251 The Caudron C.251 Et-2 was a French tandem seat, open cockpit biplane designed as an intermediate trainer and built in 1931. It did not go into production. The two seat, open cockpit C.251 was designed to replace the ubiquitous Caudron C.59, dating from 1922, as an intermediate trainer aircraft. It was a single bay biplane with N-form interplane struts, its upper wing supported over the fuselage on a pair of short, vertical, N-form cabane struts. The slightly shorter span lower wing was mounted on the lower fuselage longerons a little above the fuselage underside and, unlike the upper
Caudron C.251
14775221
Register of Historic Places in 1994. It has been restored to its original appearance and is now the part of the Augusta Historical Museum, which is operated by the Augusta Historical Society. C. N. James Cabin The C. N. James Cabin is a frontier-style log cabin, originally used as both a store and home, constructed in 1868. It was later also used as a church. It stands in what is now Augusta, Kansas, United States. The builder and proprietor of the store was Chester N. James, a merchant who moved to the area to establish a trading post. James was
C. N. James Cabin
4988477
while the center of Pin(3) is "C" × "C". The center of Pin(n,0) = Pin is "C" when n is even, "C" × "C" when n = 1 mod 4, and "C" when n = 3 mod 4. The center of Pin(0,n) = Pin is "C" when n is even, "C" when n = 1 mod 4, and "C" × "C" when n = 3 mod 4. For "p", "q" ≠ 0 the center of Pin(p,q) is an extension of either "C" × "C" or "C" by "C". The name was introduced in , where they state "This joke is
Pin group
11468905
Cunningham number In mathematics, specifically in number theory, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham. Cunningham numbers are a simple type of binomial number, they are of the form where "b" and "n" are integers and "b" is not a perfect power. They are denoted "C"("b", "n"). Establishing whether or not a given Cunningham number is prime has been the main focus of research around this type of number. Two particularly famous families of Cunningham numbers in this respect are the Fermat numbers, which are those of the form "C"(2,2),
Cunningham number
1692144
(residues 428-453) responsible for oligomerization of identical monomers. Extensive crystallographic analysis has been performed, especially on the pterin- and iron-coordinated catalytic domain to examine the active site. The structure of the N-terminal regulatory domain has also been determined, and together with the solved structure of the homologous tyrosine hydroxylase C-terminal tetramerization domain, a structural model of tetrameric PAH was proposed. Using X-ray crystallography, the structure of full-length rat PAH was determined experimentally and showed the auto-inhibited, or resting-state form of the enzyme. The resting-state form (RS-PAH) is architecturally distinct from the activated form (A-PAH). A full-length structure of A-PAH is
Phenylalanine hydroxylase
5519938
nor its structure fully determined until 1976. Full length hirudin is made up of 65 amino acids. These amino acids are organized into a compact N-terminal domain containing three disulfide bonds and a C-terminal domain that is completely disordered when the protein is un-complexed in solution. Amino acid residues 1-3 form a parallel beta- strand with residues 214-217 of thrombin, the nitrogen atom of residue 1 making a hydrogen bond with the Ser-195 O gamma atom of the catalytic site. The C-terminal domain makes numerous electrostatic interactions with an anion-binding exosite of thrombin, while the last five residues are in
Hirudin
2513851
AND or OR gates take 1 delay to complete, has a delay of The truth table for the full adder is: It is possible to create a logical circuit using multiple full adders to add "N"-bit numbers. Each full adder inputs a "C", which is the "C" of the previous adder. This kind of adder is called a ripple-carry adder (RCA), since each carry bit "ripples" to the next full adder. Note that the first (and only the first) full adder may be replaced by a half adder (under the assumption that "C" = 0). The layout of a ripple-carry
Adder (electronics)
10634734
a Latin square of order n. Estimate T(n). Describe how all Latin subsquares in multiplication tables of Moufang loops arise. A partial Latin square has "Blackburn property" if whenever the cells (i,j) and (k,l) are occupied by the same symbol, the opposite corners (i,l) and (k,j) are empty. What is the highest achievable density of filled cells in a partial Latin square with the Blackburn property? In particular, is there some constant c > 0 such that we can always fill at least c n cells? Let formula_1 be the number of Latin squares of order n. What is the
Problems in Latin squares
133823
"E", "F" are the numbers of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and "V"/2 − 10 hexagons. The smallest fullerene is the dodecahedral C. There are no fullerenes with 22 vertices. The number of fullerenes C grows with increasing "n" = 12, 13, 14, ..., roughly in proportion to "n" . For instance, there are 1812 non-isomorphic fullerenes C. Note that only one form of C, the buckminsterfullerene alias truncated icosahedron, has no pair of adjacent pentagons (the smallest such fullerene). To further illustrate the growth, there are 214,127,713 non-isomorphic fullerenes C, 15,655,672
Fullerene
17029742
CHNO.HCl, m.p. 103-104 °C. The pK of "N"-methylphenylethanolamine hydrochloride, at 25 °C and at a concentration of 10mM, has been recorded as 9.29. The presence of the hydroxy-group on the benzylic C of the "N"-methylphenylethanolamine molecule creates a chiral center, so the compound exists in the form of two enantiomers, d- and l-"N"-methylphenylethanolamine, or as the racemic mixture, d,l- "N"-methylphenylethanolamine. The dextrorotatory isomer corresponds to the S-configuration, and the levorotatory isomer to the R-configuration. The "N"-methylphenylethanolamine isolated from "Halostachys caspica", and given the alkaloid name "halostachine", was found to be the levorotatory enantiomer: "Natural" halostachine has m.p 43-45 °C, and
Halostachine
14261642
up to 400 °C. Reaction of the sodium salt with salts of other cations in ethanol affords the following salts: Nuclear magnetic resonance shows that the aromatic character of the squarate core is retained. 1,3-Bis(dicyanomethylene)squarate 1,3-Bis(dicyanomethylene)squarate is a divalent anion with chemical formula or ((N≡C−)C=)(CO). It is one of the pseudo-oxocarbon anions, as it can be described as a derivative of the squarate oxocarbon anion through the replacement of two opposite oxygen atoms by dicyanomethylene groups =C(−C≡N). The anion can be obtained by reacting squaric acid with aniline to form the diester 1,3-dianiline squarate (a yellow solid), before treating the
1,3-Bis(dicyanomethylene)squarate
11183800
domains: the central VEGF homology domain (VHD), the N-terminal domain (propeptide) and a C-terminal domain (propeptide). It is referred to as "uncleaved VEGF-C" and has a size of approximately 58 kDa. The first cleavage (which happens already before secretion) occurs between the VHD and the C-terminal domain and is mediated by proprotein convertases. However, the resulting protein is still held together by disulfide bonds and remains inactive (although it can bind already VEGFR-3). This form is referred to as "intermediate form" or pro-VEGF-C and it consists of two polypeptide chains of 29 and 31 kDa. In order to activate VEGF-C,
Vascular endothelial growth factor C
3293916
trivial bundle. The global sections of the trivial bundle form a one-dimensional vector space, so the "n"-canonical map for any "n" is the map to a point. If "C" has genus two or more, then the canonical class is big, so the image of any "n"-canonical map is a curve. The image of the 1-canonical map is called a canonical curve. A canonical curve of genus "g" always sits in a projective space of dimension "g" − 1. When "C" is a hyperelliptic curve, the canonical curve is a rational normal curve, and "C" a double cover of its canonical
Canonical bundle
7262081
is an enzyme that usually bonds to form tetramers in bacteria and dimers in eukaryotes and has a subunit mass of 40-50 kDa. Dividing the enzyme into the N-terminus and C-terminus one will notice that the N-terminus varies in composition while the C-terminus remains relatively constant (the C-terminus in plants does differ slightly from the C-terminus in other beings). In 1999 the first X-ray crystallography structure of HPPD was created and since then it has been discovered that the active site of HPPD is composed entirely of residues near the C-terminus of the enzyme. The active site of HPPD has
4-Hydroxyphenylpyruvate dioxygenase
19713853
Under normal conditions, the full-length GSDMD is inactive as the linker loop between the N-terminal and C-terminal domains stabilises the overall conformation of the full-length protein and allows GSDMD-C to fold back on and auto-inhibit GSDMD-N from inducing pyroptosis. Upon interdomain cleavage by inflammatory caspases, the auto-inhibition is relieved and GSDMD-N cytotoxicity is triggered. GSDMD can be cleaved and activated by inflammatory caspases through both the canonical and non-canonical pyroptotic pathways. Caspase-1, conserved in vertebrates, is involved in the canonical pathway and is activated by canonical inflammasomes such as NLRP3 and NLRC4 inflammasomes, which are multi-protein complexes that are formed
GSDMD
1796203
intensely red. The corrin unit has six conjugated double bonds but is not conjugated all the way around its macrocycle ring. Conjugated systems form the basis of chromophores, which are light-absorbing parts of a molecule that can cause a compound to be colored. Such chromophores are often present in various organic compounds and sometimes present in polymers that are colored or glow in the dark. Chromophores often consist of a series of conjugated bonds and/or ring systems, commonly aromatic, which can include C–C, C=C, C=O, or N=N bonds. Conjugated chromophores are found in many organic compounds including azo dyes (also
Conjugated system
6891956
c from the mitochondria induces apoptosis by initiating the assembly of caspases, or proteins responsible for degrading the cell from within. Additionally, trichothecenes such as T-2, have also been shown to increase the c-Jun N-Terminal Kinase signaling pathway in cells. Here, c-Jun N-Terminal Kinase is able to increase to phosphorylation of its target, c-Jun, into its active form. Activated c-jun acts as a transcription factor in the cell nucleus for proteins important for facilitating the downstream apoptotic pathway. The trichothecene mycotoxins are toxic to humans, other mammals, birds, fish, a variety of invertebrates, plants, and eukaryotic cells. The specific toxicity
Trichothecene
18667665
the basis for the RNPs helical conformation. NP/N proteins are also vital for the transcription and replication of full-length RNA templates. The proper function of NP/N proteins rely on their capacity to oligomerize. This defines the ability of NP/N proteins to complex together to form larger structural elements. The oligomerization mechanism is unique between the nonsegmented NSV genome (nsNSV) and segmented NSV genome (sNSV). For nsNSVs, interactions occur between the protein monomers, while the stabilization of this complex occurs through inter-monomeric contact involving N-terminal and/or C-terminal protein extensions. This contributes to the viral RNP helical structure. Oligomerization for sNSVs has
Negative-sense single-stranded RNA virus
587347
of Euclid's Book V. In Definition 5 of Euclid's Book V we read: By using modern-day notation, this is clarified as follows. If we take four quantities: "a", "b", "c", and "d", then the first and second have a ratio formula_1; similarly the third and fourth have a ratio formula_2. Now to say that formula_3 we do the following: For any two arbitrary integers, "m" and "n", form the equimultiples "m"·"a" and "m"·"c" of the first and third; likewise form the equimultiples "n"·"b" and "n"·"d" of the second and fourth. If it happens that "m"·"a" > "n"·"b", then we must
Eudoxus of Cnidus
13270166
Dinitrogen difluoride Dinitrogen difluoride is a chemical compound with the formula NF. It is a gas at room temperature, and was first identified in 1952 as the thermal decomposition product of the azide NF. It has the structure F−N=N−F and exists in both a "cis"- and "trans"-form. The "cis" configuration lies in a C symmetry and the "trans"-form has a symmetry of C. These isomers are thermally interconvertible but can be separated by low temperature fractionation. The "trans"-form is less thermodynamically stable but can be stored in glass vessels. The "cis"-form attacks glass over a time scale of about 2
Dinitrogen difluoride
18623625
the edges of the corresponding faces. The integer binary quadratic form associated with this pair of faces is defined as The quadratic form is also defined as However, the former definition will be assumed in the sequel. Let the cube be formed by the integers "a", "b", "c", "d", "e", "f", "g", "h". The pairs of matrices associated with opposite edges are denoted by ("M", "N"), ("M", "N"), and ("M", "N"). The first rows of "M", "M" and "M" are respectively ["a" "b"], ["a" "c"] and ["a" "e"]. The opposite edges in the same face are the second rows. The
Bhargava cube
3971834
odd, these algebras are mixed by "α" (the linear map on "V" defined by ): and therefore isomorphic (since "α" is an automorphism). These two isomorphic algebras are each central simple and so, again, isomorphic to a matrix algebra over C. The sizes of the matrices can be determined from the fact that the dimension of Cℓ(C) is 2. What we have then is the following table: The even subalgebra of Cℓ(C) is (non-canonically) isomorphic to Cℓ(C). When "n" is even, the even subalgebra can be identified with the block diagonal matrices (when partitioned into 2×2 block matrix). When "n"
Classification of Clifford algebras
16171870
soot is produced from two high-purity graphite electrodes by igniting an arc discharge between them in an inert atmosphere (helium gas). Alternatively, soot is produced by laser ablation of graphite or pyrolysis of aromatic hydrocarbons. C, C and C are available commercially. In the table, N represents the number of possible isomers within the "isolated pentagon rule", which states that two pentagons in a fullerene should not share edges. Symmetry is specified for the most experimentally abundant form(s), and <nowiki>*</nowiki> marks symmetries with more than one chiral form. When C or C crystals are grown from toluene solution they have
Higher fullerenes
2927344
direction (because when a protein is translated from messenger RNA, it is created from N-terminus to C-terminus - amino acids are added to the carbonyl end). Each amino acid has an amine group and a carboxylic group. Amino acids link to one another by peptide bonds which form through a dehydration reaction that joins the carboxyl group of one amino acid to the amine group of the next in a head-to-tail manner to form a polypeptide chain. The chain has two ends – an amine group, the N-terminus, and an unbound carboxyl group, the C-terminus. When a protein is translated
N-terminus
6144347
addition, U("n") acts freely on EU("n"). The spaces "F"(C) and "G"(C) are CW-complexes. One can find a decomposition of these spaces into CW-complexes such that the decomposition of "F"(C), resp. "G"(C), is induced by restriction of the one for "F"(C), resp. "G"(C). Thus EU("n") (and also "G"(C)) is a CW-complex. By Whitehead Theorem and the above Lemma, EU("n") is contractible. Proposition: The cohomology of the classifying space "H*"(BU("n")) is a ring of polynomials in "n" variables "c", ..., "c" where "c" is of degree 2"p". Proof: Let us first consider the case "n" = 1. In this case, U(1) is
Classifying space for U(n)
13695875
for the product of the above two matrices as specified by the relevant equation in Heisenberg's 1925 paper is: Where:<br> A=p(n︎←n-a)*q(n-a︎←n-b)+p(n︎←n-b)*q(n-b︎←n-b)+p(n︎←n-c)*q(n-c︎←n-b)+... B=p(n-a︎←n-a)*q(n-a︎←n-c)+p(n-a︎←n-b)*q(n-b︎←n-c)+p(n-a︎←n-c)*q(n-c︎←n-c)+... C=p(n-b︎←n-a)*q(n-a︎←n-d)+p(n-b︎←n-b)*q(n-b︎←n-d)+p(n-b︎←n-c)*q(n-d︎←n-d)+... and so forth. If the matrices were reversed, the following values would result: A=q(n︎←n-a)*p(n-a︎←n-b)+q(n︎←n-b)*p(n-b︎←n-b)+q(n︎←n-c)*p(n-c︎←n-b)+...<br> B=q(n-a︎←n-a)*p(n-a︎←n-c)+q(n-a︎←n-b)*p(n-b︎←n-c)+q(n-a︎←n-c)*p(n-c︎←n-c)+...<br> C=q(n-b︎←n-a)*p(n-a︎←n-d)+q(n-b︎←n-b)*p(n-b︎←n-d)+q(n-b︎←n-c)*p(n-d︎←n-d)+... and so forth. Note how changing the order of multiplication changes the numbers, step by step, that are actually multiplied. https://arxiv.org/pdf/quant-ph/0404009v1 Direct download for Aitchison et al. on this subject. Heisenberg's entryway to matrix mechanics Werner Heisenberg contributed to science at a point when the old quantum physics was discovering a field littered with more and more stumbling blocks. He decided
Heisenberg's entryway to matrix mechanics
11074701
Homoserine is an intermediate in the biosynthesis of threonine, isoleucine, and methionine. The enzyme can be found in a monofunctional form, in some bacteria and yeast. Structural analysis of the yeast monofunctional enzyme indicates that the enzyme is a dimer composed of three distinct regions; an N-terminal nucleotide-binding domain, a short central dimerisation region, and a C-terminal catalytic domain. The N-terminal domain forms a modified Rossman fold, while the catalytic domain forms a novel alpha-beta mixed sheet. The enzyme can also be found in a bifunctional form consisting of an N-terminal aspartokinase domain and a C-terminal homoserine dehydrogenase domain, as
Homoserine dehydrogenase
9136402
herds normally direct courtship only toward members of the same race. The valid scientific names of each of the individual populations are not universally accepted, and some researchers still consider each species to be a subspecies. The taxonomic status of the various races is not fully resolved. "C. n. nigra" (nominate subspecies) "C. n. abingdoni" "C. n. becki" "C. n. chathamensis" "C. n. darwini" "C. n. duncanensis" "C. n. hoodensis" "C. n. phantastica" "C. n. porteri" "C. n. vicina" Chelonoidis nigra darwini | synonyms_ref= All species of Galápagos tortoises evolved from common ancestors that arrived from mainland South America by
Galápagos tortoise
14268560
interactions; namely, the π electrons of the croconate rings in one layer form weak bonds with those in the adjacent layers. In the anhydrous tetrabutylammonium salt the anions are separated by more than 12 Å and no π-stacking occurs. Croconate violet Croconate violet or 1,3-bis(dicyanomethylene)croconate is a divalent anion with chemical formula or ((N≡C−)C=)(CO). It is one of the pseudo-oxocarbon anions, as it can be described as a derivative of the croconate oxocarbon anion through the replacement of two oxygen atoms by dicyanomethylene groups =C(−C≡N). Its systematic name is 3,5-bis(dicyanomethylene)-1,2,4-trionate. The term croconate violet as a dye name specifically refers
Croconate violet
5228683
N,N'-Dicyclohexylcarbodiimide "N,N<nowiki>'</nowiki>"-Dicyclohexylcarbodiimide is an organic compound with the chemical formula (CHN)C. It is a waxy white solid with a sweet odor. It primary use is to couple amino acids during artificial peptide synthesis.The low melting point of this material allows it to be melted for easy handling. It is highly soluble in dichloromethane, tetrahydrofuran, acetonitrile and dimethylformamide, but insoluble in water. The compound is often abbreviated as DCC, DCCD or DCCI. The C-N=C=N-C core of carbodiimides (N=C=N) is linear, being related to the structure of allene. The molecule has idealized C symmetry. The N=C=N moiety gives characteristic IR spectroscopic signature
N,N'-Dicyclohexylcarbodiimide
5918369
Fubini–Study metric In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CP endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study. A Hermitian form in (the vector space) C defines a unitary subgroup U("n"+1) in GL("n"+1,C). A Fubini–Study metric is determined up to homothety (overall scaling) by invariance under such a U("n"+1) action; thus it is homogeneous. Equipped with a Fubini–Study metric, CP is a symmetric space. The particular normalization on the metric depends on the application. In
Fubini–Study metric
2131303
"m"("k") = (2 − "k") ("p" − 1) − "k" (for "k" > 0). It has also been shown that the prime number "p" divides "C" when the Jacobi symbol (2 | "p") is −1, and that "p" divides "C" when the Jacobi symbol (2 | "p") is +1. It is unknown whether there exists a prime number "p" such that "C" is also prime. Sometimes, a generalized Cullen number base "b" is defined to be a number of the form "n" × "b" + 1, where "n" + 2 > "b"; if a prime can be written in this
Cullen number
14423641
where syllable breaks fall, syllable requirements are also loosely construed in braille: they do not follow the rigid application of a dictionary. These cannot follow an apostrophe or hyphen. They cannot form independent words like *"ally" or *"less", nor can they occur at the beginning of a word like *"ancestor" or *"lesson". However, then can usually occur elsewhere: "c-ount, ar-ound". They may be used across syllables, as in "c-ance-r". is used for the suffix "-ess" after "n", though not after "en" or "in", as in "baroness (b-ar-o-ness)" and "lioness", but not in "chieftainess (ch-i-e-f-t-a-in-e-s-s)". "-full" does not use in order
English Braille
19554696
heated over 260° the color changes to green, and it melts at 273 °C. A dark blue oil, bis-("o"-tolyltriethylphosphonium) tetrabromonickelate (o-CHCHPEt)NiBr can be made from the reaction of "o"-tolyl bis-triethylphosphine, nickel bromide and "o"-tolyl bromide. (o-CHOCHPEt)NiBr and (CHPEt)NiBr are made in a similar way. bis-(benzo["e"]-1,3-dithiepan-2-diethylimmonium) tetrabromonickelate, abbreviated as (xdtc)NiBr, has dark blue crystals that melt at 166 °C. It is made from α,α'-dibromo-"o"-xylene and bis-("N,N"-diethyldithiocarbamato)nickel(II) dissolved in 1,2-dichloroethane. bis-(tetra-"n"-butylphosphonium) tetrabromonickelate can form as a glass when nickel bromide is dissolved in molten tetra-"n"-butylphosphonium iodide. Blue 1,1,1-trimethylhydrazinium tetrabromonickelate [HNN(CH)]NiBr is a salt stable between 70° and 260 °C. It can be
Tetrabromonickelate
1548683
as for some integer "k" and for "i" = −1, 0, 1, 2, 3, or 4; 2 divides ; and 3 divides . So, a more efficient method is to test if "n" is divisible by 2 or 3, then to check through all the numbers of form formula_2. This is 3 times as fast as testing all "m". Generalising further, it can be seen that all primes are of the form for where "c" and "k" are integers, c# represents c primorial, and "i" represents the numbers that are coprime to c#. For example, let . Then . All
Primality test
8837492
configuration. Thus any drawing of MLA appearing before Pelletier's 1981 paper will show the structure with the incorrect stereochemistry at C-1. [1α,4(S),6β,14α,16β]-20-Ethyl-1,6,14,16-tetramethoxy-4-[[[2-(3-methyl-2,5-dioxo-1-pyrrolidinyl)benzoyl]oxy]methyl]aconitane-7,8-diol; also referred to, incorrectly, as "N-methyl lycaconitine" in a few publications. MLA is soluble in [[chloroform]], but does not dissolve well in water. The free base of MLA has not been obtained in crystalline form, and in its amorphous form it melts ultimately at 128 °C; the [[hydriodide]] salt has a melting point of 201 °C.; the [[perchlorate]] salt melts at 195 °C The [[citrate]] salt is the most common form in which MLA is currently available commercially.
Methyllycaconitine
328524
− "k") "n"th powers. For example: There can also exist "n" − 1 positive integers whose "n"th powers sum to an "n"th power (though, by Fermat's last theorem, not for "n" = 3); these are counterexamples to Euler's sum of powers conjecture. The smallest known counterexamples are A Heronian triangle is commonly defined as one with integer sides whose area is also an integer, and we shall consider Heronian triangles with "distinct" integer sides. The lengths of the sides of such a triangle form a Heronian triple ("a, b, c") provided "a" < "b" < "c". Clearly, any Pythagorean triple
Pythagorean triple
1487043
distinct primes dividing "a", "b" and "c". Andrew Granville noticed that the minimum of the function formula_16 over formula_17 occurs when formula_18 This incited to propose a sharper form of the "abc" conjecture, namely: with "κ" an absolute constant. After some computational experiments he found that a value of formula_20 was admissible for "κ". This version is called "explicit "abc" conjecture". where Ω("n") is the total number of prime factors of "n" and where Θ("n") is the number of integers up to "n" divisible only by primes dividing "n". Let "k" = rad("abc"). They conjectured there is a constant "C"
Abc conjecture
2143981
is a unique prime of period "n" in base 2 if and only if there exists a natural number "c" such that The only known values of "n" such that formula_53 is composite but formula_54 is prime are 18, 20, 21, 54, 147, 342, 602, and 889 (in these case, formula_53 has a small factor which divides "n"). It is a conjecture that there is no other "n" with this property. All other known base 2 unique primes are of the form formula_53. In fact, no prime with "c" > 1 (that is formula_54 is a "true power" of "p")
Unique prime
20917141
containing one or two equivalents of NHSi-derived silicon. Alkenes and alkynes react with NHSis only if their C-C bond is highly polarized such as is the case with phenyltrimethylsilylacetylene, which produces a silicocyclopropene with one NHSi equivalent or a disilicocyclobutene with two. With ketones two equivalents of benzo-fused NHSi react to form disilyloxetanes as well as further reaction products depending on the carbon substituents. Dienes, as well as heterodienes including benzil or the common NHSi backbone N,N'-diterbutyl-1,4diazabutadiene ([tBuN-CH=CH-tBuN]) react in a [4+1] fashion to yield molecules with two five-membered rings sharing a single silicon atom. Imines do not form simple
N-heterocyclic silylene
4733089
"Why the hell have these idiots [politicians] given so little to us despite what we have done. For the money that the government has given us we [scientists] have done much more." In his defence Rao insisted that he merely talked about the "idiotic" way the politicians ignore investments for research funding in science. C. N. R. Rao Chintamani Nagesa Ramachandra Rao FRS, also known as C. N. R. Rao (born 30 June 1934), is an Indian chemist who has worked mainly in solid-state and structural chemistry. He currently serves as the Head of the Scientific Advisory Council to the
C. N. R. Rao
10388247
for interplanetary distances, proposing an alternative to the nowadays falsified Titius-bode "law". However, the predictions here are statistical and not deterministic as in Newtonian dynamics. In addition to being statistical, the scale relativistic law has a different theoretical form, and is more reliable than the original Titius-Bode version: The Titius-Bode "law" of planetary distance is of the form "a + b × c , with "a" = 0.4 AU, "b" = 0.3 AU and "c" = 2 in its original version. It is partly inconsistent — Mercury corresponds to "n" = −∞, Venus to "n" = 0, the Earth to
Scale relativity
6508961
the projective bundle of O("-n") and the curve "C" is the zero section. This curve has self-intersection number −"n", and is the only irreducible curve with negative self intersection number. The only irreducible curves with zero self intersection number are the fibers of the Hirzebruch surface (considered as a fiber bundle over P). The Picard group is generated by the curve "C" and one of the fibers, and these generators have intersection matrix so the bilinear form is two dimensional unimodular, and is even or odd depending on whether "n" is even or odd. The Hirzebruch surface Σ ("n" >
Hirzebruch surface
1835621
that is not an integer multiple of the characteristic of "F", then "A" is diagonalizable. Proof: If "A" is diagonalizable, then "A" is annihilated by some polynomial formula_1, which has no multiple root (since formula_2) and is divided by the minimal polynomial of "A". As a rule of thumb, over C almost every matrix is diagonalizable. More precisely: the set of complex "n"×"n" matrices that are "not" diagonalizable over C, considered as a subset of C, has Lebesgue measure zero. One can also say that the diagonalizable matrices form a dense subset with respect to the Zariski topology: the complement
Diagonalizable matrix
16864706
− 6 edges. Therefore, every 2-quasi-planar graph with "n" > 2 vertices has at most 3"n" − 6 edges. It has been conjectured by Pach et al. that every "k"-quasi-planar topological graph with "n" vertices has at most "c"("k")"n" edges, where "c"("k") is a constant depending only on "k". This conjecture is known to be true for "k" = 3 . It is also known to be true for "convex geometric graphs" (that is for geometric graphs whose vertices form the vertex set of a convex "n"-gon) , and for "k"-quasi-planar topological graphs whose edges are drawn as "x"-monotone curves,
Topological graph
3984300
5-combination at position 72. The successive values of formula_15 for "n" = 4, 5, 6, ... are 0, 1, 6, 21, 56, 126, 252, ..., of which the largest one not exceeding 72 is 56, for "n" = 8. Therefore "c" = 8, and the remaining elements form the 4-combination at position . The successive values of formula_16 for "n" = 3, 4, 5, ... are 0, 1, 5, 15, 35, ..., of which the largest one not exceeding 16 is 15, for "n" = 6, so "c" = 6. Continuing similarly to search for a 3-combination at position one
Combinatorial number system
19043121
Å, c=11.104 Å, α=β=90°, γ=120°, volume 618.5 Å, Z=24. ε-nitrogen has disordered orientation. In the phase diagram ε-N appears at pressures above 2 GPa at temperatures below 50 K. Below this the γ form is stable. When heated ε-N transforms to δ-N Above 69 GPa ε-N transforms to an orthorhombic phase designated by ζ-N with a 6% reduction in volume. The space group of ζ-N is "P"222. The lattice constants are a=4.159 Å, b=2.765 Å, c=5.039 Å with eight atoms per unit cell. At 80 GPa the distance between nitrogen atoms in the molecules is 0.982 Å, but the closest
Solid nitrogen
957609
that are orthogonal to n. Let "K" be a field of scalars. Let "A" be an "m" × "n" matrix, with column vectors v, v, ..., v. A linear combination of these vectors is any vector of the form where "c", "c", ..., "c" are scalars. The set of all possible linear combinations of v, ... ,v is called the column space of "A". That is, the column space of "A" is the span of the vectors v, ... , v. Any linear combination of the column vectors of a matrix "A" can be written as the product of "A"
Row and column spaces
483015
or "in standard form") if both its first row and its first column are in their natural order. For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C. Any Latin square can be reduced by permuting (that is, reordering) the rows and columns. Here switching the above matrix's second and third rows yields the following square: This Latin square is reduced; both its first row and its first column are alphabetically ordered A, B, C. If each entry of an "n" × "n" Latin square is written as
Latin square
6518421
with metal chlorates, perchlorates, nitrates, or nitrites can cause a violent explosion. At ambient temperature and ambient pressure, Hg(CN) takes the form of tetragonal crystals. These crystals are composed of nearly linear Hg(CN) molecules with a C-Hg-C bond angle of 175.0° and an Hg-C-N bond angle of 177.0° (Aylett gives slightly different values of 189° and 175°, respectively). Raman spectra show that the molecules distort at higher pressures. Between 16-20 kbar, the structure undergoes a phase transition as the Hg(II) center changes from 2- to 4-coordinate as the C"N" groups bind to neighboring Hg centers forming via Hg-N bonds. The
Mercury(II) cyanide