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51. Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center

Creator:
Bin, Ren and Zhu, Lin Sheng
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print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, related set, basis, derivation, 13, and 51
Language:
English
Description:
A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$. 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center., Ren Bin, Zhu Lin Sheng., and Obsahuje bibliografii
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52. Classification of rings with toroidal Jacobson graph

Creator:
Selvakumar, Krishnan and Subajini, Manoharan
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Type:
model:article and TEXT
Subject:
matematika, grafy funkcí, mathematics, graphs of functions, planar graph, genus of a graph, local ring, nilpotent element, Jacobson graph, 13, and 51
Language:
English
Description:
Let R be a commutative ring with nonzero identity and J(R) the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is defined as the graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface Sn. In this paper, we investigate the genus number of the compact Riemann surface in which JR can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that JR is toroidal., Krishnan Selvakumar, Manoharan Subajini., and Obsahuje seznam literatury
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53. Coalescing Fiedler and core vertices

Creator:
Ali, Didar A, Baptist Gauci, John, Sciriha, Irene, and Sharaf, Khidir R
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, nullity, core vertex, Fiedler vertex, cut-vertices, coalescence, 13, and 51
Language:
English
Description:
The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique type in the coalescence. Moreover, the nullity of subgraphs obtained by perturbations of the coalescence G is determined relative to the nullity of G. This has direct applications in spectral graph theory as well as in the construction of certain ipso-connected nano-molecular insulators., Didar A. Ali, John Baptist Gauci, Irene Sciriha, Khidir R. Sharaf., and Obsahuje seznam literatury
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54. Cofiniteness and finiteness of local cohomology modules over regular local rings

Creator:
A'zami, Jafar and Pourreza, Naser
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Type:
model:article and TEXT
Subject:
matematika, mathematics, regular ring, cofinite module, Cohen-Macaulay ring, Krull dimension, local cohomology, 13, and 51
Language:
English
Description:
Let $(R,\mathfrak m)$ be a commutative Noetherian regular local ring of dimension $d$ and $I$ be a proper ideal of $R$ such that ${\rm mAss}_R(R/I)={\rm Assh}_R(I)$. It is shown that the $R$-module $H^{{\rm ht}(I)}_I(R)$ is $I$-cofinite if and only if ${\rm cd}(I,R)={\rm ht}(I)$. Also we present a sufficient condition under which this condition the $R$-module $H^i_I(R)$ is finitely generated if and only if it vanishes., Jafar A'zami, Naser Pourreza., and Obsahuje bibliografické odkazy
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55. Commutators of Marcinkiewicz integrals on Herz spaces with variable exponent

Creator:
Wang, Hongbin
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Type:
model:article and TEXT
Subject:
matematika, integrály, mathematics, integrals, Herz space, variable exponent, commutator, Marcinkiewicz integral, 13, and 51
Language:
English
Description:
Let \Omega \in L^{s}\left ( S^{n-1} \right ) for s\geqslant 1 be a homogeneous function of degree zero and b a BMO function. The commutator generated by the Marcinkiewicz integral μΩ and b is defined by \left[ {b,{\mu _\Omega }} \right](f)(x) = {\left( {\int_0^\infty {{{\left| {\int_{\left| {x - y} \right| \leqslant t} {\frac{{\Omega (x - y)}}{{{{\left| {x - y} \right|}^{n - 1}}}}\left[ {b(x) - b(y)} \right]f(y){\text{d}}y} } \right|}^2}\frac{{{\text{d}}t}}{{{t^3}}}} } \right)^{1/2}}. In this paper, the author proves the \left (L^{p\left ( \cdot \right )}\left ( \mathbb{R}^{n} \right ),L^{p\left ( \cdot \right )}\left ( \mathbb{R}^{n} \right ) \right )-boundedness of the Marcinkiewicz integral operator μΩ and its commutator [b, μΩ ] when p(·) satisfies some conditions. Moreover, the author obtains the corresponding result about μΩ and [b, μΩ ] on Herz spaces with variable exponent., Hongbin Wang., and Obsahuje seznam literatury
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56. Computing the determinantal representations of hyperbolic forms

Creator:
Ming-Chih Chien and Nakazato, Hiroshi
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, determinantal representation, hyperbolic form, Riemann theta function, numerical range, 13, and 51
Language:
English
Description:
The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1. We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0, 1, and present an elementary computation of the reformulation. Several examples are provided for computing the real symmetric matrices using the reformulation., Mao-Ting Chien, Hiroshi Nakazato., and Obsahuje seznam literatury
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57. Concentration-compactness principle for embedding into multiple exponential spaces on unbounded domains

Creator:
Černý, Robert
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, Sobolev space, Orlicz-Sobolev space, Moser-Trudinger inequality, sharp constant, concentration-compactness principle, 13, and 51
Language:
English
Description:
Let Ω \subset \mathbb{R}^{n} be a domain and let α < n − 1. We prove the Concentration-Compactness Principle for the embedding of the space W_{0}^{1}L^{n} log^{\alpha } L(Ω) into an Orlicz space corresponding to a Young function which behaves like (t^{n/n-1-\alpha }) for large t. We also give the result for the embedding into multiple exponential spaces. Our main result is Theorem 1.6 where we show that if one passes to unbounded domains, then, after the usual modification of the integrand in the Moser functional, the statement of the Concentration-Compactnes Principle is very similar to the statement in the case of a bounded domain. In particular, in the case of a nontrivial weak limit the borderline exponent is still given by the formula P: = \left( {1 - \left\| {\Phi (|\nabla u|)} \right\|_{L^1 (\mathbb{R}^n )} } \right)^{ - 1/(n - 1)} ., Robert Černý., and Obsahuje seznam literatury
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58. Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

Creator:
Cioabă, Sebastian M and Gu, Xiaofeng
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, spectral graph theorye, igenvalue, connectivity, toughness, spanning k-tree, 13, and 51
Language:
English
Description:
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree., Sebastian M. Cioabă, Xiaofeng Gu., and Obsahuje seznam literatury
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59. Convergence of Rump’s method for computing the Moore-Penrose inverse

Creator:
Chen, Yunkun, Shi, Xinghua, and Wei, Yimin
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Moore-Penrose inverse, condition number, ill-conditioned matrix, 13, and 51
Language:
English
Description:
We extend Rump’s verified method (S.Oishi, K.Tanabe, T.Ogita, S.M.Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse., Yunkun Chen, Xinghua Shi, Yimin Wei., and Obsahuje seznam literatury
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60. Copies of lnp’S uniformly in the spaces 2(C[0,1],X) and 1(C[0,1],X)

Creator:
Popa, Dumitru
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Type:
model:article and TEXT
Subject:
matematika, mathematics, average, multiplication operator, p-summing linear operators, copies of ln p’s uniformly, local structure of a Banach space, 13, and 51
Language:
English
Description:
We study the presence of copies of ln p ’s uniformly in the spaces 2(C[0, 1],X) and 1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite- dimensional Banach space, then 2(C[0, 1],X) contains p2-uniformly copies of ln∞’s and 1(C[0, 1],X) contains -uniformly copies of ln 2 ’s for all > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces 2(C[0, 1],X) and 1(C[0, 1],X) are distinct, extending the well-known result that the spaces 2(C[0, 1],X) and N(C[0, 1],X) are distinct., Dumitru Popa., and Seznam literatury
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