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172. Random walk centrality and a partition of Kemeny’s constant
- Creator:
- Kirkland, Steve
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, stochastic matrix, random walk centrality, Kemeny’s constant, 13, and 51
- Language:
- English
- Description:
- We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny’s constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time to the state in question, and two in terms of the transition matrix associated with the Markov chain. Several bounds are provided on the accessibility index in terms of the eigenvalues of the transition matrix and the stationary vector, and the bounds are shown to be tight. The behaviour of the accessibility index under perturbation of the transition matrix is investigated, and examples exhibiting some counter-intuitive behaviour are presented. Finally, we characterize the situation in which the accessibility indices for all states coincide., Steve Kirkland., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
173. Rank decomposition in zero pattern matrix algebras
- Creator:
- Bart, Harm, Ehrhardt, Torsten, and Bernd Silbermann
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, block upper triangularity, additive decomposition, rank constraints, zero pattern matrix algebra, preorder, partial order, Hasse diagram, rooted tree, out-tree, in-tree, 13, and 51
- Language:
- English
- Description:
- For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H.Bart, A.P.M.Wagelmans (2000). The proof involves elements from integer programming and employs Farkas’ lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred to above can be extended to other zero pattern matrix algebras. It is shown that such a generalization does indeed hold for certain digraphs determining the pattern of zeros. The digraphs in question can be characterized in terms of forests, i.e., disjoint unions of rooted trees., Harm Bart, Torsten Ehrhardt, Bernd Silbermann., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
174. Rational realization of the minimum ranks of nonnegative sign pattern matrices
- Creator:
- Fang, Wei, Gao, Wei, Gao, Yubin, Gong, Fei, Jing, Guangming, Li, Zhongshan, Shao, Yanling, and Zhang, Lihua
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, sign pattern (matrix), nonnegative sign pattern, minimum rank, convex polytope, rational minimum rank, rational realization, integer matrix, condensed sign pattern, point-hyperplane configuration, 13, and 51
- Language:
- English
- Description:
- A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set {+,−, 0} ({+, 0}, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix A is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of A. Using a correspondence between sign patterns with minimum rank r ≥ 2 and point-hyperplane configurations in Rr−1 and Steinitz’s theorem on the rational realizability of 3-polytopes, it is shown that for every nonnegative sign pattern of minimum rank at most 4, the minimum rank and the rational minimum rank are equal. But there are nonnegative sign patterns with minimum rank 5 whose rational minimum rank is greater than 5. It is established that every d-polytope determines a nonnegative sign pattern with minimum rank d + 1 that has a (d + 1) × (d + 1) triangular submatrix with all diagonal entries positive. It is also shown that there are at most min{3m, 3n} zero entries in any condensed nonnegative m × n sign pattern of minimum rank 3. Some bounds on the entries of some integer matrices achieving the minimum ranks of nonnegative sign patterns with minimum rank 3 or 4 are established., Wei Fang, Wei Gao, Yubin Gao, Fei Gong, Guangming Jing, Zhongshan Li, Yanling Shao, Lihua Zhang., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
175. Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting restricted normal Jacobi operators
- Creator:
- Hwang, Doo Hyun, Pak, Eunmi, and Woo, Changhwa
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, real hypersurface, complex hyperbolic two-plane Grassmannians, Hopf hypersurface, shape operator, Ricci tensor, normal Jacobi operator, commuting condition, 13, and 51
- Language:
- English
- Description:
- We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians ${\rm SU}_{2,m}/S(U_2{\cdot}U_m)$ with commuting conditions between the restricted normal Jacobi operator $\overline{R}_N\phi$ and the shape operator $A$ (or the Ricci tensor $S$)., Doo Hyun Hwang, Eunmi Pak, Changhwa Woo., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
176. Regularly weakly based modules over right perfect rings and Dedekind domains
- Creator:
- Hrbek, Michal and Růžička, Pavel
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, weak basis, regularly weakly based ring, Dedekind domain, perfect ring, 13, and 51
- Language:
- English
- Description:
- A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains., Michal Hrbek, Pavel Růžička., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
177. Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths
- Creator:
- Kim, Byoung Soo and Hyun Cho, Dong
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- integrály, integrals, analogue of Wiener space, analytic conditional Feynman integral, change of scale formula, conditional Wiener integral, Wiener integral, 13, and 51
- Language:
- English
- Description:
- Let $C[0,t]$ denote a generalized Wiener space, the space of real-valued continuous functions on the interval $[0,t]$, and define a random vector $Z_n C[0,t]\to\mathbb R^{n+1}$ by Z_n(x)=\biggl(x(0)+a(0), \int_0^{t_1}h(s) {\rm d} x(s)+x(0)+a(t_1), \cdots,\int_0^{t_n}h(s) {\rm d} x(s)+x(0)+a(t_n)\biggr), where $a\in C[0,t]$, $h\in L_2[0,t]$, and $0<t_1 < \cdots< t_n\le t$ is a partition of $[0,t]$. Using simple formulas for generalized conditional Wiener integrals, given $Z_n$ we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions $F$ in a Banach algebra which corresponds to Cameron-Storvick's Banach algebra $\mathcal S$. Finally, we express the generalized analytic conditional Feynman integral of $F$ as a limit of the non-conditional generalized Wiener integral of a polygonal function using a change of scale transformation for which a normal density is the kernel. This result extends the existing change of scale formulas on the classical Wiener space, abstract Wiener space and the analogue of the Wiener space $C[0,t]$., Byoung Soo Kim, Dong Hyun Cho., and Obsahuje bibliografické odkazy
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
178. Relative Gorenstein injective covers with respect to a semidualizing module
- Creator:
- Tavasoli, Elham and Salimi, Maryam
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, semidualizing module, Gc-flat module, Gc-injective module, cover, envelope, 13, and 51
- Language:
- English
- Description:
- Let R be a commutative Noetherian ring and let C be a semidualizing R-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every Gc-injective module G, the character module G+ is Gc-flat, then the class GIc(R) Ac(R) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class GIc(R) Ac(R) is covering., Elham Tavasoli, Maryam Salimi., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
179. Remarks on D-integral complete multipartite graphs
- Creator:
- Pavol Híc and Milan Pokorný
- Format:
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- Type:
- model:article and TEXT
- Subject:
- integrál, matice (matematika), mathematics, integrals, matrices, distance spectrum integral graph distance integral graph complete multipartite graph, integral graph, distance integral graph, complete multipartite graph, 13, and 51
- Language:
- English
- Description:
- A graph is called distance integral (or D-integral) if all eigenvalues of its distance matrix are integers. In their study of D-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on D-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs {K_{{p_1},{p_2},{p_3}}} with p1 < p2 < p3, and {K_{{p_1},{p_2},{p_3},{p_4}}} with p1 < p2 < p3 < p4, as well as the infinite classes of distance integral complete multipartite graphs {K_{{a_1}{p_1},{a_2}{p_2},...,{a_s}{p_s}}} with s = 5, 6., Pavel Híc, Milan Pokorný., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
180. Remarks on the behaviour of higher-order derivations on the gluing of differential spaces
- Creator:
- Drachal, Krzysztof
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, gluing of differential space, higher-order differential geometry, Sikorski differential space, 13, and 51
- Language:
- English
- Description:
- This paper is about some geometric properties of the gluing of order k in the category of Sikorski differential spaces, where k is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour of kth order tangent spaces, their dimensions, and other geometric properties, are described in the context of the process of gluing differential spaces. At the end some examples are given. The paper is self-consistent, i.e., a short review of the differential spaces theory is presented at the beginning., Krzysztof Drachal., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public