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172. Porous medium equation and fast diffusion equation as gradient systems
- Creator:
- Littig, Samuel and Voigt, Jürgen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, porous medium equation, gradient system, fast diffusion, asymptotic behaviour, order preservation, 13, and 51
- Language:
- English
- Description:
- We show that the Porous Medium Equation and the Fast Diffusion Equation, \dot u - \Delta {u^m} = f with m\in (0, \infty ), can be modeled as a gradient system in the Hilbert space H^{-1}(\Omega ), and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets \Omega \subset \mathbb{R}^{n} and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions., Samuel Littig, Jürgen Voigt., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
173. Principal blocks and p-radical groups
- Creator:
- Hu, Xiaohan and Zeng, Jiwen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, matematické výpočty, mathematics, mathematical calculations, principal block, p-radical group, p-radical block, 13, and 51
- Language:
- English
- Description:
- Let G be a finite group and k a field of characteristic p > 0. In this paper, we obtain several equivalent conditions to determine whether the principal block B0 of a finite p-solvable group G is p-radical, which means that B0 has the property that e0(kP)G is semisimple as a kG-module, where P is a Sylow p-subgroup of G, kP is the trivial kP-module, (kP)G is the induced module, and e0 is the block idempotent of B0. We also give the complete classification of a finite p-solvable group G which has not more than three simple B0-modules where B0 is p-radical., Xiaohan Hu, Jiwen Zeng., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
174. Product spaces generated by bilinear maps and duality
- Creator:
- Sánchez Pérez, Enrique A
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, Banach space, product, multiplication operator, duality, Banach function space, Hadamard product, Lipschitz map, integration, vector measure, 13, and 51
- Language:
- English
- Description:
- In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise products of Banach function spaces, spaces of integrable functions with respect to vector measures, spaces of operators, multipliers on Banach spaces of analytic functions and spaces of Lipschitz functions., Enrique A. Sánchez Pérez., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
175. Pseudo almost periodicity of fractional integro-differential equations with impulsive effects in Banach spaces
- Creator:
- Xia, Zhinan
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, hustota pravděpodobnosti, impulsive fractional integro-differential equation, pseudo almost periodicity, probability density, fractional powers of operator, 13, and 51
- Language:
- English
- Description:
- In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic PC-mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic PC-mild solution of a two-dimensional impulsive fractional predator-prey system with diffusion are investigated., Zhinan Xia., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
176. Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform
- Creator:
- Atia, Mohamed Jalel and Thabet, Faouzi
- Format:
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- Type:
- model:article and TEXT
- Subject:
- matematika, kvadratické formy, diferenciální algebra, mathematics, quadratic forms, differential algebra, algebraic equation, Cauchy transform, quadratic differential, 13, and 51
- Language:
- English
- Description:
- We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z − a)(z − b)×(z − c)−2 dz2. More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs., Mohamed Jalel Atia, Faouzi Thabet., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
177. Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs
- Creator:
- Das, Kinkar Ch and Liu, Muhuo
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, spectral radius, (signless) Laplacian spectral radius, clique number, 13, and 51
- Language:
- English
- Description:
- n this paper, the upper and lower bounds for the quotient of spectral radius (Laplacian spectral radius, signless Laplacian spectral radius) and the clique number together with the corresponding extremal graphs in the class of connected graphs with n vertices and clique number ω(2 ≤ ω ≤ n) are determined. As a consequence of our results, two conjectures given in Aouchiche (2006) and Hansen (2010) are proved., Kinkar Ch. Das, Muhuo Liu., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
178. 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
179. 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
180. 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