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  • 1
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    Stochastic evolution equations driven by Liouville fractional Brownian motion (2012)
    Springer
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    Publication Date: 2012-03-27
    Description:    Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of ℒ( H,E )-valued functions with respect to H -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 〈 β 〈 1. For 0 〈 β 〈 ½ we show that a function Φ: (0, T ) → ℒ( H,E ) is stochastically integrable with respect to an H -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H -cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations dU ( t ) = AU ( t ) dt + B dW H b ( t ) driven by an H -cylindrical Liouville fractional Brownian motion, and prove existence, uniqueness and space-time regularity of mild solutions under various assumptions on the Banach space E , the operators A : D ( A ) → E and B : H → E , and the Hurst parameter. As an application it is shown that second-order parabolic SPDEs on bounded domains in ℝ d , driven by space-time noise which is white in space and Liouville fractional in time, admit a mild solution if ¼ d 〈 β 〈 1. Content Type Journal Article Pages 1-27 DOI 10.1007/s10587-012-0011-z Authors Zdzisław Brzeźniak, Department of Mathematics, University of York, York, YO10 5DD UK Jan van Neerven, Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands Donna Salopek, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 1
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 2
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    Underlying lie algebras of quadratic Novikov algebras (2012)
    Springer
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    Publication Date: 2012-02-11
    Description:    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension 10. Content Type Journal Article Pages 323-328 DOI 10.1007/s10587-011-0077-z Authors Zhiqi Chen, School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071 P.R.China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 61 Journal Issue Volume 61, Number 2
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    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 3
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    The structure of digraphs associated with the congruence xk ≡ y (mod n) (2012)
    Springer
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    Publication Date: 2012-02-11
    Description:    We assign to each pair of positive integers n and k ⩾ 2 a digraph G ( n , k ) whose set of vertices is H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a k ≡ b (mod n ). We investigate the structure of G ( n , k ). In particular, upper bounds are given for the longest cycle in G ( n , k ). We find subdigraphs of G ( n , k ), called fundamental constituents of G ( n , k ), for which all trees attached to cycle vertices are isomorphic. Content Type Journal Article Pages 337-358 DOI 10.1007/s10587-011-0079-x Authors Lawrence Somer, Department of Mathematics, Catholic University of America, Washington, D.C. 20064, USA Michal Křížek, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Prague 1, Czech Republic Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 61 Journal Issue Volume 61, Number 2
    Print ISSN: 0011-4642
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    Topics: Mathematics
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  • 4
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    Bounds for the (Laplacian) spectral radius of graphs with parameter α (2012)
    Springer
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    Publication Date: 2012-10-16
    Description:    Let G be a simple connected graph of order n with degree sequence ( d 1 , d 2 , …, d n ). Denote ( α t ) i = Σ j : i ∼ j d j α , ( α m ) i = ( α t ) i / d i α and ( α N ) i = Σ j : i ∼ j ( α t ) j , where α is a real number. Denote by λ 1 ( G ) and µ 1 ( G ) the spectral radius of the adjacency matrix and the Laplacian matrix of G , respectively. In this paper, we present some upper and lower bounds of λ 1 ( G ) and µ 1 ( G ) in terms of ( α t ) i , ( α m ) i and ( α N ) i . Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results. Content Type Journal Article Pages 567-580 DOI 10.1007/s10587-012-0030-9 Authors Gui-Xian Tian, College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004 P.R.China Ting-Zhu Huang, School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731 P.R.China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 2
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    Topics: Mathematics
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  • 5
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    On the completeness of the system in C0(E) (2012)
    Springer
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    Publication Date: 2012-10-16
    Description:    Let E = ¥ È n = 1   I n be the union of infinitely many disjoint closed intervals where In = [ a n , b n ], 0 〈 a 1 〈 b 1 〈 a 2 〈 b 2 〈 … 〈 b n 〈 …, lim n ® ¥   b n = ∞. Let α ( t ) be a nonnegative function and { l n } n = 1 ¥ a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system { t l n log m n t } in C 0 ( E ) is obtained where C 0 ( E ) is the weighted Banach space consists of complex functions continuous on E with f ( t )e − α ( t ) vanishing at infinity. Content Type Journal Article Pages 361-379 DOI 10.1007/s10587-012-0035-4 Authors Xiangdong Yang, Department of Mathematics, Kunming University of Science and Technology, 650093 Kunming, China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 2
    Print ISSN: 0011-4642
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    Topics: Mathematics
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  • 6
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    Definability for equational theories of commutative groupoids (2012)
    Springer
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    Publication Date: 2012-10-16
    Description:    We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms. Content Type Journal Article Pages 305-333 DOI 10.1007/s10587-012-0032-7 Authors Jaroslav Ježek, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75 Praha 8, Czech Republic Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 2
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    Topics: Mathematics
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  • 7
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    Weighted endpoint estimates for commutators of multilinear fractional integral operators (2012)
    Springer
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    Publication Date: 2012-10-16
    Description:    Let m be a positive integer, 0 〈 α 〈 mn , ® b   = ( b 1 , …, b m ) ε BMO m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators I a b ® to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373. Content Type Journal Article Pages 347-359 DOI 10.1007/s10587-012-0034-5 Authors Xuefang Yan, College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024 P.R.China Limei Xue, College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024 P.R.China Wenming Li, College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024 P.R.China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 2
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    Topics: Mathematics
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  • 8
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    A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially Sr,s-graphic (2012)
    Springer
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    Publication Date: 2012-10-20
    Description:    The split graph K r + K s   on r + s vertices is denoted by S r,s . A non-increasing sequence π = ( d 1 , d 2 , …, d n ) of nonnegative integers is said to be potentially S r,s -graphic if there exists a realization of π containing S r,s as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for π to be potentially S r,s -graphic. They are extensions of two theorems due to A.R.Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series 4 (1979), 251–267 and An Erdős-Gallai type result on the clique number of a realization of a degree sequence, unpublished). Content Type Journal Article Pages 863-867 DOI 10.1007/s10587-012-0051-4 Authors Jian-Hua Yin, Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228 P.R. China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 3
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    Topics: Mathematics
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  • 9
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    Differences of weighted composition operators from hardy space to weighted-type spaces on the unit ball (2012)
    Springer
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    Publication Date: 2012-10-20
    Description:    In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of ℂ N , and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindström and E. Wolf: Essential norm of the difference of weighted composition operators. Monatsh. Math. 153 (2008), 133–143. Content Type Journal Article Pages 695-708 DOI 10.1007/s10587-012-0040-7 Authors Ze-Hua Zhou, Department of Mathematics, Tianjin University, Tianjin, 300072 P.R. China Yu-Xia Liang, Department of Mathematics, Tianjin University, Tianjin, 300072 P.R. China Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 62 Journal Issue Volume 62, Number 3
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    Topics: Mathematics
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  • 10
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    Affine connections on almost para-cosymplectic manifolds (2011)
    Springer
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    Publication Date: 2011-11-01
    Description:    Identities for the curvature tensor of the Levi-Civita connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established. Content Type Journal Article Pages 863-871 DOI 10.1007/s10587-011-0033-y Authors Adara M. Blaga, Timişoara, România Journal Czechoslovak Mathematical Journal Online ISSN 1572-9141 Print ISSN 0011-4642 Journal Volume Volume 61 Journal Issue Volume 61, Number 3
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    Topics: Mathematics
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