共查询到20条相似文献,搜索用时 15 毫秒
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Jagjit Singh Matharu Mohammad Sal Moslehian Jaspal Singh Aujla 《Linear algebra and its applications》2011,435(2):270-276
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr’s inequality due to Vasi? and Ke?ki?. 相似文献
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Mohammad Sal Moslehian 《Linear algebra and its applications》2011,434(8):1981-1987
We establish several operator versions of the classical Aczél inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the unital positive linear maps on C*-algebras and the unitarily invariant norms on matrices are presented. 相似文献
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Three schemes for shuffling a deck ofn cards are studied, each involving a random choice from [n]
n
. The shuffles favor some permutations over others sincen! does not dividen
n
. The probabilities that the shuffles lead to some simple permutations, for instance cycles left and right and the identity, are calculated. Some inequalities are obtained which lead to information about the least and most likely permutations. Numbers of combinatorial interest occur, notably the Catalan numbers and the Bell numbers. 相似文献
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L. L. Helms 《Acta Appl Math》1984,2(3-4):379-390
Methods of constructing semigroups of operators describing interacting particle systems are reviewed. A simple proof is given showing the existence of semigroups of operators on the space of bounded Borel measurable functions for nonnegative continuous attractive spin rates along with a proof of the existence of invariant measures for the semigroups so constructed. 相似文献
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Jan-Christoph Schlage-Puchta 《Archiv der Mathematik》2008,90(2):140-143
We show that an almost trivial inequality between the first and second moment and the maximal value of a random variable can
be used to slightly improve deep theorems.
Received: 25 November 2006 相似文献
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Bounds for entries of matrix functions based on Gauss-type quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, subgraph centrality, communicability) that describe properties of networks. 相似文献
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In this paper an application of the recently introduced pre-Lie Magnus expansion to Jackson’s q-integral and q-exponentials is presented. Twisted dendriform algebras, which are the natural algebraic framework for Jackson’s q-analogs, are introduced for that purpose. It is shown how the pre-Lie Magnus expansion is used to solve linear q-differential equations. We also briefly outline the theory of linear equations in twisted dendriform algebras. 相似文献
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B.G. Pittel 《Stochastic Processes and their Applications》1980,10(1):33-48
Let X1,X2,… be i.i.d. random variables with a continuous distribution function. Let R0=0, Rk=min{j>Rk?1, such that Xj>Xj+1}, k?1. We prove that all finite-dimensional distributions of a process , converge to those of the standard Brownian motion. 相似文献
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The authors give a condensed proof of the existence of Room squares for positive odd sides except 3 and 5. Some areas of current research on Room squares are also discussed.Aequationes Mathematicae launches a systematic program of expository papers. We will endeavour to publish at least one in every volume. 相似文献
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Summary We consider a walk from a stateA
1 to a stateA
n+1 in which the probability of remaining atA
i
isp
i
, and the probability of progressing fromA
i
toA
i+1 is 1 –p
i
. The probabilityW
nk
of reachingA
n+1 fromA
1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp
1,,p
n
. We determine the maximum value ofW
nk
and the (unique) choice (p
1,,p
n
) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday 相似文献
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A family of variable metric proximal methods 总被引:5,自引:0,他引:5
J. F. Bonnans J. Ch. Gilbert C. Lemaréchal C. A. Sagastizábal 《Mathematical Programming》1995,68(1-3):15-47
We consider conceptual optimization methods combining two ideas: the Moreau—Yosida regularization in convex analysis, and quasi-Newton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasi-Newton updates of the objective function itself. Also, we obtain a globally and superlinearly convergent BFGS proximal method. At each step of our study, we single out the assumptions that are useful to derive the result concerned. 相似文献
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Janusz Matkowski 《Aequationes Mathematicae》1992,43(1):106-112
Summary Leta (0, 1/2] be fixed. A functionf satisfying the inequalityf(ax + (1 – a)y) + f((1 – a)x + ay) f(x) + f(y), called herea-Wright convexity, appears in connection with the converse of Minkowski's inequality. We prove that every lower semicontinuousa-Wright convex function is Jensen convex and we pose an open problem. Moreover, using the fact that 1/2-Wright convexity coincides with Jensen convexity, we prove a converse of Minkowski's inequality without any regularity conditions. 相似文献
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Ivo Klemeš 《Linear algebra and its applications》2007,422(1):164-185
We study determinant inequalities for certain Toeplitz-like matrices over C. For fixed n and N ? 1, let Q be the n × (n + N − 1) zero-one Toeplitz matrix with Qij = 1 for 0 ? j − i ? N − 1 and Qij = 0 otherwise. We prove that det(QQ∗) is the minimum of det(RR∗) over all complex matrices R with the same dimensions as Q satisfying ∣Rij∣ ? 1 whenever Qij = 1 and Rij = 0 otherwise. Although R has a Toeplitz-like band structure, it is not required to be actually Toeplitz. Our proof involves Alexandrov’s inequality for polarized determinants and its generalizations. This problem is motivated by Littlewood’s conjecture on the minimum 1-norm of N-term exponential sums on the unit circle. We also discuss polarized Bazin-Reiss-Picquet identities, some connections with k-tree enumeration, and analogous conjectured inequalities for the elementary symmetric functions of QQ∗. 相似文献
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Aequationes mathematicae - 相似文献
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Let Ωm be the set of partitions, ω, of a finite m-element set; induce a uniform probability distribution on Ωm, and define Xms(ω) as the number of s-element subsets in ω. We alow the existence of an integer-valued function n=n(m)(t), t?[0, 1], and centering constants bms, 0?s? m, such that converges to the ‘Brownian Bridge’ process in terms of its finite-dimensional distributions. 相似文献
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Shaun Cooper 《Journal of Number Theory》2003,103(2):135-162
Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p,