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Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: In this paper, the authors offer new inequalities for differentiable-convex functions, which are connected with Hermite-Hadamard integralinequality, and apply these inequalities to special means of two positivenumbers.
Abstract: In the paper, the authors offer some new inequalities for differentiableconvex functions, which are connected with Hermite-Hadamard integralinequality, and apply these inequalities to special means of two positivenumbers.
28 citations
TL;DR: In this article, the Hermite-Hadamard type inequal-ities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established.
Abstract: Some new results related of the left-hand side of the Hermite-Hadamard type inequal- ities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established. Also, some applications to special means of real numbers are provided. 2010 Mathematics Subject Classification: 26A51; 26D07; 26D10; 26D15
28 citations
11 Jul 2005
TL;DR: An analogue of the Hadamard property of matrices for tensors in multiple dimensions is defined and it is shown that any k-party communication problem represented by a hadamard tensor must have Ω(n/2k) multiparty communication complexity.
Abstract: We develop a new method for estimating the discrepancy of tensors associated with multiparty communication problems in the “Number on the Forehead” model of Chandra, Furst and Lipton. We define an analogue of the Hadamard property of matrices for tensors in multiple dimensions and show that any k-party communication problem represented by a Hadamard tensor must have Ω(n/2k) multiparty communication complexity. We also exhibit constructions of Hadamard tensors, giving Ω(n/2k) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.
28 citations
TL;DR: In this paper, a power series with Hadamard gaps is considered, and it is shown to be convergent in |z| with respect to the power series in |Z|.
Abstract: Let be a power series with Hadamard gaps,
convergent in |z|
28 citations
TL;DR: In this paper, the stability and logarithmic decay of the solutions to fractional differential equations (FDEs) are studied and the asymptotic expansions of Mittag–Leffler function are discussed.
Abstract: In this paper, we study the stability and logarithmic decay of the solutions to fractional differential equations (FDEs). Both linear and nonlinear cases are included. And the fractional derivative is in the sense of Hadamard or Caputo–Hadamard with order $$\alpha \,(0<\alpha <1)$$
. The solutions can be expressed by Mittag–Leffler functions through applying the modified Laplace transform. In view of the asymptotic expansions of Mittag–Leffler function, we discuss the stability and logarithmic decay of the solution to FDEs in great detail.
28 citations