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81.
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf(xkv(y)k-1)dwK(k)= Φ g(x)h(y), x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d'Alembert's and Wilson's equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc. 相似文献
82.
Samir Kallel 《Potential Analysis》2014,41(1):143-169
In this work we consider the Dunkl operator on the real line, defined by $$ {\cal D}_kf(x):=f'(x)+k\dfrac{f(x)-f(-x)}{x},\,\,k\geq0. $$ We define and study Dunkl–Sobolev spaces \(L^p_{n,k}(\mathbb{R})\) , Dunkl–Sobolev spaces \({\cal L}^p_{\alpha,k}(\mathbb{R})\) of positive fractional order and generalized Dunkl–Lipschitz spaces \(\wedge^k_{\alpha,p,q}(\mathbb{R})\) . We provide characterizations of these spaces and we give some connection between them. 相似文献
83.
9-Membered rings are readily constructed through a radical addition-cyclisation sequence on a 1,6-dien-3-ol system followed by a Grob-type fragmentation. 相似文献
84.
Peter Boutillier Béatrice Quiclet-Sire Syeda Nahid Zafar Samir Z. Zard 《Tetrahedron: Asymmetry》2010,21(13-14):1649-1665
The radical addition-transfer of S-(2-fluoro-phenacyl)xanthates can be used to construct rapidly benzothiepinones, including libraries of complex aza-bridged derivatives, and highly functionalized 2,3-dihydrothieno[2,3-b]thiopyran-4-ones. 相似文献
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86.
Samir D. Mathur 《General Relativity and Gravitation》2010,42(10):2331-2336
Are there any degrees of freedom on the black hole horizon? Using the ‘membrane paradigm’ we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need ‘real’ degrees of freedom at the horizon, which can modify Hawking’s evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom. 相似文献
87.
Samir Kumar Bhowmik 《Applied mathematics and computation》2010,217(8):4217-4226
A model partial integro-differential operator (PIDO) that contains both local and nonlocal diffusion operators is considered in this article. This type of operators come in modeling various scientific and financial engineering problems. In most cases, people use finite difference schemes to generate solutions of such model problems. We compare and analyze stability and accuracy of two such finite difference schemes. We first present a discrete analogue of the PIDO and then approximate the semi-discrete time dependent problem using two different one step methods and show the stability conditions and the accuracy of the schemes. We use the Fourier transforms throughout our analysis. 相似文献
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