共查询到20条相似文献,搜索用时 15 毫秒
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We prove that every hesitant fuzzy set on a set E can be considered either a soft set over the universe or a soft set over the universe E. Concerning converse relationships, for denumerable universes we prove that any soft set can be considered even a fuzzy set. Relatedly, we demonstrate that every hesitant fuzzy soft set can be identified with a soft set, thus a formal coincidence of both notions is brought to light. Coupled with known relationships, our results prove that interval type-2 fuzzy sets and interval-valued fuzzy sets can be considered as soft sets over the universe . Altogether we contribute to a more complete understanding of the relationships among various theories that capture vagueness and imprecision. 相似文献
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Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) . This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space . The quality of the spectral approximation and the choice of the parameter c when approximating a function in by its truncated PSWFs series expansion, are the main issues. By considering a function as the restriction to of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples. 相似文献
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Fritz Gesztesy Lance L. Littlejohn Isaac Michael Richard Wellman 《Journal of Differential Equations》2018,264(4):2761-2801
In 1961, Birman proved a sequence of inequalities , for , valid for functions in . In particular, is the classical (integral) Hardy inequality and is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space of functions defined on . Moreover, implies ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite , these inequalities hold on the standard Sobolev space . Furthermore, in all cases, the Birman constants in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in (resp., ). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail. 相似文献
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Xiangfeng Yang 《Journal of Mathematical Analysis and Applications》2018,457(1):694-721
Let be the probability measures on of suitable Markov processes (possibly with small jumps) depending on a small parameter , where denotes the space of all functions on which are right continuous with left limits. In this paper we investigate asymptotic expansions for the Laplace transforms as for smooth functionals F on . This study not only recovers several well-known results, but more importantly provides new expansions for jump Markov processes. Besides several standard tools such as exponential change of measures and Taylor's expansions, the novelty of the proof is to implement the expectation asymptotic expansions on normal deviations which were recently derived in [13]. 相似文献
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Elisha Falbel 《Comptes Rendus Mathematique》2005,340(7):503-506
We propose a general method of constructing spherical CR manifolds by gluing tetrahedra adapted to CR geometry. We obtain spherical CR structures on the complement of the figure eight knot and the Whitehead link complement with holonomy in and respectively (the same integer rings appearing in real hyperbolic geometry). To cite this article: E. Falbel, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Georgij M. Kobelkov 《Comptes Rendus Mathematique》2006,343(4):283-286
For the 3D system of equations describing large-scale ocean dynamics in the Cartesian coordinate system existence and uniqueness of a solution on an arbitrary time interval is proved and the norm is shown to be continuous in time on . To cite this article: G.M. Kobelkov, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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