共查询到20条相似文献,搜索用时 31 毫秒
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《Journal of Mathematical Analysis and Applications》2014,419(2):783-795
We study restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the Stein–Tomas restriction result can be improved to the estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in dimensions. 相似文献
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Given , a compact connected Riemannian manifold of dimension , with boundary ?M, we consider an initial boundary value problem for a fractional diffusion equation on , , with time-fractional Caputo derivative of order . We prove uniqueness in the inverse problem of determining the smooth manifold (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ?M at fixed time. In the “flat” case where M is a compact subset of , two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation on are recovered simultaneously. 相似文献
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Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality , where ω is the width of the numerical range of . Some related inequalities and a reverse Lidskii majorization are given. 相似文献
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A Steiner 2- trade is a pair of disjoint partial Steiner triple systems, each on the same set of points, such that each pair of points occurs in if and only if it occurs in . A Steiner 2- trade is called d-homogeneous if each point occurs in exactly d blocks of (or ). In this paper we construct minimal d-homogeneous Steiner 2- trades of foundation and volume for sufficiently large values of . (Specifically, if is divisible by 3 and otherwise.) 相似文献
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Jianbei An Heiko Dietrich Shih-Chang Huang 《Journal of Pure and Applied Algebra》2018,222(12):4020-4039
We consider the finite exceptional group of Lie type (universal version) with , where and . We classify, up to conjugacy, all maximal-proper 3-local subgroups of G, that is, all 3-local which are maximal with respect to inclusion among all proper subgroups of G which are 3-local. To this end, we also determine, up to conjugacy, all elementary-abelian 3-subgroups containing , all extraspecial subgroups containing , and all cyclic groups of order 9 containing . These classifications are an important first step towards a classification of the 3-radical subgroups of G, which play a crucial role in many open conjectures in modular representation theory. 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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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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We investigate the following problem posed by Cabello Sanchéz, Castillo, Kalton, and Yost:Let K be a nonmetrizable compact space. Does there exist a nontrivial twisted sum of and , i.e., does there exist a Banach space X containing a non-complemented copy Y of such that the quotient space is isomorphic to ?Using additional set-theoretic assumptions we give the first examples of compact spaces K providing a negative answer to this question. We show that under Martin's axiom and the negation of the continuum hypothesis, if either K is the Cantor cube or K is a separable scattered compact space of height 3 and weight , then every twisted sum of and is trivial.We also construct nontrivial twisted sums of and for K belonging to several classes of compacta. Our main tool is an investigation of pairs of compact spaces which do not admit an extension operator . 相似文献
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Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 相似文献
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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