共查询到20条相似文献,搜索用时 31 毫秒
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《Indagationes Mathematicae》2022,33(2):494-516
Current work defines Schmidt representation of a bilinear operator , where and are separable Hilbert spaces. Introducing the concept of singular value and ordered singular value, we prove that if is compact, and its singular values are ordered, then has a Schmidt representation on real Hilbert spaces. We prove that the hypothesis of existence of ordered singular values is fundamental. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(5):106921
We prove the existence of Hall polynomials for -bounded invariant subspaces of nilpotent linear operators. 相似文献
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Jesse Geneson 《Discrete Mathematics》2019,342(5):1489-1491
Permutations of the positive integers avoiding arithmetic progressions of length 5 were constructed in Davis et al. (1977), implying the existence of permutations of the integers avoiding arithmetic progressions of length 7. We construct a permutation of the integers avoiding arithmetic progressions of length 6. We also prove a lower bound of on the lower density of subsets of positive integers that can be permuted to avoid arithmetic progressions of length 4, sharpening the lower bound of from LeSaulnier and Vijay (2011). 相似文献
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We define additive G-codes over finite fields. We prove that if C is an additive G-code over with duality M then its dual with respect to this duality is an additive G-code. We prove that if M and are two dualities, then and are equivalent codes. Finally, we study the existence of self-dual codes for a variety of dualities and relate them to formally self-dual and linear self-dual codes. 相似文献
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In this paper, we study the generalized Abreu equation on a Delzant ploytope and prove the existence of metrics with prescribed scalar curvatures of homogeneous toric bundles under the assumption of an appropriate stability. 相似文献
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This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but ) nonlinearities. 相似文献
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《Expositiones Mathematicae》2022,40(4):1181-1228
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《Discrete Mathematics》2022,345(11):113036
Let G be a cyclically 5-connected cubic graph with a 5-edge-cut separating G into two cyclic components and . We prove that each component can be completed to a cyclically 5-connected cubic graph by adding three vertices, unless is a cycle of length five. Our work extends similar results by Andersen et al. for cyclic connectivity 4 from 1988. 相似文献
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Benedetta Ferrario Margherita Zanella 《Stochastic Processes and their Applications》2019,129(5):1568-1604
We consider the two dimensional Navier–Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and colored in space. First, we prove existence and uniqueness of a weak (in the Walsh sense) solution process
and we show that, if the initial vorticity is continuous in space, then there exists a space–time continuous version of the solution. In addition we show that the solution (evaluated at fixed points in time and space) is locally differentiable in the Malliavin calculus sense and that its image law is absolutely continuous with respect to the Lebesgue measure on . 相似文献
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We consider a generalisation of a conjecture by Patterson and Wiedemann from 1983 on the Hamming distance of a function from to to the set of affine functions from to . We prove the conjecture for each q such that the characteristic of lies in a subset of the primes with density 1 and we prove the conjecture for all q by assuming the generalised Riemann hypothesis. Roughly speaking, we show the existence of functions for which the distance to the affine functions is maximised when n tends to infinity. This also determines the asymptotic behaviour of the covering radius of the Reed-Muller code over and so answers a question raised by Leducq in 2013. Our results extend the case , which was recently proved by the author and which corresponds to the original conjecture by Patterson and Wiedemann. Our proof combines evaluations of Gauss sums in the semiprimitive case, probabilistic arguments, and methods from discrepancy theory. 相似文献
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An important problem on almost perfect nonlinear (APN) functions is the existence of APN permutations on even-degree extensions of larger than 6. Browning et al. (2010) gave the first known example of an APN permutation on the degree-6 extension of . The APN permutation is CCZ-equivalent to the previously known quadratic Kim κ-function (Browning et al. (2009)). Aside from the computer based CCZ-inequivalence results on known APN functions on even-degree extensions of with extension degrees less than 12, no theoretical CCZ-inequivalence result on infinite families is known. In this paper, we show that Gold and Kasami APN functions are not CCZ-equivalent to permutations on infinitely many even-degree extensions of . In the Gold case, we show that Gold APN functions are not equivalent to permutations on any even-degree extension of , whereas in the Kasami case we are able to prove inequivalence results for every doubly-even-degree extension of . 相似文献
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Huffman (2013) [12] studied -linear codes over and he proved the MacWilliams identity for these codes with respect to ordinary and Hermitian trace inner products. Let S be a finite commutative -algebra. An -linear code over S of length n is an -submodule of . In this paper, we study -linear codes over S. We obtain some bounds on minimum distance of these codes, and some large classes of MDR codes are introduced. We generalize the ordinary and Hermitian trace products over -algebras and we prove the MacWilliams identity with respect to the generalized form. In particular, we obtain Huffman's results on the MacWilliams identity. Among other results, we give a theory to construct a class of quantum codes and the structure of -linear codes over finite commutative graded -algebras. 相似文献
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Kreweras conjectured that every perfect matching of a hypercube for can be extended to a hamiltonian cycle of . Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of for can be extended to two or more hamiltonian cycles of . In this paper, we prove that every perfect matching of for can be extended to at least different hamiltonian cycles of . 相似文献
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Bhargav Bhatt 《Journal of Pure and Applied Algebra》2019,223(5):1940-1945
Given a commutative ring A and a finitely generated ideal I, we prove that -torsion A-modules that are also I-adically complete (or merely derived I-complete) must have bounded -torsion, i.e., they are killed by for some . 相似文献