共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, we prove the energy conservation for the weak solutions of the three-dimensional ideal inhomogeneous magnetohydrodynamic (MHD) equations in a bounded domain. Two types of sufficient conditions on the regularity of the weak solutions are provided to ensure the energy conservation. Due to the presence of the boundary, we need to impose the boundedness in and the continuity in for the velocity and magnetic fields near the boundary. 相似文献
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In this paper we introduce a concept of “regulated function” of two variables, which reduces to the classical definition when v is independent of t. We then consider a scalar conservation law of the form , where F is smooth and v is a regulated function, possibly discontinuous w.r.t. both t and x. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved, relying on comparison estimates for solutions to the corresponding Hamilton–Jacobi equation.As an application, we obtain the existence and uniqueness of solutions for a class of triangular systems of conservation laws with hyperbolic degeneracy. 相似文献
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Lukas Prader 《Journal of Pure and Applied Algebra》2019,223(6):2371-2381
Let R be an affine domain of characteristic zero with finite quotients. We prove that a polynomial map over R is surjective if and only if it is surjective over , the completion of R with respect to , for every maximal ideal . In fact, the completions may be replaced by arbitrary subrings containing R. We use this result to yield a characterization of surjective polynomial maps, and remark that there does not exist a similar principle for injective polynomial maps. 相似文献
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《Discrete Mathematics》2022,345(11):113021
In 2007, Andrews and Paule published the eleventh paper in their series on MacMahon's partition analysis, with a particular focus on broken k-diamond partitions. On the way to broken k-diamond partitions, Andrews and Paule introduced the idea of k-elongated partition diamonds. Recently, Andrews and Paule revisited the topic of k-elongated partition diamonds. Using partition analysis and the Omega operator, they proved that the generating function for the partition numbers produced by summing the links of k-elongated plane partition diamonds of length n is given by for each . A significant portion of their recent paper involves proving several congruence properties satisfied by and , using modular forms as their primary proof tool. In this work, our goal is to extend some of the results proven by Andrews and Paule in their recent paper by proving infinitely many congruence properties satisfied by the functions for an infinite set of values of k. The proof techniques employed are all elementary, relying on generating function manipulations and classical q-series results. 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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Jian Wang 《Comptes Rendus Mathematique》2019,357(3):284-290
The goal of this paper is to investigate the topological structure of open simply connected 3-manifolds whose scalar curvature has a slow decay at infinity. In particular, we show that the Whitehead manifold does not admit a complete metric whose scalar curvature decays slowly, and in fact that any contractible complete 3-manifolds with such a metric is diffeomorphic to . Furthermore, using this result, we prove that any open simply connected 3-manifold M with and a complete metric as above is diffeomorphic to . 相似文献
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We consider the pseudo-Euclidean space , , with coordinates and metric , , where at least one is positive, and also tensors of the form , such that are differentiable functions of x. For such tensors, we use Lie point symmetries to find metrics that solve the Ricci curvature and the Einstein equations. We provide a large class of group-invariant solutions and examples of complete metrics defined globally in . As consequences, for certain functions , we show complete metrics , conformal to the pseudo-Euclidean metric g, whose scalar curvature is . 相似文献
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《Journal of Pure and Applied Algebra》2023,227(2):107189
For the Schur superalgebra over a ground field K of characteristic zero, we define the symmetrizer of the ordered pairs of tableaux of the shape λ. We show that the K-span of all symmetrizers has a basis consisting of for and semistandard. In particular, if and only if λ is an -hook partition. In this case, the S-superbimodule is identified as , where and are left and right irreducible S-supermodules of the highest weight λ.We define modified symmetrizers and show that their -span forms a -form of . We show that every modified symmetrizer is a -linear combination of modified symmetrizers for semistandard. Using modular reduction to a field K of characteristic , we obtain that has a basis consisting of modified symmetrizers for and semistandard. 相似文献
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We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold . We first assume the pull back Weitzenböck operator of bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when is the space form. 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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Christian Bosse 《Discrete Mathematics》2019,342(12):111595
The Hadwiger number of a graph , denoted , is the largest integer such that contains as a minor. A famous conjecture due to Hadwiger in 1943 states that for every graph , , where denotes the chromatic number of . Let denote the independence number of . A graph is -free if it does not contain the graph as an induced subgraph. In 2003, Plummer, Stiebitz and Toft proved that for all -free graphs with , where is any graph on four vertices with , , or is a particular graph on seven vertices. In 2010, Kriesell subsequently generalized the statement to include all forbidden subgraphs on five vertices with . In this note, we prove that for all -free graphs with , where denotes the wheel on six vertices. 相似文献
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