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In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields and of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each , then and are isometric and isomorphic. More generally, for , there is depending only on the ramification indices of and such that any homomorphism from the -th residue ring of to the -th residue ring of can be lifted to a homomorphism between the valuation rings. Moreover, we get a functor from the category of certain principal Artinian local rings of length n to the category of certain complete discrete valuation rings of mixed characteristic with perfect residue fields, which naturally generalizes the functorial property of unramified complete discrete valuation rings. Our lifting result improves Basarab's relative completeness theorem for finitely ramified henselian valued fields, which solves a question posed by Basarab, in the case of perfect residue fields. 相似文献
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The -additive codes are subgroups of , and can be seen as linear codes over when , -additive codes when , or -additive codes when . A -linear generalized Hadamard (GH) code is a GH code over which is the Gray map image of a -additive code. Recursive constructions of -additive GH codes of type with are known. In this paper, we generalize some known results for -linear GH codes with to any prime when , and then we compare them with the ones obtained when . First, we show for which types the corresponding -linear GH codes are nonlinear over . Then, for these codes, we compute the kernel and its dimension, which allow us to classify them completely. Moreover, by computing the rank of some of these codes, we show that, unlike -linear Hadamard codes, the -linear GH codes are not included in the family of -linear GH codes with when prime. Indeed, there are some families with infinite nonlinear -linear GH codes, where the codes are not equivalent to any -linear GH code with . 相似文献
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In the two disjoint shortest paths problem ( 2-DSPP), the input is a graph (or a digraph) and its vertex pairs and , and the objective is to find two vertex-disjoint paths and such that is a shortest path from to for , if they exist. In this paper, we give a first polynomial-time algorithm for the undirected version of the 2-DSPP with an arbitrary non-negative edge length function. 相似文献
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《Journal of Pure and Applied Algebra》2019,223(11):4583-4591
Marks showed that , the group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256. Furthermore, it is shown that although is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo. 相似文献
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A graph is -colorable if it admits a vertex partition into a graph with maximum degree at most and a graph with maximum degree at most . We show that every -free planar graph is -colorable. We also show that deciding whether a -free planar graph is -colorable is NP-complete. 相似文献
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The tensor product of graphs , and is defined by and Let be the fractional chromatic number of a graph . In this paper, we prove that if one of the three graphs , and is a circular clique, 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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In this paper, we prove the uniqueness of certain Fourier-Jacobi models for the split exceptional group over finite fields with odd characteristic. Similar results are also proved for and . 相似文献
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《Discrete Mathematics》2022,345(11):113059
Let be the finite field of q elements and let be the dihedral group of 2n elements. Left ideals of the group algebra are known as left dihedral codes over of length 2n, and abbreviated as left -codes. Let . In this paper, we give an explicit representation for the Euclidean hull of every left -code over . On this basis, we determine all distinct Euclidean LCD codes and Euclidean self-orthogonal codes which are left -codes over . In particular, we provide an explicit representation and a precise enumeration for these two subclasses of left -codes and self-dual left -codes, respectively. Moreover, we give a direct and simple method for determining the encoder (generator matrix) of any left -code over , and present several numerical examples to illustrative our applications. 相似文献
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We study standing waves of NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices Kirchhoff boundary conditions are imposed. The configuration of the graph is characterized by two lengths, and . We study the solutions with possibly nontrivial components on the half-lines and a cnoidal component on the circle. The problem is equivalent to a nonlinear boundary value problem in which the boundary condition depends on the spectral parameter ω. After classifying the solutions with rational , we turn to irrational showing that there exist standing waves only in correspondence to a countable set of negative frequencies . Moreover we show that the frequency sequence admits cluster points and any negative real number can be a limit point of frequencies choosing a suitable irrational geometry . These results depend on basic properties of diophantine approximation of real numbers. 相似文献
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