共查询到20条相似文献,搜索用时 31 毫秒
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Elena Angelini Francesco Galuppi Massimiliano Mella Giorgio Ottaviani 《Journal of Pure and Applied Algebra》2018,222(4):950-965
We prove that a general polynomial vector in three homogeneous variables of degrees has a unique Waring decomposition of rank 7. This is the first new case we are aware of, and likely the last one, after five examples known since the 19th century and the binary case. We prove that there are no identifiable cases among pairs in three homogeneous variables of degree , unless , and we give a lower bound on the number of decompositions. The new example was discovered with Numerical Algebraic Geometry, while its proof needs Nonabelian Apolarity. 相似文献
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Mohammad Daher 《Comptes Rendus Mathematique》2017,355(5):549-552
According to a previous result of the author, if is an interpolation couple, if is weakly LUR, then the complex interpolation spaces have the same property.Here we construct an interpolation couple where is LUR, but where the complex interpolation spaces are not strictly convex. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(4):1062-1078
This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator–prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists satisfying for , such that if and , then the diffusion can create nonconstant positive steady-state solutions; whereas the diffusion cannot do provided . 相似文献
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Liangchen Wang Chunlai Mu Xuegang Hu Pan Zheng 《Journal of Differential Equations》2018,264(5):3369-3401
This paper deals with a two-competing-species chemotaxis system with consumption of chemoattractantunder homogeneous Neumann boundary conditions in a bounded domain () with smooth boundary, where the initial data and are non-negative and the parameters , , and . The chemotactic function () is smooth and satisfying some conditions. It is proved that the corresponding initial–boundary value problem possesses a unique global bounded classical solution if one of the following cases hold: for ,(i) and(ii) .Moreover, we prove asymptotic stabilization of solutions in the sense that:? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution algebraically converge to as . 相似文献
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Let e be a positive integer, p be an odd prime, , and be the finite field of q elements. Let . The graph is a bipartite graph with vertex partitions and , and edges defined as follows: a vertex is adjacent to a vertex if and only if and . If and , the graph contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs containing no cycles of length less than eight and not isomorphic to the graph , even without requiring them to be edge-transitive. So far, no such graphs have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture. 相似文献
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Sunghyu Han Jon-Lark Kim Heisook Lee Yoonjin Lee 《Finite Fields and Their Applications》2012,18(3):613-633
There is a one-to-one correspondence between ?-quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every ?-quasi-cyclic self-dual code of length m? over a finite field can be obtained by the building-up construction, provided that or , m is a prime p, and q is a primitive element of . We determine possible weight enumerators of a binary ?-quasi-cyclic self-dual code of length p? (with p a prime) in terms of divisibility by p. We improve the result of Bonnecaze et al. (2003) [3] by constructing new binary cubic (i.e., ?-quasi-cyclic codes of length 3?) optimal self-dual codes of lengths (Type I), 54 and 66. We also find quasi-cyclic optimal self-dual codes of lengths 40, 50, and 60. When , we obtain a new 8-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . When , we find a new 4-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . 相似文献
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TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献
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Huyuan Chen Patricio Felmer Jianfu Yang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(3):729-750
In this paper, we study the elliptic problem with Dirac mass
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where , , , is the Dirac mass at the origin and the potential V is locally Lipchitz continuous in , with non-empty support and satisfying with , and . We obtain two positive solutions of (1) with additional conditions for parameters on , p and k. The first solution is a minimal positive solution and the second solution is constructed via Mountain Pass Theorem. 相似文献
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