共查询到20条相似文献,搜索用时 15 毫秒
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Cheng Gong 《代数通讯》2020,48(2):724-732
AbstractIn this article, we give a new upper bound for the Mordell–Weil rank of a surface fibration and we prove an analog result in positive characteristic. 相似文献
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Ya. N. Shitov 《Moscow University Mathematics Bulletin》2011,66(5):227-229
We present an example of a 6 × 6 matrix A such that rk t (A) = 4, rk K (A) = 5. This disproves the conjecture formulated by M. Chan, A. Jensen, and E. Rubei. 相似文献
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Let K be a field of characteristic p > 0, let L be a restricted Lie algebra and let R be an associative K-algebra. It is shown that the various constructions in the literature of crossed product of R with u(L) are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials. 相似文献
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Murray R. Bremner 《Linear and Multilinear Algebra》2013,61(8):921-932
We use the representation theory of Lie algebras and computational linear algebra to determine the simplest non-constant invariant polynomial in the entries of a general 2?×?2?×?3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients ±1, ±2 in the 12 indeterminates x ijk where i, j?=?1,?2 and k?=?1,?2,?3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2?×?2?×?2 arrays. 相似文献
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We compare the isoperimetric profiles of and of with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of and . Explicitly we show that and . We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions. 相似文献
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Takayuki Morisawa 《Journal of Number Theory》2013,133(6):1814-1826
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Let G be a finite abelian group. The Erd?s-Ginzburg-Ziv constant s(G) of G is defined as the smallest integer l∈N such that every sequence S over G of length |S|?l has a zero-sum subsequence T of length |T|=exp(G). If G has rank at most two, then the precise value of s(G) is known (for cyclic groups this is the theorem of Erd?s-Ginzburg-Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form , with n,r∈N and n?2, and we tackle the study of s(G) with a new approach, combining the direct problem with the associated inverse problem. 相似文献
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Carla D. Martin 《Linear and Multilinear Algebra》2013,61(8):943-950
As computing power increases, many more problems in engineering and data analysis involve computation with tensors, or multi-way data arrays. Most applications involve computing a decomposition of a tensor into a linear combination of rank-1 tensors. Ideally, the decomposition involves a minimal number of terms, i.e. computation of the rank of the tensor. Tensor rank is not a straight-forward extension of matrix rank. A constructive proof based on an eigenvalue criterion is provided that shows when a 2?×?2?×?2 tensor over ? is rank-3 and when it is rank-2. The results are extended to show that n?×?n?×?2 tensors over ? have maximum possible rank n?+?k where k is the number of complex conjugate eigenvalue pairs of the matrices forming the two faces of the tensor cube. 相似文献
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Kris Coolsaet 《Designs, Codes and Cryptography》2013,68(1-3):179-194
As a first step in the classification of nonsingular 2×2×2×2 hypercubes up to equivalence, we resolve the case where the base field is finite and the hypercubes can be written as a product of two 2×2×2 hypercubes. (Nonsingular hypercubes were introduced by D. Knuth in the context of semifields. Where semifields are related to hypercubes of dimension 3, this paper considers the next case, i.e., hypercubes of dimension 4.) We define the notion of ij-rank (with 1 ≤ i < j ≤ 4) and prove that a hypercube is the product of two 2×2×2 hypercubes if and only if its 12-rank is at most 2. We derive a ‘standard form’ for nonsingular 2×2×2×2 hypercubes of 12-rank less than 4 as a first step in the classification of such hypercubes up to equivalence. Our main result states that the equivalence class of a nonsingular 2×2×2×2 hypercube M of 12-rank 2 depends only on the value of an invariant δ 0(M) which derives in a natural way from the Cayley hyperdeterminant det0 M and another polynomial invariant det M of degree 4. As a corollary we prove that the number of equivalence classes is (q + 1)/2 or q/2 depending on whether the order q of the field is odd or even. 相似文献
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In this paper,we give a classification of real rank zero C*-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C. 相似文献
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Ya. N. Shitov 《Journal of Mathematical Sciences》2013,193(5):802-808
We consider the rank functions of matrices over semirings, functions that generalize the classical notion of the rank of a matrix over a field. We study semirings over which the factor and Gondran–Minoux ranks of any matrix coincide. It is shown that every semiring satisfying that condition is a subsemiring of a field. We provide an example of an integral domain over which the factor and Gondran–Minoux ranks are different. 相似文献
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We show the existence of a non-constant gap between the communication complexity of a function and the logarithm of the rank of its input matrix. We consider the following problem: each of two players gets a perfect matching between twon-element sets of vertices. Their goal is to decide whether or not the union of the two matcliings forms a Hamiltonian cycle. We prove:
- The rank of the input matrix over the reals for this problem is 2 O(n) .
- The non-deterministic communication complexity of the problem is Ω(nloglogn).
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The border rank of a nondegenerate m×n×(mn−q) tensor over the complex field is mn−q provided that q⩽max(m,n). 相似文献
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L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1969-1975
The lower bound
l1 (A) - ln (A) \geqslant 2||A12 ||\lambda _1 (A) - \lambda _n (A) \geqslant 2\parallel A_{12} \parallel 相似文献
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