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951.
On the number of transversals in Cayley tables of cyclic groups 总被引:1,自引:0,他引:1
It is well known that if n is even, the addition table for the integers modulo n (which we denote by Bn) possesses no transversals. We show that if n is odd, then the number of transversals in Bn is at least exponential in n. Equivalently, for odd n, the number of diagonally cyclic latin squares of order n, the number of complete mappings or orthomorphisms of the cyclic group of order n, the number of magic juggling sequences of period n and the number of placements of n non-attacking semi-queens on an n×n toroidal chessboard are at least exponential in n. For all large n we show that there is a latin square of order n with at least (3.246)n transversals.We diagnose all possible sizes for the intersection of two transversals in Bn and use this result to complete the spectrum of possible sizes of homogeneous latin bitrades.We also briefly explore potential applications of our results in constructing random mutually orthogonal latin squares. 相似文献
952.
Ioannis Konstantinos Argyros José Antonio Ezquerro Miguel Ángel Hernández-Verón Young Ik Kim Ángel Alberto Magreñán 《Mathematical Methods in the Applied Sciences》2020,43(14):8042-8050
In this paper, we propose a center Lipschitz condition for the second derivative together with the use of restricted domains in order to improve the starting points for Newton's method when compared with previous results. Moreover, we present some numerical examples validating the theoretical results. 相似文献
953.
Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to Cn ? {0}. The authors show that there exists a line bundle L over X such that E ? L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π?(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E. 相似文献
954.
Two graphs are said to be -cospectral (respectively, -cospectral) if they have the same (respectively, signless) Laplacian spectra, and a graph is said to be (respectively, ) if there does not exist other non-isomorphic graph such that and are -cospectral (respectively, -cospectral). Let be the degree sequence of a graph with vertices. In this paper, we prove that except for two exceptions (respectively, the graphs with ), if is -cospectral (respectively, -cospectral) with a connected graph and , then has the same degree sequence as . A spider graph is a unicyclic graph obtained by attaching some paths to a common vertex of the cycle. As an application of our result, we show that every spider graph and its complement graph are both , which extends the corresponding results of Haemers et al. (2008), Liu et al. (2011), Zhang et al. (2009) and Yu et al. (2014). 相似文献
955.
This paper considers a degree sum condition sufficient to imply the existence of vertex-disjoint cycles in a graph . For an integer , let be the smallest sum of degrees of independent vertices of . We prove that if has order at least and , with , then contains vertex-disjoint cycles. We also show that the degree sum condition on is sharp and conjecture a degree sum condition on sufficient to imply contains vertex-disjoint cycles for . 相似文献
956.
The conservative number of a graph is the minimum positive integer , such that admits an orientation and a labeling of its edges by distinct integers in , such that at each vertex of degree at least three, the sum of the labels on the in-coming edges is equal to the sum of the labels on the out-going edges. A graph is conservative if . It is worth noting that determining whether certain biregular graphs are conservative is equivalent to find integer Heffter arrays.In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size is for , , and otherwise. Consequently, given positive integers , , …, with for , we construct a cyclic -cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic -cycle system of the complete graph , where . Also, we prove necessary and sufficient conditions for the existence of a cyclic -cycle system of , where is a 1-factor. Furthermore, we give a sufficient condition for a subset of to be sequenceable. 相似文献
957.
本文研究一类带Poisson跳的倒向随机微分方程。在方程的系数满足非增长条件和非Lipschitz条件下,讨论方程适应解的存在唯一性和稳定性。为了证明解的存在性,首先通过函数变换,构造出一逼近序列,然后运用推广的Bihari不等式和Lebesgue控制收敛定理证明该逼近序列是收敛的,得到逼近序列的极限就是方程的适应解。解的唯一性和稳定性主要运用了Bihari不等式和推广的Bihari不等式来进行证明。 相似文献
958.
959.
研究了一类适应随机变量序列的局部收敛性,推广了文献[1]中的结论.并在假定部分和序列为极限鞅时,得到了极限鞅的强极限定理.最后给出了*-mixing序列的强大数定律. 相似文献
960.
刘朝霞 《数学物理学报(B辑英文版)》2010,30(1):55-64
Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces. 相似文献