On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.     

几类积图的团染色数

设G=（VE）为简单图,V和E分别表示图的点集和边集．图G的一个k-团染色是指点集V到色集{1,2,…,k）的一个映射,使得G的每个至少含两个点的极大团都至少有两种颜色．分别给出了任意两个图的团色数与它们通过笛卡尔积、Kronecker积、强直积或字典积运算后得到的积图的团色数之间的关系．     

矩阵乘法的推广及运用

利用矩阵的Kronecker积定义了一种矩阵乘积"*积",并且对这种乘积的性质进行了研究,发现它对于任意两个矩阵都有意义而且具有通常矩阵乘积的所有性质,并且在一些特殊情况下它比通常的矩阵乘积更和谐对称,而且当在"合适维数"下它就是通常的矩阵乘积,所以可以把这种"*积"看作是对通常矩阵乘积的推广.     

Additive multiplicative increasing functions on nonnegative square matrices and multidigraphs

It is known that if f is a multiplicative increasing function on , then either f(n)=0 for all or f(n)=n for some 0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we first study the multiplicative increasing functions over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopless multidigraphs.     

域上的线性变换

本文主要获得了任意域上的可逆线性变换群形如（1．1）的分解，是对有限域上的结果的推广。     

On well-dominated direct,Cartesian and strong product graphs

If each minimal dominating set in a graph is a minimum dominating set, then the graph is called well-dominated. Since the seminal paper on well-dominated graphs appeared in 1988, the structure of well-dominated graphs from several restricted classes has been studied. In this paper we give a complete characterization of nontrivial direct products that are well-dominated. We prove that if a strong product is well-dominated, then both of its factors are well-dominated. When one of the factors of a strong product is a complete graph, the other factor being well-dominated is also a sufficient condition for the product to be well-dominated. Our main result gives a complete characterization of well-dominated Cartesian products in which at least one of the factors is a complete graph. In addition, we conjecture that this result is actually a complete characterization of the class of nontrivial, well-dominated Cartesian products.     

Henstock-Kurzweil and McShane product integration; Descriptive definitions

The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function A is absolutely continuous. As a consequence we obtain that the McShane product integral of A over [a, b] exists and is invertible if and only if A is Bochner integrable on [a, b]. Supported by grant No. 201/04/0690 of the Grant Agency of the Czech Republic.     

Further inequalities involving the Khatri-Rao product

Styan [G.P.H. Styan, Hadamard products and multivariate statistical analysis. Linear Algebra and Its Appl. 6 (1973) 217-240] established an inequality involving the Hadamard product using statistical reasoning in the context of multivariate analysis. In this paper, the inequality is extended to involve the Khatri-Rao product in the non-negative definite matrix case and in the non-singular Hermitian matrix case. The equality conditions for these extensions are given. Also established are counterpart inequalities in the positive definite matrix case.     

Proof of a conjecture on connectivity of Kronecker product of graphs

For a graph G, κ(G) denotes its connectivity. The Kronecker product G₁×G₂ of graphs G₁ and G₂ is the graph with the vertex set V(G₁)×V(G₂), two vertices (u₁,v₁) and (u₂,v₂) being adjacent in G₁×G₂ if and only if u₁u₂∈E(G₁) and v₁v₂∈E(G₂). Guji and Vumar [R. Guji, E. Vumar, A note on the connectivity of Kronecker products of graphs, Appl. Math. Lett. 22 (2009) 1360–1363] conjectured that for any nontrivial graph G, κ(G×K_n)=min{nκ(G),(n−1)δ(G)} when n≥3. In this note, we confirm this conjecture to be true.     

The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes

The Kronecker product of two Schur functions s and s , denoted by s * s , is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions and . The coefficient of s in this product is denoted by , and corresponds to the multiplicity of the irreducible character in .We use Sergeev's Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for s [XY] to find closed formulas for the Kronecker coefficients when is an arbitrary shape and and are hook shapes or two-row shapes.Remmel (J.B. Remmel, J. Algebra 120 (1989), 100–118; Discrete Math. 99 (1992), 265–287) and Remmel and Whitehead (J.B. Remmel and T. Whitehead, Bull. Belg. Math. Soc. Simon Stiven 1 (1994), 649–683) derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product.     

A proof of a conjecture of Sabidussi on graphs idempotent under the lexicographic product

In 1960, Sabidussi conjectured that if a graph G is isomorphic to the lexicographic product G[G], then the wreath product of by itself is a proper subgroup of . A positive answer is provided by constructing an automorphism Ψ of G[G] which satisfies: for every vertex x of G, there is an infinite subset I(x) of V(G) such that Ψ({x}×V(G))=I(x)×V(G).     

批量购买下免费商品赠送对新产品扩散的影响

在非耐用品的购买过程中,批量购买的消费行为较为普遍。本文基于Bass模型,将批量购买看作一个扩散过程,建立批量购买下含免费商品的产品扩散模型;然后在扩散模型中引入重复购买和价格策略等因素的影响,构建了优化模型群。对不同购买方式下的免费商品赠送进行仿真分析,同时对模型中重要参数进行优化后分析,计算分析表明:和单量购买情形一致,当存在批量购买时,免费商品的赠送同样会加快产品的扩散速度,但值得赠送更多的免费商品以达到利润最大化。消费者的批量购买量越大,就越有必要赠送更多的免费商品来让消费者了解该产品,甚至对每个消费者发放免费商品。同时,通过对赠送时期的对比分析,发现只有在产品引入初期赠送最佳,形成了“首期赠送效应”。最后,给出了参数对免费商品赠送水平的影响范围与趋势。     

Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.     

弱Hopf代数上的ω-交叉积

在弱Hopf代数上,定义了ω-交叉积概念,并给出了ω-交叉积是弱Hopf代数的充要条件,推广了弱Hopf代数的相应结论.     

Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces

In this paper, the authors investigate the boundedness of Toeplitz product T_f T_g and Hankel product H^*_fH_g on Fock-Sobolev space for f, g ∈ P. As a result, the boundedness of Toeplitz operator T_f and Hankel operator H_g with f ∈ P is characterized.     

一类保本结构型理财产品的收益分布研究

综合运用傅里叶变换、复变函数和概率论等数学工具,研究一类保本结构型理财产品,通过严密推导得到了这类保本理财产品的预期收益计算公式,并通过数值计算得出了这类理财产品的收益分布情况.分析表明规定最高收益率的保本理财产品的理论价格的变动并不是基础资产价格波动率的单调函数,理论价格随基础资产价格波动率的增加先减小再增加,当基础资产的价格波动率较大时,购买此种理财产品并不能获得高于定期存款的收益.     

图乘积的星色数

星色数的概念最早是由Vince作为图的色数的推广而引入的.本文研究了两类图乘积G×H,G[H]的星色数.     

On anti-magic labeling for graph products

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1,2,…,q} such that the vertex sums are pairwise distinct, where the vertex sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an anti-magic labeling. Hartsfield and Ringel conjectured in 1990 that all connected graphs except K₂ are anti-magic. Recently, Alon et al. showed that this conjecture is true for dense graphs, i.e. it is true for p-vertex graphs with minimum degree Ω(logp). In this article, new classes of sparse anti-magic graphs are constructed through Cartesian products and lexicographic products.     

Domination in the hierarchical product and Vizing’s conjecture

Given a graph $G$, a set $S?V\left(G\right)$ is a dominating set of $G$ if every vertex of $G$ is either in $S$ or adjacent to a vertex in $S$. The domination number of $G$, denoted $\gamma \left(G\right)$, is the minimum cardinality of a dominating set of $G$. Vizing’s conjecture states that $\gamma (G\square H)\ge \gamma \left(G\right)\gamma \left(H\right)$ for any graphs $G$ and $H$ where $G\square H$ denotes the Cartesian product of $G$ and $H$. In this paper, we continue the work by Anderson et al. (2016) by studying the domination number of the hierarchical product. Specifically, we show that partitioning the vertex set of a graph in a particular way shows a trend in the lower bound of the domination number of the product, providing further evidence that the conjecture is true.