期刊：
Linear Algebra and its Applications,2011年435(5):1171-1186 ISSN：0024-3795
通讯作者：
Li, Shuchao
作者机构：
[He, Shushan; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Tree;Laplacian matrix;Laplacian coefficients;Matching number;Wiener index;Laplacian-like energy;Incidence energy
摘要：
Let G be a simple undirected graph with the characteristic polynomial of its Laplacian matrix L(G), P(G,x)=∑k=0n(-1)kckxn-k. Aleksandar Ilić [A. Ilić, Trees with minimal Laplacian coefficients, Comput. Math. Appl. 59 (2010) 2776–2783] identified n-vertex trees with given matching number q which simultaneously minimize all Laplacian coefficients. In this paper, we give another proof of this result. Generalizing the approach in the above paper, we determine n-vertex trees with given matching number q which have the second minimal Laplacian coefficients. We also identify the n-vertex trees with a perfect matching having the largest and the second largest Laplacian coefficients, respectively. Extremal values on some indices, such as Wiener index, modified hyper-Wiener index, Laplacian-like energy, incidence energy, of n-vertex trees with matching number q are obtained in this paper.
摘要：
In this paper, we study the nonlinear Schrodinger equation with electromagnetic fields (del/i - A(vertical bar y vertical bar))(2)u + V(vertical bar y vertical bar)u = vertical bar u vertical bar(p-1)u, u : R-N bar right arrow C, where the vector A(r) = (A(1)(r), A(2)(r), ... , A(N)(r)) is such that A(j)(r) (j = 1, 2, ... , N) is a real function on R+ and V(r) is a positive function on R+, 1 < p < N+2/N-2 if N >= 3 and 1 < p < +infinity if N = 2. We prove that the equation has infinitely many non-radial complex-valued solutions under conditions (H-1) and (H-2) which are given in Section 1. (C) 2011 Elsevier Inc. All rights reserved.
作者机构：
[李海雄] School of Mathematics and Statistics, Huazhong University of Science and Technology;[邓国泰] School of Mathematics and Statistics, Huazhong Normal Universzty
关键词：
Admissible linear estimator;Growth curve model;Inequality constraint;Matrix loss;Quadratic loss
摘要：
In terms of the theory of inequality and the vectorization transformation of a matrix, we study the admissibility problem of linear estimators in growth curve models with inequality constraints. Under the quadratic loss and the matrix loss, we obtain the necessary and sufficient conditions for a linear estimator of estimable/inestimable linear functions being admissible in the homogeneous and inhomogeneous classes separately.
期刊：
Ars Combinatoria,2011年102:47-64 ISSN：0381-7032
通讯作者：
Li, Shuchao
作者机构：
[Chen, Beifang] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
A nowhere-zero k-tension on a graph G is a mapping from the edges of G to the set {±1, ±2,..., ±(k -1)} ⊂ ℤ such that, in any fixed orientation of G, for each circuit C the sum of the labels over the edges of C oriented in one direction equals the sum of values of the edges of C oriented oppositely. We show that the existence of an integral tension polynomial that counts nowherezero k-tension on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes. The same holds for tensions on signed graphs. We develop these theories, as well as the related counting theory of nowhere-zero tensions on signed graph with values in an abelian group of odd order. Our results are of two kinds: polynomiality or quasipolynomiality of the tension counting functions, and reciprocity laws that interpret the evaluations of the tension polynomials at negative integers in terms of the combinatorics of the graph.
