一类9n2次组合混合水平正交表的构造

本文利用正交表和投影矩阵的正交分解之间的关系,给出了一类9n2次组合混合水平正交表的构造方法,作为这种方法的应用,我们构造了一些新的具有较大非素数幂水平的144次混合水平正交表,并且这些正交表具有较高的饱和率.     

非线性常微分系统的稳定性

用矩阵的Lozinskii测度的方法,得到了非线性常微分系统的一些稳定性准则,导出了关于非线性系统,x′=A（t）x（t）＋R（t,x）稳定性的充要条件．     

由n次幂等矩阵确定的交换幺半群

设R是含幺结合环,n≥2为自然数.对所有的k≥1,本文给出了n次幂等矩阵集Pk^n（R）={P｜P^n=P∈Mk（R）}上的一种等价关系,证明了P^n（R）=∪k=1^∞Pk^n（R）中的等价类在给定的加法运算下构成一个交换幺半群.     

Gold codes,Hadamard partitions and the security of CDMA systems

Let V = {1, 2, . . . , M} and let be a set of Hadamard matrices with the property that the magnitude of the dot product of any two rows of distinct matrices is bounded above. A Hadamard partition is any partition of the set of all rows of the matrices H _i into Hadamard matrices. Such partitions have an application to the security of quasi-synchronous code-division multiple-access radio systems when loosely synchronized (LS) codes are used as spreading codes. A new generation of LS code can be used for each information bit to be spread. For each generation, a Hadamard matrix from some partition is selected for use in the code construction. This code evolution increases security against eavesdropping and jamming. One security aspect requires that the number of Hadamard partitions be large. Thus the number of partitions is studied here. If a Kerdock code construction is used for the set of matrices, the Hadamard partition constructed is shown to be unique. It is also shown here that this is not the case if a Gold (or Gold-like) code construction is used. In this case the number of Hadamard partitions can be enumerated, and is very large.      

Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics

Cauchy problems for a second order linear differential operator equation

Conditioning of Random Conic Systems Under a General Family of Input Distributions

We consider the conic feasibility problem associated with the linear homogeneous system Ax≤0, x≠0. The complexity of iterative algorithms for solving this problem depends on a condition number C(A). When studying the typical behavior of algorithms under stochastic input, one is therefore naturally led to investigate the fatness of the tails of the distribution of C(A). Introducing the very general class of uniformly absolutely continuous probability models for the random matrix A, we show that the distribution tails of C(A) decrease at algebraic rates, both for the Goffin–Cheung–Cucker number C _G and the Renegar number C _R . The exponent that drives the decay arises naturally in the theory of uniform absolute continuity, which we also develop in this paper. In the case of C _G , we also discuss lower bounds on the tail probabilities and show that there exist absolutely continuous input models for which the tail decay is subalgebraic. R. Hauser was supported by a grant of the Nuffield Foundation under the “Newly Appointed Lecturers” grant scheme (project number NAL/00720/G) and through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the UK. The research in this paper was conducted while T. Müller was a research student at the University of Oxford. He was partially supported by EPSRC, the Oxford University Department of Statistics, Bekker-la-Bastide fonds, Dr. Hendrik Muller’s Vaderlandsch fonds, and Prins Bernhard Cultuurfonds.     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.     

On the upper bounds of the minimum number of rows of disjunct matrices

A 0-1 matrix is d-disjunct if no column is covered by the union of any d other columns. A 0-1 matrix is (d; z)-disjunct if for any column C and any d other columns, there exist at least z rows such that each of them has value 1 at column C and value 0 at all the other d columns. Let t(d, n) and t(d, n; z) denote the minimum number of rows required by a d-disjunct matrix and a (d; z)-disjunct matrix with n columns, respectively. We give a very short proof for the currently best upper bound on t(d, n). We also generalize our method to obtain a new upper bound on t(d, n; z). The work of Y. Cheng and G. Lin is supported by Natural Science and Engineering Research Council (NSERC) of Canada, and the Alberta Ingenuity Center for Machine Learning (AICML) at the University of Alberta. The work of D.-Z. Du is partially supported by National Science Foundation under grant No.CCF0621829.     

围长为2的本原无限布尔方阵类的本原指数集

研究了围长为2的无限布尔方阵的本原性,通过无限有向图D（A）的直径给出了这类矩阵的本原指数的上确界,最后证明了直径小于等于d且围长为2的本原无限布尔方阵所构成的矩阵类的本原指数集为Ed^0={2,3,…,3d}．     

Solution of Lane–Emden type equations using rational Bernoulli functions

In this paper, a numerical method for solving Lane‐Emden type equations, which are nonlinear ordinary differential equations on the semi‐infinite domain, is presented. The method is based upon the modified rational Bernoulli functions; these functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then given and are utilized to reduce the solution of the Lane‐Emden type equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.