Closed form summation of -finite sequences

We consider sums of the form

in which each is a sequence that satisfies a linear recurrence of degree , with constant coefficients. We assume further that the 's and the 's are all nonnegative integers. We prove that such a sum always has a closed form, in the sense that it evaluates to a linear combination of a finite set of monomials in the values of the sequences with coefficients that are polynomials in . We explicitly describe two different sets of monomials that will form such a linear combination, and give an algorithm for finding these closed forms, thereby completely automating the solution of this class of summation problems. We exhibit tools for determining when these explicit evaluations are unique of their type, and prove that in a number of interesting cases they are indeed unique. We also discuss some special features of the case of ``indefinite summation", in which .

     

基于幅度调制的非线性超声相控阵成像方法*

超声相控阵是超声检测领域常用的材料缺陷定位和成像技术,可便捷快速地对裂纹、孔洞等缺陷进行成像。但是,传统超声相控阵方法对较小缺陷如闭合裂纹不太敏感。非线性超声信号因对材料性能退化以及微小缺陷敏感而广受关注。本文针对疲劳闭合裂纹检测,提出一种基于幅度调制的非线性超声相控阵成像方法,通过测量物理聚焦和虚拟聚焦两种聚焦模式下超声扩散场中的声能差,并将其作为非线性参量,实现疲劳裂纹闭合部分的定位成像和定量表征。将该法应用于7075铝合金试样疲劳裂纹的实验测量,并研究了扩散场信号延迟时间对非线性超声相控阵成像结果的影响。结果表明：相较于传统超声相控阵全聚焦法,基于幅度调制的非线性超声相控阵成像方法能够更准确地定位和成像疲劳裂纹闭合部分;延迟时间的选择对疲劳裂纹长度的表征精度影响较大,本文研究了该延迟时间的选择方法并实现了检测结果的优化。     

Unique factorization of *-products of one-fibered monomial ideals

Let R k[x ₁,x ₂,x ₃] be a 3-dimensional polynomial ring over a field k.We show that no non-trivial relations exist among *-products of complete one-fibered (x ₁,x ₂,x ₃)-primary monomial ideals. This is connected with questions about how Zariski's work on the unique factorization of complete ideals in regular local rings of dimension two might be generalized to higher dimensions.     

Decomposing complete multipartite graphs into closed trails of arbitrary even lengths

We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:455‐462, 2011     

P3BD‐closed sets

A concept called P3BD‐closed set is introduced to describe a set of positive integers which is both PBD‐closed and 3BD‐closed. The theory of P3BD‐closure is developed and a few examples of P3BD‐closed sets are exhibited. In the process, the existence spectrum of OLIQ ^?s (overlarge sets of idempotent quasigroups with their own idempotent orthogonal mates) is almost determined. A pair of orthogonal OLIQ ^?s is shown to asymptotically exist. The existence of OLIQ s (overlarge sets of idempotent quasigroups with their own orthogonal mates not necessarily specifying idempotency) is also established with only 10 possible exceptions remained. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:407‐421, 2011     

三维随机SIERPINSKI地毯的相位和临界概率

本文用概率论的基本方法结合矩阵表示上的置换方法，证明了三维随机 Ｓｉｅｒｐｉｎｓｋｉ地毯随着保留概率从０到１变化，过程组态经历几个不同的相位，并求出各相位间的临界概率或给出其范围．     

Honest submodules

Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.     

Intersection theorems on polytopes

Received June 6, 1995 / Revised version received May 26, 1998 Published online October 9, 1998