High power CW solid-state multilaser system

A laser system containing four CW Nd:YAG double-rod lasers, transforming optics and a fibre with input-output optics has been designed and investigated. It is shown that reduction of the beam parameter product of the non-Gaussian beams in the image space of the lens has made it possible to collect the emission of four lasers to the same fibre. Independent laser operation has provided the output power control in the range of 10–900 W with a stable light spot size on the input end of the fibre.     

Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.     

THE RADICALS OF HOPF MODULE ALGEBRAS

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Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].     

应用灰色统计进行纺织产品的抉择

本文利用灰色系统理论处理问题的特点,以一纺织厂对三种产品优化抉择为例,提出了用灰色统计综合评判的方法进行产品块择,取得了较满意的效果,为纺织产品的生产抉择提供了一个新的科学方法。     

铸件成品率微机管理系统

建立了铸件成品率的数学模型，以实现铸件成品率的微机管理．该系统具有统计、分析、判断、优化等各项功能，满足了生产现场对铸件成本的控制．     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

一些特殊图类乘积的离散度

连通图的离散度是用s(G)来表示的,s(G)=max{ω(G-S)-|S|:ω(G-S)>1,SV(G)}.给出了两个完全图乘积的和一个完全图与路的乘积的离散度.还给出了两个完全图乘积的坚韧度.     

Optimally Stable Multivariate Bases

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.     

Superposition, Entanglement, and Product of States

The superposition relation extended to the statistical operators is shown to be invariant under tensor product and partial trace operations. Particular mathematical examples of superposition are characterized as well as the nature of the Schmidt decomposition of pure states superposition of other pure states.