单色光束的衍射度

受近期Gawhary和Severini在Opt.Lett.33,1360(2008)一文中引入的光束近轴度的启发,定义了一个独立于光束近轴度的衍射度参数来描述单色光束的衍射扩散程度,所定义的衍射度只依赖于光束的角谱分布,并可以定量比较不同光束的衍射扩散程度.     

基于公式真度的公式集约简

基于经典命题逻辑的真度理论,讨论了经典命题逻辑系统当中公式集的约简问题。提出了真度约简及α-真度约简的概念,为公式集的约简提供了一种可行的操作方法。     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

Density of the Medvedev lattice of Π<Superscript>0</Superscript><Subscript>1</Subscript> classes

The partial ordering of Medvedev reducibility restricted to the family of ⁰₁ classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a ⁰₁ class, which we call a ``c.e. separating class'. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes. Mathematics Subject Classification (2000): 03D30, 03D25     

光纤中高斯型伪随机序列码偏振度的理论分析和实验研究

推导了准单色光波情况下高斯脉冲伪随机序列偏振度的简洁数学表达式.理论分析结果表明,偏振度与差分群延迟之间的关系与线路啁啾和光纤色散无关,并且此关系可以由光信号频谱半宽度Δω和分光比γ唯一确定.用10 Gbit/s 7级m序列归零码进行的实验表明:实验结果与理论推导基本一致,从而验证了推导公式的正确性.     

Network formed by traces of random walks

We propose a model of time evolving networks in which a kind of transport between vertices generates new edges in the graph. We call the model “Network formed by traces of random walks”, because the transports are represented abstractly by random walks. Our numerical calculations yield several important properties observed commonly in complex networks, although the graph at initial time is only a one-dimensional lattice. For example, the distribution of vertex degree exhibits various behaviors such as exponential, power law like, and bi-modal distribution according to change of probability of extinction of edges. Another property such as strong clustering structure and small mean vertex–vertex distance can also be found. The transports represented by random walks in a framework of strong links between regular lattice is a new mechanisms which yields biased acquisition of links for vertices.     

A degree sum condition for long cycles passing through a linear forest

Let G be a (k+m)-connected graph and F be a linear forest in G such that |E(F)|=m and F has at most k-2 components of order 1, where k?2 and m?0. In this paper, we prove that if every independent set S of G with |S|=k+1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min{d-m,|V(G)|} which contains all the vertices and edges of F.     

Study of the polymerization of acrylic resins by photocalorimetry: interactions between UV initiators and absorbers

Photocurable finishes should be extensively used for industrial wood joinery in the near future even if some technical problems have still to be solved and if the durability of the finishing system has to be enhanced. In a previous work, we studied the curing reaction of acrylic resins containing some particular photoinitiators by photocalorimetry and showed that curing can be achieved under daylight with these compounds (i.e. solving the problem of restoration on site). The aim of this work is to enhance the durability of these systems by incorporating UV absorbers into the formulations. The consequences of such an addition onto the curing kinetics are again investigated by photocalorimetry.     

The minimum degree distance of graphs of given order and size

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.     

Degree sum and nowhere-zero 3-flows

Let G be a simple graph on n vertices. In this paper, we prove that if G satisfies the condition that d(x)+d(y)≥n for each xy∈E(G), then G has no nowhere-zero 3-flow if and only if G is either one of the five graphs on at most 6 vertices or one of a very special class of graphs on at least 6 vertices.