有序与无序的数学理论

我们这里所说的有序与无序是指秩序 ,通常是就体系或系统内部的基本结构单元在空间的分布或对时间发展过程中的运动状态而言的 ,有序与无序最大的特征是 :有序显示出约束性较大 ,因此表现出来的具体形式较少 ,而无序则刚好相反 .本文的目的是从数学角度去研究这个问题 .推导出与有序度及无序度有关的定理 .类似于凝聚态物理学中的序参量 ,我们给出宏观态的有序度 ,而无序度则参考统计物理学中由玻尔兹曼建立的熵公式给出的 .设系统Ｓ有ｎ个粒子 ,且有提供每个粒子选择的ｋ个自由态 ,则记此系统为 :Ｓ ={ｎ ,ｋ},若粒子是可辨的 ,则记为Ｓ·=…     

A General Alternative Procedure for Solving Negative Degree of Difficulty Problems in Geometric Programming

The degree of difficulty is an important concept in classical geometric programming theory. The dual problem is often infeasible when the degree of difficulty is negative and little has been published on this topic. In this paper, an alternative procedure is developed to find the optimal solution for the posynomial geometric programming problem with a negative degree of difficulty. First an equivalent problem was constructed with a positive degree of difficulty and the general posynomial geometric programming problem was solved using an original method previously developed by the authors. This method avoids the difficulty of non-differentiability of the dual objective function in the classical methods classified as dual. It also avoids the problem that appears when the feasible region for the dual problem is formed by an inconsistent system of linear equations.     

光扇效应对Ce：KNSBN记录偏振组态的影响

在非同时读出条件下 ,采用Ar+ 5 14 .5nm单色激光为光源。以信号光为非寻常偏振光 (e光 ) ,通过改变抽运光的偏振态 ,研究不同写入光偏振组态下Ce∶KNSBN晶体的两波耦合特性。结果表明 :由于光扇效应的影响 ,信号光和抽运光同为e光时并非如预测的那样为最佳记录偏振组态。在信号光和抽运光与晶体表面法线呈θ =11°角对称入射下 ,当抽运光的偏振方向与e光偏振方向呈 30°角时 ,光扇噪声得到明显抑制 ,两波耦合增益最大。其原因是抽运光的o光分量对光扇散射光起到了非相干擦除 ,使两波有效耦合得到提高。     

两纠缠原子与相干态光场相互作用的动力学

采用时间演化算符和数值计算方法,研究了两全同二能级纠缠原子与相干态光场相互作用的动力学,结果表明:原子布居和偶极压缩特性与两原子体系纠缠度和相干态光场强度相关联.     

区间数可能度的二维定义

利用二维空间的面积,提出了一个新的区间数可能度的定义,并给出了简单实用的计算公式和证明了相关的性质,最后,通过实例说明了该定义的实用性.     

基于对数灰关联度的加权几何平均组合预测模型的有效性

基于对数灰关联度的加权几何平均组合预测是一种新的非线性组合预测。针对该方法提出新的优性组合预测、预测方法优超、冗余度等概念,给出优性组合预测存在的充分条件,最后证明冗余预测方法的一个判定定理。     

EXISTENCE OF POSITIVE PERIODIC SOLUTION TO A CLASS OF NEUTRAL DELAY COMPETITION MODEL

By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.     

凸集上的非线性算子的固有元及固有值

本文利用拓扑度研究集上的具边界条件的非线性集压缩算子的不动点。固有元及固有值的存在性,推广了[3,5,6]中的相应结论,部分回答了[4]的一个猜测。     

经验分布函数在各种散布序下的充分必要条件

设Ｆｘ（ｘ），Ｇｎ（ｘ）是样本总体Ｘ，Ｙ，经验的分布函数，我们通过「１」，「３」，「４」中所定义的散布序≤ｍｉｓｐ、≤ｄ＾＊，≤＾ｄ来比较两个经验分布函烽间的散布程度，从而得到了Ｆｎ（ｘ），Ｇｎ（ｘ）在各种散布序下的充要条件。     

DEGREE OF SUBSTITUTION OF THE IONIZED STARCHES AND THEIR ADHESIVE CAPACITY TO POLYESTER / COTTON FIBERS

Adhesive capacity of quaternary ammonium starch and starch phosphate to the polyester / cotton fibers was studied by means roving method for the purpose of improving the sizing performance and decreasing the cost. By introducing different amount of quaternary ammonium or phosphate groups onto starch molecules, the modified starch with a series of defferent degree of substitution was prepared. Therefore the regularity of adhesive capacity, extended property and size-absorbing ability with the change in degree of substitution (DS) was obtained through the researches. The experiments demonstrate that the DS of the two modified starches show a marked influence upon the properties mentioned above. The starch phosphate is superior to quaternary ammonium starch as warp size for polyester / cotton yarns from the viewpoint of adhesive capacity and cost, although both of them are better than natural one. To improve the adhesive capacity to polyester / cotton fibers, DS≥0.027 is necessary for quaternary ammonium s