The Existence of Solutions of （k, n - k） Conjugate Boundary Value Problems in Banach Spaces

In this paper,by use of the Schauder fixed-point theorem,the existence of solution of (k,n-k) Conjugate boundary value problems in Banach spaces is investigated.     

On the ionic conductivity of polymer electrolytes in terms of hole fraction

A theoretical model to interpret the conductivity of ions through polymer electrolytes is established in terms of the temperature and pressure‐dependent hole fraction computed from Simha‐Somcynsky hole theory. The model successfully linearizes the logarithm of PPG and PEG conductivity data with NaCF₃SO₃ in a 20:1 ratio for a broad range of temperature and pressure. The conductivity parameter and transmission coefficient with an additive hole fraction constant are discussed and compared for both species. The derivative of the logarithm of conductivity with respect to the hole fraction decreases inversely with the hole fraction and saturates at about 0.08 and 0.12 hole fractions for PPG and PEG, respectively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2249–2254, 2008     

The complex Monge–Ampère equation with infinite boundary value

In this article we consider the complex Monge–Ampère equation with infinite boundary value in bounded pseudoconvex domains. We prove the existence of strictly plurisubharmonic solution to the problem in convex domains under suitable growth conditions. We also obtain, for general pseudoconvex domains, some nonexistence results which show that these growth conditions are nearly optimal.     

Methods of statistical modeling in the process of sieve separation of heterogeneous particles

In the article we undertook the attempt of using the theory of random fields in the analysis of the separation process of particles in non-contiguous systems. The presentation of the complete model is a complicated problem. We can say that this article is start point of the theory, which will be supplemented gradually in the future. The separation process of particles on sieves is a phenomenon with random character. It is a result of random character of cleaned mixture and the nature of the separation process. Undoubtedly, an important part is played by the theory of random fields in which system-events, inherently not determined, are described in undetermined-probabilistic way. However, we can perceive one paradox in such actions – correctly constructed probabilistic models serve to impose deterministic frames on the given random process. We can say that stochastic models generate the matrix of the causal-consecutive dependence, which will give the ability of controlling a given process.     

Implicit two-phase solvation model as a tool to assess conformation and energetics of proteins in membrane-mimetic media

 A heterogeneous implicit membrane-mimetic model is applied to simulations of membrane proteins. The model employs atomic solvation parameters for gas–water and gas–cyclohexane transfer. It is used to analyze structure, energetics, and orientation with respect to the bilayer of two polypeptides with different modes of membrane binding – hydrophobic segment of human glycophorin A (GpA) and cytotoxin II from Naja naja oxiana snake venom (CTX). The native state of GpA represents a transmembrane (TM) α helix, while CTX is a water-soluble protein, which is able to interact with the cell membrane. The conformational space of the polypeptides was explored in Monte Carlo simulations. The results show that the most stable conformers of GpA represent a TM α helix. They are additionally stabilized by an applied TM voltage. The results also show that CTX inserts with its three loops, does not cross the hydrophobic layer, and stays partially immersed in the membrane. This agrees well with the experimental data, thus confirming the validity of the solvation model. Received: 13 June 2000 / Accepted: 15 September 2000 / Published online: 19 January 2001     

Temperature induced rotation in a [4.4]cyclophane

The synthesis, the X-ray, NMR and molecular modeling structure determination of a new orthopara[4.4]cyclophane are reported. The similarity of the π(CO)-π(Ar) driven conformational equilibrium of this compound to the work of an amusement ride machinery is also revealed.     

Modeling the mechanical properties of highly oriented polymer films: A fiber/gel composite theory approach

Controlling the extent of orientation is of great interest in polymer processing and is effected by the choice of polymer, the fabrication technique and the processing conditions. Understanding the crystalline transitions that form highly oriented fibrils is necessary for modeling the changes in physical properties, relative to degree of orientation. A model is proposed to describe the mechanical properties of drawn semicrystalline polymer films based on structural transitions. With a minimal amount of experimental data (requiring testing on only two drawn films samples), this model can be used to predict film properties. These properties include the critical and maximum draw ratios, the moduli at the maximum draw ratio, the moduli of the fiber, the modulus of the nonfibrous gel relative to draw ratio, the volume fraction of fibers, and the rate of fibrillation. Where high degrees of uniaxial orientation are required, the polymer is typically drawn in the solid state, meaning the polymer is stretched in a single direction at temperatures below the melting point. During this process, pre‐existing crystallites are transformed into fiber‐like structures with large aspect ratios. The presence of these rigid asymmetric structures significantly enhances the moduli and break strength of the polymer. This work presents a model that describes the formation of fiber‐like structures. The volume fraction of fibers is predicted to be linear in draw ratio. The derived relationship between volume fraction of fibers and draw ratio can then be used for the prediction of the various properties of the oriented film. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 607–618, 2008     

最佳粮库地址的选择

管理部门通常要选择适当的地方建造粮库 ,所需服务范围已知 ,各部门运输量给定 .需为他们选择合适的地方 ,使总运费最少 .某乡的九个村 (A,B,C,… ,H,I)如图 1 ,各村距离给出 ,并标明它们各自上缴公粮数 .管理部门希望在村内或道路上建立一个粮库 ,最大限度地减少运输费用 .问题的解法有几种方案 ,对于本题来说 ,穷举搜索法是可行的 .另外 ,我们提出一种分析求解法 ,可找到优化解 .它利用图论的基础知识先求出图 1的各顶点间的最小路径 ,再进一步求出图的绝对中心 (即粮库的地址 ) ,其中的有关计算利用了 C++语言程序 .在此基础上 ,还可对问题的参数作更精细的分析 .概括地说 ,穷举搜索法对于简单的区域是行之有效的 .但对于更加一般化的问题 ,利用计算机可快捷准确地得到答案 .通过建立模型 ,我们得到下面两个结论 :(1 )我们找到最优解是 E点 ,其总运费为 1 2 775元 .(2 )模型具有广泛性 ,对于更一般的区域 ,可利用计算机总可以求出最优解 .     

General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution （Ⅰ）

In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.     

一类p-Laplace方程边值问题解的存在性

主要讨论一维p-Laplace方程在Neumann边值条件u(0)=0,u(1)=0下,对应的边值问题解的存在性.通过使用度理论,在适当的条件下,建立了对于p-Laplace方程在Neumann条件下解的存在性的充分条件.