Nonlinear Correlations of Protein Sequences and Symmetries of Their Structures

We investigate the nonlinear correlations of protein sequences by using the nonlinear prediction method developed in nonlinear dynamical theory. It is found that a lot of protein sequences show strong nonlinear correlations and have deterministic structures. Further investigations show that the strong nonlinear correlations of these protein sequences are due to the symmetries of their tertiary structures. Furthermore, the correlation lengths of the sequences are related to the degrees of the symmetries. These results support the duplication mechanism of protein evolution and also reveal one aspect how amino acid sequences encode their spatial structures.     

Optical and Acoustical Frequencies in a Nonlinear Helicoidal Model of DNA Molecules

We compare optical and acoustical frequencies in the Peyrard-Bishop-Dauxois model, i.e. an extended Peyrard-Bishop model, of DNA molecules. We discuss how ratio of those frequencies depends on a value of the harmonic constant of the helicoidal spring K. Also, we suggest that the most favourable mode could be a resonance mode.     

聚芳香杂环甲烯的三阶非线性光学效应与时间分辨光克尔效应

合成了一系列聚芳香杂环甲烯,包括聚吡咯甲烯和聚噻吩甲烯.采用四波混频法研究材料的共振三阶非线性光学效应(λ＝532nm),其共振二阶超分子极化率γ三阶非线性光学系数分别达到10^-30esu和10^-8esu.选择具有良好溶解性、成膜性的聚吡咯对二甲氨基苯甲烯(PPDMAB),采用飞秒时间分辨光克尔效应方法研究材料的非共振三阶非线性光学效应(λ=790nm).实验表明,翠绿亚胺碱溶液的光克尔信号仅表现一超快响应的成分,归功于π电子云扭转产生的非共振激发.PPDMAB的非共振二阶超分子极化率γ三阶非线性光学系数分别达到γ=5.78×10^-32esu和χ⁽³⁾=1.26×10^-10esu.     

带有单模糊映射的一般变分不等式解的存在性

众所周知，在各种变分不等式问题中，解的存在性是最基础也是最重要的问题之一．本文的目的是在Hilbert空间中研究带有单模糊映射的一般变分不等式解的存在性．此外，还讨论了几种特殊情况．     

纳米PIC-I分子聚集体的超辐射和Z-扫描研究

分子聚集体在非线性光学和集成光学等领域有潜在的应用前景。纳米结构一维染料分子J—聚集体有许多既不同于单个分子又不同于体材料的奇异性质，即超辐射和巨光学非线性。这种超辐射是由于在几个本征态内振于强度结合在一起，得到一巨跃迁偶极于，因而是超辐射的。跃迁速率与耦合分子个数N成正比。分子聚集体的J—吸收和超辐射发射是共振的。利用Z—扫描技术测量PIC在不同配比下的非线性折射率、非线性吸收系数和非线性极化率。观测到随着链长变短，样品的三阶非线性极化率增大。对这种非线性增强的机制进行了分析和讨论。     

激光水下扫描成像系统的图像修正机理

同步扫描系统可以克服后向散射，但同时也产生了两种非线性，一是扫描线速度的非线性，一是由于距离对光能衰减造成的非线性，两种非线性都需要修正，本文从原理上讨论水下激光成像时能量衰减的修正原理与修正方法，并给出仿真结果。     

厚高阶光学非线性介质Z扫描的变分法分析

利用变分法对具有五阶光学非线性介质的Z扫描特性进行了研究。通过比较，发现当介质在具有较大的五阶非线性系数或较大光强的情况下，五阶非线性项的作用是不可忽略的。这对光限制器的设计和Z扫描实验都具有一定的指导意义。     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

凸度量空间中单值和集值映象的公共不动点定理

§ 1.　Introduction　　Anecessaryandsufficientconditionandasufficientconditiontoensurethataset valuedmappingandasingle valuedmappinginacompletemetricspaceandacompleteconvexmetricspacehavingacommonfixedpointarerespectivelygivenin [1 ] .Meanwhilethemainresultsin[2 ]— [5]areimprovedandextendedin [1 ] .Inthispaper ,theexistenceatcommonfixedpointsoftwoset valuedmappingandasing valuedmappingwerestudied ,andthecorrespond ingresultsin [1 ]— [5]wereextendedandimproved .Let(X ,d)beanon emptymetricspa…     

非线性不适定问题一种双循环的牛顿型迭代格式

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。