关于亚纯函数据有三个公共值以及它们的导函数据有一个公共值的问题

这篇论文研究的是亚纯函数的唯一性。这篇论文的主要结论是：如果两个非常数亚纯函数ｆ和ｇ有三个ＣＭ公共值或四个ＩＭ公共值,并且ｆ’和ｇ’以零为ＩＭ公共值,则ｆ和ｇｒＭｏｂｉｕｓ变换。其中一个结论是Ｋ．Ｔｏｈｇｅ有一个结果的改进,而且我们采用了与Ｋ．Ｔｏｈｇｅ不同的方法。『     

基于一维分子线的甲醛分子探针研究

甲醛为公认的致癌物质,本文针对目前甲醛分析需使用专用仪器和试剂盒的不便现状,合成了分子探针(km2bn),通过晶体结构分析发现其苯并二氮杂卓基团与水自组装为一维分子线材料(km2bn·H2O),可与甲醛分子发生固-气相Hantzsch反应,生成具有更大共轭体系二氢吡啶杂环结构,双官能团反应使其生成一维伸展的线性聚合物,共轭体系得到更大的拓展,具有深色与光谱红移效应,其颜色坐标与甲醛浓度具有线性关系,兼具检测选择性,因而可通过该可视显色反应检测甲醛,并可制成试纸,方便普通家庭使用。     

无穷可数个Brown运动驱动的随机微分方程解的分布唯一性及路径唯一性

研究如下形式的随机微分方程Xit =xi + ∑∞j=1∫t0σijs(Xs)dBjs +∫t0bis(Xs)ds,i=1,2,…,n,( * )其中{Bjt}∞j=1是相互独立的标准Brown运动的无穷可数序列.主要证明如下结论:1)解的分布唯一性蕴含了解的联合分布唯一性；2)解的分布唯一性与强解的存在性可以保证解的轨道唯一性.结论2)是Yamada定理的对偶命题.     

NON-UNIQUE SOLUTIONS FROM SURFACE ELASTICITY FOR FUNCTIONALLY GRADED MATERIALS

This paper considers the unusual behavior of functionally graded materials/structures when the surface effect is involved. It is found that on the assumption that the surface energy is not positive semi-definite, the solution can be non-unique. Several examples are given for simple spherically-symmetric and axisymmetric FGM bodies with surface effects characterized by Gurtin-Murdoch surface elasticity. The results show that the conditions for non-uniqueness of solution emerge when the magnitude of negative effective surface modulus is of the order of a characteristic dimension of the problem multiplied by the bulk modulus near the surface, which is quite different from that for homogeneous materials.     

On edge colorings of 1-toroidal graphs

A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree Δ≥ 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree Δ for each Δ≤ 8.     

利用金兹堡-朗道理论研究无序光晶格中超冷玻色系统的相变问题

在冷原子物理中,对无序和温度效应的研究一直是一个非常重要的课题。基于金兹堡-朗道理论,我们从解析上研究了无序和有限温度对光晶格中超冷玻色系统相变的影响。我们的计算结果显示,无序强度的增加会使得系统的Mott绝缘相区域减小;热涨落的存在将进一步破坏Mott绝缘相,同时使得系统中出现了正常流体相。这里的金兹堡-朗道理论在最低阶近似下得到的相界方程与平均场结果一致,原则上很容易将计算结果推广到高阶从而给出超越平均场的结果。     

The Scalar Photon Light-Cone Distribution Amplitude in the Instanton Vacuum Model of QCD

Based on the principle of the Lorentz covariance, the transition matrix elements from an off-shell photon state to the vacuum are parameterized by the light-cone photon distribution amplitudes （DAs）. Both the scalar off-shell photon light-cone DA and the corresponding coupling are calculated in the instanton vacuum model of quantum chromodynamics （QCD）, and their explicit analytical expressions and the numerical results are given. The results for the other chiral-odd light-cone photon DAs and their couplings are presented as well.     

Nonautonomous dark soliton solutions in two-component Bose–Einstein condensates with a linear time-dependent potential

We report the analytical nonantonomous soliton solutions （NSSs） for two-component Bose-Einstein condensates with the presence of a time-dependent potential. These solutions show that the time-dependent potential can affect the velocity of NSS. The velocity shows the characteristic of both increasing and oscillation with time. A detailed analysis for the asymptotic behavior of NSSs demonstrates that the collision of two NSSs of each component is elastic.     

热色液晶无损检测技术

本文介绍了热色液晶在无损检测技术中的应用研究，并获得了非常成功的结果。通过液晶显示出的缺陷周围温度分布的色彩奇异性，可以明显地指示出缺陷的位置。