Shift Harnack inequality and integration by parts formula for semilinear stochastic partial differential equations

Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.     

Time Operators and Approximation of Continuous Functions

The main purpose of this paper is to study time operators associated with generalized shifts and determined by the Haar and Faber–Schauder bases on the space of continuous functions. It is given the characterization of the domains of the constructed time operators and their scalings. It is also shown how scalings of time operators affect the dynamics of associated semigroups of shift operators.     

基于新的整数型分子图论指数M系统探索烷烃核磁共振碳谱(13C NMR)化学位移和CSS规律

系统研究了核磁共振碳谱与化学位移和规律,以及拓扑图论方法在定量结构波谱关系(QSSR)中的应用.本文基于路径长度矢量p=p1,p2,p3,…,pm)组合研究提出了一种新的整数型拓扑图论指数M=(p1+p2)+(p1-p3),并发现它与烷烃¹³C NMR化学位移和有良好线性相关性:回归方程及其统计参数为CSS=+14.329^* M-21.089;n=65,R=0.991,SD=7.684,F=3648.021,U=215381.656,Q=3719.563;交互校验CV结果为:R=0.990,R²(01)=0.981,SD(01)=8.086,F(01)=3288.113,U(01)=214982.172,Q(01)=4119.042.     

序列伪轨跟踪性与拓扑可迁

给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。     

两种DⅢ型有界对称域的逆ABEL变换

利用ｂｃ２型根系的三个转移算子Ｄｉ（１≤ｉ≤３）,我们在本文中给出了有界对称域ＳＯ＊（８）／Ｕ（４）及ＳＯ＊（１０）／Ｕ（５）上初等球函数和逆Ａｂｅｌ变换的显式表达。     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

微波强场中的光谱激发及其谱线特征

本文报道了关于微波强场中的光谱激发现象的最新研究,并对微波强场激发光谱（ＭＳＥＳ）和普通的原子发射光谱（ＡＥＳ０的比较光谱进行了分析,对其中出现的谱线偏移现象进行了重复性实验。     

一个计算次甲基质子NMR化学位移的经验式

本文提出了一个计算次甲基质子NMR化学位移的经验式δ_CHXYZ=δ_(CH3)2CHZ+△_xy主要用来计算那些Bell、Bowles和Senese关系式不适用的、含有无去屏蔽作用的次甲基质子体系中次甲基质子的化学位移。     

A New Class of Completely Unitary Invariants in B_n(Ω) and the Commutant of Weighted Unilateral Shift Operators

ＡＮｅｗＣｌａｓｓｏｆＣｏｍｐｌｅｔｅｌｙＵｎｉｔａｒｙＩｎｖａｒｉａｎｔｓｉｎＢ_ｎ（Ω）ａｎｄｔｈｅＣｏｍｍｕｔａｎｔｏｆＷｅｉｇｈｔｅｄＵｎｉｌａｔｅｒａｌＳｈｉｆｔＯｐｅｒａｔｏｒｓＹａｎＣｏｎｇｑｕａｎ（严从荃）（ＤｅｐａｒｔｍｅｎｔｏｆＭ?..     

二阶变系数线性差分方程的Mikusinski算符解法

本文利用Mikusinski算符域中变数算符的概念和相应的变系数移动算符幂级数的概念和结果,成功地获得二阶变系数线性差分方程的解。