变换中含有孤立稳定点的第二积分换元定理

在不定积分第二积分换元定理的条件中,要求变换x=φ(t)不含有稳定点,即:φ′(t)≠0.当变换x=φ(t)中含有孤立稳定点时,给出了变换中含有孤立稳定点的第二积分换元定理.拓宽了第二积分换元定理的应用范围.     

On meromorphic functions that share three values of finite weights

A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood-Yang's conjecture and Mues' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained.     

Minimax Theorems Involving Two Functions and Strictly Monotone Transformations of Their Values

Two two-function minimax theorems are proved.The concavity-convexity conditions of the twofunctions involve strictly monotone transformations and mixing of the values of the two functions,and aredescribed by the inequalities as upward and weakly downward conditions.     

一类具有转向点问题的n阶近似解

用Langer变换和Olver变换求得一类具有转向点问题的n阶近似解:y(x)=v(x)ψ(x),其中ψ=λ12-14×(x2-1)14,2332=-λx∫11-τ2dτ,v(z)=A(z,λ)ξ(λ23z)+B(z,λ)'ζ(λ23z).并探讨了其特征值问题,得到λn=4n+1112,n=0,1,2….由此给出了该类问题的解的一般性结论.     

Synthetic studies toward the immunosuppressant FR901483. Facile construction of the azatricyclic skeleton

A concise synthesis of the azatricyclic core structure of FR901483, a potent immunosuppressant, has been accomplished. The key elements of the approach involve a nucleophilic addition to an acyl iminium ion, a ring closing metathesis and a lactone-lactam rearrangement to provide the tricyclic structure.     

Total synthesis of malayamycin A and analogues

The total synthesis of the bicyclic C-nucleoside malayamycin A is described starting with d-ribonolactone. A new method was developed to obtain preparatively important quantities of β-pseudouridine, which was used as an intermediate. The synthesis of a carba N-nucleoside analogue of malayamycin A is also described.     

Investigation and reduction of variance of a weighted estimate in numerical statistical simulation

The efficiency of the “value” and “partial value” modeling related to the construction of a modeling distribution for an auxiliary random variable by multiplying the initial density by a value function is investigated. The value function usually corresponds to a solution of the adjoint equation. Conditions under which the value modeling of the initial distribution reduces the variance compared to the direct simulation are obtained. It is proved that the variance of the weighted estimate is bounded in the case of the partial value modeling. This proposition provides a basis for a method for determining whether or not the variance of the weighted estimate is bounded. This method uses the majorizing adjoint equation. Using a practically important problem in transport theory as an example, the asymptotic optimization of the distribution of the mean free path is presented. The application of the proposed method of the investigation of the variance boundedness for the analysis of the classical exponential transformation method of simulating the mean free path of a particle in the one-dimensional and the spherical variants is discussed.     

沿直线的垂直方向匀速直线运动的带电直线的电场

本文利用相对论变换关系计算了沿直线的垂直方向匀速运动的带电直线的电场.     

一种基于功率谱对数变换的联合变换相关器

联合功率谱的高频成份对相关峰识别具有重要作用,实验中记录的联合功率谱随着频率的增加其强度迅速降低。为增强联合功率谱的高频成分,改善其调制程度,可对功率谱进行对数变换,从而有效保留更多的高频成份,压低零级衍射光斑,提高联合变换相关器的识别能力。