关于三次高斯和的均值

主要研究三次高斯和的均值性质，并给出一个较强的渐近公式。     

几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

The uniqueness of solutions of perturbed backward stochastic differential equations

We prove a result on the preservation of the pathwise uniqueness property for the adapted solution to backward stochastic differential equation under perturbations.     

“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

KNbO3：Fe晶体的时间微分效应及图像追踪

本文观察到了KNbO_3:Fe晶体的时间微分效应,并用这个微分效应进行了图像追踪的演示,为KNbO_3:Fe晶体在光折变器件领域的应用进行了有益的探索。     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.