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.     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

“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。     

Scattering Problem for a Classical Particle with Spin in a Coulomb Field

We investigate the scattering problem for a relativistic electron with spin in a Coulomb field in the framework of pseudoclassical mechanics. We obtain an analytic expression for the scattering angle and limiting estimates for the scattering parameters for the spinless and nonrelativistic cases. For small angles, the pseudoclassical model under consideration leads to the well-known quantum-mechanical Mott formula.     

Algebraic and Differential Nonlinear Superposition Formulas

Knowledge of the Lax pair and the Darboux transformation for a completely integrable system provides an iterative approach for generating exact solutions. This approach involves solving for the eigenfunction of the Lax pair at each step. But this process can be considerably simplified using the Bäcklund transformation and Bianchi's permutability theorem. This allows constructing the so-called nonlinear superposition formula, which provides a new solution of the system in terms of three previous solutions. The advantage of this approach is that the differential order of the nonlinear superposition formulas is lower than that of the Lax pairs, and in some cases, these formulas reduce to algebraic equations. We consider the construction of new nonlinear superposition formulas in the form of both differential equations and algebraic equations.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

关于L——函数的积分均值公式

利用 Hurwitz zeta—函数的函数方程及其解析方法给 Dirichlet L—函数的二次均值的一个较强的渐近公式.     

一种Cr─Mo─V冷轧辊钢回火工艺参数的研究

利用光学显微镜和电子显微镜对一种Cr－Mo－V冷轧辊钢淬火后的回火组织进行了观察．通过Hollomon关系式建立了该钢回火参数曲线，并在此基础上，建立了等效回方程，为该钢的热处理参数的选择提供必要的理论依据和试验依据．     

自然数同次幂级数求和的方法

本文利用微积分方法，推导出自然数同政幂级数的求和公式。