超几何函数与Tricomi算子

加性时空高斯白噪声扰动下双曲半平面中的Tricomi方程

The Tricomi equation in the hyperbolic half plane under additive space-time Gaussian White Noise perturbation

研究加性时空高斯白噪声扰动下Tricomi方程的柯西问题，通过傅里叶变换和艾里函数积分分析解的存在唯一性、平方可积性、样本路径连续性及空间平稳性。

变系数Hyperbolic Operators的基本解

Fundamental Solutions for Hyperbolic Operators with Variable Coefficients

本文描述了构造变系数算子基本解的新方法。该方法在“A note on the基本解for the Tricomi-type equation in the hyperbolic domain”（J.微分方程，206（2004）227--252）中被引入来研究Tricomi型方程。更精确地说，提出了一种新的积分算子，它将常系数方程Cauchy问题的基本解族转化为变系数算子的基本解族.

多元汇合型超几何函数的分解公式

Decomposition formulas associated with the multivariable confluent hypergeometric functions

这项工作的主要目的是显示如何一些相当基本的技术的基础上，某些逆对的符号运算符将很容易导致我们几个分解公式与汇合型超几何函数的两个和更多的变量。许多涉及这些符号运算符对的运算符恒等式首先是为此目的而构造的。利用这些算子恒等式，找到了几个分解公式，这些分解公式将上述超几何函数表示为高斯超几何函数的乘积等较简单的函数。

超几何函数$H_A, H_B,H_C$的分解

Decompositions for hypergeometric function $H_A, H_B,H_C$

借助符号算子的某些逆对技巧，研究了Srivastava三元超几何函数的几个分解公式.在这个问题上已经构造了一些操作者身份。借助于这些算子形式，我们找到了15种分解，它们都是用超几何高斯函数和Appell函数的乘积表示的。

通过超几何函数和谐振子研究 Prandtl 方程的线性不稳定性

Linear Instability of the Prandtl Equations via Hypergeometric Functions and the Harmonic Oscillator

本文利用 Kummer 函数与二次势 Schrödinger 算子，显式刻画二次剪切流附近线性化 Prandtl 方程的不稳定准本征模，并验证其与已有数值结果一致。

Hypergeometric Functions and Feynman Diagrams

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $ε$-expansion. As an example, we present a detailed discussion of the construction of the epsilon-expansion of the Appell function $F_3$ around rational values of parameters via an iterative solution of differential equations. As a by-product, we have found that the one-loop massless pentagon diagram in dimension $d=3-2ε$ is not expressible in terms of multiple polylogarithms. Another interesting example is the Puiseux-type solutio…

Linear peridynamics Fourier multipliers and eigenvalues

A characterization for the Fourier multipliers and eigenvalues of linear peridynamic operators is provided. The analysis is presented for state-based peridynamic operators for isotropic homogeneous media in any spatial dimension. We provide explicit formulas for the eigenvalues in terms of the space dimension, the nonlocal parameters, and the material properties. The approach we follow is based on the Fourier multiplier analysis developed for the nonlocal Laplacian. The Fourier multipliers of linear peridynamic operators are second-order tensor fields, which are given through integral represen…