Integral Geometry of Real Surfaces in the Complex Projective Plane

We give a Poincaré formula for any real surfaces in the complex projective plane which states that the mean value of the intersection numbers of two real surfaces is equal to the integral of some terms of their Kähler angles.     

Gauss整数环诸类问题探

本文主要探讨：（１） Ｇａｕｓｓ 整数环的定义及性质;（２） 其商环及性质;（３） Ｚ（ｘ）ｘ２＋ １同构于 Ｚ（ｉ）;（４） 两点猜想     

Φ~n空间中有界域上一种积分表示

本文应用单位分解的观点及积分表示中核函数的构造理论,得到~n空间中有界域上积分表示的一种抽象的一般形式,根据这种一般形式,可以得到至今许多区域上光滑函数和全纯函数种种已有的抽象公式和具体的积分公式。     

重积分和线面积分中的一个典型题目

针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻.     

Mixed Measures and Functionals of Translative Integral Geometry

The iterated translative versions of classical kinematic integral formulae for intrinsic volumes and curvature measures have led to a series of mixed functionals and mixed measures of convex bodies. Here, we present a systematic study of the integral geometric relations which hold for these mixed measures and functionals. We give new formulae involving halfspaces, reduction formulae and some spherical representations and also generalize some earlier results.     

Cn空间中有界域上一种积分表示

本文应用单位分解的观点及积分表示中核函数的构造理论,得到Cⁿ空间中有界域上积分表示的一种抽象的一般形式,根据这种一般形式,可以得到至今许多区域上光滑函数和全纯函数种种已有的抽象公式和具体的积分公式。     

一类曲面积分的解法

本文对定义在柱面上的一类函数给出了用定积分求曲面积分的方法 ,并证明了方法的可行性 .     

一类奇异积分的正则化方法

本文给出了一类奇异积分的一个正则化方法     

圆外平面弹性问题的边界积分公式

将边界上的应力函数及其法向导数展开为罗朗级数,与复应力函数的罗朗级数的表达式对比,可以确定罗朗级数的各系数,再利用傅利叶级数和卷积的几个公式进行计算,得到应力函数边界积分公式．通过边界的应力函数及其法向导数的积分,直接得到圆外应力函数值,并给出几个算例,表明结果用于求解单位圆外平面弹性问题十分方便．     

一道Lebesgue积分题目的注记

设E为n维欧氏空间Rn的可测子集,m E+∞,f(x)为E上的非负可测函数,并记Ek=E{x|k≤f(x)k+1}(k=0,1,2,…),利用Lebesgue积分的性质,通过构造反例,指出"级数∑k km Ek收敛"并不是f(x)在E上Lebesgue可积的充分条件.进一步,通过增加条件"f在E上a.e.有限",得到相应的充分必要条件.     

An Asymptotic Series for the Weber--Schafheitlin Integral

We obtain an asymptotic power series for the Weber--Schafheitlin integral whose coefficients are distributions.     

三次数域的整基和幂元整基

如何有效地找出数域的整基,是人们长期思考的问题.本文给出了求三次数域的整基的一个简单方法.此外,人们还对数域是否存在幂元整基的问题感兴趣.二次域和分圆域均存在幂元整基,而对于三次数域情形,则尚不清楚.本文给出了三次数域存在幂元整基的充要条件,从而对于三次数域情形给出了完整的答案.     

在整环上的几何空间中运动的分解

在整环R的几何空间V(R)上,给出运动A的座标阵的规范形,研究了用初等二平延中的旋转和伸缩,分解运动A的构作方法.并指出:当detA=1时,只须用的旋转个数L=r(r-1)个,就足以串成运动A;当1≠detA∈R*时,用一个伸缩和L=r(r-1)个旋转,也足够地串成运动A,其中r=resA.     

Solutions of the Equation of a Spinorial Yamabe-type Problem on Manifolds of Bounded Geometry

We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler–Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hijazi inequality for the underlying spin manifold.     

一个重积分问题的解法探究

滥演百题不如精做一题.一题多法是精做的重要途径、方式.本文讨论了一个二重积分问题不同的解法.     

傅里叶变换中一个含参变量广义积分的计算

本文利用含参变量广义积分计算中常用的求导和变量替换等技巧等给出了傅里叶变换中一个重要的含参变量广义积分的计算方法.     

Integral models of representations of current groups

We suggest a new construction of nonlocal representations of the current group. Instead of the Fock space, which is usually used in this situation, we consider the direct integral of countable tensor products of representations over the trajectories of some stochastic process. The construction substantially uses the invariance of the so-called infinite-dimensional Lebesgue measure.     

Initial Value Problem for a Nonlinear Evolution System with Singular Integral Differential Terms

The initial value problem for a nonlinear evolution system with singular integral differential terms is studied. Dy means of a priori estimates of the solutions and Lcray-Schauder's fixed point theorem, we demonstrate the existence and uniqueness theorems of the generalized and classical global solutions to the problem.     

Nonconvex optimization for third-order tensor completion under wavelet transform

The main aim of this paper is to develop a nonconvex optimization model for third-order tensor completion under wavelet transform. On the one hand, through wavelet transform of frontal slices, we divide a large tensor data into a main part tensor and three detail part tensors, and the elements of these four tensors are about a quarter of the original tensors. Solving these four small tensors can not only improve the operation efficiency, but also better restore the original tensor data. On the other hand, by using concave correction term, we are able to correct for low rank of tubal nuclear norm (TNN) data fidelity term and sparsity of $l_1$-norm data fidelity term. We prove that the proposed algorithm can converge to some critical point. Experimental results on image, magnetic resonance imaging and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and other methods.