一种基于过滤与反卷积的新型高阶浸没边界法

传统浸没边界法在边界附近只有一阶精度,而高精度的改进方法都需要额外引入跳跃条件,因此不具备普适性．文中设计了一种基于过滤和反卷积的新型算法,既在一定程度上提高了精度,又避免了以往方法中引入额外跳跃条件的难题．通过一个简单的一维算例验证了新算法可以达到接近二阶精度,其具体的精度值与反卷积步骤中选取的逆核函数在积分域边界的连续性有关．     

一种新的退卷积解谱技术

本文介绍一种新的退卷积方法,它是将退卷积问题化为求解逆矩阵问题,用奇异值分解(SVD)法处理病态矩阵体系,结合本文提出的最佳判据,求得退卷积结果。该方法已用 FORTRAN 5编成程序,对实验观测能谱及计算机模拟谱进行了退卷积处理,方法可靠,且退卷积解是稳定的。     

无穷远点处亚纯单叶函数的拟Hadamard卷积(英文)

本文研究了圆环域U内亚纯星象和凸象函数的某些新子类的拟Hadamard卷积.利用卷积方法,获得了该类函数的与拟Hadamard卷积有关的某些性质,推广了一些已知结果.     

扩展G-期望下的最小卷积问题(英文)

文章研究了在多维的G-分布期望下的最小卷积问题,并且得到了多维G-分布期望的最小卷积和生成元G的最小卷积的关系.此外,我们还研究了此问题的连续性性质和动态性质.     

软卷积代数

利用软集的概念定义软卷积代数,这一概念将卷积代数与关联代数统一到软卷积代数的概念下,给出软卷积代数的基本性质并研究了它的幂等性和二元关系"≤"性质。     

不同分布的卷积的局部封闭性及局部渐近性的充分条件和必要条件

得到了支撑在[O,∞)上的不同分布的卷积(包括卷积根)的局部封闭性及局部渐近性的充分条件和必要条件,它揭示了不同分布的卷积及两两卷积之间的内在关系.这一结果的充分性部分推广了Geluk等非局部的相应结果,并且两者使用的方法是不同的;而这一结果的必要性部分是Geluk等人的结果中所没有的.最后,讨论了(-∞,∞)上不同分布卷积的局部封闭性及局部渐近性.     

广义次指数密度的两个新的等价条件

得到了广义次指数密度的两个新的等价条件,刻划了它们的卷积封闭性和卷积根封闭性.     

球面卷积算子逼近

研究d维欧氏空间R~d中单位球面上卷积算子的逼近问题.利用球面乘子理论以及K-泛函与光滑模等价关系,建立一类球面卷积算子逼近的正、逆定理.特别地,给出了逼近的强型逆向不等式,从而揭示了该类球面卷积算子的本质逼近阶.此外,作为应用,给出了球面Jackson-Matsuoka卷积算子与Abel-Poisson卷积算子逼近上、下界的相同阶估计.     

一类解析函数的广义λ-Hadamard卷积

首先引进一类具有负系数的广义星象函数子类及其广义λ-Hadamard卷积;其次,利用从属关系证明了属于该类函数的充要条件;最后,研究了在函数类上广义λ-Hadamard卷积及其相关特殊卷积的封闭性质.所得结果改进和推广了Choi等人的主要结果,并得到了一些新结果.     

超大型二维循环卷积的FPT和FNT混合算法

本文将FPT和FNT相结合提出了一种计算超大型二维循环卷积的迭代算法,它的基础是应用了FPT.与二维循环卷积的FPT算法相比,乘法量减少了一个数量级,同时实际取消了FNT算法中卷积规模所受到的字长的限制.     

Brunn–Minkowski and Zhang inequalities for convolution bodies

A quantitative version of Minkowski sum, extending the definition of θ$\theta$-convolution of convex bodies, is studied to obtain extensions of the Brunn–Minkowski and Zhang inequalities, as well as, other interesting properties on Convex Geometry involving convolution bodies or polar projection bodies. The extension of this new version to more than two sets is also given.     

一类全不连通群上的BMO和奇异积分算子

本文主要讨论了定义在局部紧的全不连通群Ｇ上的一类卷积算子在加权Ｌ^∞（Ｇ）和ＢＭＯ（ａ）空间的性态．证明了如果卷积算子的核满足适当的条件,则算子是Ｌ^∞（Ｇ）到ＢＭＯ（ａ）有界的或是ＢＭＯ（ａ）到ＢＭＯ（ａ）有界的．     

Fractional Crank–Nicolson–Galerkin finite element scheme for the time‐fractional nonlinear diffusion equation

This article presents a finite element scheme with Newton's method for solving the time‐fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank–Nicolson scheme based on backward Euler convolution quadrature. We discuss the existence‐uniqueness results for the fully discrete problem. A new discrete fractional Gronwall type inequality for the backward Euler convolution quadrature is established. A priori error estimate for the fully discrete problem in L²(Ω) norm is derived. Numerical results based on finite element scheme are provided to validate theoretical estimates on time‐fractional nonlinear Fisher equation and Huxley equation.     

On integral convolution operators

We study integral convolutions defined on functions ofn variables in symmetric spaces and obtain new additive estimates for the mean value of the nonincreasing permutation(K ^* f) ^** (t) of the absolute value of the integral convolution on the interval [0,t] for anyt>0. As an example of application of the estimates obtained, we prove the boundedness of the integral convolution operator acting from the intersection of symmetric spaces into the Marcinkiewicz space. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 551–555, October, 1999.     

On the blow-up of solutions to a nonlinear dispersive rod equation

Using a variational approach we prove an optimal nonlinear convolution inequality. This result is then applied to give criteria for finite-time blow-up of solutions to a nonlinear model equation in elasticity, improving considerably upon recent blow-up results.     

Two-weight inequalities for convolution operators in Lebesgue space

In this paper, we prove a theorem on the boundedness of a convolution operator in a weighted Lebesgue space with kernel satisfying a certain version of Hörmander’s condition.     

Fefferman-stein不等式和齐次群上Herz型Hardy空间的极大特征

本文延拓Fefferman-Stein加权极大不等式到齐次群上，作为其应用，建立了齐次群上伴随于Herz空间和Beurling代数的Hardy空间极大特征。同时，得到了具(α，r)型核的卷积算子在这些Hardy空间上的有界性。     

Convolution theorems associated with some integral operators and convolutions

In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.     

Near Equality in the Riesz–Sobolev Inequality

The Riesz–Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of appropriately situated intervals. We characterize ordered triples of subsets of R~1 that nearly realize equality, with quantitative bounds of power law form with the optimal exponent.