立方公式论中的多重和的整表示与计算

基于Larman-Rogers-Seidel定理的最小立方公式存在性问题的新方法

A new approach for the existence problem of minimal cubature formulas based on the Larman-Rogers-Seidel theorem

针对球对称积分，研究在Möller下界取等号的4k+1次立方公式的存在性，证明高维最小公式中同心球面上任意两点的内积均为有理数，并由此证明对某些特殊积分，d>2时不存在13次和21次的最小公式。

Cubature formulas and Sobolev inequalities

We study a problem in the theory of cubature formulas on the sphere: given $θ\in (0, 1)$, determine the infimum of $\|ν\|_θ= \sum_{i = 1}^n ν_i^θ$ over cubature formulas $ν$ of strength $t$, where $ν_i$ are the weights of the formula $ν$. This problem, which generalizes the classical problem of bounding the minimal cardinality of a cubature formula -- the case $θ= 0$ -- was introduced in recent work of Hang and Wang (arXiv:2010.10654), who showed the problem to be related to optimal constants in Sobolev inequalities. Using the elementary theory of reproducing kernel Hilbert spaces on $S^{n - 1…

哈拉里和积分和图——详细综述

Harary's Sum and Integral Sum Graphs -- A Survey in detail

本文详细综述不同作者关于哈拉里提出的和图与积分和图的研究成果，其顶点标记分别为不同正整数与任意不同整数，介绍了相关概念及不同作者在其上的研究所得。

A study on edge coloring and edge sum coloring of integral sum graphs

Frank Harary introduced the concept of integral sum graph. A graph $G$ is an \emph{ integral sum graph} if its vertices can be labeled with distinct integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on vertices $u$ and $v$ is also a label in $G.$ For any non-empty set of integers $S$, let $G^+(S)$ denote the integral sum graph on the set $S$. In $G^+(S)$, we define an \emph{edge-sum class} as the set of all edges each with same edge sum number and call $G^+(S)$ an \emph{edge sum color graph} if each edge-sum class is considered as an edge color class of $G^+(S)$.…

$q$-analogs of sinc sums and integrals

$q$-analogs of sum equals integral relations $\sum_{n\in\mathbb{Z}}f(n)=\int_{-\infty}^\infty f(x)dx$ for sinc functions and binomial coefficients are studied. Such analogs are already known in the context of $q$-hypergeometric series. This paper deals with multibasic `fractional' generalizations that are not $q$-hypergeometric functions.

整表示系数的Egorychev方法的新应用及组合和的计算

New applications of the Egorychev method of coefficients of integral representation and calculation of combinatorial sums

本文介绍作者在70年代末提出的关于整表示系数和组合和计算的Egorychev方法的新应用及其在C^n中的代数和全纯函数理论等方面的应用。