关于重积分与线面积分内容体系的探讨

本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分，并且用第一类曲线、曲面积分定义第二类曲线、曲面积分。     

Some combinatorial identities via Fibonacci numbers

The Pascal matrix and the Stirling matrices of the first kind and the second kind obtained from the Fibonacci matrix are studied, respectively. Also, we obtain combinatorial identities from the matrix representation of the Pascal matrix, the Stirling matrices of the first kind and the second kind and the Fibonacci matrix.     

An algorithm based on the regularization and integral mean value methods for the Fredholm integral equations of the first kind

In this paper, an algorithm based on the regularization and integral mean value methods, to handle the ill-posed multi-dimensional Fredholm equations, is introduced. The application of this algorithm is based on the transforming the first kind equation to a second kind equation by the regularization method. Then, by converting the first kind to a second kind, the integral mean value method is employed to handle the resulting Fredholm integral equations of the second kind. The efficiency of the approach will be shown by applying the procedure on some examples.     

On an identity for zeros of Bessel functions

In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind.     

Stability analysis of methods employing reducible rules for volterra integral equations of the first kind

The concept of (A ₀,S)-stability for Volterra integral equations of the second kind will be extended to that of the first kind equations. We will show that stability polynomials for methods employing reducible quadrature rules, as applied to the first kind equations, can be trivially obtained from the results for the second kind equations.     

一类块三对角阵特征值的求解及应用

提出了求一类块三对角矩阵A的特征值和特征向量的方法,求得了该类矩阵的特征值和特征向量的表达式,并写出了用迭代法解该类方程组Au=f时迭代矩阵的特征值.     

Shapiro polynomials of the second kind

In this work by replacing the initial data in recursive relations the Shapiro polynomials of the second kind were introduced and their relation to the Shapiro polynomials of the first kind was established. In addition to the results similar to the known for the Shapiro polynomials of the first kind the following was defined: the relation was established between the coefficients of the basic and complementary polynomials of the first and second kind, namely, their pairwise orthogonality was proved and the number of the positive coefficients for all polynomials was counted.     

Dedekind和及第一类Chebyshev多项式

本文利用分析方法、Dedekind和及第一类Chebyshev多项式的算术性质,研究了一类关于Dedekind和及第一类Chebyshev多项式混合均值的渐近估计问题,并得到了一个较强的渐近公式.     

一些包含Chebyshev多项式和Stirling数的恒等式

利用初等方法研究Chebyshev多项式的性质,建立了广义第二类Chebyshev多项式的一个显明公式,并得到了一些包含第一类Chebyshev多项式,第一类Stirling数和Lucas数的恒等式.     

一类值型双层凸规划的Johri一般对偶

本文首先给出一类特殊的值型凸二次双层规划一其下层子规划只含有线性约束(简记为VBCP)；然后证明了一般形式的VBCP可以等价变换为非增值型凸二次双层规划的形式；最后给出该类双层规划VBCP的Johri对偶规划及其对偶性质．     

我国教育统计与教育统计指标体系

建立中国教育统计指标体系具有重要的现实意义，本文提出了第一类教育统计与第二类教育统计，分析了第二类教育统计的现状，指出了它的弊端，其目的是为了更好实现对基层教育的改革．     

A recursive algorithm for Bernstein operators of second kind

The Bernstein operators of second kind were introduced by Paolo Soardi in 1990, in terms of a random walk on a certain hypergroup. They have the same relation with Chebyshev polynomials of second kind as the classical Bernstein operators have with Chebyshev polynomials of first kind. In this paper we describe a de Casteljau type algorithm for these operators.     

Restricted Dumont permutations, Dyck paths, and noncrossing partitions

We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths. Finally, we enumerate Dumont permutations of the first kind simultaneously avoiding certain pairs of 4-letter patterns and another pattern of arbitrary length.     

第二类曲线(面)积分的向量学习法再探

以通量概念引入第二类曲面积分、以环流量概念引入第二类曲线积分,并用向量形式表达高斯公式、斯托克斯公式等关系,以期达到第二类曲线(面)积分部分的知识点符号表达简明、计算和公式容易记忆的目的.     

煤炭资源最佳开采时期研究

煤炭资源是一种不可再生资源,即耗竭性资源.现在的煤炭资源开采策略是一种掠夺式的开采,不仅浪费资源,而且会使我国的煤炭将来很难满足现代化建设的需要.为此,本文采用经济控制论模型试图探讨煤炭资源的最佳开采时期.     

Central simple superalgebras with anti-automorphisms of order two of the first kind

By a theorem of Albert's, a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the Brauer group. Our main purpose is to develop the theory of existence of anti-automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over K, where K is a field of arbitrary characteristic. First we need to generalize the Skolem–Noether Theorem to the superalgebra case. Then we show which kind of finite dimensional central simple superalgebras have an anti-automorphism of order 2 of the first kind.     

Error bounds of the Galerkin method for singular integral equations of the second kind

For solving singular integral equations of the first kind Erdogan proposed a method of Galerkin type, and convergence was proved by Linz. In this paper we consider equations of the second kind, and it is found that the method converges also in this case. However, stronger conditions than for the first kind equations must be imposed. The computational aspect of the convergence problem is also considered.     

Solutions to systems of linear Fredholm integral equations of the third kind with multipoint singularities

A new approach is used to show that the solution for one class of systems of linear Fredholm integral equations of the third kind with multipoint singularities is equivalent to the solution of systems of linear Fredholm integral equations of the second kind with additional conditions. The existence, nonexistence, uniqueness, and nonuniqueness of solutions to systems of linear Fredholm integral equations of the third kind with multipoint singularities are analyzed.     

On linear Fredholm integro-differential equations of first kind

We study the question whether linear one-dimensional integro-differential equations with constant limits of integration (equations of Fredholm type) containing no free differential expression (equations of first kind) can be reduced to integral equations of first kind and to Fredholm integro-differential equations of second kind.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 20–27.     

交叉数学规划问题

本文提出了一个新的数学规划概念──交叉数学规划问题．该问题的提出是以经济问题为其背景的．许多已有的规划问题上。对偶规划问题、双水平规划问题、多目标规划问题、参数规划问题以及对策问题均可作为交叉规划问题的特例．本文除系统地给出交及数学规划问题的基本定义外，还分别对各类交叉规划问题的有关理论及求解方法进行了初步的探讨．