狭长矩形梁弯曲问题的多项式应力函数解法

本文给出了求双调和方程和脱里谷米方程的部分特解的一些公式;并得到了分布载荷的集度按纵向坐标的四次幂规律变化时,狭长矩形梁弯曲问题的有限项数形式的多项式精确解.     

用摄动法和有限条法分析矩形板的大挠度

本文将摄动法和有限条法结合起来进行矩形板的大挠度弯曲分析.用摄动的概念,将非线性微分方程组化为一系列线性微分方程组,然后用有限条法解这些线性微分方程组.     

二维矩形条带装箱问题的改进左下角定位模型

针对不可旋转二维矩形条带装箱问题(2DR-SPP),基于两矩形的左下角单元坐标及其覆盖区域的关系,提出并证明了两矩形在条带箱中发生重叠的充分必要条件,然后根据此充分必要条件得到了禁止矩形重叠的约束条件,建立了问题的线性整数规划模型.增添旋转90~0后所得的矩形数据至原有的矩形数据中,基于更新后的矩形数据,修改不可旋转2DR-SPP的数学模型,得到了可旋转情形下问题的线性整数规划模型.算例结果验证了所建模型的有效性和准确性.     

关于矩形和斜带模型的反强迫数和反凯库勒数

在苯类化合物的凯库勒结构的研究中引入了反强迫数和反凯库勒数.通过分析矩形和斜带模型苯类化合物的分子图的结构,证明了具有k行l列的矩形R[k,l]和斜带模型Z[k,l]的反凯库勒数是2,R[k,l]的反强迫数是l,Z[k,l]的反强迫数不超过[(l+1)/2],其中[x]表示不超过x的最大整数.     

Rectangular group congruences on a semigroup

We study rectangular group congruences on an arbitrary semigroup. Some of our results are an extension of the results obtained by Masat (Proc. Am. Math. Soc. 50:107–114, 1975). We show that each rectangular group congruence on a semigroup S is the intersection of a group congruence and a matrix congruence and vice versa, and this expression is unique, when S is E-inversive. Finally, we prove that every rectangular group congruence on an E-inversive semigroup is uniquely determined by its kernel and trace.     

指数多项式在半带形中的闭包

该文对一类复指数多项式组成的线性空间$M(\Lambda )$ 在Banach 空间 H_α中的不完备性给出了充分必要条件, 其中 H_α为在半带形 I_α={z=x+iy: x≥ 0, |y|≤α} (α > 0 )中连续, 在I_α的内部解析且当 x→∞时, f(x+ iy)在I_α中关于 y 一致地 趋向 0 的函数 f(x+ iy)全体, 其范数为上确界范数. 同时指出, 如果$M(\Lambda )$ 在 H_α中不完备, 则它的闭包cl$(M(\Lambda ))$中所有的函数都可以延拓为由Dirichlet级数表示的解析函数.     

有限高狭长压电体中半无限反平面裂纹分析

利用保角变换和复变函数方法,研究了裂纹面上受反平面剪应力和面内电载荷共同作用下的有限高狭长压电体中半无限裂纹的断裂问题,给出了电不可通边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解．当狭长体高度趋于无限大时,可得到无限大压电体中半无限裂纹的解析解．若不考虑电场作用,所得解可退化为纯弹性材料的已知结果．此外,通过数值算例,分析了裂纹面上受载长度、狭长体高度以及机电载荷对机械应变能释放率的影响规律．     

Extrapolation of Finite Element Approximation in a Rectangular Domain

Recently, the Richardson extrapolation for the elliptic Ritz projection with linear triangular elements on a general convex polygonal domain was discussed by Lin and Lu. We go back in this note to the simplest case, i.e. the bilinear rectangular elements on a rectangular domain which is a parallel case of the one-triangle model in the early work of Lin and Liu. We find that the finite element argument for the Richardson extrapolation with an accuracy of $O(h^4)$ needs only the regularity of $H^{4,\infty}$ for the solution $u$ but the finite difference argument for extrapolation with $O(h^{s+\alpha})$ accuracy needs $u\in C^{5+\alpha}(0＜\alpha＜1)$. Moreover, a formula is suggested to guarantee the extrapolation of $O(h^4)$ accuracy at fine gridpoints as well as at coarse gridpoints.     

Rectangular arrays

In this paper we studied m×n arrays with row sums $\text{nr}\text{(n,m)}$ and column sums $\text{mr}\text{(n,m)}$ where (n,m) denotes the greatest common divisor of m and n. We were able to show that the function H_m,n(r), which enumerates m×n arrays with row sums and column sums $\text{nr}\text{(m,n)}$ and $\text{mr}\text{(n,m)}$ respectively, is a polynomial in r of degree (m?1)(n?1). We found simple formulas to evaluate these polynomials for negative values, ?r, and we show that certain small negative integers are roots of these polynomials. When we considered the generating function G_m,n(y) = Σ_r?0H_m,n(r)y^r, it was found to be rational of degree less than zero. The denominator of G_m,n(y) is of the form (1?y)^(m?1)(n?1)+3, and the coefficients of the numerator are non-negative integers which enjoy a certain symmetric relation.