复合材料平面断裂中的J积分

本文采用复变函数方法,首先将裂纹尖端应力和位移代入J积分的一般公式得到了线弹性正交异性复合材料单向板复合型裂纹尖端的J积分的复形式,其次证明了该J积分的路径无关性,最后推出了该J积分的计算公式.作为特例,给出了线弹性正交异性复合材料单向板Ⅰ,Ⅱ型裂纹尖端的J积分的复形式,路径无关性和计算公式.     

线弹性正交异性复合材料板Ⅰ,Ⅱ型裂纹尖端的J积分

本文借助于复变函数方法,通过将J积分化为复形式,首先证明了线弹性正交异性复合材料板Ⅰ、Ⅱ型裂纹尖端附近的J积分的路径无关性,继而推出了该J积分在Δ<0和Δ>0两种情况下的计算公式.这对于将J积分应用于复合材料平面断裂的理论研究和实验校核中去,具有一定的参考价值.     

关于平面断裂中的J积分

本文利用复变函数和微积分的理论讨论线弹性各向同性均匀材料板和正交异性复合材料板Ⅰ、Ⅱ型裂纹尖端附近的J积分,得到了下列结果: (1)将各个J积分统一化为对坐标的曲线积分的标准形式:J=∫_rP(x,y)dx+Q(x,y)dy (2)证明了各个J积分的路径无关性. (3)推出了各个J积分的具体计算公式.     

含圆形孔口和水平直裂纹的平面问题的应力分析

利用复变函数方法和积分方程理论研究了既含有圆形孔口又含有水平裂纹的无限大平面的平面弹性问题,将复杂的解析函数的边值问题化成了求解只在裂纹上的奇异积分方程的问题.此外,还给出了裂纹尖端附近的应力场和应力强度因子的公式.     

带裂纹的弹性狭长体基本问题

利用复变方法和积分方程理论，讨论带任意裂纹的各向同性弹性狭长体的基本问题。通过适当的函数分解和积分变换，将问题简化为一正则型奇异积分方程。对方程解的情况和求解方法进行了研究，并导出裂纹尖端的应力强度因子。     

正交异性复合材料板复合型裂纹尖端的J积分

本文采用复变函数和微积分理论两种途径探讨线弹性正交异性复合材料板复合型裂纹尖端的Ｊ积分，得到了该Ｊ积分在△＞０和△＜０两种情况下的表示式，证明了它们的路径无关性，推出了它们的计算公式。     

受弯正交异性复合材料板的裂纹尖端场

本文对受对称弯曲载荷作用的线弹性正交异性复合材料板的裂纹尖端场进行了有关的力学分析。采用复变函数方法推出了裂纹尖端附近的弯矩、扭矩、应力、应变和位移的计算公式。     

椭圆孔边裂纹对SH波的散射及其动应力强度因子

采用复变函数和Green函数方法求解具有任意有限长度的椭圆孔边上的径向裂纹对SH波的散射和裂纹尖端处的动应力强度因子．取含有半椭圆缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移解作为Green函数,采用裂纹“切割”方法,并根据连续条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．讨论了孔洞的存在对动应力强度因子的影响．     

纯扭正交异性复合材料板的断裂分析

对受纯扭载荷作用的线弹性正交异性复合材料板裂纹尖端附近的断裂性态进行探讨。利用复变函数方法，通过求解偏微分方程的边值问题，推出了裂纹尖端附近的弯矩、扭矩、应力和位移的表达式，最后给出了数值算例。     

具水平直裂纹的弹性半平面运动载荷问题

利用平面弹性复变方法和积分方程理论，讨论具水平直裂纹的弹性半平面运动载荷问题，最后，得出应力函数封闭形式的解。     

OSCILLATION CONVERGENT THEOREMS FOR THE V^2-INTEGRAL

The V^t-integral as defined in[2], which is eqnivalent to M^2-integrsl as defined in Trigonometre series by Zygmund is used to sum trigonometric seies in[1]. In this paper, some convergent theorems of V^2-integral are established.     

A denjoy-type integral for Banach-valued functions

In this paper, we shall show that theHL ϕ-integral and the Denjoy ϕ-integral, defined in [2] are equivalent.     

Right closure of martingale sequences in the sense of theA-integral

In this paper new sufficient (necessary and sufficient for martingales of special form) conditions for the martingale closure from the right in the sense of theA-integral are given. These results follow from the theorem about passing to the limit under theA-integral. The theorem is established using the criterion for transposing iterated limits with respect to the base. It is shown that the sufficient conditions thus obtained are stronger than those previously known. Translated fromMatematicheskie Zametki, Vol.68, No. 1, pp. 98–104, July, 2000.     

The <Emphasis Type="Italic">A</Emphasis>-integral and its application in the study of P. L. Ul’yanov and other matematicians

In this paper we consider the A-integral and its application in the theory of trigonometric series.     

Connected Q-integral graphs with maximum edge-degree less than or equal to 8

Graphs with integral signless Laplacian spectrum are called Q-integral graphs. The number of adjacent edges to an edge is defined as the edge-degree of that edge. The Q-spectral radius of a graph is the largest eigenvalue of its signless Laplacian. In 2019, Park and Sano [16] studied connected Q-integral graphs with the maximum edge-degree at most six. In this article, we extend their result and study the connected Q-integral graphs with maximum edge-degree less than or equal to eight. Further, we give an upper bound and a lower bound for the maximum edge-degree of a connected Q-integral graph with respect to its Q-spectral radius. As a corollary, we show that the Q-spectral radius of the connected edge-non-regular Q-integral graph with maximum edge-degree five is six, which we anticipate to be a key for solving the unsolved problem of characterizing such graphs.     

关于C1-积分

本文利用Riemann和的Moore-Smith极限来定义并研究C1-积分.利用C1-积分的有关性质,讨论了C1-积分与C-积分之间的关系,并给出了一个零测度集特征函数C1-可积的充要条件,从而推广了文献[5]的有关结论.     

Ostrowski Type Inequalities on Time Scales for Double Integrals

In this paper we first derive an Ostrowski type inequality on time scales for double integrals via ΔΔ-integral which unify corresponding continuous and discrete versions. We then replace the ΔΔ-integral by the ∇ ∇-, Δ∇-, and ∇Δ-integrals and get completely analogous results.     

q-Laguerre polynomials and related q-partial differential equations

In this paper, we define two homogenous q-Laguerre polynomials, by introducing a modified q-differential operator, we prove that an analytic function can be expanded in terms of the q-Laguerre polynomials if and only if the function satisfies certain q-partial differential equations. Using this main result, we derive the generating functions, bilinear generating functions and mixed generating functions for the q-Laguerre polynomials and generalized q-Hahn polynomials. Cigler’s polynomials and its generating functions discussed in [J. Cao, D.-W. Niu, A note on q -difference equations for Cigler’s polynomials, J. Difference Equ. Appl. 22 (2016), 1880–1892.] are generalized. At last, we obtain an q-integral identity involving q-Laguerre polynomials. These applications indicate that the q-partial differential equation is an effective tool in studying q-Laguerre polynomials.