混合料配合比矿料组成设计的改进正规方程法

混合料配合比组成设计常用的数解方法是正规方程法,由于该方法不能直接考虑理论设计级配范围的约束条件,故按其计算结果配制的混合料不能保证一定满足理论设计级配要求.本文的改进方法以普通正规方程法得到的混合料级配为基础,对超出理论设计级配范围的筛分数据直接赋界限值,并作为目标级配再利用正规方程法进行迭代计算,最终得到满足理论设计级配范围要求的解.改进后的正规方程法算法简单明了、应用方便,计算结果收敛、稳定,且与二次规划法的计算结果完全相同,具有良好的工程适用性.     

具五次强非线性项的Lienard方程的新精确解

通过构造辅助方程,求出了具五次强非线性项的L ienard方程的多种新精确解,包括孤波解、三角函数解、Jacob i椭圆函数解.利用所得结果可以求出Kundu方程、导数Schr d inger方程和力学中重要的具五次强非线性项的波方程以及PC方程等重要非线性发展方程的精确解.     

Fe（Ⅱ）／UV对染料废水的脱色降解

主要研究了十种模拟染料废水在硫酸亚铁及紫外光作用下的脱色降解情况。结果表明：在适当的实验条件下，硫酸亚铁对所研究的模拟染料废水都具有脱色降解作用，紫外光不起作用，染料溶液的初始pH值、硫酸亚铁投加量、染料溶液初始浓度对溶液的脱色率均有影响。     

半正Neumann边值问题的解和正解的存在性与多解性

利用锥拉伸与锥压缩型的Krasnosel＇skii不动点定理考察了一类非线性Neumann边值问题的解和正解，其中允许非线性项有非正的下界．研究表明，只要非线性项在某些有界集上的最大高度和最小高度是适当的，这个问题便具有n（n为任意自然数）个解或者正解．     

子矩阵约束下三类矩阵方程的对称正交对称迭代解法

讨论了子矩阵约束下三类矩阵方程的对称正交对称迭代解,利用广义共轭梯度法构造了迭代算法,并证明了算法的有限终止性.该算法能自动判定解的情况:当矩阵方程(组)相容时,得到矩阵方程(组)的解;当矩阵方程(组)不相容时,得到矩阵方程(组)的最小二乘解.     

Fundamental formulation for frictional contact with graded materials

In the paper, we develop the fundamental solutions for a graded half-plane subjected to concentrated forces acting perpendicularly and parallel to the surface. In the solutions, Young's modulus is assumed to vary in the form of E(y) = E0e(ay) and Poisson's ratio is assumed to be constant. On the basis of the fundamental solutions, the singular integral equations are formulated for the unknown traction distributions with Green's function method. From the fundamental integral equations, a series of integral equations for special cases may be deduced corresponding to practical contact situations. The validity of the fundamental solutions and the integral equations is demonstrated with the degenerate solutions and two typical numerical examples.     

广义凸集值映射优化问题的强有效解

在局部凸Hausdorff拓扑向量空间中,研究了集值优化问题的强有效解.首先,在广义锥次似凸集值映射下,获得了集值优化问题的强有效解的标量化的特性,最后,获得了带广义不等式约束集值优化问题的强有效解的La-grange型最优性条件.     

广义凸集值映射优化问题的强有效解

在局部凸Hausdorff拓扑向量空间中,研究了集值优化问题的强有效解.首先,在广义锥次似凸集值映射下,获得了集值优化问题的强有效解的标量化的特性,最后,获得了带广义不等式约束集值优化问题的强有效解的La-grange型最优性条件.     

素数模19的同余方程的整数解

证明了连续正整数偶次幂之和,关于素数模19同余方程的若干性质,并给出了全部整数解。     

Adomian’s Method applied to solve ordinary and partial fractional differential equations

This paper presents a method to solve the problems of solutions for integer differential and partial differential equations using the convergence of Adomian’s Method. In this paper, we firstly use the convergence of Adomian’s Method to derive the solutions of high order linear fractional equations, and then the numerical solutions for nonlinear fractional equations. we also get the solutions of two fractional reaction-diffusion equations. We can see the advantage of this method to deal with fractional differential equations.     

基于格序偏好的模糊多目标决策方法

运用格论,将方案优选的全序刻画拓展为格序刻画.基于决策理论和模糊集理论,提出了模糊多目标格序决策的概念,建立了模糊多目标格序决策模型.基于正、负理想解的概念,提出了该模型的2种算法.算法1是先对模糊指标值进行加权,然后确定模糊正、负理想解,通过比较每个方案与两者之间的差异选择满意解.算法2是直接在原模糊指标值的基础上确定模糊正、负理想解,并引入满意度的概念刻画每个方案与两者之间的差异,最后通过加权得到满意解.算法1较简单,算法2则能始终保持模糊元素的线性性质.算例表明,2种算法结果一致.     

斜拉索静力解及其应用

为得到斜拉索的解析解，从索微元体的平衡方程出发，推导出含待定参数的解析式，并利用这些解析式探讨了各变量之间的关系。当测量中测得或设计中给出某些参数后，这些解析式便成为可用于工程设计和基于测量的强度检算的精确解。     

三阶边值问题解的存在性与唯一性

本文利用上下解方法研究了三阶边值问题解的存在性和唯一性。     

Travelling Wave Solutions for Generalized KdV-mKdV Equation

A technique based on reduction of order for solving ordinary differential equations is developed to find exact solutions for a generalized KdV-mKdV equation that possesses high order nonlinear terms. The analytical expressions of several types of travelling wave solutions for the equation are obtained in terms of sin, cos, tan, cot, sinh, cosh, tanh, coth and algebraic profiles. It is shown that the wave speed of travelling wave solutions and the coefficient of low order derivative term in the equation are two main factors to determine the change in the physical structures of solutions.     

盾构隧道管片力学模型的一种修正方法

为更准确的分析盾构隧道管片的变形特性,对常用的惯用法模型进行修正。并基于修正模型推导管片的位移解析解。结合哈尔滨地铁1#线工程资料,基于修正模型计算管片位移的数值解和解析解,同时计算基于惯用法模型的位移数值解,并将特殊位置处的位移进行对比分析。结果表明,对惯用法模型的修正是合理的,基于修正模型求得的位移解析解是正确的。     

Inflation Cosmological Solutions in Two-Dimensional Brans-Dicke Gravity Model

Introduction Inflation cosmology is an important theory fordescribing the evolution of the early universe. Thistheory attracts wide attention[1-3]because it can suc-cessfully explain the flatness, horizon and magnticmonopole problems, and may be supported experi-mently in observation of microwave background radia-tion. There are two basic types of inflation models:one is the higher-derivative gravity model; another isbased on the model of scalar field. These models areusually studied within th…     

互惠共生系统解的存在性和唯一性

利用上下解方法研究了某一类Ｖｏｌｔｅｒａ型互惠共生系统，得到了解的存在性和唯一性．     

向量优化问题的严有效解的最优性条件

在局部凸Hausdorff拓扑向量空间中,研究了集值映射向量优化问题的严有效解.首先,在广义锥次似凸集值映射下,获得了向量优化问题的严有效解的标量化的特性,最后,获得了带广义不等式约束向量优化问题的严有效解的Lagrange型最优性条件.     

向量优化问题的严有效解的最优性条件

在局部凸Hausdorff拓扑向量空间中,研究了集值映射向量优化问题的严有效解.首先,在广义锥次似凸集值映射下,获得了向量优化问题的严有效解的标量化的特性,最后,获得了带广义不等式约束向量优化问题的严有效解的Lagrange型最优性条件.     

Structural Multi-objective Probabilistic Design for Six Sigma

Uncertainties in engineering design may lead to low reliable solutions that also exhibit high sensitivity to uncontrollable variations. In addition, there often exist several conflicting objectives and constraints in various design environments. In order to obtain solutions that are not only "multi-objectively" optimal, but also reliable and robust, a probabilistic optimization method was presented by integrating six sigma philosophy and multi-objective genetic algorithm. With this method, multi-objective genetic algorithm was adopted to obtain the global Pareto solutions, and six sigma method was used to improve the reliability and robustness of those optimal solutions. Two engineering design problems were provided as examples to illustrate the proposed method.