查询词典 consistent system of equations

The so-called indeterminate equation is the solution in the range of integers, positive integers, rational numbers or integers of the equation or algebraic equations, whose unknowns are usually more than the number of equations ...

所谓不定方程是指解的范围为整数、正整数、有理数或代数整数的方程或方程组，其未知数的个数通常多于方程的。。。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

In this article, we study the solutions of several operator equations and the stability of operator equations and inequalities.

本文研究了几类算子方程的解与算子方程和不等式的稳定性问题。

To inequality constraint s, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

在无约束非线性规划问题全局优化的模拟退火算法基础上，进行有约束问题求解的进一步探讨，对不等式约束条件提出了检验法和罚函数法的处理方法，对等式约束条件开发了罚函数法和解方程法的求解步骤，并进行了分析比较，从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。

At the same time, the characteristic equations of the controlled systems with time delays are transcendental equations and belong to infinite dimensional systems, so it is difficult to study the time delay systems in mathematics theory and also difficult to obtain good performance for the time delay systems using the controller designed by classical control theory.

同时，由于含有时滞的控制系统的特征方程是超越方程，属于无穷维系统，对时滞系统的研究在数学理论上是非常困难的，有很高的理论价值，而且通过经典控制理论设计出来的控制器对时滞系统很难得到良好的控制效果。

There exists a dual symmetry between the equations of motion and the Maurer-Cartan equations of the type IIB superstring on AdS〓 S〓. We generalize the finite dual transformation to the infinitesimal dual transformation by the twisted dual.

根据Euler-Lagrange运动方程与Maurer-Cartan方程的扭曲对偶变换，我们可得到AdS〓×S〓中IIB超弦的Lax平联络及其相应的可积的相容条件，由此可以说明体系是一个可积系统。

2Nd order - Transport Equations: Integrability Conditions Yield Transport Equations, Complete Specification of Zero Order f

二阶- 传输方程式：可积分条件决定传输方程式，零阶f的完整描述

In the second chapter, modefied Taylor\'s expansion method is studied for solving Fredholm-Volterra integral equations, several illustative examples are given to show the efficiency of the proposed method. More over, by simple algebra, the modified Taylor\'s expansion can also be used to solve integral equations with weakly singular kernel, and the corresponding accuracy is dramatically promoted.

第二章重点讨论了应用Taylor展开方法解Fredholm-Volterra积分方程，通过数值例子，表明了该方法的简单有效性，特别应用于具有弱奇异核积分方程获得了更高精度的解。

New boundary integral equations for the torsion problem of an isotropic bar with curvilinear cracks are derived by using integration by parts and other techniques to the traditional boundary integral formulations. And the boundary integral equations for the torsion problem of an anisotropic bar with curvilinear cracks are also derived by using the isotropicalized boundary element method. Then the anisotropic problem can be solved on the base of the boundary element method of isotropic problem.

然后用各向同性化方法，将各向异性材料裂纹柱体的扭转问题转化为各向同性材料的问题，在各向同性材料裂纹柱体扭转问题的新的边界积分方程的基础上，推导出了适用于各向异性材料裂纹柱体扭转问题的边界积分方程，然后按已推导出的各向同性问题的边界元法求解。

Thin film equations; nonlinear cross-diffusion systems; two-dimensional nonlinear reaction-diffusion equations; invariant subspace method; invariant sets

基础科学，数学，数学分析薄膜方程；非线性交错扩散方程组；二维非线性反应扩散方程；不变子空间方法；不变集

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。