模拟结果与微扰理论和平均球近似积分方程理论的预测值进行了比较。
The simulated results are analyzed and compared with those predicted from perturbation theory and integral equation theory under mean spherical approximation.
同时利用带位的奇异积分方程理论得到了这一问题可解的主要条件及指数计算公式。
By the singular integral equation theory we obtain the resolvable sufficient and necessary condition and the formula of counting index for the problem.
运用泛函分析和积分方程理论，证明了系统解的存在性与唯一性，得到系统解的解析表达式。
Applying the theory of integral equation and functional analysis, we prove the existence and uniqueness of the system solution to the equation, and get the analytical expression of the solution.
用近代统计力学研究成果——积分方程理论和微扰理论简要评述了电解质和非电解质溶液的国内外研究进展。
A brief review by the progress of advanced statistical mechanics, integral equation and perturbation theory for electrolyte and non-electrolyte solutions in recent years is presented.
笔者通过适当的函数分解和积分变换，将寻求复应力函数的问题转化为求解一正则型奇异积分方程，并借助积分方程理论给出了方程的求解方法。
Using proper decomposition of the functions and integral transformation, the problem is reduced to a singular integral equation, whose solution is given of the theory of integral equation.
讨论了解常微分方程的积分因子法在极限理论、微分学、积分学中的一些应用。
Some simple application of method of integrating factor that solve ordinary differential equation is discussed on the limit theory, differential and integral.
利用不动点理论，给出了一类时滞积分方程渐近概周期解的存在性定理。
Using the theory of fixed point, we give a theorem about the existence of asymptotically almost periodic solution for a class of delay integral equations.
本文利用不动点理论，给出了一类非线性延迟积分方程正的概周期型解的存在性条件。
In this paper, we give the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations.
利用不动点理论，给出了一类非线性积分方程正的遍历解存在的充分条件。
Applying fixed points theorem, we give the sufficient conditions of the existence of positive ergodic solutions for a class of infinite nonlinear integral equations.
本文研究拖索稳态理论的三维问题，建立了微分方程，提出了一个简便的积分方法，并且用优化方法处理与此相联系的边值问题。
The three-dimensional steady state theory of towing cable is studied, with differential equations derived and a simple method of integration suggested.
对于离子液体的研究理论上主要是用解析或数值计算求解积分方程组。
The theoretical investigation in ionic fluids has been done with analytical or numerical calculation of integral equations.
本文在严格、完整的基础上，利用矩阵范数理论研究了结构非线性动力分析中数值积分格式的稳定性问题，给出了判别单自由度非线性动力方程积分格式稳定性的一般数学准则。
The problem of stability in the numerical integration schemes of nonlinear dynamic analysis of structures is discussed by using matrix and norm theory on a rigorous and complete basis in this paper.
从边界层动态微分方程出发，按照速度边界层有关理论，推导出了边界层动态积分方程。
Based on the dynamical differential equations for the velocity boundary layer, dynamic integrate equation is drawn.
在求解动力学系统的方程中，动力学系统的第一积分与积分不变量是求解运动方程积分理论的重要内容之一。
The first integration and integrated invariant of dynamic system belongs to important contents of solving equations of motion integrated theory during solving equations in dynamic system.
在分数阶微积分的理论框架下，将分形动力学的机制引入到生物黏弹性本构方程的研究中。
Within the framework of the fractional calculus theory, the mechanism of fractal dynamics is introduced to the constitutive equation research of viscoelastic materials.
得到的积分方程中的积分核具有奇异性，再根据R -函数理论，可以选择适当的边界规范化方程，消除核的奇异性。
By choosing suitable boundary normalized equation in according to R-function theory, the irregularity of integral kernel in integral equation can be eliminated.
使用边界积分方法求解已知第二类边界条件的拉普拉斯方程或泊松方程时，理论上解是不唯一的。
Theoretically the numerical solution of Poisson's equation or Laplace's equation plus Neumann boundary condition calculated by the boundary integration method is not unique.
利用不动点理论，给出了一类非线性延迟积分方程正的渐近概周期解存在的充分条件。
Using fixed point theorems, in this paper we give sufficient conditions of the existence of asymptotically-almost-periodic solution for some nonlinear delay integral equations.
通过对能量方程进行体积分得到了三维流场中场协同理论的表达式。该式不仅含速度矢量与温度梯度矢量的点积项，还含有速度矢量与压力梯度矢量的点积项。
In this article the mathematical expression of field synergy theory for three dimensional flow with centrifugal force was derived by integrating the energy equation in the concerned volume.
应用广义特征线理论得到了沿特征线上的相容方程，并采用数值积分方法分析了有限长圆柱壳的波传问题。
By using the generalized characteristics method, the compatibility equations on the characteristics are obtained. And the wave propagation of the finite length cylindrical shell is analyzed.
偏微分方程数值方法，积分方程法，课程3：离散收敛理论(PDF)。
Numerical Methods for PEDs, Integral Equation Methods, Lecture 3: Discretization Convergence Theory (PDF).
利用更新理论和随机过程等方法，给出了模型生存概率所满足的微积分方程关系式和破产概率的一个上界估计。
The differential and integral equation for survival probability and a upper bound of ruin probability are given by using renewal theory and stochastic process approach.
至于解第一类积分方程机械求积法，由于 相关的聚紧理论对弱奇异第一类 积分方程失效，未得到充分研究。
On the one hand, the mechanical quadrature methods (MQM) for solving BIE of the first kind are void of the collectively compact theory, so they have not been sufficiently analyzed yet;
至于解第一类积分方程机械求积法，由于 相关的聚紧理论对弱奇异第一类 积分方程失效，未得到充分研究。
On the one hand, the mechanical quadrature methods (MQM) for solving BIE of the first kind are void of the collectively compact theory, so they have not been sufficiently analyzed yet;
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