查询词典 structure equations

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.

首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。

Rumjantsev used Hamilton's principle with Lagrange's multipliers to generate the dynamical equations of a rigid-fluid coupled system in 1954 and the dynamical equations and their dynamical boundary conditions of a fluid-elastic coupled system in 1969, where the fluid is incompressible and inviscid. In 1990, Liu used Jourdain's principle with Lagrange's multipliers to generate the dynamical equations of a rigidfluid coupled system, where the fluid is incompressible and viscid.

Rumjantsev利用带Lagrange乘子Hamilton变分原理于1954年建立了刚—流耦合系统的动力方程，于1969年建立了流—弹耦合系统的动力方程及其动力边界条件，其中所考虑的流体是不可压无粘液体；Liu利用带Lagrange乘子Jourdain变分原理于1990年建立了刚—流耦合系统的动力方程，其中所考虑的流体是不可压粘性液体。

The dynamical equations of a liquid-filled tank were deduced using Jourdain principle,including the momentum and angle momentum equations for the coupling system and Navier-Stokes equations for the liquid sloshing.

液体模块采用Lagrange-Euler描述方法建立有限元计算模型；充液刚体模块利用二阶显式Runge-Kutta格式离散的常微分方程组。

On the basis of classical lamination theory and large deflection hypotheses of plate, the equilibrium and compatibility equations of simply supported composite laminated plates were obtained. The nonlinear partial differential equations are transformed into the ordinary differential equations of Kronecker tensor product by series expansion and solved numerically by the fourth-order Runge-Kutta method.

基於经典的层合板理论及板的大挠度基本假设，得到四边简支层合板的非线性运动方程及变形协调方程；用级数展开把非线性偏微分方程组化为易於求解的Kronecker张量积形式的二阶常微分方程组，并由四阶Runge-Kutta法数值求解。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

We calculate the differential characteristic set of determining equations for source evolution equations (include several linear and nonlinear differential system of equations).

用算法′计算了几个微分方程对称的确定方程组(包括线性微分方程组以及非线性微分方程组)的微分特征列集，并在计算量上对算法′与算法进行了比较。

By employing the local Lipschitz condition and Picard sequence, the local existence-uniqueness of solutions of stochastic functional differential equations of Ito-type is firstly obtained. Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition. Finally, by establishing some delay differential inequalities and using properties of H_m-functions, a stochastic version of Wintner theorem and the global existence-uniqueness of solutions of stochastic functional differential equations of Ito-type are given. The results generalize the earlier publications.

首先，利用局部Lipschitz条件和Picard序列，获得了伊藤随机泛函微分方程解的局部存在唯一性；其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；最后，通过建立一些时滞微分不等式和利用H_m-函数的特性，得到了Wintner定理的随机版本和伊藤随机泛函微分方程解的全局存在唯一性，推广了已有的一些结果。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

The subject of equations in mathematical physics includes partial differential equations and integral equations arise in physics and engineering.

数学物理方程主要研究物理或工程问题中所涉及的各种偏微分方程和积分方程。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。