通解

发动机故障诊断的MonteCarlo通解算法

Monte Carlo general solution algorithm for engine fault diagnosis

联结Burgers方程与扩散方程的Cole-Hopf变换实际上是Backlund变换，而扩散方程众所周知是具有通解的。

The Cole-Hopf transformation join up with Burgers equation and the diffusion equation is Backlund transformation in fact , and the diffusion equation has the general solution as everyone knows .

给出B为非负定时的通解。

The general solutions with nonnegative definite matrix B are obtained .

n元一次不定方程的通解

The Solution of N-Variables Indefinite Equation of the First Degree

N阶常系数线性非齐次方程通解的积分表达式

An integral representation for general solution of n-order constant coefficient nonhomogeneous linear equation

（f，g）-反演的函数方程的通解

General Solution of ( f , g ) - Inversion

利用矩阵的初等行变换，简洁地给出了n元一次不定方程的通解公式。

By elementary rank transformations of matrix , the solution of n-variables indefinite equation of the first degree is obtained .

总论；二维Poisson方程的通解

The general solution of two dimensional Poisson equation

等幂和与Bernoulli数的通解公式

The General Expressions for Sum of Equal Powers and Bernoulli Number

其方法与Bлох的将已有的平衡方程通解带入到应力协调方程的方法恰好相反，得到的通解形式和Bлох的结果完全一致。

Different from B лох, the general solution is obtained by substituting the general solution of stress compatibility equations into equilibrium equations . This solution is identical with B лох 's .

用乘积的高阶导数莱布尼兰公式推导出了n阶常系数线性非齐次方程通解的积分表达式。

Leibniz ' formula of the product derivative of higher order has been adopted to derive an integral representation for general solution of n-order constant coefficient nonhomogeneous linear equation .

为研究n阶常系数非齐次线性常微分方程解的问题，求证了n阶常系数非齐次线性常微分方程的通解和特解的积分表达式。

To obtain the general solution and their special solutions in integration form , the way to get the n order non-homogeneous linear ordinary equation with constant coefficients was studied .

并参考圆薄板轴对称/反轴对称变形的弹性曲面微分方程及通解，获得E膜片的应力应变解析解。

The analytical solutions of the strain and stress are obtained from the elastic surface differential equations about the axisymmetric / non - axisymmetric deformation of circular plate .

构造出了符拉索夫板弯曲问题的Hamilton正则方程，给出了它的分离变量通解。

In this paper , the Hamilton canonical equation for Vlasov plates and its solution with seperation of variables is presented .

约束线性方程组通解的显式表示及Cramer法则

Explicit expression and Cramer rule for solution of restricted linear equations

利用分离变量方法即得到Helmholtz方程完备的通解。

Solving the Helmholtz equations by separating variable methods leads to the complete solutions of the potentials .

弹性地基上Vlasov板的位移通解

A general solution of displacement for Vlasov plates on elastic foundations

本文利用MATLAB符号工具箱，通过编程可求出齐次方程的解，通过自动寻找积分因子，从而求出全微分方程的通解，另外指出文献[3]中的一个错误。

This paper applies symbol toolbox of MATLAB to solve the implicit solution of the homogeneous and complete differential equation by programming and point out one error in reference [ 3 ] .

通过水冷受激光辐射产生极化倍频的非线性光学晶体工作特性的分析，建立了热分析物理模型，使用半解析热分析方法得出了KTP晶体温度场的通解表达式。

Through analysing the work characteristics of water-cooling nonlinear optical crystal irradiating with laser , thermal physics model was built .

在分析3D横向各向同性介质中平面波的通解形式时，发现似P波、似SV波及似SH波是相互耦合的，且同时并存。

Analysing the general solution of plane wave in 3D transversely isotropic medium , we found that quasi P-wave , quasi SV-wave and qu - asi SH-wave are coupling and coexistent .

本文应用李群方法，通过求解Hamilton-Jacobi方程，得出了一类可积的Lagrange系统的通解。

The general solution of a kind of Lagrange system is obtained by using Lie group method and Hamilton Jacobi theorem .

第二种通过右互质既约分解，给出了通解关于一组自由参量和矩阵J的特征值的显式表达式。

By utilizing some right coprime fractions , the second solution is given in an explicit form with respect to the free parameter vectors and the eigenvalues of the matrix J.

其次证明了广义多圆柱区域上正则函数的Dirichlet边值问题的可解性并给出了通解表达式；

Prove the solvability of the Dirichlet boundary value problem for regular quaternion functions in a generalized polycylinder and obtain its expressions of solution ;

首先，利用Hankel积分变换方法，直接对频域内的Biot波动方程进行求解，得出Biot波动方程的通解；

The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique .

一类4×4退化上三角量子色Yang-Baxter矩阵方程的通解（Ⅰ）

General Solutions of 4 × 4 Singular Upper Triangle Quantum Coloured Yang-Baxter Matrix Equation (ⅰ);

通过建立相对运动的通解公式，针对不同性质的初值深入地分析了其相对运动轨迹的本质特征，并给出了Hill方程的适用条件。

By using necessary geometry mapping , general expression is built up , and then the relative motions under different initial conditions are so comprehensively characterized that the applicability condition of Hill 's approximation is obtained .

获得Biot固结方程和简化Biot固结方程的位移、应变和应力的势函数通解表达式。

The generalized expressions of displacements , strains and stresses for general and simplified Biot 's equations of consolidation are expressed in terms of the potential functions .

几类CLAIRAUT型常微分方程的通解公式

Formulae of General Solutions to Some Kinds of Clairaut Constant Differential Equations

并在τ度规下，解torus上的玻色弦及其鬼的运动方程，得到了弦场和鬼场通解形式；

Then we solve the equations of motion for bosonic string and their ghost fields under the general metric , and obtain the general solutions of the equations .

依据线性微分方程系统的通解，可以通过实验和数学方法求取速率常数矩阵K的特征向量和特征值，从而解决了计算速率常数矩阵的问题。

Based upon the general solution of systems of linear differential equations and from certain experimental and mathematical procedures , it is possible to determine the eigenvectors and eigenvalues of the coefficient matrix , and from which the coefficient matrix itself can be evaluated .