查询词典 galerkin equations

Initial boundary value problem of two dimensional unsteady diffusion equations is solved in this paper. By using time-dependent fundamental solution of two dimensional diffusion equations and the extension of double layer potential, we establish virtual boundary integral expression of diffusion equations. Then virtual boundary element method is used to implement the numerical computation.

本文在求解二维非定常扩散方程的初边值问题时，利用二维扩散方程与时间有关的基本解，基于双层位势的延拓，建立二维扩散方程的虚边界积分表达式，然后利用虚边界元法进行数值计算。

Due to equivalent transformation during the simplification procedure of equations, the solution set of equations can neither expand and nor contract, and also the transformed equations for four displacement functions are compact in the form and easy to find their solutions.

由于方程化简过程是等价变形，从而可以保证方程的解集既不会扩大也不会缩小，而位移势函数便给出了一维六方准晶中弹性解的一个通解公式。

For the long composite cylindrical panels, including the influences of the transverse shear deformation, rotatory inertia and initial geometric imperfections, the nonlinear dynamic equations of the long composite cylindrical panels were derived from Hamilton's philosophy. The nonlinear partial differential equations were transformed to ordinary differential equations by expansion in series and solved numerically by fourthorder Runge-Kutta method.

针对含初始几何缺陷的复合材料圆柱曲板，考虑横向剪切变形、转动惯量、初始几何缺陷以及非扁壳等诸多因素，利用Hamilton原理导出复合材料长圆柱曲板的非线性动力方程；用级数展开把非线性偏微分方程组转化为二阶常微分方程组，并由四阶Runge-Kutta方法数值求解。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

The influence of initial imperfections on the stability ofcomposite laminated plates was studied by solving the nonlinear governing equations for laminated plates with elastical restraints subject to in-plane loading using the energy variational principle and nonlinear geometric equations incorporating the initial imperfection. The governing equations were solved using generalized Fourier series to obtain the effect of the non-uniform order term.

为深入研究初始缺陷对复合材料层板稳定性的影响，利用能量变分原理和考虑初始缺陷的非线性几何方程，建立了具有弹性约束的层合板在面内载荷作用下的非线性稳定性控制方程组，运用广义傅立叶级数法对其进行求解，并进一步获得了影响非线性稳定性控制方程组的性质的非齐次项。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

The Hankel transformation method has been used to turn the basicdisplacement equations and displacement-stress constitutive equations intoa system of first order non-homogenous ordinary differential equations inwavenumber domain,and by us of the matrix method,the transfer matrix ofthe medium layered is established.

利用Hankel变换，将轴对称静力问题的位移基本方程和位移应力本构方程转化为波数域内非齐次一阶常微分方程组，利用矩阵法，建立了介质层的传递矩阵，导出了层状弹性半空间轴对称静力问题奇异解的一般解析表达式。

The model is usually an inhomogeneous system of linear equations. It is pointed out that the general solution of the homogeneous system of linear equations can satisfy the request of making the wires tight, and the special solution of the inhomogeneous system of linear equations are not smaller than zero, so their sum is greater than a given mumble.

由于多自由度绳牵引并联机构的静力学模型一般是一个非齐次线性方程组，本文指出可让对应齐次方程组的通解的最小值满足绳保持张紧的条件；让非齐次线性方程组的特解非负，而避免利用对应齐次线性方程组的通解保证非齐次线性方程组的解不小于给定的最小值。

Based on the hydrokinetics study of jigging process, the free vibration equations of ideal fluid and actual flow vibration equations have been established. These equations are the theoretical foundation to set the operation parameters and air pressure of the jig. The similar criteria and their related equation of model jig have been deducted by actual flow vibration equation. These similar criteria can be used for parameter transformation between model jig and industrial jig. One set of single cell model jig with measuring system has been constructed in laboratory.

本文通过对跳汰过程的流体动力学研究，建立了跳汰机中理想流体的自由振动方程和实际水流的振动方程，为跳汰机工作制度及风源风压的确定提供了理论依据；利用跳汰机中实际水流的振动方程推导出了跳汰机模型试验的相似准数，建立了模化准则关系式，为工业跳汰机与实验室跳汰机之间的参数转换提供了理论依据；并设计建造了一套实验室单槽模型跳汰机及其实验检测系统，为深入开展跳汰理论的研究创造了条件。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。