查询词典 solvable equation

Using Biot's 2D elastodynamic theory solves the saturated soil equation. The Fredholm integral equation of the second kind can be built by using the fundamental solution of circular load, the compatibility condition and superposition method. The Fredholm integral equation of the second kind of pile groups can be solved by using numerical method. The numerical solutions of pile groups axial forces, pore pressures under vertical harmonic loading and shear forces, moments and pore pressures under horizontal harmonic loading can be obtained.

采用Biot提出的三维波动原理，利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件，并采用叠加原理得到饱和土中群桩的第二类Fredholm积分方程，应用数值法求解群桩的第二类Fredholm积分方程，得到在垂直简谐载荷作用下群桩的轴力、孔压随桩身变化的数值结果以及在水平简谐载荷作用下群桩的剪力、弯矩和孔压随桩身变化的数值结果。

Then the momentum P in the acquired motion equation is replaced by quantum operator, thus we obtain Schrodinger equation for charged particle moving in magnetic fields in Quantum Mechanics. Then we discuss the Gauge transformation and gauge invariance of Schrodinger equation, following which the Dirac phase is introduced.

然后把经典力学中的哈密顿量量子化，得到量子化的带电粒子在磁场中运动的薛定谔方程，之后是薛定谔方程的规范变换和规范不变性，并引入Dirac不可积相因子的概念。

After descibing the concepts, definitionsand operation approaches of quantum group and SLq(2) Lie algebra, the physicalmeaning of quantum group particles is explained in the present thesis. The gaugeinvariance in SLq(2) gauge field and its thermodynamics model is considered basedon the idea of q-deformation. The zero energy gap equation and q-deformed energygap equation are derived under the assumption of q-quantization and semi-classical q-quantization, then the zero-temperature energy gap A(0,q) and crititical temperature〓 can be calculated from the q-energy gap equation.

在介绍了量子群和SLq(2)李代数的基本概念，定义和运算方法后，文中进一步阐述了量子群粒子的物理意义；在q变形思想基础上，本文研究了SLq(2)规范场及其热力学模型中的规范不变性质，并在q量子化和半经典q量子化的假设下导出了零能隙方程和q变形能隙方程；然后从q能隙方程计算了与零温度能隙△(0，q)和临界温度〓。

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

When the solution for the linear equation is not unique, this thesis discusses the solution space of homogeneous equation and gives an orthonormal system, which yields all solutions of linear equation.

同时在再生核空间W_2~1中给出了一种求解该问题的稳定数值算法。对实际数据用该算法进行数值模拟，并与以前的工作相比较，得到了较好的结果。

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

Based on the modem FEM with the dynamic substructure method, itd dynamic equation is established with almost no limits to DOFs of the system, in which the left side is the first approach of the nonlinear system and the right side is the excitation and coupling nonlinear pseudo forces. The modal analysis method is used to get the eigen solution to the reduced linear homogeneous dynamic differential equation. When the system is excited by the harmonic excitation at the right side of the equation, the nonlinear dynamic response can be calculated by the numerical method to give quantitative analysis.

基于近代有限元和子结构模态综合法的动力学建模方法，获得非线性系统动力学微分方程，其自由度几乎没有限制，对左端首次近似齐次方程进行模态分析，选取对响应有贡献的部分本征对，同样对右端激励和非线性伪力作模态变换，得到减缩后非线性系统耦合动力学微分方程。

The nonexistence of global weak solution to elliptic equation and the evolution equation, together with the nonexistence of local weak solution to hyperbolic equation is contained in this paper.

本文运用试验函数法研究了带有非局部源的偏微分方程的全局弱解的不存在性，内容包括椭圆方程、发展方程全局解的不存在性以及双曲型方程的局部弱解的不存在性。

For that, using Darcy law, ideal gas state equation, mass conservation law and moment equation, the paper presents the pressure distribution equation in the porous media and lubricated film including hydrostatic and aerostatic porous thrust bearings (circular pad and rectangular pad), hydrostatic and aerostatic porous journal bearings and hydrostatic and aerostatic porous spherical bearings.

为此，本文利用Darcy定律、理想气体状态方程、质量守恒定律、动量方程以及相应的边界条件，给出流体在多孔质内部和流体薄膜内部压力分布方程，结果表明这两个流动域内部流体压力分布方程是相互耦合的。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。