问题求解

Suppose G is a finite group, then QG is a semisimple Q-algera, obviously ZG is a Z-order of QG,we denote the maximal Z-order by ?.If G is not abelian, it is not an easy thing to determine г; if G is an abelian group, then QG is isomorphic to the direct sum of a finite number of number fields, and r is the direct sum of these rings of algebraic integers of those number fields, but which elements of QG belong to r is not clear.

设G是一个有限群，那么QG是一个半单代数，ZG是QG的一个Z-序，设Γ是QG的一个极大Z-序，当G是一个非交换群时，Γ的求解是困难的问题；当G是一个交换群时，QG同构于有限多个数域的直和，Γ相应的就是各数域代数整数环的直和，但Γ具体是QG中那些元素不清楚。

Asymmetrical dynamic propagation problems under the action of variable loads and (P^3t/x^2) located at the origin of the coordinates respectively, are resolved by the measures of self-similar functions, and the universal expressions of analytical solutions to stresses, displacements and stress intensity factors are gained.

采用自相似函数的方法对坐标原点分别受到变载荷Px/t、Pt^3/x^2作用下的非对称动态扩展问题进行求解，获得了应力、位移和动态应力强度因子解析解的一般表达式。

Adjoint function algorithms and direct collocation and nonlinear programming methods are applied to resolve the non-coplanar optimal orbit transfers problem.

分别利用了共轭函数法与直接配置和非线性规划方法对异面最优变轨问题进行了求解。

On the basis of the conversion relation of inverse matrix and adjoint matrix, by using 1/ω instead of |B'(xBx(subscript k|, a new Landweber iteration formula x(superscript δ subscript k+1)=x(superscript δ subscript k)-ωB'(x(superscript δ subscript k)Bx(superscript δ subscript kB'x(superscript δ kf(x(superscript δ subscript k)-y(superscript δ)is constructed for solving rank deficiency nonlinear least squares problem, with which the phenomenon that leads to ill-posed problem because the iteration matrix is rank-deficient and very ill-conditioned in numerical iterative process is avoided.

基于逆矩阵和矩阵伴随算子的换算关系，并用1/ω代替|B′(xBx(下标k|，构造出一个新的求解秩亏非线性最小二乘问题的Landweber迭代格式，x(上标δ下标 k+1)=x-ωB'(xBx(上标δ下标 k*B'x(上标δ下标 kf(x-y，从而避免了在迭代过程中由于迭代矩阵的秩亏和病态而产生的不适定现象。

Please design an algorithm to solve the aforementioned problems.

请设计一个算法求解上述问题。

With Airy stress function, a plane elasticity problem can be simplified to solve a biharmonic function equation.

通过引入Airy应力函数，平面问题可以归结为在给定的边界条件下求解一个双调和方程。

As a result,an algebraic curve is obtained which is the zero level set of the algebraic function.

曲线重建过程可以归结为求解线性方程组问题。

The differential equation and algebraic equation are calculated separately so as to use proper methods based their own characteristics.

将微分方程与代数方程的解算问题分离，根据各自的特点选用适当的方法求解。

Using orthogonal function expansion technique the problem can be summa-rized into the solution of infinite algebraic equation systems.

用正交函数展开的方法，将待解的边值问题归结为求解一组无穷代数方程组。

Governing equation discrete, solving of the conjugated algebraic equation set and SIMPLE method are also discussed in this paper.

同时对方程离散、方程组的耦联求解及SIMPLE算法等数值计算以及湍流及其模型等问题进行了论述。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷