在闭合时间路径的实时温度场论的框架下，导出了热重整化群方程。
Thermal Renormalization Group equations are derived in the framework of Closed Time Path formalism in real time temperature field theory.
介绍了重正化群方程的一种有效的数值解法，并与多项式展开的传统解法作了比较。
An effective numerical solution of renormalization group equations is introduced, and compared with the traditional solution of polynomial expansion.
研究完整力学系统准坐标表示的运动微分方程在群的无限小变换下的形式不变性。
The paper studies the form invariance of differential equations of motion for holonomic systems in terms of quasi coordinates, under the infinitesimal transformations of groups.
本文建立带观测方程的库群月径流综合生成模型。
In this paper, a model for synthetical generation of monthly runoff of reservoirs, which includes an observation equation, is established.
本文提出了一种基于蚁群算法求方程组数值解的新方法。
A new method for resolving equation groups is proposed, which is based on Ant Colony System.
主要考虑非线性波方程组的一些简单对称及其构成的李代数，并利用所得对称给出该方程组的一些单参数变换群。
In this paper, the symmetries and Lie algebra of a coupled nonlinear wave equation were discussed. One-parameter transformation groups of this equation were obtained by using the symmetries.
在经典的刚架弹性稳定理论基础上推导了考虑节点刚度的四弯矩方程和构件群稳定方程，并将其应用于桁架结构。
Based on classic elastic stability theory of framework, the four-moment equation and the stability equations of member group considering joint rigidity are derived and extended to study trusses.
基本思想是首先利用圆盘状单裂纹之解以及局部坐标展开法将裂纹群问题化为求解一组线代数方程。
The basic idea is to use the single crack solution and the expansions of the local coordinates to reduce the complicated problem into a set of linear algebraic equations.
广义条件对称；精确解；非线性反应扩散方程；对称群。
The generalized conditional symmetry; Exact solutions; The nonlinear reaction diffusion equations; symmetry group.
在第二章中我们主要利用群分支法来求解非线性扩散方程(2.4)的分离变量解。
In the chapter 2, we find the separation of variables solutions for nonlinear reaction diffusion equation (2.4) by utilizing the group foliation method.
接着于1984年出版了“模糊群子论”，系统地论述了线性群子理论方程及其某些应用。
Then in 1984, "on Vague sub-cluster", which systematically, expounded the linear sub-cluster equation and its application, was off the press.
并提出在数值模拟控制方程中，如何考虑加入桩(群)影响的阻力项。
In the governing equation of numerical simulation, factors of resistance considering effects of pile or pile group were applied.
并且依据广义条件对称和所考虑方程的相容性求得了相应方程的群不变解。
Exact solutions to the resulting equations are constructed via the compatibility of the generalized conditional symmetry and the considered equation.
构造了求解二维两群中子扩散方程的混合间断有限元格式，研制了相应的计算程序。
A variational formula combining mixed finite element method with discontinuous finite element method is derived for solving the two-group neutron diffusion equation in 2d.
运用活动标架和回转运动群对其啮合方程和啮合效率进行了分析研究；
The meshing equation and the formula of meshing efficiency are drawn by using active coordinate and rotating matrix operators.
应用主成分分析方法构建了前兆震群判别方程，对震群活动的异常特征进行了分析。
The anomalous characteristic of the swarm activity is analyzed using the precursor swarm distinguishing equation constructed by the principal component analysis method.
主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解。
Some nonclassical potential symmetry generators and group-invariant of heat equation and wave equation were determined.
提出一种两群替代微粒群优化算法(TSSPSO)，并对算法参数进行分析和对算法方程进行修正。
In this paper, two sub-swarms substituting particle swarm optimization algorithm (TSSPSO) is proposed. The algorithm parameters are analyzed and the iteration equations are amended.
可解方程的群都是交换群。
依据模糊群子论的基本原理，导出了水泥体系粒径分布的群子本征方程，并计算得到水泥体系的群聚度。
The sub cluster intrinsic equation for the cement particles size distribution was derived on the base of fuzzy sub cluster theory.
研究完整力学系统准坐标表示的运动微分方程在群的无限小变换下的形式不变性 。
On the form invariance of differential equations of motion for generalized mechanical system in terms of quasi-coordinates;
研究了板几何控制临界本征方程多群逼近的合理性。
In this paper, the rationality of the multigroup approximation of the control critical eigenvalue equation for the slab geometry is studied.
介绍一种求解瞬态两群多维中子扩散方程的动力学节块方法。
A kinetics nodal method for the solution of transient two-group multi - dimensional neutron diffusion equation is described.
该方法是基于最小相位滤波器的复倒谱系数和其群迟延函数以及其系统函数之间的关系，通过一个非线性的递归方程求解分母多项式的系数。
Based on the relationship between the group delay function and the cepstral coefficients, the denominator polynomial coefficients can be determined through a nonlinear recursive difference equation.
本文给出了建立在含幺半群基础上的范畴语法的代数结构 ，定义了范畴方程和它的解并对范畴方程的解作了分类 ：相容性的相关性。
In this article, we showed the algebraic structure of syntactic categories based on monoid and defined categorial equation whose solutions are described by consistency and correlation .
讨论描述希尔伯特空间最终范数连续半群特征的一个算子方程的解，给出这个解的一个显式表达式。
A new perturbation result on the Hilbert space for the eventually norm-continuous semigroups is obtained, which makes the perturbation of the semigroups more abundant.
非古典对称方法在经典的李对称方法的基础上添加了初始方程的表面不变条件，从而既简化了计算，又有助于得到更多的对称及群不变解。
Compared with the classical Lie method, it adds an invariant surface condition in the formation. Consequently, it makes calculation easy and obtains more group-invariant solutions.
非古典对称方法在经典的李对称方法的基础上添加了初始方程的表面不变条件，从而既简化了计算，又有助于得到更多的对称及群不变解。
Compared with the classical Lie method, it adds an invariant surface condition in the formation. Consequently, it makes calculation easy and obtains more group-invariant solutions.
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