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随着科学的发展，重整化群有了不同的内涵。As science develops, different connotations of renormalization group come into being.

讨论了极性半导体中表面极化子重正化质量的性质。In this paper, renormalization mass of the surface polaron in polar crystals were studied.

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描述了基于重构性的复杂网络自相似模型。This paper describes the self-similarity model of complex networks based on renormalization procedure.

本文利用实空间重整化群方法对渗流、岩裂、飞蚁模型进行了研究。The models of percolation, rock fracture and flit ant are studied on the real-space renormalization group approach.

当时的想法所谓的重整和规范理论已成为富有成果，我感到非常兴奋地说。It was a time when ideas called renormalization and gauge theories were becoming fruitful and I was very excited by that.

利用重整化群方法研究煤层底板岩层单元体破裂的随机性和关联性。The renormalization group method is used to study the randomness and connectivity of the failture for coal floor element.

介绍了用重整化群方法描述临界现象的基本思路和做法。The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced.

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正规化和重整化是量子场论的一个十分重要的成功。One of the key elements in the triumph of quantum field theory was the development of regularization and renormalization theory.

目前处理临界相变问题的方法主要有重正化群和数值模拟。Nowadays people mostly apply renormalization group theory and numerical simulation methods to deal with critical phase transition problem.

重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.

根据所得演化函数分别从时间和增长率两个方面求出了股市系统演化方程的重正化群解。Correspondingly, the renormalization group solutions of stock system evolutional equation are solved from the angel of time and increasing rate.

详细介绍了在二维情况下孔隙介质逾渗流的基本理论、重正化群方法的原理及其在逾渗研究中的应用。The basic theory of porous mediums in 2D condition is introduced and the theory of Renormalization method is applied to research the percolation.

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用一种新的处理线性或非线性方程的重整化数学方法求解了碰撞等离子体中的平行动力学方程。A new renormalization mathematics method of treating linear or nonlinear questions is used in solving parallel-kinetic equation in collision plasmas.

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.

另外，我们采用位置空间重整化群方法，对二维次近邻三角格子键渗流模型进行了研究。We study the two-dimension triangular-bond lattice percolation with next-nearest-neighbor interactions on the renormalization group approach as well.

利用重正化群方法，构造了该边值问题解的一致有效渐近展开式。By using the so called renormalization group method, we give a uniformly valid asymptotic expansions of the boundary value problems under consideration.

我们将讨论诸如匹配，重整化，算符乘积展开，幂次计数，和重整化群跑动等概念。Concepts such as matching, renormalization , the operator product expansion, power counting, and running with the renormalization group will be discussed.

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重整化群方法是研究相变的临界现象最有力的工具，它是一种由理论求得分形维数的方法。Renormalization group method which calculates fractal dimension theoretically is the most useful tool when we study critical phenomena of phase transition.

用实空间中的重整化群理论，对二维正方形格点上的高分子模型自踪迹规避链进行了求解。In this article, the critical exponents of the polymer model SAT in two dimensional square lattice have been studied with the real space renormalization theory.

将结合重整化群和盒计数方法，探讨对复杂网络的这三个特征的产生机理和它们之间相互关系的内在机制。The paper will probe into origins of three features of complex networks and underlying mechanism of their relation using renormalization and box-covering method.