在每次约化后，余下的方程是保持对称和带状的。
After each reduction, the remaining equations remain symmetric and banded.
依据约化理论，建立了维修费用的VAR模型。
VAR model on maintenance cost is put forward according to the theory of simplification.
通过这些测量提取约化跃迁几率B（E2 ） 。
The reduced transition probabilities B (E2) are extracted from these measurements.
通过广义条件对称方法得到了其对称约化和精确解。
Its symmetry reduction and exact solutions are obtained through the generalized conditional symmetry approach.
得到简并双光子过程中原子约化密度算符非对角元。
The non-opposite angle element of two-level atom's reducible density rectangular array is obtained.
特别地，约化模型应用了随机过程中的马尔科夫理论。
Particularly, the markov theory of random process has been used in reduced model.
利用中心流形约化方法证明了霍普夫分歧解的稳定性。
By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.
对于标量粒子，其质量的获得则主要通过推广的平群约化方法。
And the mass for scalar particles is mainly given by generalized reduction on trivial group.
又对允许广义条件约化的方程的反应系数和热源项的函数形式作了分类。
A complete classification of the functional forms of the reaction coefficients and source terms is presented when the equation admits the generalized conditional symmetry reduction.
结果表明，约化速度、拖缆倾角、拖曳速度等是影响涡激振动的主要因素。
Result shows that the dip Angle, the towed velocity and reduced velocity are main influence factors to the vortex-induced vibration of a circular cylinder.
本文给出了分别由约化环类和s -弱正则环类确定的上根的一些基本性质。
Some basic properties of the upper radicals determined by the classes of reduced rings ands-weakly regular rings are presented respectively.
本文利用约化摄动重整化方法研究了光纤零色散波长点附近光孤子传输的特征。
Propagation feature of optical soliton near the zero-dispersion wavelength point is researched by using Reductive Perturbation Method (RPM) and Renormalization Method in this paper.
再利用多参数稳定性理论及归一化技术，对约化方程进行求解，得到了分岔方程。
Then, using the multi-parameter stability theory and unification technique, we solved the reduced equation and obtained the bifurcation equations and their solution.
引入空间群消光规律，用计算机模拟电子衍射图，提出选取约化四边形的新方法。
Adopting the space-group extinction rule and simulating the electron diffraction pattern with computer, this paper proposed a new method for selecting the reduced quadrangle.
也证明了弱整体有限的凝聚环是约化环，以及弱整体为有限的凝聚连通环是整环。
It is also proved that a coherent connected ring with finite weak global dimension is a domain.
结果表明，奇偶约化多核并行算法在三次样条曲线拟合中的应用是有效及可行的。
The results indicate that multi-core parallel algorithm of odd-even reduction used in cubic spline curve fitting is effective and feasible and the research results have good practical significance.
研究了依赖强度耦合多光子J—C模型的演化算符，约化密度算符及其场熵特性。
The evolution opera tor, the reduce density operator and the dynamical properties of the field entropy evolution in the intensity - dependent coupling multiphoton J - C model are studied.
本文证明了多项式正常算子具有性质(P)和多项式正常的约化算子必为正常算子。
It is proved that the polynomial normal operators have the property (p) and the polynomial normal reductive operators must be normal operators.
也就是说，一般多线性变量分离可解性在对称约化下从高维系统到低维系统得到了保持。
Namely, the applicability of the method is retained from high dimensional systems to low dimensional systems in the symmetry reduction sense.
我们发现在有能级交叉的有限大尺寸系统中，约化保真度是一个测量量子相变的有效工具。
We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems.
本文从漫射理论出发，推导出了组织体漫反射率与约化散射系数和吸收系数之间的唯一性关系。
Based on the principles of diffuse reflectance, the unique relationship between diffuse reflectance and transport scattering coefficient and absorption coefficient of biotissue is deduced.
本文应用多重尺度约化微扰方法研究了充满流体的圆形弹性管壁上应力波的弱非线性调制问题。
The reductive perturbation method of multiple-scales is used to investigate the weak nonlinear modulation of the stress wave on the wall of a fluid-filled elastic circular tube.
根据约化密度矩阵与基态能量之间的关系，我们给出了约化保真率和量子相变之间的一般关系。
A general connection between the reduced fidelity susceptibility and quantum phase transitions is given in terms of the relation between reduced density matrix and ground-state energy.
运用量子约化熵研究了V型三能级原子与双模奇偶纠缠相干光场相互作用系统中场熵的演化特性。
The quantum reduced entropy evolution of a V-type three-level atom interacting with the two - mode odd-even entangled coherent field is investigated.
这些约化方法在其可应用的系统类型上有一定的局限性，比如其不能应用于不 完整 约束系统等。
There are restrictions on what type of systems these techniques can be applied to, e. g. , these reduction techniques do not apply to systems that are nonholonomically constrained.
在惯性驰豫时间与德拜时间的对比中，研究了初始磁化率随频率的变化关系以及随约化温度的变化关系。
The relation between initial susceptibility and frequency has been studied by the comparison of inertia time to Debye time.
在本文中我们主要研究了等变调和映照、及其约化定理和等变变分公式，得到了等变调和映照的调和性方程。
In this paper, we mainly study equivariant harmonic maps, the theorem of reduction, the equivariant variational formula, and the harmonic equation.
本文第二章介绍了无穷维动力系统的惯性流形与近似惯性流形的约化思想，并讨论了KS方程的直接约化方法。
In this paper, the second chapter introduces the reducing idea of inertial manifolds and approximate inertial manifolds, and discuss the similarity reduction of KS equation.
该方法能方便、简洁地将密度主方程转化为对应的普通微分方程，并能从微分方程的解中提取出约化密度算符。
Using it we can conveniently and simply convert a ME into its corresponding differential equation and from solution of which we can extract the reduced density operator.
该方法能方便、简洁地将密度主方程转化为对应的普通微分方程，并能从微分方程的解中提取出约化密度算符。
Using it we can conveniently and simply convert a ME into its corresponding differential equation and from solution of which we can extract the reduced density operator.
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