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consistency equation
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     For the equation
     我们称方程(?)
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     equation
     方程(之14)
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     THEOREMS ON CONSISTENCY OF A MATRIX EQUATION OVER RINGS
     环上矩阵方程可解的几个定理
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     THE CONSISTENCY CONDITIONS IN INVERSE PROBLEMS OF GENERALIZED LOGISTIC EQUATION
     关于广义Logistic方程反问题的相容性条件
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     2. Data Consistency.
     2.数据一致性保证。
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  consistency equation
Under these conditions, we represent the solution of the self-consistency equation continuously depending on the momentum of the relative motion of the pair.
      
Local current conservation is guaranteed by ensuring that the order parameter satisfies the self-consistency equation at each point.
      
Then the self-consistency equation for the 4 × 4 matrix self-energy reduces to three equations for δ1, δ2, and cos θ, and a fourth equation for the renormalized Larmor frequency.
      
We also show that the self-consistency equation for the order parameter Δ(x) can be expressed in terms of ? and a generalization of it.
      
This is supplemented by a self-consistency equation for the order parameter, and we show that a simple trial form gives quite a good solution of it.
      
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An analytical method is used to investigate the chiral symmetry restoring phase transition at finite temperature and density. The self-consistency equations for the order parameter at T=0 are generalized and the corresponding equations at finite temperature and density are established. The order parameter as a function of the temperature and the phase diagram are obtained.

本文用解析方法研究了有限温度和密度下的手征相变.把零温情形下序参量的自洽方程加以推广,建立了有限温度情形下的相应方程.由此得到了序参量随温度的变化关系,证实了手征对称性恢复的相交的存在,求出了理论的相图.

The Hamiltonian of comb polymer molecule is set up by using interaction model of liquid crystal proposed by Freiser. The order parnameter self-consistency equations of combined phase of polymer liquid crystal are derived by derivation procedure. The phase transition from isotropic to uniaxial nematics and from uniaxial to biaxial nematies are obtained for given molecular structure. The results show that when the repulsion in coupling term of main chain and side chain, the magnetude of strong nematic field...

The Hamiltonian of comb polymer molecule is set up by using interaction model of liquid crystal proposed by Freiser. The order parnameter self-consistency equations of combined phase of polymer liquid crystal are derived by derivation procedure. The phase transition from isotropic to uniaxial nematics and from uniaxial to biaxial nematies are obtained for given molecular structure. The results show that when the repulsion in coupling term of main chain and side chain, the magnetude of strong nematic field of combined phase increase, the phase transition temperature from uniaxial to biaxial will rise and gradually changes from first order to second order phase transition.

利用Freiser关于液晶分子相互作用模型,建立了梳型高聚物分子的哈密顿量,适用变分程序导出高聚物液晶结合相序参数自洽方程,得到在给定分子结构参数时的各向同性相至单轴向列相以及单轴至双轴向列相的相变。结果表明,当分子主、侧链间隔基团的耦合项中排斥作用以及结合相中较强向列相场者强度增大时,单轴至双轴向列相相变温度升高,并从一级相变逐渐变为二级相变。

The existence of concentration shocks due to nonlinearity of the adsorption isotherm is the feature of simultaneous adsorption and reaction processes in a fixed bed. A new approach to the shock is suggested in this paper. The shocks are regarded as moving boundaries which cut the spatial domain into separate "smooth" subregions, and the consistency equations on the shocks are taken as boundary conditions or connection ones that link the adjacent subregions. Then, a moving coordinate following the movement...

The existence of concentration shocks due to nonlinearity of the adsorption isotherm is the feature of simultaneous adsorption and reaction processes in a fixed bed. A new approach to the shock is suggested in this paper. The shocks are regarded as moving boundaries which cut the spatial domain into separate "smooth" subregions, and the consistency equations on the shocks are taken as boundary conditions or connection ones that link the adjacent subregions. Then, a moving coordinate following the movement of the shocks is introduced and the shock discontinuities are transformed into fixed boundaries in the coordinate. Finally, simple trial functions are used to approximate concentration profiles in the smooth region , and the integral form of the governing equations provide a close set of first order ordinary differential equations. By the method, the problem of migration of two components with Langmuirian adsorption and reversible reactions is greatly simplified to that of four ODEs. A complete solution for the problem is obtained , and the characteristics of the shock movement under various conditions are discussed. It is found that when the weakly adsorptive reactant A is initially dominant, a maximum of distance between the two shocks exists there, and for irreversible reactions, the A - rich region does not disapear even when A is depleted, it becomes a constant thin layer between two shocks in the end of the movement.

浓度激波现象是固定床中非线性吸附-反应过程的重要特征。本文将激波面考虑为分割空间光滑区域的运动边界,将激波间断条件作为相应的边界条件,采用移动坐标系中的试验函数来近似浓度剖面,将双组分吸附反应问题化为4个简单的一阶常微分方程的求解,获得了问题的完整解答,据此讨论了浓度激波的运动特征。

 
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