传统有限元的研究，要求对区域的剖分满足正则性条件。
The researches of classical finite elements need the meshes of triangulation satisfying the regular condition.
本文在一个正则性条件下，给出了渐近最优EB估计的一个充要条件。
In this paper, we have given a sufficient and nfcessary condition for the asymptotic optimum EB estimate on ceatain regular condition.
利用各向异性单元分析方法得到了二阶问题的误差估计，从而避开了正则性条件的限制。
Using the analytic method of the anisotropic element, error estimate for the second order problem is obtained without the limitation of regularity conditions.
第四章我们首先证明了算法是有定义的，其次在没有正则性条件的假设下证明了算法的全局收敛性。
We prove that the algorithm is well defined and the global convergence of method is obtained without regular conditions.
一个有限半群是满足左正则性条件的IC富足半群当且仅当它是一个幂等元形成左正则带的纯整超富足半群，但满足左正则性条件的无限IC富足半群不都是幂等元形成左正则带的纯整超富足半群。
A finite semigroup is an IC abundant semigroup satisfying the left rgularity condition if and only if it is an orthodox superabundant semigroup whose idempotents form a left regular band.
尤其是本文把正则阶作为约束条件之一，从而保证了滤波器通带的平坦性和阻带的快速衰减，并且在阻带滤波器的频谱值非常接近于零。
Especially, regularity as one of the constraints assure the flatness in passband and the high attenuation in stopband, even the value of stopband response is very close to zero.
考虑具有可控增长条件的非线性椭圆方程组弱解的部分正则性。
In this paper, we consider the nonlinear elliptic systems under the controllable growth condition.
给出了多导单步方法正则性的概念，并给出了多导单步方法具有正则性的条件。
The concept of regularity was given in this paper. The conditions, which ensure the regular-method is also obtained.
本文主要研究了广义分散控制系统的正则性，并给出了可以正则化的一个充要条件。
In this short poper, the regularizability of descriptor decentralized systems is studied and a necessary and sufficient condition is given.
主要研究了在适当的正则性假设条件下液晶流的稳定有限元逼近的数值分析。
This paper is devoted to the numerical analysis of a stabilized finite element approximation for a liquid crystal flow under appropriate regularity hypothesis.
根据纹理特征的局部马尔可夫性和高斯变量的条件回归之间的关系，将复杂的模型选择转变为较简单的变量选择，应用惩罚正则化技巧同步选择邻域和估计参数。
The structure of the GGM is explored by the connection between the local Markov property of texture features and the conditional regression of Gaussian random variables.
本文运用正则化方法证明了一类退化抛物方程解的存在唯一性，讨论了解的全局存在性与爆破，并在一定的初值条件下得到了解的爆破速率。
In this paper, we establish the local existence and uniqueness of the solution by using regularization method. We also obtain the global existence and nonexistence. Finally, we get the blow-up rate.
本文运用正则化方法证明了一类退化抛物方程解的存在唯一性，讨论了解的全局存在性与爆破，并在一定的初值条件下得到了解的爆破速率。
In this paper, we establish the local existence and uniqueness of the solution by using regularization method. We also obtain the global existence and nonexistence. Finally, we get the blow-up rate.
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