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正则嵌入

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The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容:第一章研究了该模型正平衡解的性质,可分为三部分:第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件;第二部分利用分歧理论给出了平衡态系统正分歧解的结构,并讨论了局部分歧解的稳定性;第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性,并讨论了参数对解的影响。

A pointwise characterization of fuzzy complete regularity is yielded by means of the Q- neighborhood structures and some algebraic properties of certain class of maps in lattices. The Weil theorem on fuzzy uniformity and the general imbedding theorem in the fuzzy basic cube are established.

其次给出不分明完全正则的点式刻划与关于一致结构的著名Weil定理的不分明推广并从而建立了在不分明单位方体中一般性的嵌入定理。

The main aim of this thesis is to study the properties of the maps for Heisenberg group target, which include Lipschitz and Holder continuity, L~#,H~(n , W~(1,p)#,H~(n , BMO and John-Nirenberg estimates, embedded theorems, Poincare inequalities and reverse Poincare inequalities, the regul-arities about the minimizers.

本文的主要目的是系统研究靶流形为Heisenberg群的函数及其空间的性质,其中包括Lipschitz及Hlder连续性、空间L~p及W~(1,p)的性质、空间BMO的性质及其上的John-Nirenberg估计、嵌入定理、Poincare不等式和逆Poincare不等式、能量极小映射的存在性、正则性及用调和函数逼近能量极小映射等问题。

In general, prefer embedding regular expressions by value rather than by reference.

通常,应该优先以值的方式而不是引用的方式嵌入正则表达式。

The next section shows how to define a recursive regular expression by embedding a regex by reference.

下一节将示范如何通过以引用方式嵌入regex来定义一个递归的正则表达式。

Simulation results show that both freezing and coalescing processes have distinct stages.

对这些小尺寸团簇的结构变化采用基于嵌入原子方法的正则系综分子动力学进行计算机模拟。

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在对危险的南部地区访问时,他斥责什叶派民兵领导人对中央集权的挑衅行为。

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