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1.
We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.  相似文献   
2.
使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.  相似文献   
3.
In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-Güneri-Stichtenoth (GGS) curve are discovered.  相似文献   
4.
In this paper, we prove the uniqueness of stationary standing wave solutions of an optical model generated by Type II Second Harmonic Generation (SHG) with behaviors tending to zero at infinity under certain conditions on parameters. In addition, we provide the same issues for the Dirichlet boundary value problems on the ball centered at the origin. A classification of solutions for radial case is also established.  相似文献   
5.
This paper deals with the blowup behavior of the radially symmetric solution of the nonlinear heat equation ut = ?u + e~u in R~N. The authors show the nonexistence of type II blowup under radial symmetric case in the lower supercritical range 3 ≤ N ≤ 9,and give a sufficient condition for the occurrence of type I blowup. The result extends that of Fila and Pulkkinen(2008) in a finite ball to the whole space.  相似文献   
6.
We consider a Schrödinger operator L=?d2/dx2+V(x) on R, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).  相似文献   
7.
This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the Lp linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an Lp well-posed system.  相似文献   
8.
9.
In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.  相似文献   
10.
This paper deals with a stochastic system which models the population dynamics of a chemostat including species death rate. On the basis of the theory on Markov semigroup, we demonstrate that the probability densities of the distributions for the solutions are absolutely continuous. The densities will convergence in L1 to an invariant density or weakly convergence to a singular measure under appropriate conditions. We also give the sufficient criteria for extinction exponentially of the species. To be specific, when D1>D and the strength of perturbation is relatively small, we derive a precise threshold for the species survival.  相似文献   
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