碰撞分支Q-矩阵生成的Markov积分半群

首先证明了碰撞分支Q-矩阵在Banach空间l∞上能生成一个积分半群T(t),且当m1≤0时它的生成元是Q∞,当m1＞0时它的生成元是Qo**.事实上,T(t)是一个Markov积分半群.然后论证了当m1＞0时,T(t)满足Feller性质.

Abstract：

This paper aims to prove that the collision branching q-matrix can generate an integrated semigroup T(t)on l∞ and that if m1 ≤ 0, its generator is Q∞; if m1 ＞ 0, its generator is Qo** . In fact, T(t) is just a Markov integrated semigroup. Also, we obtain that if m1 ＞ 0, this integrated semigroup has the Feller property.     

一致突变人口半群的渐近行为

证明了一致突变人口矩阵Q在l∞上生成一个正压缩积分半群T(t)且该压缩积分半群T(t)是随机单调的.讨论了压缩积分半群T(t)关于状态i及时间t的渐近行为,证明了一致突变人口过程具有强遍历性.     

一类抽象半线性泛函微分方程的小时滞鲁棒稳定性

研究Banach空间X中的抽象半线性泛函微分方程d/dtx(t) = Ax(t)+F(t, x_t(·))的小时滞鲁棒稳定性,其中无界线性算子A在X上生成一个C0-半群T(t)_t≥0, F是非线性函数.在F是全局Lipschitz连续的条件下,利用算子半群理论以及扰动方法,证明了上述方程的解的指数稳定性对小时滞是鲁棒的.

Abstract：

The robust stability of the abstract semi-linear functional differential equationd/dtx(t)= Ax(t)+F(t, x_t(·))is considered in Banach space X, where the linear operator A generates a C_0-semigroup [T(t)]_t≥0in X, and F is a nonlinear function. Under the condition that F is globally Lipschitz continuous, and the robust stability of the above equation is proved with the operator semi-group theory and perturba-tion method.     

一般突变过程诱导的积分半群

研究了一般突变q-矩阵Q在l∞上生成一个压缩积分半群的充要条件, 并且Q可在l∞上生成一最小的积分Q-半群T(t), 讨论了T(t)单调的充要条件, 给出了T(t)是Feller的充分条件, 并讨论了T(t)关于时间t的极限行为.     

一致突变人口半群的渐近行为

证明了一致突变人口矩阵Q在l∞上生成一个正压缩积分半群T（t）且该压缩积分半群T（t）是随机单调的.讨论了压缩积分半群T（t）关于状态i及时间t的渐近行为,证明了一致突变人口过程具有强遍历性.     

一般突变过程诱导的积分半群

研究了一般突变q-矩阵Q在l∞上生成一个压缩积分半群的充要条件,并且Q可在l∞上生成一最小的积分Q-半群T（t）,讨论了T（t）单调的充要条件,给出了T（t）是Feller的充分条件,并讨论了T（t）关于时间t的极限行为.     

伴随积分算子半群及其性质

研究了伴随积分算子半群的性质,给出了经典的Phillips定理的一个简单证明,并明确了伴随算子半群成c0算子半群的最大子空间.

Abstract：

The properties of adjoint integrated semigroups are studied. As an application, the classical Phillips Theorem for adjoint semigroups is proved with a different and somewhat simple way. Furthermore, the maximal subspace to which the restriction of adjoint semigroups is a c0 semigroup is specified.     

非自治二阶哈密顿系统周期解的存在性

利用临界点理论中的极大极小作用原理获得了非自治二阶哈密顿系统{ǔ=▽F(t,u(t),a.e.t∈[0,T] u(0)-u(T)=ú(0)ú(T)=0周期解的存在性结果.其中T>0,F:[0,T]× RM→R满足:对每个x∈RN,F(t,x)关于t是可测的;对几乎处处的t∈[0,T],F(t,x)关于x是连续可微的;存在a∈C(R+,R+)和b∈L1(0,T;R+)使得| F(t,x)|≤a(|x|)b(t)| ▽F(t,x)|≤a(|x|)b(t)对所有的x∈RN和几乎处处的t∈[0,T]都成立.

Abstract：

The existence of periodic solutions is obtained for nonautonomous second order Hamiltonian systems{ǔ=▽F(t,u(t),a.e.t∈[0,T] u(0)-u(T)=ú(0)ú(T)=0- where T ＞ 0,and F:[0,T]× RN →R satisfies assumption:which says that F(t,x)is measurable in t for every x ∈ RN and continuously differentiable in x for a.e.t ∈[0,T],and there exist a ∈C(R+,R+),b ∈L1(0,T;R+)such that｜ F(t,x)｜≤a(｜x｜)b(t)｜ ▽F(t,x)｜≤a(｜x｜)b(t)for all x ∈ RN and a.e.t ∈[0,T].The existence of solutions is proved by the minimax method in critical point theory.     

一类富足半群的结构

利用左正则带和(F)~*-幂单半群,给出了具有S-恰当断面的富足半群的一个结构定理.

Abstract：

By means of a left regular band and an (F)~*-unipotent semigroup,the structure theorem for an abundant semigroup with an S-adequate transversal is established.     

Markov积分半群的弱对称性

介绍了Markov积分半群的弱对称性,对于一个单流出保守的Q-矩阵,给出了Markov积分Q-半群忠实且弱对称的充要条件.

Abstract：

This paper introduces weak symmetry of Markov integrated semigroups. For a conservative single-exit q-matrix Q, sufficient and necessary conditions for a Markov integrated Q -semigroup to be honest and weakly symmetric are given.