一类三种群竞争合作系统的传播问题

本文主要研究一类三种群竞争合作系统的波前解存在性及最小波速的选择机制问题.通过构造合适的上下解并结合严格的分析过程,得到了系统存在波前解的一些充分条件.本文的结果改进了已有文献中的相关结果,特别地,在存在性结果的基础上,我们进一步给出最小波速线性决定的一些充分条件.这些结果丰富了三种群竞争合作系统的相关研究.     

具有弱凸性合作系统解的收敛性

本文研究合作系统解的收敛性．基本假设是f(x)满足凸性并且Df(0)的主特征值是非负的．如果系统是合作和不可约的，且每个解是有界的，则每个解收敛于奇点．特别，如果Df(0)的主特征值是负的，则正奇点在第一象限内部是全局稳定的．把这些结果应用于经典的Lotka－Volterra系统，可以获得只要关联矩阵A是合作和不可约的，且所有解是有界的，那么每个解收敛于奇点．     

具有离散时滞和反馈控制的Lotka-Volterra合作系统的动力学行为研究

研究了具有离散时滞和反馈控制的两种群Lotka-Volterra合作系统的正周期解的存在性和全局吸引性.基于Gaines和Mawhin的叠合度定理和构造Lyapunov函数的方法,给出了具有离散时滞和反馈控制的两种群周期合作系统的正周期解的存在性和全局吸引性的充分条件.     

半群的拟紧性和不可约性

利用算子半群生成元的边界扰动方法,给出了Banach格上C0半群的拟紧性和不可约性的充分条件.并利用该结果对一串联可修复系统的拟紧性和不可约性进行了研究.     

Banach空间上的闭强不可约算子

本文首先给出Banach空间上闭强不可约算子的定义,并给出一个无界强不可约算子的例子;其次给出闭强不可约算子的性质,特别地,给出了闭强不可约算子的一些等价描述;最后给出上三角算子矩阵表示的闭算子具有强不可约性的一些充分条件.     

具有热储备的并行可修复系统指数稳定性分析

应用泛函分析的方法讨论了有两个相同部件和一个热储备的并行可修复系统的指数稳定性.我们通过分析系统算子生成C0半群的本质谱增长阶,证明了该半群是拟紧的.此外,该半群还是不可约的.于是作为半群拟紧性和不可约性的直接结果,得到了系统的时间依赖解指数收敛到其静态解,并且该静态解即为系统算子简单特征值0对应的正的特征向量.     

一类无界区域中的椭圆型系统非局部边值问题

本文讨论了一类在无界区域中的非线性椭圆系统的非局部边值问题。在适当的条件下,相对边值问题解的存在性及其比较定理作了研究。     

随机环境中马氏链的常返性和瞬时性

讨论了随机环境马氏链中具有强π不可约性链的常返性的判定,从而得到了强π不可约链常返性判定的充分必要条件,同时给出了在一定条件下随机环境中的马氏链的瞬时性判定的几个充分条件.     

一类华氏宏观经济数学模型的均衡增长路径

利用非负矩阵最大特征值及非负特征向量的存在性和特征值的取值范围,研究一类华氏宏观经济数学模型的均衡增长路径.证明了无论直接消耗系数矩阵是否是不可约的,一类华氏宏观经济数学模型存在均衡增长解的必然性,并给出了模型的均衡增长解.说明在实际生产中相对于本部门总投入,当本部门的生产消耗掉本部门产品数量较少时,经济系统稳定增长.     

基于PI控制器的不确定广义系统的非脆弱耗散控制

主要研究了一类不确定广义系统的耗散控制问题,基于线性矩阵不等式的处理方法给出了使广义系统容许且严格耗散的充要条件,并利用线性矩阵不等式的解给出了耗散控制器的设计方法,得到了一个具有非脆弱性的状态反馈PI控制器的显示表达,使得对所允许的不确定性闭环广义系统容许且严格耗散.最后用数值例子说明了所提出方法的正确性和有效性.     

Strongly irreducible operators on Banach spaces

This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w*-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.     

On Hilbert's Irreducibility Theorem

A method for obtaining very precise results along the lines of the Hilbert Irreducibility Theorem is described and then applied to a special case. In addition, the relationship of the irreducibility theorem to other tools of diophantine analysis is investigated. In particular, we give a proof of the irreducibility theorem that uses only Noether's lemma and the fact that an absolutely irreducible curve has a rational point over a finite field of large order.     

A resultant condition for the irreducibility of the polynomials

We prove a criterion for the irreducibility of the polynomials in one indeterminate with the coefficients in the valuation ring of a discrete valued field. From this result we deduce the Schönemann, Eisenstein, and Akira irreducibility criteria. The results obtained can also be used for proving that some polynomials in several indeterminates are irreducible.     

New generic quasi-convergence principles with applications

In this paper, essentially strongly order-preserving and conditionally set-condensing semiflows are considered. Obtained is a new type of generic quasi-convergence principles implying the existence of an open and dense set of stable quasi-convergent points when the state space is order bounded. The generic quasi-convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations, giving some results of theoretical and practical significance.     

A C*-ALGEBRA APPROACH TO THE IRREDUCIBILITY OF COWEN-DOUGLAS OPERATORS

LetHbeaseparableindnitedimensionalHilbertspaceoverthefieldCandletL(H)(resp.K(H))denotethealgebraofallboundedlinearoperators(resp.allcompactoperators)onH.ForTEL(H),wedenotebyR(T)(resp.KerT)therange(resp.thenullspace)ofT.Accordingto[2],Bit(fl)consistsofallCowen-DouglasoperatorsTEL(H)satisfyingfollowingconditions:(l)fiCa(T)isaconectedopensubsetinC;(2)R(w--T)=HanddimKer(w--T)=n相似文献   

Correction: On the Severi problem in arbitrary characteristic

In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any characteristic. Following Severi’s original idea, this gives a new proof of the irreducibility of the moduli space of smooth projective curves of a given genus in positive characteristic. It is the first proof that involves no reduction to the characteristic zero case. As a further consequence, we generalize Zariski’s theorem to positive characteristic and show that a general reduced planar curve of a given geometric genus is nodal.

     

On a mild generalization of the Schönemann - Eisenstein - Dumas irreducibility criterion

We state a mild generalization of the classical Schönemann and Eisenstein- Dumas irreducibility criterion in ?[x] and provide an elementary proof. In the end of the paper, we also provide a concrete example of a polynomial which is irreducible by the main result of the paper but whose irreducibility does not follow from existing criteria.     

Irreducible positive linear maps on operator algebras

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible positive linear maps on von Neumann algebras are explicitly constructed, and a criterion for the irreducibility of decomposable positive maps on full matrix algebras is given.

     

The irreducibility of almost all Bessel Polynomials

The irreducibility of the Bessel Polynomials y_n(x) (described below) has been investigated by Emil Grosswald. He has obtained several interesting results on this subject; in particular, using his ideas, it is possible to prove that a positive proportion of the Bessel Polynomials are irreducible. This paper uses a different approach to deduce the stronger result that almost all Bessel Polynomials are irreducible.     

Periodic orbits of competitive and cooperative systems

In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincaré-Bendixson theorem holds for such three dimensional systems.