We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T⊕Mg is universal, where Mg is multiplication by a generating element of a compact topological group. We use this result to characterize R+-supercyclic operators and to show that whenever T is a supercyclic operator and z1,…,zn are pairwise different non-zero complex numbers, then the operator z1T⊕?⊕znT is cyclic. The latter answers affirmatively a question of Bayart and Matheron. 相似文献
Let f(l, t, n) be the maximal size of a family such that any l2 sets of have an exactly t1-element intersection. If l3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine Let g(l,t,n) be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: g(3, 1, n) = n2/3(1 + o(1)). 相似文献
This paper concerns the integration of ε-Fenchel subdifferentials of proper lower semicontinuous convex functions defined on arbitrary topological vector spaces. We make use of integration tools to provide a representation formula of the approximate subdifferential of convex functions, and also to identify the class of maximal cyclically monotone families of operators. 相似文献
Every Banach space either contains a subspace isomorphic to , or it has an infinite-dimensional closed subspace which is a quotient of a Hereditarily Indecomposable (H.I.) separable Banach space.
In the particular case of , it is shown that the space itself is a quotient of a H.I. space. The factorization of certain classes of operators, acting between Banach spaces, through H.I. spaces is also investigated. Among others it is shown that the identity operator admits a factorization through a H.I. space. The same result holds for every strictly singular operator .
Interpolation methods and the geometric concept of thin convex sets together with the techniques concerning the construction of Hereditarily Indecomposable spaces are used to obtain the above mentioned results. 相似文献
Parametric multiple regression models for the claim number and the claim amount of an individual risk are introduced allowing explanatory variables to influence the mean claim number (amount). A model for an entire portfolio of risks is established on this basis. Then an extensive and in many cases efficient statistical analysis of this model is presented. 相似文献
In this paper, a class of nonlinear damped wave equations of the form αu?(t)+u″(t)=βAu(t)+γAu′(t)+f(t,u(t)), t?0, satisfying αβ<γ with prescribed initial conditions are studied. Some sufficient conditions are established for the existence and uniqueness of an asymptotically almost periodic solution. These results have significance in the study of vibrations of flexible structures possessing internal material damping. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. 相似文献
In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions: sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system (M system, P system) has positive lower density ( Fs , Fr resp.)-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some exampl... 相似文献