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91.
Yu Qing Chen 《Discrete Mathematics》2008,308(13):2764-2775
In this paper, we give a characterization of a group G which contains a semiregular relative difference set R relative to a central subgroup N containing the commutator subgroup [G,G] of G such that 1∈R and rRr=R for all r∈R. In particular, these relative difference sets are fixed by inversion and inner automorphisms of the group are multipliers. We also present a construction of such relative difference sets. 相似文献
92.
We construct inertial manifolds for a class of random dynamical systems generated by retarded semilinear parabolic equations subjected to additive white noise. These inertial manifolds are finite-dimensional invariant surfaces, which attract exponentially all trajectories. We study the corresponding inertial forms, i.e., the restriction of the stochastic equation to the inertial manifold. These inertial forms are finite-dimensional Ito equations and they completely describe the long-time dynamics of the system under consideration. The existence of inertial manifolds and the properties of inertial forms allow us to show that under mild additional conditions the system has a global (random) attractor in the sense of the theory of random dynamical systems. 相似文献
93.
研究一类具有多时滞Holling II型功能性反应非自治捕食-被捕食系统, 利用重合度理论得到系统全局正周期解存在的充分条件.推广了相关的已有结果. 相似文献
94.
95.
96.
B. Krishna Das J. Martin Lindsay Orawan Tripak 《Journal of Mathematical Analysis and Applications》2014
A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which Lévy processes on compact quantum groups is a special case. 相似文献
97.
Letαbe a flow on a Banach algebra(?),and t(?)u_t a continuous function from Rt into the group of invertible elements of(?)such that u_sα_s(u_t)=u_s+t,s,t∈R.Thenβ_t=Adu_t oα_t,t∈R is also a flow on(?),where Adu_t(B)(?)u_tBu_t~(-1)for any B∈(?).βis said to be a cocycle perturbation ofα.We show that ifα,βare two flows on a nest algebra(or quasi-triangular algebra),thenβis a cocycle perturbation ofα.And the flows on a nest algebra(or quasi-triangular algebra)are all uniformly continuous. 相似文献
98.
Take σ to be a continuous semiflow on the locally compact metric space Θ, and let {A(θ)}θ∈Θ be a family of (possibly unbounded) densely defined closed operators on the Banach space X. 相似文献
99.
A class of linear stochastic retarded functional differential equations is considered. These equations have diffusion coefficients that do not look into the past. It is shown that the trajectories of such equations form a continuous linear cocycle on the underlying state space. At times greater than the delay the cocycle is almost surely compact. Consequently, using an infinite-dimensional Oseledec multiplicative ergodic theorem of Ruelle, the existence of a countable non-random Lyapunov spectrum is proved. In the hyperbolic case it is shown that the state space admits an almost sure saddle-point splitting which is cocycle-invariant and corresponds to an exponential dichotomy for the stochastic flow 相似文献
100.
Roland Kempf 《Journal of Difference Equations and Applications》2013,19(12):1121-1131
The paper investigates z -limit sets for discrete-time dynamical systems of the form x n +1 = f n +1 ( x n ), n S 0, with each f n mapping an interval I of R into itself. For autonomous systems, i.e. f n = f for all n , and f continuous on I =[ a , b ], the case that all z -limit sets consist of one point only is characterized by several equivalent conditions, one being that f has no 2-periodic points. The non-autonomous case assumes that the functions f n converge uniformly to a continuous function f X that has no 2-periodic points. It is shown that the z -limit sets are closed intervals consisting of fixed points of f X only. Under certain conditions these closed intervals contain exactly one point each. This allows a treatment of certain discrete-time dynamical systems in R n . 相似文献