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731.
In this paper,we prove the Mohebi-Radjabalipour Conjecture under an ad-ditional condition,and obtain an invariant subspace theorem on subdecomposableoperators. 相似文献
732.
Zhongkai Guo Xingjie Yan Weifeng Wang Xianming Liu 《Journal of Mathematical Analysis and Applications》2018,457(1):214-232
Random invariant manifolds and foliations play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. In a general way, these random objects are difficult to be visualized geometrically or computed numerically. The current work provides a perturbation approach to approximate these random invariant manifolds and foliations. After briefly discussing the existence of random invariant manifolds and foliations for a class of stochastic systems driven by additive noises, the corresponding Wong–Zakai type of convergence result in path-wise sense is established. 相似文献
733.
Consider the scalar delay differential equation x(t) + ∑ akx(t-rk) = 0 (1) where ak and rk ≥ 0, (0 ≤k ≤ m), are real numbers.In this paper we show that there exists an invariant cone of the positive initial functions if and only if the characteristic equation of Eq. (1) has a real root. We also give the constraction of the maximal invariant cone among the positive initial functions with respect to Eq. (1). At the end of the paper we show the generalizations of these results for systems 相似文献
734.
Arthur C. Heinricher Richard H. Stockbridge 《Applied Mathematics and Optimization》1993,28(2):181-195
We analyze optimal control problems for systems subject to random deterioration and failure. The system is replaced at failure and our objective is to optimize the utilization of the system between failures. The problems are new in that the payoff depends on the running maximum of a diffusion. This provides an intuitively appealing model for naturally monotone phenomena such as wear. The long-term average control problem is reduced to a family of simpler, single-cycle problems, a formula for the invariant measure for the (controlled) process is determined and a computational scheme based on the decomposition and formula is given. 相似文献
735.
J.D. Meiss 《Communications in Nonlinear Science & Numerical Simulation》2012,17(5):2108-2121
Invariant tori are prominent features of symplectic and volume-preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an n-dimensional volume-preserving map, such tori are prevalent when the map is nearly “integrable,” in the sense of having one action and n − 1 angle variables. As the map is perturbed, numerical studies show that the originally connected image of the frequency map acquires gaps due to resonances and domains of nonconvergence due to chaos. We present examples of a three-dimensional, generalized standard map for which there is a critical perturbation size, εc, above which there are no tori. Numerical investigations to find the “last invariant torus” reveal some similarities to the behavior found by Greene near a critical invariant circle for area preserving maps: the crossing time through the newly destroyed torus appears to have a power law singularity at εc, and the local phase space near the critical torus contains many high-order resonances. 相似文献
736.
Hirohiko Shima 《Transactions of the American Mathematical Society》1999,351(12):4713-4726
We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.
737.
738.
739.
This paper is concerned with the convergence of invariant measures in the Wasserstein sense for fractional stochastic reaction–diffusion equations defined on unbounded domains as the noise intensity approaches zero. Based on uniform estimates of solutions, we prove the family of invariant measures of the stochastic equations converges to the invariant measure of the corresponding deterministic equations in terms of the Wasserstein metric. We also provide the rate of such convergence. 相似文献
740.
In this paper, we found a special non-isentropic gas dynamics system, whose invariant region is the opposite of the corresponding isentropic case. This shows that the powerful invariant region theory introduced by Chueh, Conley and Smoller for general hyperbolic system of two conservation laws cannot be obviously applied to obtain the a priori estimates for systems of more than two equations. 相似文献