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1.
Consider a vector measure of bounded variation m with values in a Banach space and an operator T:XL1(m), where L1(m) is the space of integrable functions with respect to m. We characterize when T can be factorized through the space L2(m) by means of a multiplication operator given by a function of L2(|m|), where |m| is the variation of m, extending in this way the Maurey–Rosenthal Theorem. We use this result to obtain information about the structure of the space L1(m) when m is a sequential vector measure. In this case the space L1(m) is an ℓ-sum of L1-spaces.  相似文献   

2.
We consider a class of multitype particle systems in d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).  相似文献   

3.
Skeide  M. 《Mathematical Notes》2002,71(5-6):836-843
We generalize Bhat's construction of product systems of Hilbert spaces from E0-semigroups on B(H) for some Hilbert space H to the construction of product systems of Hilbert modules from E0-semigroups on Ba(E) for some Hilbert module E. As a byproduct we find the representation theory for Ba(E) if E has a unit vector. We establish a necessary and sufficient criterion for the conditional expectation generated by the unit vector to define a weak dilation of a CP-semigroup in the sense of [1]. Finally, we also show that white noises on general von Neumann algebras in the sense of [2] can be extended to white noises on a Hilbert module.  相似文献   

4.
In this paper, considering full Logistic proliferation of CD4+ T cells, we study an HIV pathogenesis model with antiretroviral therapy and HIV replication time. We first analyze the existence and stability of the equilibrium, and then investigate the effect of the time delay on the stability of the infected steady state. Sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delay. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold, and investigate the existence of Hopf bifurcation by using a delay τ as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the main results.  相似文献   

5.
Pyrex glasses with different ZnS: Mn2+ contents were prepared by melting method. It has been found that Mn ion may occupy two sites: (Mn2+)sub, and (Mn2+)int from photoluminescene (PL) and photoluminescence excitation (PLE) spectra. The results were confirmed by the further electron panmagnetic resonance (EPR) experiments and the three types of states (Mn2+)sub, (Mn2+)int,and Mn clusters were identified. It was observed that theg-factor and the hyperfine structure (HFS) constant increase with the decreasing size of nanocrystallite. This may result from hybridization of sp3 electron states of ZnS and 3d5 electron states of Mn by the effects of quantum confinement and the surface states. Project supported by the National Natural Science Foundation of China and Laboratory of Excited State Processes, Chinese Academy of Sciences.  相似文献   

6.
Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C : K → 2Y a point-to-set mapping such that for any χ ε K, C(χ) is a pointed, closed, and convex cone in Y and int C(χ) ≠ 0. Given a mapping g : KK and a vector valued bifunction f : K × KY, we consider the implicit vector equilibrium problem (IVEP) of finding χ* ε K such that f g*), y) -int C(χ) for all y ε K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems.  相似文献   

7.
The purpose of this paper is to study systems of vector equilibrium problems. We establish some existence theorems for systems of vector equilibrium problems by using (S)+-conditions and Kakutani–Fan–Glicksberg fixed point theorem *This work was supported by the Kyungnam University Research Fund 2004  相似文献   

8.
In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L2-stability and error estimate of order Or+1+hk+1/2) are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.  相似文献   

9.
Stability for parametric implicit vector equilibrium problems   总被引:6,自引:0,他引:6  
In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters and λ, respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S:Λ1×Λ2→2X for such parametric implicit vector equilibrium problems.  相似文献   

10.
A key tool in the study of the dynamics of vector fields near an equilibrium point is the theory of normal forms, invented by Poincaré, which gives simple forms to which a vector field can be reduced close to the equilibrium. In the class of formal vector valued vector fields the problem can be easily solved, whereas in the class of analytic vector fields divergence of the power series giving the normalizing transformation generally occurs. Nevertheless the study of the dynamics in a neighborhood of the origin can very often be carried out via a normalization up to finite order. This paper is devoted to the problem of optimal truncation of normal forms for analytic vector fields in Rm. More precisely we prove that for any vector field in Rm admitting the origin as a fixed point with a semi-simple linearization, the order of the normal form can be optimized so that the remainder is exponentially small. We also give several examples of non-semi-simple linearization for which this result is still true.  相似文献   

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