关于赋范空间在“*弱”拓扑下的隔离性定理

给出了赋范共轭空间的点与(紧)凸集、紧凸集之间被原空间中的点分隔的定理.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

The Roughness of Model Function to the Basis Functions

The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ＂h＂, the shift in the slope of two consecutive segments. If the distribution of design is uniform, f（x） is continuous segment function, and h is constant, then the maximum roughness is h2/192 obtained at the midpoint of the observations. Suppose that we have a sequence of designs {Pn（x）} then its corresponding distribution {Fn （x）} converges weakly to some distribution F（x）. Let D（f） be a set of discontinuous points off（x）, it is possible to take the limit of the roughness if D（f） has zero （dF）-measure. The behavior of maximum roughness of the discontinuous segment function has been studied by using grid points.

Asymptotic Behavior on Cox Risk Process Perturbed by Diffusion

In this paper, the asymptotic behavior on the Cox risk model perturbed by diffusion is studied. The sufficient and necessary conditions for the process when it weakly convergence to Normal distribution and th.e rate of weakly convergence are received. Finally discuses the exponential upper bound for ruin probability of this risk model.

Whitehead＇s Categoreal Scheme as a Social-Psychiatric Game Autism and Metaphysics

The lack of emotional relations is not replaced by the ＂savant＂ characteristics （see Asperger syndrome） but by their immersing into stereotypic instincts. In other words, they compensate their divergent intrinsic emotions with imitated convergences （eg., the monotonous ＂convergence obsessed＂ logic of hammering, wringing hands etc.） Today＇s science cannot declare this to be convergent, especially for the fact that psychotic autist patients prove to be weak at convergence, but the male/female proportion reflects on notable facts （with Kanner syndrome it is 3：1 or 4：1, while Rett syndrome only affects females）. Can we declare Kanner and Rett syndromes to be basically female brain disorders？ Asperger-autism has been scientifically considered as a type of ＂male-brain disorder＂ since 199l （Baron-Cohen theory）. The proportion of male-female is approximately 6：1 with this disease. The author would like to demonstrate a very special case, the Asperger-autism as a ＂cognitive autism.＂ It is common to address autistic disorder as ＂pervasive＂ or ＂comprehensive＂ ontogenetic disorders because they affect all areas of adolescent psychological development negatively. But as the expression itself suggests, we are not aware of the specific disorders directly. As it will turn out we cannot deal with autism as on complex disorder, we should rather use the term in plural, i.e., autisms and autistic disorders.

Convergence Theorems for Fuzzy Superpramarts

The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.

Interaction of strong converging shock wave with SF6gas bubble

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Test for autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes

In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge. The test statistics are evaluated by some empirical results.

Well-posedness for the stochastic 2D primitive equations with Lévy noise

The two-dimensional primitive equations with Lévy noise are studied in this paper.We prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak convergence method and monotonicity arguments.

Stochastic Systems Arising from Markov Modulated Empirical Measures

This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.

Long-time behavior of a stochastic predator-prey model with modified Leslie-Gower and Holling-type II schemes

In this paper, we consider a stochastic predator-prey model with modified Leslie-Gower and Holling-type II schemes. We analyze long-time behavior of densities of the distri- butions of the solution. We prove that the densities can converge in L1 to an invariant density or can converge weakly to a singular measure under appropriate conditions.

Conditional limit theorems for critical continuous-state branching processes

We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф（λ） = λ 1＋αL（1/λ）, where （α∈ [0, 1] and L is slowly varying at co. We prove that if α ∈ （0, 1], there are norming constants Qt →0 （as t ↑ ＋ ∞） such that for every x 〉 0, Px（QtXt ∈ · ｜Xt 〉 0） converges weakly to a non-degenerate limit. The converse assertion is also true provided the regularity of ψ at 0. We give a conditional limit theorem for the case α = 0. The limit theorems we obtain in this paper allow infinite variance of the branching process.

Strong representation of weak convergence

Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.