Banach and Statistical Cores of Bounded Sequences

In this paper, we are mainly concerned with characterizing matrices that map every bounded sequence into one whose Banach core is a subset of the statistical core of the original sequence.     

SOME GENERALIZATIONS OF KY FAN＇S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map onmetrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derivedfor the map studied. Our work generalizes severl results in approximation theory.     

On the Manifold of Almost Complex Structures

Let (M, g ₀) be a smooth closed Riemannian manifold of even dimension 2_n admitting an almost complex structure. It is shown that the space of all almost complex structures on M determining the same orientation as the one determined by a fixed almost complex structure J ₀ is a smooth locally trivial fiber bundle over the space of almost complex structures orthogonal with respect to g ₀ and determining the same orientation as J ₀.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 66–71.Original Russian Text Copyright © 2005 by N. A. Daurtseva.     

On nonregular ideals and <Emphasis Type="Italic">z</Emphasis>°-ideals in <Emphasis Type="Italic">C</Emphasis>(<Emphasis Type="Italic">X</Emphasis>)

The spaces X in which every prime z°-ideal of C(X) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X, such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z°-ideal in C(X) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C(X) a z°-ideal? When is every nonregular (prime) z-ideal in C(X) a z°-ideal? For instance, we show that every nonregular prime ideal of C(X) is a z°-ideal if and only if X is a ?-space (a space in which the boundary of any zeroset is contained in a zeroset with empty interior).     

Actions of SL $$(n,\mathbb{Z})$$ on Homology Spheres

Any continuous action of SL , where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n −1. In particular, any continuous action of SL on the n-dimensional sphere factors through a finite group action.Mathematics Subject Classiffications (2000). Primary 57S25; Secondary 37C85, 57S17     

On decompositions of Banach spaces of continuous functions on Mrówka's spaces

It is well known that if is infinite compact Hausdorff and scattered (i.e., with no perfect subsets), then the Banach space of continuous functions on has complemented copies of , i.e., . We address the question if this could be the only type of decompositions of into infinite-dimensional summands for infinite, scattered. Making a special set-theoretic assumption such as the continuum hypothesis or Martin's axiom we construct an example of Mrówka's space (i.e., obtained from an almost disjoint family of sets of positive integers) which answers positively the above question.

     

EXPONENTIAL STABILITY FOR A CLASS OF SWITCHED STOCHASTIC SYSTEMS

In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently "small".     

锯齿型通道流动和换热的周期性研究

本文对锯齿型通道内流动与换热的周期性进行了数值模拟.在Re=550～700范围内,入口段后的各几何周期的平均Nu数已随时间发生振荡,且随Re数增大,振荡起始位置朝入口方向移动;发生振荡的各几何周期的流场、无量纲温度场虽然在同一时刻不尽相同,但在不同的时刻可以找到近乎相同的流场和温度场,而且各几何周期平均Ⅳu数其振荡幅度基本相同,对时间求平均值后也基本相同,因此仍具有周期性充分发展的一些特性.     

A dengue fever model with free boundary incorporating the time-periodicity and spatial-heterogeneity

Propagation of dengue fever is characterized by periodicity and seasonality and further influenced by geographic heterogeneity. To account for these characteristics, we formulate a dengue model in a spatial-heterogeneous and time-periodic environment. Moreover, the free boundary is additionally incorporated into our model to reflect the boundary change of region where dengue virus spreads. Employing the properties of the contagion risk threshold, that is the spatial-temporal basic reproduction ratio, we derive some sufficient conditions regarding the vanishing and spreading of virus. Importantly, the long-time asymptotic behavior of solution is studied in depth when spreading happens. Our findings manifest that as time goes on, dengue virus will behave periodically when spreading. Finally, these phenomena are numerically simulated and epidemiologically explained.     

Direct Method of Constructing H 2-Suboptimal Controllers: Continuous-Time Systems

An H ₂-suboptimal control problem is defined and analyzed. Then, an algorithm called H ₂-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H ₂-suboptimal state feedback gains. Also, although the sequence of H ₂-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter , the construction procedure itself does not require explicitly the value of the parameter . Next, attention is focused on constructing a sequence of H ₂-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H ₂-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The direct method of constructing H ₂-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.