Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性

考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.     

SWITRIM��������ƺ�ʹ�øſ�

研制出了用于计算氚投料量在FEB聚变堆各个子系统中的分布及其随时间变化的数值模拟程序包SWITRIM。通过近5年的使用，表明其运行良好、计算结果可靠。用SWITRIM数值模拟研究了聚变堆起动过程中的“氚坑深度和氚坑时间”新现象。简单介绍了SWITRIM程序包的组成和用户使用说明以及最新的运用等。     

Titanium nanocarbides: Synthesis and modeling

The present state of research on the production and modeling of nanostructures based on titanium carbide-a typical representative of an extensive class of carbides of d-and f-metals-is reviewed. Methods for the synthesis of various Ti-C nanostructures (molecular clusters, nanocrystallites, nanospheres, nanofibers, nanowires) are examined, and their morphology, atomic structure, and known physicochemical characteristics are described. Theoretical models of the atomic structure and properties of new types of nanostructures in the titanium-carbon system (endo-and exohedral titanofullerenes, “hybrid” structures based on carbon nanotubes, the so-called peapods, nanocables, and a number of others) and the prospects for their application as components of nanoceramics, hydrogen accumulators, materials for spintronics, etc. are discussed. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 1, pp. 1–23, January–February, 2007.     

L-S category of quaternionic Stiefel manifolds

By calculating certain generalized cohomology theory, lower bounds for the L-S category of quaternionic Stiefel manifolds are given.     

Lévy processes and their subordination in matrix Lie groups

Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasi-invariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail.     

加权Herz—type Triebel—Lizorkin空间的特征及应用

当s∈ R,0,〈q, p〈∈∞,0,〈β≤∞且 max{-n/q,-nδ2/qδ1}〈a时，定义了加权Herz—type　Triebel-Lizorkin空间kq^q,pF^s β（R^n,ω1，ω2）和Kq^a,pF^sβ（R^n，ω1，ω2），并给出这些空间的一些特征及在这些空间上的Hard—Littlewood极大算子不等式．     

Countably compact topological group topologies on free Abelian groups from selective ultrafilters

Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c² using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom.     

On cellularization for simplicial presheaves and motivic homotopy

We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky.     

QN-spaces, wQN-spaces and covering properties

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).