S.I.S.向量随机测度在弱拓扑及相容拓扑下的收敛性

本文主要研究ｓ．ｉ．ｓ．向量随机测度在弱拓扑及相容拓扑下的收敛性,给出了ｓ．ｉ．ｓ．向量随机测度在弱拓扑 容拓扑下的Ｖｉｔａｌｉ－Ｈａｌｍ－Ｓａｋｓ定理,作为应用,我们建立了Ｒ＾１－值有界可测函数关于Ｂａｎａｃｈ空间值ｓ．ｉ．ｓ．向量随机测度的随机积分的收敛定理,并得到了具ｔｙｐｅｐ的Ｂａｎａｃｈ空间中ｓ．ｉ．ｓ．向量随机测度的大数定律及中心极限定理。     

R/M的局部分配性

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｍｂｏｓ－Ｓｐｉｅｓ,Ｊｏｃｋｕｓｃｈ,ＳｈｏｒｅａｎｄＳｏａｒｅ［１９８４］ｐｒｏｖｅｄｔｈａｔＭ,ｔｈｅｓｅｔｏｆａｌｌｔｈｅｃａｐ－ｐａｂｌｅｒ．ｅ．ｄｅｇｒｅｅｓ,ｉｓａｎｉｄｅａｌｉｎＲａｎｄＮＣ,ｔｈｅｓｅｔｏｆａｌｌｔｈｅｎｏｎｃａｐｐａｂｌｅｒ．ｅ．ｄｅｇｒｅｅｓ,ｉｓａｆｉｌ－ｔｅｒｉｎＲａｎｄＮＣ＝ＰＳ,ｔｈｅｓｅｔｏｆａｌｌｔｈｅｐｒｏｍｐｔｌｙｓｉｍｐｌｅｄｅｇｒｅｅｓ．Ｗｅｈａｖｅａｑｕｏｔｉｅｎｔｐａｒｔｉａｌｏｒｄｅｒｏｆｔｈｅｒ．…     

分离定理的应用

ＬｅｔＬｅｍｍａ［１］ｓｕｐｐｏｓｅｔｈａｔＣ１ａｎｄＣ２ｉｓＲｎ′ｓｔｗｏｎｏｎｉｎｔｅｒｓｅｃｔｉｎｇｎｏｎｅｍｐｔｙｃｏｎｖｅｘｓｅｔｓａｎｄｔｈｅｒｅｅｘｉｓｔｓａｓｕｐｅｒｐｌａｎｅｓｅｐａｒａｔｉｎｇｔｈｅｍ,ｉ．ｅ．ｖｅｃｔｏｒｙａｎｄｒｅａｌｎｕｍｂｅｒβｅｘｉｓｔｉｎｔｈｅｍ．Ｉｄｅｎｔｉｆｙｕ∈Ｃ１,ｖ∈Ｃ２,ｔｈｅｒｅｉｓｉｎｆｕ∈Ｃ１ｙＴｕβｓｕｐｖ∈Ｃ２ｙＴｖ．（１）　　Ｔｈｅｆｏｌｌｏｗｉｎｇｒｅｓｕｌｔｓｃａｎｂｅｐｒｏｖｅｄｂｙａｐｐｌｙｉｎｇｔｈｉ…     

关于自相似集的Hausdorff测度

得到了 Ｈａｕｓｄｏｒｆｆ容度与 Ｈａｕｓｄｏｒｆｆ测度相等的集的充分必要条件．对于满足开集条件的自相似集,验证了它的Ｈａｕｓｄｏｒｆｆ容度与Ｈａｕｓｄｏｒｆ测度相等并给出了它的Ｈａｕｓｄｏｒｆｆ测度的一个便于应用的公式．作为例子,给出了均匀康托集的Ｈａｕｓｄｏｒｆｆ测度的一种新的计算方法,对于Ｋｏｃｈ曲线的Ｈａｕｓｄｏｒｆｆ测度的上限也作了讨论．     

离散的Painlevé方程Ⅱ的有理解

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＮｏｎｌｉｎｅａｒｉｎｔｅｇｒａｂｌｅｄｉｓｃｒｅｔｅｓｙｓｔｅｍｓａｒｅｎｏｗａｔｔｒａｃｔｉｎｇｍｕｃｈａｔｔｅｎｔｉｏｎ．Ａｍｏｎｇｔｈｅｍ,ｔｈｅｄｉｓｃｒｅｔｅＰａｉｎｌｅｖéｅｑｕａｔｉｏｎｓａｒｅｅｘｐｅｃｔｅｄｔｏｂｅｔｈｅｍｏｓｔｆｕｎｄａｍｅｎｔａｌｏｎｅｓｉｎａｎａｌｏｇｙｔｏｔｈｅｃｏｎｔｉｎｕｏｕｓｃａｓｅ．Ｃｌｏｓｅｒｓｔｕｄｉｅｓａｒｅｈｏｗｒｅｖｅａｌｉｎｇｔｈｅｉｒｒｉｃｈｍａｔｈｅｍａｔｉｃａｌｓｔｒｕｃｔｕｒｅｓ,ｓｕｃｈａｓ…     

在条件lim(n→∞)(infP(X_n= 0)>0)下的一类独立随机变量和的收敛定理

设｛Ｘ_ｎ,ｎ≥ １｝是一独立随机变量序列．受概率数论中Ｅｒｄｏｓ猜想的启发,我们研究了在条件lim(n→∞)(infP(X_n= 0)>0)下的独立项级数ｓｕｍ　ｆｒｏｍ　ｎ＝１ Ｘ_ｎ的 ａ．ｓ．收敛性,并且获得了该级数ａ．ｓ．收敛的两个充分必要条件和一个充分条件．这些定理分别改进了文献［３］、［５］中关于Ｅｒｄｏｓ猜想的研究结果．     

螺线的Steinhaus维数

Ｄｕｐａｉｎ Ｙ,Ｆｒａｎｃｅ Ｍ．Ｍ．和 Ｔｒｉｃｏｔ Ｃ．［１］利用积分几何中的经典的Ｓｔｅｉｎｈａｕｓ定理,引入 Ｓｔｅｉｎｈａｕｓ维数,并研究了螺线的 Ｓｔｅｉｎｈａｕｓ维数与盒维数的关系．本文深入这一研究,对Ｓｔｅｉｎｈａｕｓ维数的值域,单调性等基本性质作了进一步的考察．     

欧氏空间中具有共形Gauss映照的曲面

本文考虑欧氏空间中具有共形Ｇａｕｓｓ映照的曲面．从Ｇａｕｓｓ映照的观点给出了 ｖｅｒｏｎｅｓｅ曲面的一个新特征．     

偏好意义下的Pareto极值存在性定理及其应用

本文给出了偏好意义下的Ｐａｒｅｔｏ极值存在性定理．作为应用,得到了推广的Ｗｅｉｅｒｓｔｒａｓｓ定理以及非连续集值增算子的不动点定理．     

用多网格方法研究Poisson方程的解

本文给出了二种颜色的双网格方法．渐近缩减到一种颜色的双网格方法．用付立叶分析，通过红黑Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代，对Ｐｏｉｓｓｏｎ方程讲行研究，取得了较为满意的结果．     

On free products in varieties of associative algebras

Varieties of associative algebras over a field of characteristic zero are considered. Belov recently proved that, in any variety of this kind, the Hilbert series of a relatively free algebra of finite rank is rational. At the same time, for three important varieties, namely, those of algebras with zero multiplication, of commutative algebras, and of all associative algebras, a stronger assertion holds: for these varieties, formulas that rationally express the Hilbert series of the free product algebra via the Hilbert series of the factors are well known. In the paper, a system of counterexamples is presented which shows that there is no formula of this kind in any other variety, even in the case of two factors one of which is a free algebra. However, if we restrict ourselves to the class of graded PI-algebras generated by their components of degree one, then there exist infinitely many varieties for each of which a similar formula is valid. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 693–702, May, 1999.     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

基于覆盖上近似算子的拟阵结构及其关系

Covering-based rough sets,as a technique of granular computing,can be a useful tool for dealing with inexact,uncertain or vague knowledge in information systems.Matroids generalize linear independence in vector spaces,graph theory and provide well established platforms for greedy algorithm design.In this paper,we construct three types of matroidal structures of covering-based rough sets.Moreover,through these three types of matroids,we study the relationships among these matroids induced by six types of covering-based upper approximation operators.First,we construct three families of sets by indiscernible neighborhoods,neighborhoods and close friends,respectively.Moreover,we prove that they satisfy independent set axioms of matroids.In this way,three types of matroidal structures of covering-based rough sets are constructed.Secondly,we study some characteristics of the three types of matroid,such as dependent sets,circuits,rank function and closure.Finally,by comparing independent sets,we study relationships among these matroids induced by six types of covering-based upper approximation operators.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.     

Generalized Weyl–Wigner–Moyal–Ville Formalism and Topological Groups

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal, and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, theory of unitary projective representations of groups, and theory of groups algebras. Later on, we present some generalization to quantum mechanics on locally compact Abelian groups. It is based on Pontryagin duality. Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of ‘Umklapp–Prozessen’. Copyright © 2011 John Wiley & Sons, Ltd.     

On the potential of norm-governed behavior in different categories of artificial societies

Based on a classification of artificial societies and the identification of four different types of stakeholders in such societies, we investigate the potential of norm-governed behavior in different types of artificial societies. The basis of the analysis is the preferences of the stakeholders and how they influence the state of the society. A general conclusion drawn is that the more open a society is the more it has to rely on agent owners and designers to achieve norm-governed behavior, whereas in more closed societies the environment designers and owners may control the degree of norm-governed behavior. Paul Davidsson is professor at the Department of Systems and Software Engineering, School of Engineering, Blekinge Institute of Technology, Sweden. He received his Ph.D. in Computer Science in 1996 from Lund University, Sweden. His research interests include the theory and application of multi-agent systems, autonomous agents, and machine learning. Application areas include logistics, transport systems, district heating systems, building automation, and telecommunications systems. The results of this work have been reported in more than 75 peer-reviewed scientific articles published in international journals and conference proceedings. Moreover, he has been the co-editor of three books on Multi Agent Based Simulation and member of program committees of numerous international conferences, such as the International Joint Conference on Autonomous Agents and Multi-Agent Systems Stefan Johansson is an assistant professor at Department of Systems and Software Engineering, Blekinge Institute of Technology, Sweden, where he also finished his PhD in 2002. The main research areas cover coordination issues in multi-agent systems and theories of autonomous agents. Applications of special interests are agents in game ai, robotics, telecommunication networks. On his list of publications are more than 35 peer-reviewed papers published in conference proceedings and scientific journals in the areas of agents, ai, robotics and games. He has also been a member of a variety of programme committees of scientific conferences, including e.g. Intelligent Agent Technology.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

Rolling-ball method for estimating the boundary of the support of a point-process intensity

We suggest a generalisation of the convex-hull method, or ‘DEA’ approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation.     

Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities

We study the existence, uniqueness and asymptotic behavior, as well as the stability of a special kind of traveling wave solutions for competitive PDE systems involving intrinsic growth, competition, crowding effects and diffusion. The traveling waves are exclusive in the sense that as the variable goes to positive or negative infinity, different species are close to extinction or carrying capacity. We perform an appropriate affine transformation of the traveling wave equations into monotone form and construct appropriate upper and lower solutions. By this means, we reduce the existence proof to application of well-known theory about monotone traveling wave systems (cf. [A. Leung, Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, MIA, Kluwer, Boston, 1989; J. Wu, X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001) 651-687] and [I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994]). Then, by using spectral analysis of the linearization over the profile, we prove the orbital stability of the traveling wave in some Banach spaces with exponentially weighted norm. Furthermore, we show that the introduction of some weight is necessary in the sense that, in general, traveling wave solutions with initial perturbations in the (unweighted) space C₀ are unstable (cf. [I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994] and [D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981]).