Hilbert-type inequalities with a product-type homogeneous kernel and Schur polynomials

The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a product-type homogeneous kernel, thus generalizing a result obtained in [Z. Xie, Z. Zheng, A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3, J. Math. Anal. Appl. 339 (2008) 324-331]. In some cases the best possible constants obtained in these inequalities are expressed using the Schur polynomials.     

Arithmetics of binary quadratic forms,symmetry of their continued fractions and geometry of their de Sitter world

This article concerns the arithmetics of binary quadratic forms with integer coefficients, the De Sitters world and the continued fractions.Given a binary quadratic forms with integer coefficients, the set of values attaint at integer points is always a multiplicative tri-group. Sometimes it is a semigroup (in such case the form is said to be perfect). The diagonal forms are specially studied providing sufficient conditions for their perfectness. This led to consider hyperbolic reflection groups and to find that the continued fraction of the square root of a rational number is palindromic.The relation of these arithmetics with the geometry of the modular group action on the Lobachevski plane (for elliptic forms) and on the relativistic De Sitters world (for the hyperbolic forms) is discussed. Finally, several estimates of the growth rate of the number of equivalence classes versus the discriminant of the form are given.Partially supported by RFBR, grant 02-01-00655.     

Catalytic performance and structural characterization of ferric oxide and its composite oxides supported gold catalysts for low-temperature CO oxidation

The preparation and catalytic activity of ferric oxide and its composite oxides supported gold catalysts for low-temperature CO oxidation were investigated detailedly, and characterized extensively by XRD, XPS, TPR, EC and XAFS techniques. It was found that containing highly dispersed Au of partially oxidized state, these nano-structured oxides supported Au/Fe2O3 and Au/NiFe2O4 catalysts had higher low-temperature activities. The possible catalytic active center is the gold of partially oxidized state (Auζ+).     

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.     

On Small World Semiplanes with Generalised Schubert Cells

The well known “real-life examples” of small world graphs, including the graph of binary relation: “two persons on the earth know each other” contains cliques, so they have cycles of order 3 and 4. Some problems of Computer Science require explicit construction of regular algebraic graphs with small diameter but without small cycles. The well known examples here are generalised polygons, which are small world algebraic graphs i.e. graphs with the diameter d≤clog  _k−1(v), where v is order, k is the degree and c is the independent constant, semiplanes (regular bipartite graphs without cycles of order 4); graphs that can be homomorphically mapped onto the ordinary polygons. The problem of the existence of regular graphs satisfying these conditions with the degree ≥k and the diameter ≥d for each pair k≥3 and d≥3 is addressed in the paper. This problem is positively solved via the explicit construction. Generalised Schubert cells are defined in the spirit of Gelfand-Macpherson theorem for the Grassmanian. Constructed graph, induced on the generalised largest Schubert cells, is isomorphic to the well-known Wenger’s graph. We prove that the family of edge-transitive q-regular Wenger graphs of order 2q ⁿ , where integer n≥2 and q is prime power, q≥n, q>2 is a family of small world semiplanes. We observe the applications of some classes of small world graphs without small cycles to Cryptography and Coding Theory.     

关于弱DEA有效性的本质特征

弱DEA有效单元与偏序集的极大元之间关系密切,从偏序集理论出发刻画了四种典型DEA模型所描述的弱DEA有效性的本质特征,揭示了可能集结构变化对弱DEA有效性的影响,并对弱DEA有效性的含义给出了新的解释.最后,探讨了偏序集理论在研究DEA数据变换性质、讨论DEA模型关系、分析决策单元变更以及指标增减对弱DEA有效性影响等方面的应用.     

一门崭新的交叉科学:网络科学(上)

本文试图比较系统地概括和评述正在兴起的一门崭新的交叉科学—网络科学,内容涉及网络科学的发展简史,基本概念,网络分类,主要理论模型及其特性,目前国内外该领域的若干重要课题的研究进展概况。全文结构分为:序言,主体部分共12章,最后是结束语,分别概述和涵盖网络科学的主要课题的研究成果和近年的进展,特别是着重介绍和总结了我们"一院二校"(原子能科研院、上海交大和北京师大)国家自然科学基金重点项目联合研究组开展的复杂网络研究所取得的若干成果和进展。分两期发表,下篇请见《物理学进展》27卷4期。     

Stabilization of the Hierarchy in Brane-World Scenarios

We consider a class of warped brane models with topology M ₄ × × S¹/Z ₂, where is a D₂-dimensional compact manifold, and two branes are placed at the orbifold fixed points. In a scenario where supersymmetry is broken not far below the cutoff scale, the hierarchy between the electroweak and the Planck scales is generated by a combination of the redshift and the large volume effects. We evaluate the effective potential induced by bulk scalar fields in these models and show that it can stabilize the moduli and the hierarchy without fine-tuning, provided that the internal space is flat. We also comment on the relation between these models and the five-dimensional scalar-tensor models that describe them classically when the compactification scale is small.     

Nonlinear Dynamical Behavior in Neuron Model Based on Small World Network with Attack and Repair Strategy

In this paper, we investigate the effect due to the change of topology structure of network on the nonlinear dynamical behavior, by virtue of the OFC neuron evolution model with attack and repair strategy based on the small world. In particular, roles of various parameters relating to the dynamical behavior are carefully studied and analyzed. In addition, the avalanche and EEC-like wave activities with attack and repair strategy are also explored in detail in this work.     

Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes

We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some “rewired“ longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model‘s avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with “added“ long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].