微课在大学物理实验教学中的应用

微课是以单一知识点为教学内容,通过简短的视频或音频等多媒体形式记载并结合一定的学习任务而形成的一种教学资源。介绍了微课的概念和特点,探索了如何将微课与大学物理实验课程教学相结合,以达到提高教学效果和培养学生创新能力为目的。     

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.     

同伴指导影响师范生课堂教学基本技能的实验研究

为了找寻训练师范生课堂教学行为的有效策略，对某师范大学的38名师范生进行教育实验，探讨了教师单向指导训练策略和同伴相互指导训练策略对师范生课堂教学行为变化的影响。结果表明，相比教师单向指导策略，同伴相互指导策略能激发全体师范生的积极主动性，是一种低消耗、高效率的训练师范生教学基本技能的有效策略。     

外资评级机构进入中国能否发挥“鲶鱼效应”?

近年来,中国信用评级行业逐步对外开放。我国监管部门相继批准标普、惠誉等具有国际影响力的外资评级机构进入我国市场。在此背景下,本文采用博弈模型分析了外资评级机构进入中国市场对本土评级机构评级质量的影响。研究发现,高声誉外资评级机构进入中国市场能够起到激励本土评级机构公正评级并促进评级行业形成良性循环的作用。本文研究结论为我国信用评级行业对外开放以及引入更多具有国际影响力的外资评级机构提供了理论支撑。     

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.     

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.     

Effects of Different Connectivity Topologies in Small World Networks on EEG-Like Activities

Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension, and the Hurst exponent within the rescaled range analysis (R/S). We find that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.     

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.].