基于知识资本的大学学术竞争力自组织机理研究

学术性是大学的本质所在,大学的核心竞争力本质上是基于知识资本的学术竞争力。大学学术竞争力是大学人力、科教、文化、组织与社会等五种(知识)资本学术竞争力的整体协同涌现,其自组织演进,既受到大学内部因素的协同作用,又离不开外部环境作用的影响。     

地方综合性院校开展数学建模协会活动的实践与研究

简要介绍了济南大学数学建模协会的开展情况,分析了地方综合性院校开展建模协会时存在的困难,指出了做好建模协会工作应当遵循的一些原则.     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

一流课程建设背景下大学物理线上线下混合课程的建设与实践

大学物理课程是高校理工科专业学生非常重要的一门必修公共基础课,一流本科课程建设对大学物理教学提出了新的要求.本文从教学内容、教学方法、教学手段、考核方式等方面探索了实施大学物理混合式教学较为有效的策略和方法,以期为物理学科一流课程建设助力.     

结合专业特色的大学物理课程教学改革探索

制定大学物理课程的授课计划不仅仅要关注物理学知识体系的系统性,同时要注重与后续专业课程的结合,因材施教;根据学生的专业课程内容和特点,结合学生需求精选教学内容,让学生感受到学以致用．教师要精心进行教学设计,将物理学理论和专业课程知识巧妙衔接,同时还要引导学生重视大学物理学提供的科学研究的基本训练．结合专业特色的大学物理教学改革实践,不仅突出了大学物理课程基础理论的重要性,而且还激发了学生对大学物理学习的兴趣和对专业研究的动力．     

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.     

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.     

论工科高等数学精品课程建设

系统论述了工科高等数学精品课程建设产生的历史背景、指导思想、建设内容和在建设中所应遵循的基本原则.     

大学一年级物理实验教学的对策

分析了中学物理实验教学现状,指出大学与中学物理实验教学衔接存在的问题,根据现代教育理论,提出了大学一年级物理实验教学的对策。     

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.