抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

Orders of Indescribable Sets

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.     

Mackey Theory for p-adic Lie Groups

This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G - H × t A to systems of imprimitivity.     

牛顿弦截法预估校正迭代格式的收敛阶

研究如下形式的牛顿弦截法的预估校正(P.C.)格式:P(预估):~xk+1=xk-(xk-xk-1)f(xk)f(xk)-f(xk-1)C(校正):xk+1=xk-(~xk+1-xk)f(xk)f~(xk+1)-f(xk)证明了它的收敛阶为2.618.     

Little higgs models and T parity

Little Higgs models are an interesting extension of the Standard Model at the TeV scale. They provide a simple and attractive mechanism of electroweak symmetry breaking. We review one of the simplest models of this class, the Littlest Higgs model, and its extension with T parity. The model with T parity satisfies precision electroweak constraints without fine-tuning, contains an attractive dark matter candidate, and leads to interesting phenomenology at the Large Hadron Collider (LHC).     

Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).     

Fourth-order problems with fully nonlinear boundary conditions

Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented.     

Scheduling orders for multiple product types to minimize total weighted completion time

We consider the problem of scheduling orders for multiple different product types in an environment with m dedicated machines in parallel. The objective is to minimize the total weighted completion time. Each product type is produced by one and only one of the m dedicated machines; that is, each machine is dedicated to a specific product type. Each order has a weight and may also have a release date. Each order asks for certain amounts of various different product types. The different products for an order can be produced concurrently. Preemptions are not allowed. Even when all orders are available at time 0, the problem has been shown to be strongly NP-hard for any fixed number (?2) of machines. This paper focuses on the design and analysis of efficient heuristics for the case without release dates. Occasionally, however, we extend our results to the case with release dates. The heuristics considered include some that have already been proposed in the literature as well as several new ones. They include various static and dynamic priority rules as well as two more sophisticated LP-based algorithms. We analyze the performance bounds of the priority rules and of the algorithms and present also an in-depth comparative analysis of the various rules and algorithms. The conclusions from this empirical analysis provide insights into the trade-offs with regard to solution quality, speed, and memory space.     

狭缝式高速摄影机胶片的计算机判读

根据狭缝摄影机胶片的成象原理,运用数字图象处理技术,对狭缝式高速摄影机胶片判读工作的计算机化进行研究.应用结果表明,该技术先进实用,极大地提高了判读的精度和效率,将是这种胶片判读技术的发展方向.     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002