财经类院校数学建模的教学与实践

针对经济、管理类专业学生的特点 ,介绍了在财经类院校开展数学建模活动的意义、方法和步骤 ,总结了开展数学建模竞赛的经验 .     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Corrections of proofs for Hansen and Mélot's two theorems

The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot [Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs.     

Experience Gained Using Second-Moment Closure Modeling for Transitional Flows Due to Boundary Layer Separation

This paper presents detailed information on the experience gained during the attempts to model a set of transitional flows due to boundary layer separation. These flows are developed on a flat plate with a semi-circular leading edge and they have been coded by the ERCOFTAC Special Interest Group on Transition, as T3L flows. Different freestream velocities and turbulence intensities configure these transitional flows and, by consequence, govern the transition mechanism, resulting in larger or smaller transitional regions. The modeling of the T3L flows has been performed by adopting a low-Reynolds number second-moment closure turbulence model. The results showed satisfactory agreement with the experimental measurements, although some difficulties regarding successful convergence have been faced. The final conclusion is that turbulence modeling can present quite accurate results for transitional flows without any additional use of ad-hoc modifications or additional equations based on various transition models and intermittency transport modeling.     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．     

Towards understanding the increase in strength of thermotropic polyesters with heat treatment

Thermotropic copolyester fibers of oxynaphthoate and oxybenzoate have been subjected to conditions that promote solid-state polymerization as well as annealing. The annealing process causes the crystals to perfect with a simultaneous increase in heat of fusion and melting temperature. Solid-state polymerization, a reaction rate-controlled process, causes the polymer viscosity average molecular weight to increase by chain extension from about 14,000 g/mole to more than 87,000 g/mole with a simultaneous impressive increase in tenacity from about 10 g/d (1.2 GPa) to almost 30 g/d (3.7 GPa). To understand the changes in mechanical properties, we have modeled the fiber structure as short rod-like molecules poorly bonded to a continuous matrix of parallel molecules. Lengthening of the reinforcing molecules facilitates better transfer of load from matrix to molecules, resulting in higher tenacity fibers. © 1994 John Wiley & Sons, Inc.     

Manganese(II) complexes with diethylamine in aqueous solutions

Interaction between MnCl₂ and diethylamine (DEA) in aqueous solutions has been studied by UV, IR, and EPR spectroscopy as part of the design and research program on models of natural photosystems. The composition of the precipitate for comparable concentrations of reagents and solute oxygen has been investigated. Mn(II) was found to be oxidized with oxygen to give MnO₂·H₂O as a precipitate. In the solution over the precipitate, Mn(III) complexes with DEA are formed; the complex molecule has four and six amine molecules in the coordination sphere.     

同输入M/M/∞排队群的联合队长过程

本提出一个偏微分方程方法，用这一方法研究同输入M/M／∞排队群中的联合队长分布。在任意初始条件下，给出了瞬时联合队长分布的多元母函数，也讨论了稳态队长的联合分布及各排队系统之间的相关性。