仓库容量有限条件下的随机存贮管理问题的评注

给出2005年全国部分高校研究生数学建模竞赛D题的研究背景,对参赛论文作了简要评注,并提供了一种参考解答.     

Convergent Flows of Molten Polymers Modeled by Generalized Second-Grade Fluids of Power-Law Type

The molding processes of polymer melts involve geometrically complex dies. Such dies are usually tapered or streamlined to achieve a maximum output rate under conditions of laminar flow. The model of a generalized second-grade fluid of power-law type is used and the results obtained are illustrated by examples of convergent flows in conical and wedge-shaped dies.     

具有模糊数的模糊多目标群体决策优选模型与方法

多目标群体决策问题是运筹学的一个重要研究领域，目前已经提出了一些有效的决策方法。但对目标值和权重均为模糊数的模糊多目标群体决策问题却研究不多，本对此类模糊多目标群体决策问题进行了探讨，利用相对正理想方案与相对负理想方案概念定义了相对差异距离，进而建立了模糊多目标群体决策优选模型与方法，并通过战役决心方案的评价说明了该方法是可行、有效的，可作为军事决策与决策支持系统的备选方法。     

Two-component model of solar plages

By use of the 2-m Mcmath-Pierce telescope at Kitt Peak, the high-quality spectra of a plage with moderate brightness near the center of solar disk were obtained. The data include seven spectral lines, which are Hα, Hβ, CaII H and K lines and the infrared triplet. With the consideration of fine structures of solar plages, a two-component atmospheric model is constructed by keeping the cool component to be the quiet atmosphere. Three cases of the hot component are given for different filling factors where the temperature and density distribution are adjusted in order to reproduce the seven observed spectral profiles. We also briefly discuss the influence of the column density at the base of the corona, m0, and the macro-turbulent velocity on the required filling factor and computed profiles. The two-component model is compared with precious one-component semi-empirical models. The limitation of the model is pointed out and further improvement is indicated.     

Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Er3+掺杂的Bi2O3-B2O3-SiO2玻璃的光谱性质

测试了Bi₂O₃-B₂O₃-SiO₂玻璃中的Er³⁺离子的吸收光谱、发射光谱、⁴I_13/2的荧光寿命、拉曼光谱,及OH^-的傅里叶红外吸收光谱。应用Judd-Ofelt理论计算了该玻璃中的Er³⁺离子的J-O参数、振子强度、⁴I_13/2能级的寿命,从而利用测得的⁴I_13/2的荧光寿命得出了⁴I_13/2能级的量子效率(15%)。由于较低量子效率可能与OH^-有关,所以计算了玻璃中的OH^-浓度,发现其浓度较高(1.66×10¹⁹cm^-1,相当于Er³⁺浓度的3倍)。应用McCumber理论和四能级模型计算了Er³⁺离子的受激发射截面和荧光发射光谱的半峰全宽,结果与通过吸收光谱计算所得基本吻合。根据透射率和折射率的关系计算了折射率,发现和测量值相差很大,说明有较大的散射,通过拉曼光谱和显微镜测试,认为是玻璃中的微小气泡造成的。     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Theory of interfacial phase transitions in surfactant systems

The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discretization of the solutions to Poisson’s equation

Sharp estimates (in the power scale) are obtained for the discretization error in the solutions to Poisson’s equation whose right-hand side belongs to a Korobov class. Compared to the well-known Korobov estimate, the order is almost doubled and has an ultimate value in the power scale.