Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

The transmission of meningococcal infection: a mathematical study

The most common type of bacterial meningitis in the developed countries is caused by Neisseria meningitidis bacteria, which cause meningococcal meningitis. Case fatality rate can be between 3% and 10% in developed countries and as high as 20% in African countries. During epidemics in sub-Saharan countries, the so-called meningitis belt, the case fatality rate can peak to 70% or higher. Some people who have bacterial meningitis experience some form of after effects: epilepsy, damaged eyesight, hearing loss, brain damage. There is no immunity after infection. Approximately on average 10% of the population at any time carry the germs for days, weeks, or months. Carriers can infect other individuals by close contacts, even though they do not become ill themselves. An age-structured mathematical model is formulated that enables the understanding of the dynamics of the infection transmission. The model is used to study the conditions for the stability of the disease-free steady state (which imply extinction of the disease) and the existence of an endemic state (which leads to persistence of the disease in the population). The results of the model are applied to identify the contribution of the carriers to the transmission of the disease. Final epidemiological conclusions are given.     

MSE's of prediction in growth curve model with covariance structures

We consider the growth curve model with covariance structures: positive-definite, uniform covariance structure and serial covariance structure. Two types of prediction problems are studied in this paper. One is called the conditional prediction problem and the other is called the extended prediction problem. For both types of prediction problems, the mean squared error for a serial covariance structure is obtained for the estimates based on the conditional expectation: the mean squared error for an unrestricted covariance structure is compared with the mean squared error for a uniform covariance structure or a serial covariance structure. These results are exemplified by two sets of real data.This research was supported in part by Grant-in-Aid for general Scientific Research, The Ministry of Education, Science and Culture under Contract Number 03640239.     

Multicolor particle systems with large threshold and range

In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of debris or fire fronts. The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems.     

Researches of DC—Problem Under the Model S in which the Numbers of Defective Coins are not Fixed

In this paper,we research general Defective Cion Problem under the model S,i.e,the number d of Defective cions is not fixed. For d=O,1,or 2. we get some good results.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.     

低密度氢气的分子间平均相互作用势理论和计算

本文提出了分子单中心模型,并通过对构型的平均,两个定理的提出与证明,色散能修正的证明,从数学上论证了这个模型的合理性。由此模型可以直接求出两个氢分子间的平均相互作用势,从而改变了长期以来,总是先算有限几种构型然后再作平均的传统作法。通过数字计算,得到了迄今为止最好的全程平均相互作用势曲线。势阱深度及平衡分子间距分别为-2.91meV和3.44(实验值:-2.85～-3.00meV,3.43～3.49)。     

闭壳层原子相关效应的多体理论计算：Ne原子基态相关能

对coupled-pair many-electron theory(CPMET)展开中的非线性四体效应采取了近似处理,用角动量图技术和两体函数方法得到了适用于一般闭壳层原子的径向微分方程。然后以X_a模型作为零级近似,通过迭代求解成功地计算了Ne原子基态的任意阶相相关能,从而说明至少对于闭壳层原子体系而言,用X_a模型作零级近似同样可以进行成功的多体理论计算。     

F－L模型的状态方程与退禁闭相变图象

用温度场论方法计算了Ｆ－Ｌ模型在有限温度和密度下的状态方程，分析了压强对净重子数密度的等温线．结果表明，在平均场近似下，Ｆ－Ｌ模型所给出的退禁闭相变为一级相变．