Mathematical modeling of the dissolving and deposition processes during solution seepage in a porous medium

A mathematical model that describes solution seepage in a porous medium and the processes of mineral dissolving and secondary deposition is proposed. Self-similar solutions describing the motion of the leading and trailing fronts, that is, the boundaries of the complete-dissolving zone, are determined. The main features of the processes under consideration are studied and numerical calculations are performed. It is shown that the model describes well the experimental data on mineral leaching by sulfate solutions. The dynamics of mineral extraction from productive solutions in a medium with a nonuniformacidity distribution are investigated. It is shown that, in the elevated-PH zones, the mineral is dissolved; whereas, in the low-acidity zones, secondary deposition of the mineral occurs. In the latter case, after the work has been completed, the bed may contain more or less considerable mineral resources, depending on the extent of the low-PH zone and its proximity to an extraction well.     

A model for the problem of ground vibration induced by the wheels of a moving train

This paper presents a three-dimensional model for the analysis of ground vibrations excited by forces transmitted to the ground from the wheels of a moving train through the track. The field equations are solved by using scalar wave functions. From the computed results presented here, certain qualitative conclusions can be made to enhance our understanding of the physical problem.     

学生学习成绩相关性的研究

从大学生学习成绩出发,应用广义线性回归模型研究了学生学年间成绩的相关性,揭示了大学一年级,尤其是一年级的二学期是影响学生后期学习的关键阶段.进一步应用聚类分析,得到学生成绩在大学一年级就已经埋下了两极分化的隐患,应用判别分析得出了两极分化的关键课程.该结论为教育教学和学生管理提供决策依据.     

Analyzing the sustainability of harvesting behavior and the relationship to personality traits in a simulated Lotka–Volterra biotope

For the analysis presented in this paper we use experiments to study human behavior in a simulation environment based on a simple Lotka–Volterra predator–prey ecology. The aim is to study the influence of different harvesting strategies and of certain personality traits derived from the Hamburg Personality Inventory (HPI) [Andresen, B., 2002. HPI – Hamburger Persönlichkeitsinventar. Hogrefe, Göttingen] on the outcome in terms of sustainability and economic performance.     

Fluid models of single-particle kinematics

A family of trajectories of a single particle, parameterized by initial velocities on some space-like hypersurface, is somewhat analogous to streamline fluid flow. This model is applied to electromagnetism and gravity by introducing velocity and displacement fields. The resulting kinetic field equations are of simpler form than the original equations of motion, and have certain advantages for solution. The gravitational kinetic field equation is, in fact, linear. Some simple solutions are given for illustration.     

负二项分布类的条件概率封闭性

在研究只允许部分服务台进入休假状态的多服务台M／M／c排队系统时，我们发现了条件Erlang分布的一些有趣的性质，进一步研究我们发现相对应离散随机状态的负二项分布也具有很好的性质（概率封闭性．本文证明了一类负二项分布的概率封闭性．它们对导出复杂排队系统中离散状态下顾客等待时问分布及保险公司中破产概率上界的计算起着重要作用．     

飞行员数量的宏观估计与调控模型

本文提出一种估计与调控飞行员宏观数量的方法.文章给出了当航空兵的兵力规模保持稳定、只考虑飞行员年龄分布的情况下,战斗部队飞行员和航校教员总数量与每年的补充量、淘汰率、服役年限之间的函数关系;给出了当航空兵的兵力规模需要变更时,尽快达到变更目标的数学规划模型,模型考虑了每年的补充量、淘汰率、服役年限以及航校学制、规模和效率之间的关系.     

On projective group properties of the 6D pseudo-Riemannian space

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic definition of projective motion in the 6-dimensional rigid h-space. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

数学建模与聚类分析方法在企业经营效绩评价中的综合运用

本论文通过CT总公司所属九个分公司财务指标即:财务效益状况指标,资产营运状况指标,偿债能力状况指标,发展能力状况指标和稳固程度状况指标五个方面的财务状况数据,一方面采用数理统计方法进行数据分析,建立数学模型,设定了评分办法及评分标准.做出了CT总公司所属九个分公司2 0 0 0年的经营业绩(量化)评价结果.另一方面按九个公司财务指标的原始数据用聚类分析的方法将其归类,进一步揭示出各个公司之间的联系与差别.     

关于Alzer不等式的一个简单证明

利用数学归纳法和函数的单调性，本给出了Alzer不等式的一个简单证明．