饮酒驾车

针对酒后驾车问题,根据微分方程理论以及合理的假设,建立了体液中酒精含量随时间变化的数学模型,并求得其特解.再根据给定的数据,运用MATLAB软件确定回归方程的系数.由此,对于不同的喝酒方式以及喝下的不同数量的酒,进行血液中酒精浓度的分析,可以预测喝酒后任意时刻血液中的酒精浓度,并能预测不同喝酒方式以及喝下的不同数量的酒后能否驾车的时间分界点.从而对问题作出科学的解释和证明.     

线性流量阀的内孔设计模型

在详细分析线性流量阀工作原理的基础上,应用平面解析几何、微积分等相关概念,给出了不存在呈严格线性的流量阀的数学论证.在设计近似线性流量阀时,首先构造了"线性误差函数"用以刻画"过流面积"与角度之间的线性误差.之后在分析内孔为对称直线、对称1/2次曲线的基础上,设计出内孔为倒"S"形内孔曲线图,通过最小化线性误差函数,得到内孔曲线的最佳参数.最后针对外孔有磨损时,给出了设计方案.     

基于线性状态反馈的非线性混合系统的实用稳定化

研究非线性混合系统的实用稳定化问题,其中该系统具有时变子系统和时变跳转函数.首先,通过状态跳转函数,确定系统一条严格递增的切换时间序列.然后在该序列中的每一段时间区间内,明确地构造出相应的线性状态反馈控制律,由此实现闭环系统的实用稳定.最后,给出一个数值例子说明文中方法的有效性.     

波莱尔“关联函数法”思想研究

利用历史比较和分析的方法,探讨波莱尔提出"关联函数法"的思想背景,分析了波莱尔利用该法研究函数奇点、函数解析开拓等问题的思想方法和意义.     

平面弹性问题自适应有限元方法的收敛性分析

针对平面弹性问题,首先采用基于最新顶点二分法的网格加密方法,给出一种不需要标记振荡项和加密单元、不需要满足"内节点"性质的自适应有限元方法.其次,通过对各层网格上解函数和误差指示子的分析,利用相邻网格层上解函数的正交性、解函数和真解函数的能量误差的上界估计、相邻网格层上误差指示子的近似压缩性等结果,从理论上严格证明了该自适应有限元方法是收敛的.最后数值实验验证了该自适应有限元方法是收敛的和鲁棒的.     

向量法解截距型线性规划问题

在线性约束条件下,对于形如"z=ax+b(a,b∈R)"的目标函数的最值问题,"课程标准"中的例题和"教材"都是介绍平移法.该解法运用函数平移的思想,思路简单,但步骤较     

一类新的求全局优化问题的填充函数

填充函数方法是一种寻找全局极小解的有效方法.本文首先对现有的填充函数进行研究分析,然后构造出一类新的填充函数,设计算法,并通过数值试验验证了该函数和算法的有效性.     

内P-显性信息规律显性-隐性特征与显性信息规律发现

函数P-集合(function packet sets)是把函数概念引入到P-集合内(packet sets),改进P-集合得到的,函数P-集合具有动态特性,规律(函数)特性。函数P-集合是由函数内P-集合SF(function internal packet set SF)与函数外P-集合SF(function outer packet set SF)构成的函数集合对;或者,(SF,SF)是函数P-集合.利用函数内P-集合与生物遗传学中的"显性","隐性"概念交叉,渗透,给出内P-显性信息规律的显性-隐性特征,给出内P-显性信息规律的显性-隐性定理,给出内P-显性信息规律发现准则;利用这些结果,给出内P-显性信息规律发现的应用.     

有限域上一类代数簇ζ函数的计算

对于有限域上给定代数簇的ξ函数,Weil提出了著名的系列猜想,其中"有理性"和"黎曼猜想的模拟"先后被Dwork和Deligne用p-adic分析和l-adic上同调等高深的代数几何工具所解决.本文发现,若代数簇的增广次数矩阵的Smith标准形满足一定的条件,则可计算出其ξ函数,从而用初等的方法证明了Weil猜想中的"有理性"和"黎曼猜想的模拟"对于这类代数簇是成立的.     

复合Poisson模型中“双界限”分红问题

引入了复合Poisson模型中的"双界限"分红模型,在这种模型中,当盈余超过上限时分红以不超过保费率的速率付出,低于下限后保费率增大.文中利用Gerber- Shiu函数来分析这种模型,先导出了Gerber-Shiu函数m_1,m_2,m_3满足的积分-微分方程,再给出m_1,m_2,m_3的解析表示,最后通过几步把Gerber-Shiu函数m(u;b_1,b)的解析式表示出来.     

血液中酒精浓度的数学模型

把人体对酒精的吸收、排放简化为一般的房室模型,提出了吸收因子、消除因子的概念.针对短时间饮酒、长时间饮酒以及间断饮酒等情况,分别建立了关于人体体液中酒精浓度的微分方程模型,并且给出了显式解.对于特殊的周期性间断饮酒的模型,给出了更便于计算的叠加公式,并通过分析酒精浓度函数的极限过程,证明了其有界性.对短时间饮酒和长时间饮酒的情况分别计算了酒精浓度的最大值、取得最大值的时间和禁止驾车的时间范围,而且进行了比较,所得结论与实际吻合.     

慢速饮酒血液中酒精含量的数学模型

描述的是在一定时间内慢慢地匀速喝完一定数量酒的问题,并建立了相应的数学模型.同时也建立了快速饮酒的数学模型,以及证明了在各次饮酒后的某时刻酒精含量的可叠加性.     

Alcohol consumption among college students: An agent‐based computational simulation

An agent‐based C++ program was developed to model student drinking. Student‐agents interact with each other and are randomly subjected to good or bad drinking experiences, to stories of other students' experiences, and to peer pressure. The program outputs drinking rates as functions of time based on various input parameters. The intent of this project is to simulate alcohol use, eventually adding other drugs, and possibly creating a simulation game for use as an educational tool. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

Modelling alcohol problems: total recovery

Binge drinking in the UK is an increasing problem, resulting in negative health, social and economic effects. Mathematical modelling allows for future predictions to be made and may provide valuable information regarding how to approach solving the problem of binge drinking in the UK. We develop a 3-equation model for alcohol problems, specifically binge drinking, which allows for total recovery. Individuals are split into those that are susceptible to developing an alcohol problem, those with an alcohol problem and those in treatment. We find that the model has two equilibrium points: one without alcohol problems and one where alcohol problems are endemic in the population. We compare our results with those of an existing model that does not allow for total recovery. We show that without total recovery, the threshold for alcohol problems to become endemic in the population is lowered. The endemic equilibrium solution is also affected, with an increased proportion of the population in the treatment class and a decreased proportion in the susceptible class. Including totally recovery does not determine whether the proportion of individuals with alcohol problems increases or decreases, however it does effect the size of the change. Parameter estimates are made from information regarding binge drinking where we find an increase in the recovery rate decreases the proportion of binge drinkers in the population.     

An infrared spectroscopic study of the breakdown of polymers under load

It has been found that when a uniaxial tension is applied to highly oriented polymer films of polypropylene, polyvinyl alcohol, or polyethylene, an increase in the intensity of the absorption bands corresponding to the vibrations of the C=O carbonyl groups is observed. These groups are produced by the oxidation of the free radicals formed on the rupture of the chemical bonds under the influence of mechanical stress. The composition of the products has been studied, and their concentration has been estimated. Curves giving the accumulation of C=O groups with time at constant load and with increase in stress for a fixed period of time under load have been studied. It is suggested that the rate of accumulation of C=O groups in both cases is determined chiefly by the rate of rupture of the molecular chains under load.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 433–436, May–June 1970.     

酒后驾车问题的数学模型

就酒后驾车问题,仿照药物动力学原理,考虑吸收系统和迟滞时间,建立了二房室模型,得出了饮酒者饮酒后血液中的酒精含量与饮酒量、饮酒方式及时间的关系.根据提供的测量数据,通过多种方法计算模型参数,选用了总体残差平方和最小的阻尼最小二乘法的计算结果作为模型参数.最后对相关问题进行了解答,结果表明,模型是合理和有效的.     

A Theoretical Analysis of Smoking and Alcoholism

A mathematical model for the spread of alcoholism and smoking is designed and analysed to gain insights into this growing health and social problem. The reproduction number and equilibria states of the model are determined and their local asymptotic stabilities investigated. Analysis of the reproduction number have shown conditions under which encouraging and supporting moderate alcohol drinkers (smokers) to quit alcohol consumption (smoking) is more effective in the control of alcoholism (smoking) than supporting and encouraging alcoholics (smoking addicts) to quit and vice-versa. Numerical simulations show that smoking greatly enhances alcoholism and vice-versa. Thus, as shown by the numerics encouraging and supporting all smokers (alcohol drinkers) to quit smoking (alcohol drinking) also contribute meaningfully to alcohol (smoking) control programmes.     

On a bi-scale and tri-phasic model for the description of growth in biological tissue using the example of the human liver

The human liver is important for hepatic metabolism regulations which depend on complex and time depending biochemical reactions coupled to the hemodynamic blood perfusion. Growth effects can impair the perfusion and therefore affect the metabolism. Such influences can be observed during the accumulation of fat in the liver tissue. The fat accumulation results from the lipid metabolism which comprises synthesis and degradation of lipids in liver cells. Individual addictions to alcohol and high fat diets are possible causes which result in an excessive synthesis of lipids. The liver sensitively reacts to such changes which could affect the viability of the organ. To observe these coupled influences of perfusion-metabolism-growth effects we use a computational model with a multi-component/tri-phasic/bi-scale approach to simulate the functionality of the human liver with respect to fat deposition. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of the long-term strength of polymer materials under arbitrary loading histories

A nonlinear version of the phenomenological theory of long-term strength of polymer materials (viscoelastic bodies) is proposed. It is based on the introduction of a function accounting for the damage accumulation connected with changes in the load intensity. The form of this function may be determined from the results of testing the material with a load changing with time in a certain way, for instance, periodically. As a parameter, the function contains the rate of the changing load or the frequency for periodic loads. For a quasi-isotropic material, the basic relationships of the theory proposed are generalized to the case of combined stresses. The durability (failure time) calculations of the material based on this theory are compared with experimental data for a number of polymer and composite materials in a wide range of loading modes. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 585–594, September–October, 1999.