两个数学建模问题的探讨

探讨了两个在教科书中作为例题的数学建模问题，一个是关于渔业生产的，另一个关于体育训练，对于前者，提出一个更为合理的解法；对于后者，则提出其中数学推导上的错漏并得出新的结论。     

发动机的曲轴转速方程及其近似解

从活塞发动机的动力分析中得到本文中的微分一积分方程(4),其中α为曲轴转角,θ为角速度的平方,而ε<<1为总等效转动惯量的倒数。本文利用压缩映象原理和摄动方法证明了所得方程解的存在性和唯一性,并给出了这个解的渐近展开。     

416例湘西苗族学生手纹研究

<正>皮纹是人体稳定的体表特征.它的各种性状具有遗传特征,种族差异和民族差异,并且在刑侦及其某些遗传性疾病的诊断中起重要作用.为积累我国各民族正常群体的皮纹学参数值,为人类学、遗传学及临床医学等相关研究提供正常对照数据,我们对416例湘西苗族学生的手纹进行了研究,为了对照分析,引用了有关文献.     

Quantitative genetic models of sexual selection

Summary Quantitative genetic models of sexual selection have disporven some of the central tenets of both the handicap mechanism and the sexy son hypothesis. These results suggest that the good genes approach to sexual selection may generally lead to erroneous results.Runaway sexual selection seems possible under a wide variety of circumstances. Quantittive genetic models have revealed runaway processes for sexually selected attributes expressed in both sexes and for attributes of parental care. Furthermore, the runaway could occur simultaneously in a series of populations that straddle an environmental gradient. While the models support the feasibility of runaway processes, empirical studies are needed to evaluate whether runaways actually happen. Estimates of critical genetic parameters are particularly needed, as well as measures of natural and sexual selection acting on the same population.The models also show that sexual selection has tremendous potential to produce population differentiation, particularly in epigamic traits. Differentiation is promoted by indeterminancy of evolutionary outcome, transient differences among populations during the final slow approach to equilibrium, sampling drift among equilibrium populations, and the tendency of sexual selection to amplify geographic variation arising from spatial differences in natural selection. Recent work with two- and three-locus models of sexual selection has produced results that parallel the results of the polygenic models^36–38,58. Thus the feature of indeterminate equilibria (outcome dependent on initial conditions) is common to both types of model.     

南水北调东线工程调水期洪泽湖水质变化规律分析

为了解南水北调东线工程调水期间洪泽湖水质变化,基于2013—2020年洪泽湖调水期水质监测数据,采用Daniel趋势检验分析水质年变化趋势,通过空间插值得出各湖区水质分布规律,并进一步用主成分分析法分析水质主要污染类型。结果表明：2013—2020年洪泽湖调水期水质在合格至轻度污染之间,TP和TN为主要超标因子;时间上水质有变好趋势,空间上过水区水质最差,但有转好趋势,而成子湖区和溧河洼区有所恶化;污染类型以富营养化污染为主,氮磷营养盐影响较大;水质污染以入湖河流输入和建设用地增加人类活动的污染为主要来源,还伴有偶发污染事故;时间上洪泽湖对东线输水的综合水质有改善趋势,建议进一步加强相关污染防治工作,保护洪泽湖水环境,保障南水北调东线工程输水水质安全。     

计算旋转螺旋面三维边界层的一种积分方法

本文将计算二维层流边界层的Thwaites方法和计算二维湍流边界层的Truckenbrodt方法推广,用以求解旋转系统的“准三维”边界层方程,得到了计算旋转螺旋面上三维边界层的一种可迭代求解的积分方法.应用此方法进行了两例计算.计算结果与理论精确解或实验测量的对比表明,本文方法是有效的.     

Error rates in quadratic discrimination with constraints on the covariance matrices

In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions. We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following four models: (i) arbitrary covariance matrices, (ii) common principal components, (iii) proportional covariance matrices, and (iv) identical covariance matrices. Using Monte Carlo simulation to estimate expected error rates, we study the performance of the four discrimination procedures for five different parameter setups corresponding to standard situations that have been used in the literature. The procedures are examined for sample sizes ranging from 10 to 60, and for two to four groups. Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.The authors wish to thank the editor and three referees for their helpful comments on the first draft of this article. M. J. Schmid supported by grants no. 2.724-0.85 and 2.038-0.86 of the Swiss National Science Foundation.     

凸轮实测中角度基准偏移误差的消除方法

引起凸轮测量误差的主要原因之一是实测时的角度基准与理论设计时的角度基准不一致,本文利用凸轮的一次离散实测数据,采用分段抛物线拟合函数,以角度搜索法插值得到不同角度基准下的多组测量数据．从各组测量数据与设计数据的各个最大偏差值中,找到最小值,它所对应的角度基准即为该凸轮的准确的角度基准．通过编程并在实测凸轮中验证了此方法的可靠性．     

基于雷达导引头角度跟踪特性的战斗机机动控制方法

通过分析导弹导引头角度自动跟踪系统的跟踪特性,明确了跟踪误差产生机理及对跟踪系统的影响,提出了战斗机规避导弹攻击的机动控制目标。以二维平面内导弹攻击为例,建立了导弹与战斗机的相对追逃运动模型。基于动态逆理论,对中断导引头角度跟踪的机动控制方法进行分析,推导了战斗机的规避机动控制律。通过仿真验证了该方法的有效性。     

战斗机网络攻击指令引导控制方法

对战斗机网络攻击指令引导控制方法进行了研究。建立了导弹拦射攻击模型和导弹发射边界模型;以航向角和高度为引导指令建立网络指令引导解算模型;基于典型作战场景对上述模型进行仿真实验分析。仿真结果表明:不管针对非机动目标还是机动目标,采用网络攻击指令引导方法都能实现最大火力包线的战斗机网络攻击引导。