一个体现新课程理念的教学内容设计——“圆锥曲线第二定义”的教学体会

正新课程实验教材已完成了一轮教学.由于新课程的理念变了,编写意图也发生了变化,新教材相对于与原教材而言,内容变了、体系改了、要求不同了、方法更新了.因此,在教学中新     

绿色食品需求函数的一种求解方法

本分析了影响绿色食品消费的因素，建立了消费消费绿色食品及同类一般食品的效用最大化数学规划模型，给出了Kuhn-Tucker条件；引入了绿色食品置信度参数并建立了一个可计算的二次效用函数，导出了该二次效用函数对应的需求函数，并详细地表述了求解过程和方法，讨论了绿色食品需求函数的性质。     

基于粗糙集的患者满意度评价模型及其实证分析

在文献阅读及实地调研的基础上,本文提出了患者满意度的定义,建立了影响患者满意度的指标体系,介绍了粗糙集的相关概念及利用粗糙集进行评价的步骤,提出了新的约简方法,构建了基于粗糙集的患者满意度评价模型并进行了实证分析,得出了影响患者满意度的关键指标,并计算了关键指标权重,对江西省十个医院进行了综合评价值的计算.     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

数学是……

数学是一首悠扬的歌
　　直线成了五线谱
　　圆连成了音符
　　唱出了奇妙的快乐
　　数学是一幅清新的画
　　曲线成了浪花
　　线性规划调出了最佳
　　绘出了斑斓的色彩     

分数阶抛物方程控制系统最优控制的稳定性

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

广义不变凸非线性分式规划的对偶性

Craven研究了一类非线性分式规划的对偶性．本文减弱了文献中主要定理的条件，得到了相同的结果．同时，还获得了几个新结果及讨论了逆对偶性．     

数学小报，我来也

数学小报好处多
　　1.开阔了视野,开发了思维。
　　2.给学习增添了新鲜感,激发了学习数学的积极性。
　　3.能够复习、梳理已学知识点,锻炼了整理知识的能力。
　　4.培养了动手、动脑的习惯,培养了想象力和创造力。     

分数阶抛物方程控制系统最优控制的稳定性（英文）

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

基于泊松过程的理想纱条的数学建模与条干不匀分析

在Rao给出的理想纱条的数学定义的基础上,进一步提出利用泊松过程来描述纤维在理想纱条中的随机排列.由此得出纱条片段中纤维左头端数服从泊松分布,相邻纤维的左头端间隔距离服从指数分布,纤维左头端在纱条中的位置服从均匀分布,纱条截面的纤维根数服从泊松分布,这对理解纤维在纱条中的排列结构以及模拟纤维在纱条中的随机排列提供了基础.在此模型的基础上对纱条的条干不匀进行了分析,给出了考虑纤维细度因素之后的条干不匀公式.     

Anomalous scaling in statistical models of passively advected vector fields

We use the methods of the renormalization group and the operator product expansion to consider the problem of the stochastic advection of a passive vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The external velocity field satisfies the Navier-Stokes equation. We show that the correlation functions have anomalous scaling in the inertial range. The corresponding anomalous exponents are determined by the critical dimensions of tensor composite fields (operators) built from only the fields themselves. We calculate the anomalous dimensions in the leading order of the expansion in the exponent in the correlator of the external force in the Navier-Stokes equation (the oneloop approximation of the renormalization group). The anomalous exponents exhibit a hierarchy related to the anisotropy degree: the lower the rank of the tensor operator is, the lower its dimension. The leading asymptotic terms are determined by the scalar operators in both the isotropic and the anisotropic cases, which completely agrees with Kolmogorov’s hypothesis of local isotropy restoration.     

The calculation of the energy losses in a sliding elastic contact with friction and wear (the plane problem)

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.     

基于随机模糊投资乘数的离散CPPI资产配置研究

以传统CPPI投资策略的分析框架为基础,在风险资产为连续价格波动的条件下,构建离散投资决策时点的CPPI投资策略。引入模糊决策的分析方法度量投资决策者的心理预期,将传统CPPI投资策略中的投资乘数修正为随机模糊投资乘数,采用马尔科夫链蒙特卡洛模拟风险资产未来市场价格,利用模糊隶属函数描述投资决策者对未来市场运行状况预期的不确定性,保证即使投资决策者预期不精确的条件下,也能保证离散CPPI投资策略获得相对稳定的投资效果。利用中国证券市场上的真实数据进行实证检验,认为:随机模糊投资乘数最大限度地涵盖了投资决策者主观预测的不确定性;基于随机模糊投资乘数的离散CPPI投资策略在不同的市场运行状况中,较传统的CPPI投资策略更具投资的灵活性,可以在保证投资保险的前提下,追求较高的投资收益。     

基于加总和乘积的方差分解法及其应用

研究了加总式和乘积式的方差分解问题,证明了在因变量等于各自变量之和的条件下,因变量方差等于各自变量与因变量的协方差之和;在因变量等于各自变量之乘积的条件下,因变量对数值的方差等于各自变量对数值与因变量对数值的协方差之和．以中国31个省份2005－2012年的居民人均收入及其影响因素的统计数据资料为例,说明了加总式和乘积式的方差分解法的具体应用．     

The equilibrium problem for a Timoshenko-type shallow shell containing a through crack

Under study is the nonlinear equilibrium problem for an elastic Timoshenko-type shallow shell containing a through crack. Some boundary conditions in the form of inequalities are imposed on the curve defining the crack. We establish the unique solvability of the variational statement of the nonlinear problem of the equilibrium of a shell. We prove that, for sufficient smoothness of the solution, the initial variational statement is equivalent to the differential formulation of the problem. We deduce the boundary conditions on the inner boundary that describes the crack. In the case of the zero opening of the crack, we prove the local infinite differentiability of the solution function with additional assumptions on the functions defining the curvatures of the shell and the external loads.     

运动机械质心数学模型及其在机构质心稳定中的应用

以四连杆机械为例,其自由度是1,整个机构的质心只需一个独立参变数描述.故机构的质心对该参数的导数等于零即机构质量中心保持固定的充要条件.通过对线性方程组基础理论的巧妙利用,给出了四连杆在工作状态下质心保持稳定的几何特征.     

援疆效果满意度的公因子分析:综合评价和政策取向——以南疆三地州数据为例

以居民对援疆政策满意度为出发点,前学者的研究基础上确定援疆政策效果的满意度的衡量指标,选取6个大方向31个指标来测量援疆效果满意度.通过南疆三地州进行实地问卷调查获得数据为样本,采用因子分析方法确定二级指标及三级指标的权重,进行对援疆政策效果满意度综合评价.研究结论是南疆居民对援疆效果的满意度总得分接近70分,说明总体满意度较高,其中满意度最高的为收入及补贴,排在第一位,排在末尾的就是教育领域,排在第二位的是住房建设,而基层服务的满意度仅仅高于教育领域,排在第五位.排在第三位的就是医疗,第四位才是居民出行为核心内容的基础设施建设.从而为援疆政策效果满意度优化,解决存在的问题,全面改善援疆政策效果提出政策建议.     

Asymptotics of a Solution of a Three-Dimensional Nonlinear Wave Equation near a Butterfly Catastrophe Point

We consider an optimal distributed control problem in a planar convex domain with smooth boundary and a small parameter at the highest derivatives of an elliptic operator. The zero Dirichlet condition is given on the boundary of the domain, and the control is included additively in the inhomogeneity. The set of admissible controls is the unit ball in the corresponding space of square integrable functions. Solutions of the obtained boundary value problems are considered in the generalized sense as elements of a Hilbert space. The optimality criterion is the sum of the squared norm of the deviation of the state from a given state and the squared norm of the control with a coefficient. This structure of the optimality criterion makes it possible to strengthen, if necessary, the role of either the first or the second term of the criterion. In the first case, it is more important to achieve the desired state, while, in the second case, it is preferable to minimize the resource consumption. We study in detail the asymptotics of the problem generated by the sum of the Laplace operator with a small coefficient and a first-order differential operator. A feature of the problem is the presence of the characteristics of the limit operator which touch the boundary of the domain. We obtain a complete asymptotic expansion of the solution of the problem in powers of the small parameter in the case where the optimal control is an interior point of the set of admissible controls.     

Crosslinking of an unsaturated polyester resin in the mould: Modelling and heat transfer studies

The crosslinking of unsaturated polyester was studied by using an experiment and a mathematical model of the process. Temperature–time profiles were recorded in the centre of the sample inside the mould at the outer wall of the cylindrical copper mould, and in the bulk of the heated air bath. A numerical model was constructed by taking into account the heat transferred by convection from the air to the mould surface and the heat transferred by conduction through the resin, as well as the heat generated by the crosslinking reaction. The convection heat transfer coefficient was determined in independent experiments with the empty copper mould. Introduction of the carbon base filler reduced the amount of heat generated in the composite due to the less reactive component in the composite. As a result, it lowered the temperature of the resin. By recording the temperature-time and the degree of crosslinking time profiles developed within the sample extensive knowledge of the process can be obtained. The effects of the convection heat transfer on the rate of mould heating, and the conduction heat transfer through the mould as well as the internal heat generated by the crosslinking reaction are visibly shown, despite a complexity of the process.