负数的使用—中国人的骄傲

中国人很早就开始使用负数.在古代商业活动中,以收入为正,支出为负;以盈余为正,亏欠为负,在古代农业活动中,以增产为正,减产为负.著名的中国古代数学著作《九章算术》的"方程"一章,在世界数学史上首次正式引入负数及其加减法运算法则.书中涉及用不同颜色的算筹(小棍形状的记数工具)分别表示正数     

基于广西少数民族文化的小学数学课程资源的开发

以广西少数民族文化为依托,以中小学数学知识为载体,探索了基于广西少数民族文化的小学数学课程资源开发.以《用数学的眼光了解广西》拓展课为实践案例,将民族文化融入数学课程与教学,引导学生在真实情景中发现问题、解决问题.在感受民族文化的过程中领略我国少数民族的智慧,增强民族自豪感.     

两类基于向前差分的分数阶差分方程的解的存在唯一性

主要研究了Riemann-Liouvile型和Caputo型分数阶差分方程解的存在唯一性.结合分数阶差分方程已有的研究理论,以向前差分为出发点,参考已有的向后差分的研究方法及相关的结论,推导出适用于向前差分方程的结论,运用相关结论及两个特殊函数的收敛性,证明了两类类分数阶差分方程解的存在唯一性.向后差分是就想要得到的目标状态推算出当前状态,而向前差分可以由目前状态推算出未来的目标状态.然而,迄今已有一系列以向后差分为出发点分数阶差分方程理论的专著问世,而鲜见以向前差分为出发点的分数阶差分方程理论.经过推导总结,得出了以向前差分为出发点的两类分数阶差分方程解的存在唯一性.     

打造以学为中心的“教学评”一体化的小学数学课堂

研究学生是一切教育活动的起点.以学为中心的数学课堂,是充满生命力的课堂.教师可从学前调研起步,了解学生的认知起点和心理特征,把握“出发点”;择机退后,把时间和空间给予学生,突破“生长点”;适时向前,提供必要的学习指导,提升“关键点”.以学促教,以学评教的课堂理念,让学生自主站在课中央,成为靓丽的风景线.     

车灯光源的优化设计

通过建立直角坐标系,利用线、面方程得出以下结论:1.根据由光源发射的辐射能均匀分布在以点光源为中心的球形波阵面上,把所求的总功率之比转化为以线光源一点F′为球心,|F′B|为半径(B为灯口边缘最上的顶点)的球面被灯口所截得的两个球冠面积之比,经计算得直射光总功率反射光总功率≈0.690683.2.直射光的亮区是由圆滑动而成.3.光源放在车灯焦点处效果最佳.     

个人信用评分的Adaptive Lasso-Logistic回归分析

以个人信用风险为研究对象,分析影响个人信用评分的因素.利用某商业银行个人信用数据,并采用.Adaptive Lasso-Logistic回归模型对影响顾客的个人信用风险的因素进行分析,并与传统Logistic回归模型以及Lasso-Logistic回归模型进行比较.以对顾客"好"与"坏"的二分类结果的正确比例为主要衡量标准,实证发现以.Adaptive Lassi-Logistic回归方法建立的个人信用评分模型,在变量选择和解释上,以及预测的准确性上,均优于传统的Logistic和Lasso-Logistic方法.     

带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性

研究了带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性问题.通过构造合适的Lyapunov泛函,得到了判定带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定的充分条件.并举例说明结论的有效性.     

带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性

讨论了带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性.通过构造合适的Lyapunov函数,获得了判定带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性的充分条件.     

错解数学问题的辨析与对策

解答数学试题难免出现错误,如何使解题中的错误率降到最低程度,以达到提高考试成绩的目的,是每一位学生渴望解决的问题.本文就此问题作以探讨.     

例谈椭圆双曲线离心率取值范围的求法

求离心率取值范围问题有两种题型,即显示约束条件和隐藏约束条件两种题型.两种解题方向,即以"形"为主的解题的方向和以"数"为主的解题方向.两种求取值范围的方法,即解不等式法和函数值域法.下面举例说明.……     

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.     

On Green’s functions for positive,elliptic differential operators on closed,Riemannian manifolds and some consequences for semi-linear PDE

In this article, we establish the non-negativity of Green’s functions for a class of elliptic differential operators on closed, Riemannian manifolds. The method used is the calculus of variations with a unilateral constraint. Consequences of this result are then explored, with a maximum principle-type result established for a broad class of semi-linear elliptic PDE as a result. Finally, a result regarding the positivity of the principal eigenfunction of an operator in this class is proven as well.     

Minkowski空间中具有常值支持函数的子流形

在Mlinkowski空间中证明了完备连通且具有常值支持函数的子流形必为Finsler球面或者为一个平面．利用支持函数研究的两类子流形是Euclid空间中结果的推广，同时优化了Euclid空间中子流形的相应结果．     

Addendum to “Distribution of points on the circle” [J. Number Theory 127 (1) (2007) 127-135]

In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a new proof of our earlier result and to improve upon the marginal result.     

Existence of nonzero solutions for a class of damped vibration problems with impulsive effects

In this paper, a class of damped vibration problems with impulsive effects is considered. An existence result is obtained by using the variational method and the critical point theorem due to Brezis and Nirenberg. The obtained result is also valid and new for the corresponding second-order impulsive Hamiltonian system. Finally, an example is presented to illustrate the feasibility and effectiveness of the result.     

Homogenization and corrector for the wave equation with discontinuous coefficients in time

In this paper we analyze the homogenization of the wave equation with bounded variation coefficients in time, generalizing the classical result, which assumes Lipschitz-continuity. We start showing a general existence and uniqueness result for a general sort of hyperbolic equations. Then, we obtain our homogenization result comparing the solution of a sequence of wave equations to the solution of a sequence of elliptic ones. We conclude the paper making an analysis of the corrector. Firstly, we obtain a corrector result assuming that the derivative of the coefficients in the time variable is equicontinuous. This result was known for non-time dependent coefficients. After, we show, with a counterexample, that the regularity hypothesis for the corrector theorem is optimal in the sense that it does not hold if the time derivative of the coefficients is just bounded.     

化肥需要量灰色预测模型参数的四阶求法

针对文［１］化肥需要量灰色预测模型误差较大且预测结果与定性分析矛盾的问题，本文提出和应用了确定Ｖｅｒｈｕｌｓｔ模型参数的四阶方法，并重新合理配置建模数据而得一预测模型．计算表明新模型与实际值的拟合精度提高近十倍，而且预测结果与定性分析完全一致．     

General Decay for a Viscoelastic Equation of Variable Coefficients in the Presence of Past History with Delay Term in the Boundary Feedback and Acoustic Boundary Conditions

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function \(g\). Our result extends the decay result obtained for problems with finite history to those with infinite history.     

Automatic Linear Correction of Rounding Errors

A new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a confidence threshold are computed using algorithmic differentiation, computation of elementary rounding error and running error analysis. Algorithms for which the accuracy of the result is not affected by higher order terms are identified. The correction is applied to the final result or to sensitive intermediate results to improve the accuracy of the computed result and/or the stability of the algorithm.This revised version was published online in October 2005 with corrections to the Cover Date.     

Effective stability for slow time-dependent near-integrable Hamiltonians and application

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.