一元二次方程的根的判别式的应用

一元二次方程的根的判别式是初中代数的重要内容之一 ,它在中学数学中有着广泛的应用 ,成为近几年全国各地中考的热点问题 .为了帮助读者更好地掌握好这部分知识内容 ,现对它在初中数学中的应用进行归纳 ,以餮读者 .应用一 :判断一元二次方程 (或二元二次方程组 )的根的情况 ;或已知根的情况 ,求方程 (或组 )中的待定系数的取值范围 .一元二次方程ａｘ2 +ｂｘ +ｃ =0 (ａ≠ 0 )的根的判别式为△ =ｂ2 - 4ａｃ,它与这个方程的根有着十分密切的关系 :( 1)△ >0 方程有两个不等的实数根 ;( 2 )△ =0 方程有两个相等的实数根 .( 3)△ <0 方程…     

纯正的群的正则带的构造

本文研究纯正的群的正则带.在给出这类半群的若干特征后,建立了纯正的群的正则带的构造定理.作为应用,同时给出了纯正的群的右拟正规带的构造定理.     

图的邻域复形的同调群的不变性

本文研究了图的邻域复形同调群的不变性质。设G是一个简单连通图,x是G的一个顶点,以G/x表示G中剔去点v及其关联边而得到的图,给出了G和G/x的邻域复形的同阶同调群同构的充要条件。     

单圈图的最大特征值的上界的改进

Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.     

多项式的根的一个性质的判定

文献[1]在讨论多项式型的函数迭代方程的局部解析解的存在性时涉及到了多项式的根的一个性质.本文给出了判定该性质是否成立的一个简洁的条件,证明了多项式λ_nzⁿ+…+λ₂z²+λ₁z+λ₀有一个根α满足inf{｜λ_nα^nm+…+λ₂a^2m+λ₁α^m+λ₀｜：m=2,3,…｝>0当且仅当如下两个条件之中至少有一个成立：(i)该多项式有一个根β满足｜β｜>1;(ii)该多项式有一个根β满足｜β｜<1,且λ₀≠0.     

数的概念的发展

编者按:李邦河院士于2009年4月中国数学会厦门学术年会上荣获"华罗庚数学奖".本文是李院士在这次年会上所做的公众报告,他在报告中谈到一个重要的思想:数学玩的是概念,而不是纯粹的技巧.因为中小学数学里面的概念比较少,所以就在一些难题、技巧上下功夫,这恰恰是舍本逐末的做法,值得所有的数学教育工作者深思.     

圆锥曲线的割线的性质

如果一条直线与圆锥曲线有两个公共点,我们称该直线为圆锥曲线的一条割线,当割线的斜率不为零时,它必与主轴所在直线(x轴)相交.下面以椭圆为例探究与割线有关的一些数学问题.引例过椭圆x2a2 y2b2=1(a>b>0)的左焦点F(-c,0)作直线l交椭圆于P、Q两点,Q′是Q关于x轴的对称点(Q′与P不重合),直线PQ′交x轴于点M.则图1(1)PFFQ=M PMQ;′(2)点M为定点(-2ac,0).(1)证法1如图1,连结MQ,易知得等腰△MQQ,′∴M F平分∠QMQ.′由角平分线性质定理可得M P MQ=PF FQ,又MQ=MQ′,∴M P MQ′=PF FQ,所以PFFQ=M PMQ.′证法2设QQ′与x轴…     

ZFC的模型的上限序数的一个性质

S1 引言 Forcing方法假设存在ZFC的一个可数可传的模型M。记满足αM的最小序数α为,显然M中一切序数所成的集合即。由于M是ZFC的模型,故应具有某些性质。本文证明了它满足关系,故为ε数或1级关键数,进而证明了是H级关键数(H为任意自然数)。文中的记号等引用。     

基于酉几何的等概的具有仲裁的认证码的构造

具有仲裁的认证码既要防止敌手的欺骗,又要防止收入和发方的互相欺骗,本文给出一种由酉几何构造等概的具有仲的认证码的方法,并计算了有关参数,分析了各种攻击成功的概率。     

保险风险模型的序关系及其误差

从停止损失序的角度,探讨了用集体风险模型来近似个体风险模型时,随机风险理赔总额S的一般情况,我们推广现有文献(如Goovaerfs)的关于单因模型的结果,得到了各模型间S的序的关系(定理1),并给出了各模型S之间的误差公式(定理3).     

Constant barrier strategies in a two-state Markov-modulated dual risk model

In this paper,we consider the dividend problem in a two-state Markov-modulated dual risk model,in which the gain arrivals,gain sizes and expenses are influenced by a Markov process.A system of integrodifferential equations for the expected value of the discounted dividends until ruin is derived.In the case of exponential gain sizes,the equations are solved and the best barrier is obtained via numerical example.Finally,using numerical example,we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model.Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.     

基于违约风险的Vasicek利率风险研究

本文将非瞬时利率作为状态变量,通过Vasicek双因素期限结构模型得到了随机久期和凸度,并且讨论了考虑违约风险的Vasicek随机久期和凸度,使得对债券进行投资时,用Vasicek模型进行利率风险管理更加符合实际情况。     

Criterion of semi-Markov dependent risk model

A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.     

On multivariate modifications of Cramer–Lundberg risk model with constant intensities

ABSTRACT

The paper considers very general multivariate modifications of Cramer–Lundberg risk model. The claims can be of different types and can arrive in groups. The groups arrival processes have constant intensities. The counting groups processes are dependent multivariate compound Poisson processes of Type I. We allow empty groups and show that in that case we can find stochastically equivalent Cramer–Lundberg model with non-empty groups. The investigated model generalizes the risk model with common shocks, the Poisson risk process of order k, the Poisson negative binomial, the Polya-Aeppli, the Polya-Aeppli of order k among others. All of them with one or more types of policies. The numerical characteristics, Cramer–Lundberg approximations, and probabilities of ruin are derived. During the paper, we show that the theory of these risk models intrinsically relates to the special types of integro differential equations. The probability solutions to such differential equations provide new insights, typically overseen from the standard point of view.     

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai (Probability in the Engineering and Informational Sciences, 16(2002), 309-324). We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.     

考虑公众风险感知的突发事件风险传播模型及仿真研究

突发事件应对过程中,公众对突发事件的风险感知会在一定程度上决定其行为选择从而影响事件风险的传播。为此,本文通过分析突发事件风险信息、风险感知和风险传播的路径关系,在风险传播过程中引入传染病传播机制,构建基于微分方程的风险传播模型。综合考虑风险传播阈值、媒体报道力度、群体风险感知度、个人风险知识水平四类因素并结合仿真实验分析对风险感知和风险传播行为的影响。最后,通过实例研究表明模型结论的有效性。本文研究结论有助于为相关职能部门调节公众风险感知,制定风险防控措施提供理论依据与支持。     

有红利界限的平稳更新模型的红利现值

本文研究平稳更新风险模型下的红利现值,将其用普通更新模型下的红利现值表示出来.这个关系式统一并推广了已有的某些结果.     

中证开放式基金指数和GARCH-M模型

基于开放式基金指数周收益率时间序列的非正态性和厚尾特性,以中证开放式基金指数为例,运用GARCH-M模型进行研究,系统地分析我国不同类型的开放式基金的投资风险.实证分析表明:GARCH-M模型对中证开放式基金指数周收益率的拟合效果较好,并为预测我国开放式基金的投资风险提供了科学依据.     

Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary

In this paper, we propose two risk hedge schemes in which a life insurer (an annuity provider) can transfer mortality (longevity) risk of a portfolio of life (annuity) exposures to a financial intermediary by paying the hedging premium of a mortality-linked security. The optimal units of the mortality-linked security which maximize hedge effectiveness for a life insurer (an annuity provider) can be derived as closed-form formulas under the risk hedge schemes. Numerical illustrations show that the risk hedge schemes can significantly hedge the downside risk of loss due to mortality (longevity) risk for the life insurer (annuity provider) under some stochastic mortality models. Besides, finding an optimal weight of a portfolio of life and annuity business, the financial intermediary can reduce the sensitivity to mortality rates but the model risk; a security loading may be imposed on the hedge premium for a higher probability of gain to compensate the financial intermediary for the inevitable model risk.