拟Lipschitz函数的广义梯度及其在优化理论中的简单应用

本文总假定:R~n为n维欧氏空间,R为全体实数,D(?)R~n为开子集,‖·‖为R~n中的欧氏模,co为凸包,co为闭凸包,f:R~n→R为R~n上的实值函数。     

具有指定亏函数和指定亏量的素函数

设F(z)为亚纯函数,若F可表为 F(z)=f°g(z) (1) 其中g为整函数,f为亚纯函数(当f为有理函数时,g可为亚纯函数)。我们称(1)为F的一个分解。若F的任何形如(1)的分解都只能是f或g为线性函数,则称F为素的。如果F的任何形如(1)的分解都只能以g为多项式或f为有理函数的形式出现,则称F为拟素的。     

一类锥体的外接球半径公式及其应用

设圆锥的母线长为l，高为h，或侧棱长都相等的棱锥的侧棱长为l，高为h，则它们的统一外接球半径公式为R=l^2/2h（1）     

具有扫描的混合环路的数学分析

本文研究这样的锁相环路,其环路的滤波器为理想滤波器,特性为(s α)/s,而扫描速度为R,鉴相器特性为sinφ k sin 2φ。因而相应的环路方程为:     

等差等比递归数列性质初探

1问题的提出观察数列一般地,我们给出：定义1若数列{an}满足递推关系其中u．v（v=0)为常数，则称{an}为一型等差等比速归数列．称u为为公差，v为公比．定义2若数列{an}满足递推关系其中u，v（v=0）为常数，则称{an}为二型等差等比递归数列．称u为公差，v为公比．显然，非军常数列是以上两型数列当公差为年同时公比为1的特例．由定义可得定理1若｛an｝为互型数列，则{an 1}:为Ⅱ型数列；若{an}为Ⅲ型数列，则{an＋1}为I型数列．21型数列的性质定理ZI型数列｛a。｝的通项公式为证明由递推关系（互）可得由此递推式得将上面诸式相加得；从而…     

素特征的"李定理"

设L为代数闭域F上有限维李代数,著名的李定理说若char F=0,则L为可解当且仅当L的任一有限维不可约模为1维的.在这里特征为0及模为有限维两个条件都是本质的.(1)若charF=p＞o,则L为交换当且仅当L的任一(有限维)不可约模为1维的;(2)若char F=0,则L为交换当且仅当L的任一(有限维或无限维)不可约模为1维的;(3)若charF=p＞7,L为李代数(限制李代数),则L为可解当且仅当L的任一不可约模(限制模)的维数为p的幂.     

素特征的“李定理”

设L为代数闭域F上有限维李代数,著名的李定理说:若char F=0,则L为可解当且仅当L的任一有限维不可约模为1维的.在这里特征为0及模为有限维两个条件都是本质的.(1)若charF=P>0,则L为交换当且仅当L的任一(有限维)不可约模为1维的;(2)若char F=0,则L为交换当且仅当L的任一(有限维或无限维)不可约模为1维的; (3)若char F=P>7,L为李代数(限制李代数),则L为可解当且仅当L的任一不可约模(限制模)的维数为p的幂.     

长期预报相空间模式的预报误差估计

§1.预报误差与资料个数、相空间维数和模式阶数的关系 设时间序列的点间隙为ε,模式的阶数为q,相点数为N,资料数为n,相空间维数为d,则:     

无理数的一个性质

无理数的一个性质黄炳生（东南大学）命题若Ｃ为无理数，ｎ为奇素数，且Ｃ”为有理数，则除夕（ｋ为一切自然数）为有理数外，其它一切Ｃ”（ｍ为自然数，但ｍｆｋ，；）皆为无理数。证（１）由Ｃ’为有理数，且Ｃ‘”一（Ｃ“）‘（ｋ为自然数），则显然可见此少为有理数...     

一类SierPinski地毯的Hausdorff测度的初等证明

在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM.     

Pricing catastrophe options with counterparty credit risk in a reduced form model

In this paper, we study the price of catastrophe options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model. We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.     

基于PLSR的多级制造过程关键质量特性识别方法

为解决多级制造过程关键质量特性识别中多质量特性之间的相关性问题,将偏最小二乘回归方法(Partial Least Squares Regression, PLSR)引入模型构建与分析中。首先应用状态空间方法建立多级制造过程关键质量特性识别模型,进而利用PLSR方法解决质量特性间的多重共线性问题并进行模型分析,识别关键质量特性,最后以卷烟生产过程为例介绍了该方法的应用。实例表明,该方法不仅可以有效识别多级制造过程关键质量特性,而且能够建立各级过程的输出质量对最终产品质量的影响及其质量特性之间相互关系的模型,反映多级生产过程的结构特征和各级过程质量特性之间的因果关系,为多级制造过程质量分析与控制提供依据。     

A new uncertain insurance model with variational lower limit

Uncertainty theory provides a new tool to deal with uncertainty. The paper employs it to propose a new uncertain insurance model with variational lower limit, and gives a ruin index and uncertainty distribution for the uncertain insurance risk process that claim process is a renewal reward process. The model extends and improves uncertain insurance model presented by Liu. Finally, it also provides examples to illustrate the effectiveness of the model.     

随机赔偿,随机折现下的保险概率模型及若干结果

本文首先构造了保险的随机过程模型，即随机赔偿和随机折现的双随机模型．运用测度扩张理论将赔偿过程发展为随机赔偿恻度，在模型的基本假定之下研究赔偿过程的性质，给出保险和年金的测度表示以及诸多精算公式．最后针对随机利率的Gauss过程模型得到Hoem模型随机赔偿测度的现值矩发展了［7］中的主要结果．     

Diffusion and survival models for the process of entry into marriage

In this paper different survival models with a non‐parametric hazard rate function are applied to the process of entry into marriage. The hazard function of the Hernes model of the marriage process as well as the log‐logistic survival model are both derivable from a differential equation for a social diffusion process. The log‐logistic model might be appropriate for modelling the marriage rate because of its non‐monotonic hazard function. Moreover, in light of our analysis, application of this model to the marriage process can be justified by the theoretical rationale of a process of social diffusion. Both models are tested using German age‐at‐marriage data and the U.S. cohort data analyzed by Hernes (1972). It can be shown that the three parameter Hernes model yields a good fit while the log‐logistic model, with only two parameters, leads to a moderate approximation of the data.     

马氏风险过程

研究了一般马氏风险过程,它是经典风险过程的拓广．具有大额索赔的风险过程用此马氏风险模型来描述是适合的．在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数．主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界．     

广义复合Poisson风险模型下的生存概率

In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model, then for the generalized model and the classical compound poisson risk model, we respectively get its survival probability in finite time period in case of exponential claim amounts.     

Recursive parameter identification for fermentation processes with the multiple model technique

This paper considers parameter identification problems for a fermentation process. Since the fermentation process is nonlinear, it is difficult to use a single-model for describing such a process and thus we use the multiple model technique to study the identification methods. The basic idea is to establish the model of the fermentation process at each operation point by means of the least squares principle, to obtain multiple models with different points, and then use the weighting functions or interpolation methods to compute the total model or the global model. Finally, a numerical example is provided to test the effectiveness of the proposed algorithm.     

稀疏过程在破产问题中的应用

本讨论一类人寿保险的风险过程，其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏．对此模型给出其破产概率的具体上界，并与其它一类风险模型进行比较．     

A Markov modulated Poisson model for software reliability

In this paper, we consider a latent Markov process governing the intensity rate of a Poisson process model for software failures. The latent process enables us to infer performance of the debugging operations over time and allows us to deal with the imperfect debugging scenario. We develop the Bayesian inference for the model and also introduce a method to infer the unknown dimension of the Markov process. We illustrate the implementation of our model and the Bayesian approach by using actual software failure data.