The structure and the sufficint and necessary conditions for generalized statistically self-similar sets

We constructed a class of generalized statistically self-similar sets and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson, Falconer, Graf are the special cases of ours. Foundation item: Supported by the National Natural Science Foundation of China Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate, research interes: is in stochastic process and random ractal     

The classification of statistically recursive sets

The main aim of this paper is to make a classification of random setsK _m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK _m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification. Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China Hu Dihe: born in May 1935, Professor     

在Sparre Andersen模型中破产前发生的理赔次数

研究在Sparre Andersen模型中保险公司破产前发生的理赔次数,这里理赔时间间隔服从Erlang(2)分布;令p(u;n)表示破产前发生n次理赔的概率,(s;n)表示p(u;n)的拉普拉斯变换,给出了(s,n)的递推公式,由此运用Mathematics等数学软件可以算出p(u;n).     

WOD样本密度函数和失效率函数递归核估计的逐点强相合性

考虑同分布宽象限相依(WOD)随机样本未知密度函数的一类递归型密度核估计量.利用WOD序列的Rosenthal型不等式,在一定条件下证明了该估计量的逐点强相合性,并讨论了失效率函数估计的逐点强相合性.     

关于Diophantine方程x~3±1=2pqry~2

设p,q,r为奇素数,p≡13 mod 24,q≡19 mod 24,(p/q)=-1.利用同余式、平方剩余、递归序列、Legendre符号的性质、Pell方程解的性质等证明了:(A)若r≡5 mod 12,则方程G:x3-1=2pqry2仅有平凡解(x,y)=(1,0);若r≡11 mod 12,则方程G最多有2组正整数解.(B)若r≡11 mod 12,则方程H:x3+1=2pqry2仅有平凡解(x,y)=(-1,0);若r≡5 mod 12且(pq/r)=-1,则方程H最多有2组正整数解.     

一类二维分数阶偏微分方程解的适定性

研究一类二维分数阶偏微分方程的边值问题,主要包括两方面内容:一是研究了合适的分数阶Sobolev空间及分数阶算子的性质;二是发展了一个弱解的理论框架,并建立了弱解的适定性理论.这是构造数值方法(如有限元和谱方法等)求解二维分数阶偏微分方程的理论基础.     

金刚石膜中的黑色层状缺陷及非相关成因

对高功率直流电弧等离子体喷射法制备的金刚石膜中的黑色层状缺陷进行了研究。沉积过程中通过改变沉积速率；适量加氧、加水、加氮；采用高纯气体；调整漏气率；多台设备并联运行；单台设备反复运行和交换零部件多种手段，均未找到其成因。中对用黑厚时位式新理念的研究作了报导。证实夹层成因和膜制备过程中的上述因素间无密切关系。     

一个考虑到炮检距的速度反演递推公式

由于实际地震资料是一定炮检距范围内共中心点道集叠加的结果，建立于地震波垂直入射似设基础之上的常规人工合成地震记录与波阻抗反演方法，常导致错误的解释结果，垂直入积压假设不能反映地震波传播的实际情况，通过对Ｚｏｅｐｐｒｉｔｚ方程的合理简化，推导出了一个考虑炮检距变化的反射系数递推公式。经地质模型试算，证明了该公式的正确性。     

A BI-LEVEL FORMULATION AND QUASI-NEWTON ALGORITHM FOR STOCHASTIC EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND

1 IntroductionThe network design problem (NDP) is to select link improvements or add new links to anexisting network suCh that social welfare is maximized while according for the route choicebehavior of network users and/or changes in demand. Two sets of decision-makers with differedsobjectives are involved in the NDP. The network users individually select their routes suchthat their individual travel costs are minimized, while the planners aim to make the bestnetwork improvements for reduc…     

非-Lipschitz条件下随机微分效用

研究了由Ｄｕｆｆｉｅ 和Ｅｐｓｔｅｉｎ 等创立的随机微分效用理论．在非－Ｌｉｐｓｃｈｉｔｚ条件下，讨论了随机微分效用的存在性和唯一性以及效用过程的时间相容性，并对消费的单调性、对终值的单调性和风险厌恶及凹性进行了讨论．