Estimating the Prevalence of Illegal Drug Use

A generic globally applicable integral equation allows the estimation of hidden drug use. Formulas for estimating the prevalence of drug use are provided for both the assumed and known latency period. Estimates of prevalence of opiate use in Ireland ranging from 7,955 [5,789, 10,122] to 11,986 [8,792, 15,181] with prevalence rates ranging from 2.7 [2.0, 3.5] per 1,000 to 4.1 [3.0, 5.2] were obtained. The model can be implemented by service providers and planners if numbers of first treatments for drug use and the latency period are known or assumed.     

E-Capacities and the Ellsberg Paradox

Ellsberg's (1961) famous paradox shows that decision-makers give events with known probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity is the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them.     

关于一个恒等式

给出Δu的一个新的表示式     

对零势点选择若干问题的探讨

讨论几种典型电场的零势点位置的确定 ,说明选择零势点的原则     

Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

In this paper we consider the problem of estimating a coefficient of a strongly elliptic partial differential operator in stochastic parabolic equations. The coefficient is a bounded function of time. We compute the maximum likelihood estimate of the function on an approximating space (sieve) using a finite number of the spatial Fourier coefficients of the solution and establish conditions that guarantee consistency and asymptotic normality of the resulting estimate as the number of the coefficients increases. The equation is assumed diagonalizable in the sense that all the operators have a common system of eigenfunctions.     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

Strong previsions of random elements

LetC be a class of arbitrary real random elements andP an extended real valued function onC. Two definitions of coherence forP are compared. Both definitions reduce to the classical de Finetti's one whenC includes bounded random elements only. One of the two definitions (called strong coherence) is investigated, and some criteria for checking it are provided. Moreover, conditions are given for the integral representation of a coherentP, possibly with respect to a δ-additive probability. Finally, the two definitions and the integral representation theorems are extended to the case whereC is a class of random elements taking values in a given Banach space.     

一类二阶拟线性微分方程的非振动定理

考虑二阶拟线性微分方程 :( |y′|α -1y′)′+q(t) |y|α -1y=0 ,获得了在 q(t)振动的条件下该方程非振动的一些充分 (必要 )条件 ,改进和推广了已有文献的结果     

一类n阶非线性微分方程多点边值问题解的存在性

利用Leray-Schauder度理论建立了n阶非线性微分方程y(n)=f(x,y,y′,…,y(n-1)),n≥3,满足多点边界条件yn-1(0)-hyn-2(0)=0,y(i)(ηi)=0,i=0,1,…,n-3,y(n-1)(1)+ky(n-2)(1)=0.的多点边值问题的解存在性的几个充分条件,并给出了应用举例.     

分析电磁散射问题的MGFFT方法

采用多重网格法（ＭＧ）分析电大尺寸物体的电磁散射，这种ＭＧ方法与已有的几种多重矩量法有本质的不同，与其他多层方法相比，它是一种高效率的迭代方法。再利用积分方程的卷积特性引入ＦＦＴ方法快速计算迭代过程中矩阵与矢量的乘积，从而构成ＭＧＦＦＴ新算法，数值结果表明ＭＧＦＦＴ方法具有很高的计算效率，适用于电大尺寸问题的分析。