与中心极限定理有关的几个随机试验的模拟

用Excel来模拟与中心极限定理有关的几个随机试验,以此来说明满足一定条件的随机变量之和的极限分布是正态分布,即从实验的角度验证了中心极限定理.

基片上二元组份薄膜的定量分析的Monte Carlo模拟计算方法

本文用Ｍｏｎｔｅ Ｃａｒｌｏ方法对入射电子在薄膜中的散射和特征Ｘ射线的发射进行数学模拟，提出了基片上 二元组份薄膜成份的模拟计算方法．用这一方法模拟计算了若干个二元组份薄膜的成份，得到了与实验测定值相一致的模拟计算结果．

Some Notes of Property of Distribution Function of Many Variables

In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then

The quantified analysis of China's GM cotton yield capacity by C-D function and stochastic frontier model

Using a modified C D function and stochastic frontier model, the paper analyzed China's cotton yield capacity and found that the yield and technical efficiency of China's cotton planting system can be increased by the use of genetically modified (GM) varieties.

试题库的计算机构建

利用计算机软件构建了试题库 ,可随意按章节、难度、题型等随机定量组题 ,可以对试题库的试题进行增、删。

Inequalities of Maximum of Partial Sums and Convergence Rates in the Strong Laws for ρ^-mixing Random Variables

In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.

Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.

Coffee drinking and pancreatic cancer risk:A meta-analysis of cohort studies

AIM:To quantitatively assess the relationship between coffee consumption and incidence of pancreatic cancer in a meta-analysis of cohort studies. METHODS:We searched MEDLINE,EMBASE,Science Citation Index Expanded and bibliographies of retrieved articles.Studies were included if they reported relative risks(RRs)and corresponding 95%CIs of pancreatic cancer with respect to frequency of coffee intake.We performed random-effects meta-analyses and metaregressions of study-specific incremental estimates to determine the risk of pancreatic cancer associated with a 1 cup/d increment in coffee consumption. RESULTS:Fourteen studies met the inclusion criteria, which included 671 080 individuals(1496 cancer events) with an average follow-up of 14.9 years.Compared with individuals who did not drink or seldom drank coffee per day,the pooled RR of pancreatic cancer was 0.82 (95%CI:0.69-0.95)for regular coffee drinkers,0.86 (0.76-0.96)for low to moderate coffee drinkers,and 0.68(0.51-0.84)for high drinkers.In subgroup analyses,we noted that,coffee drinking was associated witha reduced risk of pancreatic cancer in men,while this association was not seen in women.These associations were also similar in studies from North America,Europe, and the Asia-Pacific region. CONCLUSION:Findings from this meta-analysis suggest that there is an inverse relationship between coffee drinking and risk of pancreatic cancer.

Grammar Consciousness-Raising Tasks and Intermediate Learners＇ Achievement and Perceptions

While there is lots of empirical evidence showing that grammar consciousness raising tasks （GCRTs） have an edge over the traditional modes of grammar instruction, there is very little qualitative evidence reflecting learners＇ perceptions of externally imposed educational changes including GCRTs. To extrapolate the previous findings and fill in this gap, this study aims to： （I） test the alleged superiority of GCRTs in grammar instruction and （2） explore learners＇ perceptions of learning grammar through GCRTs. To this end, this study used a mixed-method design including a quantitative and a qualitative dimension. The former dimension aimed at testing the superiority of GCRTs on a random sample of intermediate learners from Simin language school in Karaj, Iran through the robust Solomon-four-group design and the latter dimension aimed at collecting and analyzing qualitative interview data on learners＇ perceptions of GCRTs. The quantitative results clearly showed that learners being taught through GCRTs significantly outperformed those instructed through the traditional mode of grammar instruction and the qualitative analysis of learners＇ perspectives showed that the participants had a positive perception of GCRTs and this positive perception was rooted in GCRTs＇ potential to： （1） facilitate the internalization of grammar and （2） involve learners in discovery learning. The findings have clear implications for syllabus designers and practitioners.

On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update： to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1 - f1 - f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.

The Hierarchical Stochastic Schrodinger Equations: Theory and Applications

The hierarchical stochastic Schrodinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath.Starting from the influence-functional description of open quantum systems,this review outlines the general theoretical framework of HSSEs and their concrete forms in different situations.The applicability and efficiency of HSSEs are exemplified by the simulations of ultrafast excitation energy transfer processes in large-scale systems.

RANDOM SETS: A UNIFIED FRAMEWORK FOR MULTISOURCE INFORMATION FUSION

The more diverse the ways and means of information acquisition are,the more complex and various the types of information are. The qualities of available information are usually uncertain,vague,imprecise,incomplete,and so on. However,the information is modeled and fused traditionally in particular,name some of the known theories: evidential,fuzzy sets,possibilistic,rough sets or conditional events,etc. For several years,researchers have explored the unification of theories enabling the fusion of multisource information and have finally considered random set theory as a powerful mathematical tool. This paper attempts to overall review the close relationships between random set theory and other theories,and introduce recent research results which present how different types of information can be dealt with in this unified framework. Finally,some possible future directions are discussed.

Benford＇s Law and Invariances

Benford＇s law is logarithmic law for distribution of leading digits formulated by P[D=d]= log（1＋1/d） where d is leading digit or group of digits. It＇s named by Frank Albert Benford （1938） who formulated mathematical model of this probability. Befbre him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number.The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford＇s law and Y is arbitrary random variable with continuous density then XY follows Benford＇s law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.

On the Second Borel-Cantelli Lemma for α-mixing Sequences of Events

In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

Determination of Ash Contents in Coal by Means of Ordinary Kriging Method

The ash contents in coal particles were examined in the paper dependably on particle size and its density. So, the two-dimensional regressive function Z = Z（P, D） was the searched object, where Z is random variable describing ash contents, P---density and D---particle diameter. This dependence was determined based on experimental data concerning the coal of type 31. For this coal, the method of ordinary kriging was applied to calculate the values of random variable Z. This method required the proper selection of so-called variogram function, in which four forms were considered in this paper in purpose to select the best solution. The given results were then evaluated by the mean standard error value and compared with empirical data.

Random Walk Based Method for Automatic Segmentation of Intravascular Ultrasound Images

Intravascular ultrasound( IVUS) is an important imaging technique that is used to study vascular wall architecture for diagnosis and assessment of the vascular diseases. Segmentation of lumen and media-adventitia boundaries from IVUS images is a basic and necessary step for quantitative assessment of the vascular walls.Due to ultrasound speckles, artifacts and individual differences,automated segmentation of IVUS images represents a challenging task. In this paper,a random walk based method is proposed for fully automated segmentation of IVUS images. Robust and accurate determination of the seed points for different regions is the key to successful use of the random walk algorithm in segmentation of IVUS images and is the focus of the present work. Performance of the proposed algorithm was evaluated over an image database with 900 IVUS image frames of nine patient cases. The preliminary experimental results show the potential of the proposed IVUS image segmentation approach.

CHOVER'S LAW OF THE ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED SEQUENCES

Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.

Stochastic quantization and ergodic theorem for density of diffusions

For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.

Music electric stimulation of points for anxiety:a multi-center randomized controlled clinical trial

To observe the therapeutic efficacy of music electric stimulation of points in treating anxiety. Methods： By adopting a design of multi-centered randomized controlled trial （RCT）, a total of 270 patients with anxiety were randomized into a treatment group and a medication group. The treatment group was intervened by music electric stimulation of points, while the medication group was intervened by oral administration of doxepin. The two groups were evaluated by using Hamilton anxiety rating scale （HAMA） and Chinese revised edition of self-rating anxiety scale （SAS-CR） before and after the intervention. The therapeutic efficacies were also compared. Results： The total effective rate was 93.6% in the treatment group versus 92.3% in the medication group, and the between-group difference was statistically insignificant （P〉O.05）. After the treatment, the aggregate scores of HAMA and SAS-CR were significantly changed in both groups （both P〈0.001）, and the inter-group differences were statistically insignificant （P〉O.05）. Conclusion： Music electric stimulation of points can produce equivalent efficacy in treating anxiety compared to doxepin. Thus, it can be taken as a choice in the treatment of anxiety.

THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.