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China’s urban green innovation:Regional differences,distribution dynamics,and convergence
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作者 Yuting Xue Shumin Dong +1 位作者 Guixiu Ren Kai Liu 《Chinese Journal of Population,Resources and Environment》 2023年第4期239-248,共10页
Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above t... Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above the prefecture level.Then,using the Dagum Gini coefficient,kernel density estimation(KDE),and con‐vergence models,we examined regional differences,distribution dynamics,and convergence of UGI across China.The study’s findings are as follows:(1)Overall,regional differences in UGI tended to narrow,and the main contributor to these differences was the difference between economic zones.(2)KDE showed that the level of UGI was rising,which was polarized within each economic zone.(3)The national UGI in economic zones other than the Northeast and Middle Yellow River Economic Zones featured significantσconvergence,while each economic zone showed absolute and conditionalβconvergence. 展开更多
关键词 Urban green innovation Regional difference distribution dynamic convergence Green patent
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The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition
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作者 Xilai Dai 《Journal of Applied Mathematics and Physics》 2024年第5期1597-1605,共9页
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ... In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition. 展开更多
关键词 convergence Rate Second-Order Regular Variation Condition Fréchet distribution Extreme Value index
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Fully asynchronous distributed optimization with linear convergence over directed networks
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作者 SHA Xingyu ZHANG Jiaqi YOU Keyou 《中山大学学报(自然科学版)(中英文)》 CAS CSCD 北大核心 2023年第5期1-23,共23页
We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it f... We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem. 展开更多
关键词 fully asynchronous distributed optimization linear convergence Polyak-Łojasiewicz condition
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一类Lindley模型参数的经验Bayes检验收敛速度的改进
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作者 黄金超 《吉首大学学报(自然科学版)》 CAS 2024年第3期13-18,共6页
利用递归核估计和单调性,构造了Lindley模型参数的经验Bayes检验函数,并在适当的条件下,证明了收敛速度的阶可任意接近O(n^(-1)).
关键词 Lindley分布族 递归核估计 Bayes检验 经验BAYES检验 收敛速度
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CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT 被引量:2
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作者 Yingqiu LI Xulan HUANG Zhaohui PENG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第3期957-974,共18页
We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ... We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law. 展开更多
关键词 Branching process with immigration random environment convergence rates central limit theorem convergence in law convergence in probability
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Push-Pull Finite-Time Convergence Distributed Optimization Algorithm 被引量:1
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作者 Xiaobiao Chen Kaixin Yan +3 位作者 Yu Gao Xuefeng Xu Kang Yan Jing Wang 《American Journal of Computational Mathematics》 2020年第1期118-146,共29页
With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution r... With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive. 展开更多
关键词 DISTRIBUTED Optimization FinITE Time convergence Linear Parameterized Neural Network PUSH-PULL Algorithm Undirected GRAPH
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Convergence in the r-th Mean and the Marcinkiewicz Type Weak Law of Large Numbers for Weighted Sums of L_q-mixingale Arrays
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作者 Gan Shi-xin School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 《Wuhan University Journal of Natural Sciences》 CAS 2003年第04A期1047-1050,共4页
L_r convergence and convergence in probability for weighted sums of L_q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers for L_q-mixingale arrays has been obtained.
关键词 L_q-mixingale array L_r convergence convergence in probability Marcinkiewicz type weak of large numbers
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A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES
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作者 孔繁超 唐启鹤 《Acta Mathematica Scientia》 SCIE CSCD 2001年第3期331-338,共8页
Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hilde... Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well. 展开更多
关键词 sums of independent random variabies essential convergence limit distribution Levy distance three series theorem
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On Convergence for TrigonometricInterpolation of Analytic Function
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作者 Liu Hua Du Jing-yuan 《Wuhan University Journal of Natural Sciences》 EI CAS 1999年第3期275-277,共3页
In this paper, we give a necessary and sufficient condition of sequence of nodes, such that, the error of trigonometric interpolation for analytic function converges to 0.
关键词 trigonometric interpolation convergence well-distributed
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A Whale Optimization Algorithm with Distributed Collaboration and Reverse Learning Ability 被引量:2
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作者 Zhedong Xu Yongbo Su +1 位作者 Fang Yang Ming Zhang 《Computers, Materials & Continua》 SCIE EI 2023年第6期5965-5986,共22页
Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used ... Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used to solve practical engineering optimization problems.However,with the increased dimensions,higher requirements are put forward for algorithm performance.The double population whale optimization algorithm with distributed collaboration and reverse learning ability(DCRWOA)is proposed to solve the slow convergence speed and unstable search accuracy of the WOA algorithm in optimization problems.In the DCRWOA algorithm,the novel double population search strategy is constructed.Meanwhile,the reverse learning strategy is adopted in the population search process to help individuals quickly jump out of the non-ideal search area.Numerical experi-ments are carried out using standard test functions with different dimensions(10,50,100,200).The optimization case of shield construction parameters is also used to test the practical application performance of the proposed algo-rithm.The results show that the DCRWOA algorithm has higher optimization accuracy and stability,and the convergence speed is significantly improved.Therefore,the proposed DCRWOA algorithm provides a better method for solving practical optimization problems. 展开更多
关键词 Whale optimization algorithm double population cooperation distribution reverse learning convergence speed
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Nonlinear Analysis of Axial-load and Stress Distribution for Threaded Connection 被引量:21
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作者 LIAO Ridong SUN Yujuan ZHANG Weizheng 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2009年第6期869-875,共7页
Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded co... Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded connection is difficult to measure. So it is necessary to study the reliable numerical method. At present neither the convergence analysis of the computational results nor the elastic-plastic analysis in the loading-unloading process are studied. In this paper, von Mises plasticity and kinematic hardening model is used to describe the material response. A new convergence criterion for nonlinear finite element analysis of the loading-unloading process is proposed. An axisymmetric finite element model according to the proposed convergence criterion is developed and used to analyze the distributions of axial-load and stress. It can be conclude that the stress distribution analysis is more dependent on the mesh density than the axial-load distribution analysis. The stress distribution result indicates that with increasing of applied load, the engaged threads close to the nut-bearing surface become plastic firstly. The axial-load distribution result reveals that the load percentage carried by single thread depends on the position of thread and load intensity. When the load is relatively small, the applied load is mainly carried by the engaged threads near the nut-bearing surface, when the load is larger, the differences of percentages for all threads become small. The proposed convergence analyzing procedure is applicable for other nonlinear analyses. The obtained distributions of axial-load and stress can be a reference of engineering application. 展开更多
关键词 threaded connection finite element method (FEM) axial-load distribution stress distribution convergence criterion
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One-sided empirical Bayes test for location parameter in Gamma distribution 被引量:1
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作者 YUAN Min ZHANG Qian WEI Lai-sheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第3期287-297,共11页
In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is as... In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied. 展开更多
关键词 three parameter Gamma distribution location parameter one-sided empirical Bayes test asymptotically optimality convergence rate
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Probability Inequalities for Extended Negatively Dep endent Random Variables and Their Applications 被引量:1
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作者 TANG Xiao-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第2期195-202,共8页
Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant ... Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results. 展开更多
关键词 extended negatively dependent sequence negatively orthant dependent se-quence probability inequality complete convergence
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有向网络分布式优化的Barzilai-Borwein梯度跟踪方法
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作者 高娟 刘新为 《控制理论与应用》 EI CAS CSCD 北大核心 2023年第9期1637-1645,共9页
本文研究有向网络上的分布式优化问题,其全局目标函数是网络上所有光滑强凸局部目标函数的平均值.受Barzilai-Borwein步长改善梯度方法表现的启发,本文提出了一种分布式Barzilai-Borwein梯度跟踪方法.与文献中使用固定步长的分布式梯度... 本文研究有向网络上的分布式优化问题,其全局目标函数是网络上所有光滑强凸局部目标函数的平均值.受Barzilai-Borwein步长改善梯度方法表现的启发,本文提出了一种分布式Barzilai-Borwein梯度跟踪方法.与文献中使用固定步长的分布式梯度算法不同,所提出的方法中每个智能体利用其局部梯度信息自动地计算其步长.通过同时使用行随机和列随机权重矩阵,该方法避免了由特征向量估计引起的计算和通信.当目标函数是光滑和强凸函数时,本文证明了该算法产生的迭代序列可以线性地收敛到最优解.对分布式逻辑回归问题的仿真结果验证了所提出的算法比使用固定步长的分布式梯度算法表现更好. 展开更多
关键词 分布式优化 多智能体系统 有向图 Barzilai-Borwein方法 优化算法 收敛速度
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Influence of spectral distribution on accommodation-vergence and reading performance 被引量:1
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作者 Shiva Ram Male Rishi Bhardwaj Chiranjib Majumder 《Annals of Eye Science》 2017年第1期127-132,共6页
Background:To assess the influence of different spectral energy distribution on accommodation,vergence and reading performance.Methods:A Randomized experimental study was conducted after getting the approval of the Et... Background:To assess the influence of different spectral energy distribution on accommodation,vergence and reading performance.Methods:A Randomized experimental study was conducted after getting the approval of the Ethical Committee of University of Hyderabad.Forty participants with an age group of 18-21 years was integrated,out of which 50%was male and 50%was female.Subjects with emmetropia and no history of ocular pathology were included in the study.Near point of accommodation(NPA)&near point of convergence(NPC)was measured with the help of royal air force(RAF)ruler followed by near visual task of a readability passage.Results:A statistically significant result was obtained when reading rate,reading speed and NPC was compared among different spectral distribution of light(P<0.001)except NPA(P=0.43).Post hoc analysis showed a significant difference(P<0.001)when tungsten was compared with fluorescent light(FLOU),compact fluorescent light(CFL),and light emitting diode(LED)for reading rate,reading speed and NPC.But there is no noteworthy difference exist when fluorescent was compared with CFL for reading rate(P=0.530)&reading speed(P=0.595).Similarly,LED also showed no considerable difference when compared with CFL(P=0.682)and fluorescent(P=0.490)for NPC.When NPA was assessed within the group LED showed insignificant difference with CFL(P=0.205)and fluorescent(P=0.275)similar like fluorescent and tungsten(P=0.482).Conclusions:This study concluded that reading performance(reading rate and reading speed)and NPC has a significance change if we use inappropriate lighting during visual tasks.It will cause visual fatigue and strain after sustained near work.In addition,tungsten spectral energy influences the convergence which can also show an impact on reading and near visual tasks because of its brightness and miosis.Prolonged reading and working under this lighting can cause convergence disorders and visual fatigue. 展开更多
关键词 ACCOMMODATION convergence reading rate reading speed READABILITY spectral distribution correct word per minute(CWPM)
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Higher-order expansions of powered extremes of logarithmic general error distribution
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作者 TAN Xiao-feng LI Li-hui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期47-54,共8页
In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor... In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v). 展开更多
关键词 logarithmic general error distribution convergence rate higher-order expansion powered ex-treme
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PROBABILITY INEQUALITIES FOR SUMS OF INDEPENDENT UNBOUNDED RANDOM VARIABLES
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作者 ZHANG Dixin(张涤新) +1 位作者 WANG Zhicheng(王志诚) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期597-601,共5页
The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random ... The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Omega, T, P). The probability exponential inequalities for sums of the results, some independent unbounded random variables were given. As applications of interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables. 展开更多
关键词 probability exponential inequality unbounded random variables convergence
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On Continuous Limiting Behaviour for the <i>q(n)</i>-Binomial Distribution with <i>q(n)</i>→1 as n→∞
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作者 Malvina Vamvakari 《Applied Mathematics》 2012年第12期2101-2108,共8页
Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence of the q-binomial distribution to a Stieltjes-W... Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence of the q-binomial distribution to a Stieltjes-Wigert continuous distribution. In the present article, assuming a sequence q(n) of n with q(n)→1 as n→∞, the study of the affect of this assumption to the q(n)-analogue of the Stirling type and to the asymptotic behaviour of the q(n)-Binomial distribution is presented. Specifically, a q(n) analogue of the Stirling type is provided which leads to the proof of deformed Gaussian limiting behaviour for the q(n)-Binomial distribution. Further, figures using the program MAPLE are presented, indicating the accuracy of the established distribution convergence even for moderate values of n. 展开更多
关键词 Stirling Formula q(n) -Factorial Number of Order N Saddle Point Method q(n)-Binomial distribution POinTWISE convergence Gauss distribution
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Strong Convergence of Empirical Distribution for a Class of Random Matrices
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作者 LIANG Qing-wen MIAO Bai-qi WANG Da-peng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期28-32,共5页
Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = (ai1,…, aiM) be random vectors with {aij} being i.i.d, random variables. Define XN =(x1,…, xk) and SN =XNXN^T,where xi=ai... Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = (ai1,…, aiM) be random vectors with {aij} being i.i.d, random variables. Define XN =(x1,…, xk) and SN =XNXN^T,where xi=ai×si and si=1/√N(v1i,…, vN,i)^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions. 展开更多
关键词 empirical spectral distribution function sample covariance matrix Stieltjes transform strong convergence
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An Approach to Resolving Two Paradoxes in Probability Theory
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作者 刘道建 黄天民 陈亚波 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第3期362-365,共4页
A new mathematical expectation formula with some hypotheses, notions and propositions was given to get rid of the challenge of St. Petersburg paradox and Pascal's wager. Relevant results show that it is very effec... A new mathematical expectation formula with some hypotheses, notions and propositions was given to get rid of the challenge of St. Petersburg paradox and Pascal's wager. Relevant results show that it is very effective to apply the model to solve the expected revenue problems containing random events with low proba-bility but high revenue. This work also provides the probability theory with a more widely applied perspective in group decision-making. 展开更多
关键词 conservative probability function conservation degree conservative mathematical expectation St. Petersburg paradox and Pascal's wager convergence group decision-making
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