In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.展开更多
针对黑猩猩优化算法(Chimp optimization algorithm,ChOA)存在收敛速度慢、精度低和易陷入局部最优值问题,提出一种融合多策略的黄金正弦黑猩猩优化算法(Multi-strategy golden sine chimp optimization algorithm,IChOA).引入Halton序...针对黑猩猩优化算法(Chimp optimization algorithm,ChOA)存在收敛速度慢、精度低和易陷入局部最优值问题,提出一种融合多策略的黄金正弦黑猩猩优化算法(Multi-strategy golden sine chimp optimization algorithm,IChOA).引入Halton序列初始化种群,提高初始化种群的多样性,加快算法收敛,提高收敛精度;考虑到收敛因子和权重因子对于平衡算法勘探和开发能力的重要作用,引入改进的非线性收敛因子和自适应权重因子,平衡算法的搜索能力;结合黄金正弦算法相关思想,更新个体位置,提高算法对局部极值的处理能力.通过对23个基准测试函数的寻优对比分析和Wilcoxon秩和统计检验以及部分CEC2014测试函数寻优结果对比可知,改进的算法具有更好的鲁棒性;最后,通过2个实际工程优化问题的实验对比分析,进一步验证了IChOA在处理现实优化问题上的优越性.展开更多
利用致密性定理获得有界数列{y_n}收敛的一个充分条件:∨ε>0,■N∈Z+,使得当n>Z时,不等式yn-yn-1<ε恒成立。并发现任意项级数收敛的一个判定定理:如果级数sum from n=1 to ∞ a_n有界,且limn→∞a_n=0,则该级数收敛。由此获...利用致密性定理获得有界数列{y_n}收敛的一个充分条件:∨ε>0,■N∈Z+,使得当n>Z时,不等式yn-yn-1<ε恒成立。并发现任意项级数收敛的一个判定定理:如果级数sum from n=1 to ∞ a_n有界,且limn→∞a_n=0,则该级数收敛。由此获得:级数sum from n=1 to ∞ sin^(1+2s/t)=n/n~α收敛,其中s∈Z,t∈Z+,0<α≤1。并进行推广:如果s∈Z,t∈Z^+,0<α≤1,则级数sum from n=1 to ∞sin^1+2s/t)(an)/n~α收敛。再获得一个一般性结论:设有界函数f(n)满足0≤f(n)<M,且0<α≤1,则级数sum from n=1 to ∞sin(an)/n^af(n)收敛。同时利用确界定理得到:正项级数sum from n=1 to ∞sinn^(2s)n/n发散,其中s∈Z。并推广:正项级数sum from n=1 to ∞nsin^(2s)(an)/n发散,其中0<a≤π/2,s∈Z。利用数学归纳法获得:正项级数sum from n=1 to ∞ sin^(2s)(ann+b)/n发散,其中s∈Z,(a-2kπ)~2+(b-2lπ)~2>0,k,l∈Z。展开更多
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c...In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].展开更多
针对黏菌优化算法(Slime Mould Algorithm,SMA)的寻优过程存在收敛效率较低、容易陷入局部最优解等问题,文中提出融合多策略改进的黏菌优化算法(Improved SMA Fused with Multi-strategy,MISMA).引入Halton序列,丰富初始种群的多样性,...针对黏菌优化算法(Slime Mould Algorithm,SMA)的寻优过程存在收敛效率较低、容易陷入局部最优解等问题,文中提出融合多策略改进的黏菌优化算法(Improved SMA Fused with Multi-strategy,MISMA).引入Halton序列,丰富初始种群的多样性,提升算法寻优的遍历性和收敛精度.融入差分变异思想,改进算法的全局位置更新公式,强化全局探索能力,增强算法的持续寻优性能.糅合改进收敛因子和精英选择机制的局部搜索策略,提升算法的局部开采能力,更好地平衡算法的全局探索与局部开发进程.基于动态边界的透镜成像学习策略改善个体的质量,加强算法反早熟及摆脱局部最优解的能力.在13个基准函数及部分CEC2014测试函数上的数值仿真实验表明,MISMA具有较强的鲁棒性.此外,在光伏电池组件模型参数优化实验上进一步验证MISMA在处理实际工程优化问题时的优越性及适用性.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
基金the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
文摘针对黑猩猩优化算法(Chimp optimization algorithm,ChOA)存在收敛速度慢、精度低和易陷入局部最优值问题,提出一种融合多策略的黄金正弦黑猩猩优化算法(Multi-strategy golden sine chimp optimization algorithm,IChOA).引入Halton序列初始化种群,提高初始化种群的多样性,加快算法收敛,提高收敛精度;考虑到收敛因子和权重因子对于平衡算法勘探和开发能力的重要作用,引入改进的非线性收敛因子和自适应权重因子,平衡算法的搜索能力;结合黄金正弦算法相关思想,更新个体位置,提高算法对局部极值的处理能力.通过对23个基准测试函数的寻优对比分析和Wilcoxon秩和统计检验以及部分CEC2014测试函数寻优结果对比可知,改进的算法具有更好的鲁棒性;最后,通过2个实际工程优化问题的实验对比分析,进一步验证了IChOA在处理现实优化问题上的优越性.
文摘利用致密性定理获得有界数列{y_n}收敛的一个充分条件:∨ε>0,■N∈Z+,使得当n>Z时,不等式yn-yn-1<ε恒成立。并发现任意项级数收敛的一个判定定理:如果级数sum from n=1 to ∞ a_n有界,且limn→∞a_n=0,则该级数收敛。由此获得:级数sum from n=1 to ∞ sin^(1+2s/t)=n/n~α收敛,其中s∈Z,t∈Z+,0<α≤1。并进行推广:如果s∈Z,t∈Z^+,0<α≤1,则级数sum from n=1 to ∞sin^1+2s/t)(an)/n~α收敛。再获得一个一般性结论:设有界函数f(n)满足0≤f(n)<M,且0<α≤1,则级数sum from n=1 to ∞sin(an)/n^af(n)收敛。同时利用确界定理得到:正项级数sum from n=1 to ∞sinn^(2s)n/n发散,其中s∈Z。并推广:正项级数sum from n=1 to ∞nsin^(2s)(an)/n发散,其中0<a≤π/2,s∈Z。利用数学归纳法获得:正项级数sum from n=1 to ∞ sin^(2s)(ann+b)/n发散,其中s∈Z,(a-2kπ)~2+(b-2lπ)~2>0,k,l∈Z。
文摘In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].
文摘针对黏菌优化算法(Slime Mould Algorithm,SMA)的寻优过程存在收敛效率较低、容易陷入局部最优解等问题,文中提出融合多策略改进的黏菌优化算法(Improved SMA Fused with Multi-strategy,MISMA).引入Halton序列,丰富初始种群的多样性,提升算法寻优的遍历性和收敛精度.融入差分变异思想,改进算法的全局位置更新公式,强化全局探索能力,增强算法的持续寻优性能.糅合改进收敛因子和精英选择机制的局部搜索策略,提升算法的局部开采能力,更好地平衡算法的全局探索与局部开发进程.基于动态边界的透镜成像学习策略改善个体的质量,加强算法反早熟及摆脱局部最优解的能力.在13个基准函数及部分CEC2014测试函数上的数值仿真实验表明,MISMA具有较强的鲁棒性.此外,在光伏电池组件模型参数优化实验上进一步验证MISMA在处理实际工程优化问题时的优越性及适用性.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
