The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infini...Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).展开更多
Letζ =（0,z1,z2,···,zn） with ｜zj｜〈1for1≤j≤n,ω=（1,w1,w2,···,wn）,and P（ζ,ω） denote the set of functions p（z） that are analytic in D={z：｜z｜〈1} and satisfy Rep（z）〉0（｜...Letζ =（0,z1,z2,···,zn） with ｜zj｜〈1for1≤j≤n,ω=（1,w1,w2,···,wn）,and P（ζ,ω） denote the set of functions p（z） that are analytic in D={z：｜z｜〈1} and satisfy Rep（z）〉0（｜z｜〈1）,p（0）=1,p（zj）=wj,j=1,2,···,n.In this article we investigate the extreme points of P（ζ,ω）.展开更多
Let P-n(c(1),c(2),...,c(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + c(1)z + c(2)z(2) +...+ c(n-1)z(n-1) + d(n)z(n) +..., where c(1),c(2),...,c(n-1) are fixed complex constants}. Le...Let P-n(c(1),c(2),...,c(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + c(1)z + c(2)z(2) +...+ c(n-1)z(n-1) + d(n)z(n) +..., where c(1),c(2),...,c(n-1) are fixed complex constants}. Let P-R,P-n(b(1),b(2),...,b(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + b(1)z + b(2)z(2) +...+ b(n-1)z(n-1) + d(n)z(n) +..., where b(1),b(2),...,b(n-1) are fixed real constants and the coefficients of p(z) are real}. Let T-n(l(1),l(2),...,l(n-1)) = {f(z) : f(z) is analytic in \z\ < 1 and f(z) = z + l(1)z(2) + l(2)z(3) +...+ l(n-1)z(n) + d(n)z(n+1) +...; where l(1),l(2),...,l(n-1) are fixed real constants and the coefficients of f(z) are real}. It is understood that P-n(c(1),c(2),...,c(n-1)), P-R,P-n(b(1),b(2),...,b(n-1)) and T-n(l(1),l(2),...,l(n-1)) are not empty when the constants c(k)(k = 1,...,n-1), b(k)(k = 1,2,...,n-1) and l(k)(k = 1,...,n-1) satisfy certain conditions. This paper obtaines the extreme points of P-n(c(1),...,c(n-1)), P-R,P-n(b(1),...,b(n-1)) and T-n(l(1),...,l(n-1)).展开更多
By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
In this paper, the extreme points of the unit ball of diagonal-disjoint ideals L in nest algebras are characterized completely; Furthermore, it is shown that every extreme point of the unit ball of L has essential-nor...In this paper, the extreme points of the unit ball of diagonal-disjoint ideals L in nest algebras are characterized completely; Furthermore, it is shown that every extreme point of the unit ball of L has essential-norm one.展开更多
Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
An objective identification technique is used to detect regional extreme low temperature events(RELTE) in China during 1960-2009.Their spatial-temporal characteristics are analyzed.The results indicate that the lowest...An objective identification technique is used to detect regional extreme low temperature events(RELTE) in China during 1960-2009.Their spatial-temporal characteristics are analyzed.The results indicate that the lowest temperatures of RELTE,together with the frequency distribution of the geometric latitude center,exhibit a double-peak feature.The RELTE frequently happen near the geometric area of 30 N and 42 N before the mid-1980s,but shifted afterwards to 30 N.During 1960-2009,the frequency,intensity,and the maximum impacted area of RELTE show overall decreasing trends.Due to the contribution of RELTE,with long duration and large spatial range,which account for 10% of the total RELTE,there is a significant turning point in the late 1980s.A change to a much more steady state after the late 1990s is identified.In addition,the integrated indices of RELTE are classified and analyzed.展开更多
光伏电池板所处环境的非线性变化使得光伏电池的功率保持在最大功率点(maximum power point,MPP)非常困难。传统的最大功率点跟踪(maximum power point tracking,MPPT)方法普遍存在技术缺陷,无法满足当前需求。针对光伏发电MPPT问题,该...光伏电池板所处环境的非线性变化使得光伏电池的功率保持在最大功率点(maximum power point,MPP)非常困难。传统的最大功率点跟踪(maximum power point tracking,MPPT)方法普遍存在技术缺陷,无法满足当前需求。针对光伏发电MPPT问题,该文提出了一种基于麻雀搜索算法优化的极限学习机(sparrow search algorithm-extreme learning machine,SSA-ELM)神经网络控制器的MPPT方法。与传统技术相比,该MPPT方法在稳定性、速度、超调和MPP的振荡等方面的效果均较好。使用MATLAB/Simulink平台进行仿真实验,验证了所提控制策略及理论分析的正确性。展开更多
In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting p...In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.展开更多
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
文摘Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).
基金Supported by Educational Commission of Hubei Province of China(D2011006)
文摘Letζ =（0,z1,z2,···,zn） with ｜zj｜〈1for1≤j≤n,ω=（1,w1,w2,···,wn）,and P（ζ,ω） denote the set of functions p（z） that are analytic in D={z：｜z｜〈1} and satisfy Rep（z）〉0（｜z｜〈1）,p（0）=1,p（zj）=wj,j=1,2,···,n.In this article we investigate the extreme points of P（ζ,ω）.
文摘Let P-n(c(1),c(2),...,c(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + c(1)z + c(2)z(2) +...+ c(n-1)z(n-1) + d(n)z(n) +..., where c(1),c(2),...,c(n-1) are fixed complex constants}. Let P-R,P-n(b(1),b(2),...,b(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + b(1)z + b(2)z(2) +...+ b(n-1)z(n-1) + d(n)z(n) +..., where b(1),b(2),...,b(n-1) are fixed real constants and the coefficients of p(z) are real}. Let T-n(l(1),l(2),...,l(n-1)) = {f(z) : f(z) is analytic in \z\ < 1 and f(z) = z + l(1)z(2) + l(2)z(3) +...+ l(n-1)z(n) + d(n)z(n+1) +...; where l(1),l(2),...,l(n-1) are fixed real constants and the coefficients of f(z) are real}. It is understood that P-n(c(1),c(2),...,c(n-1)), P-R,P-n(b(1),b(2),...,b(n-1)) and T-n(l(1),l(2),...,l(n-1)) are not empty when the constants c(k)(k = 1,...,n-1), b(k)(k = 1,2,...,n-1) and l(k)(k = 1,...,n-1) satisfy certain conditions. This paper obtaines the extreme points of P-n(c(1),...,c(n-1)), P-R,P-n(b(1),...,b(n-1)) and T-n(l(1),...,l(n-1)).
文摘By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
基金This work was supported by the National Natural Science Foundation of China.
文摘In this paper, the extreme points of the unit ball of diagonal-disjoint ideals L in nest algebras are characterized completely; Furthermore, it is shown that every extreme point of the unit ball of L has essential-norm one.
文摘Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
基金supported by the Special Scientific Research Projects for Public Interest(No.GYHY201006021 and GYHY201106016)the National Natural Science Foundation of China(No.41205040 and 40930952)
文摘An objective identification technique is used to detect regional extreme low temperature events(RELTE) in China during 1960-2009.Their spatial-temporal characteristics are analyzed.The results indicate that the lowest temperatures of RELTE,together with the frequency distribution of the geometric latitude center,exhibit a double-peak feature.The RELTE frequently happen near the geometric area of 30 N and 42 N before the mid-1980s,but shifted afterwards to 30 N.During 1960-2009,the frequency,intensity,and the maximum impacted area of RELTE show overall decreasing trends.Due to the contribution of RELTE,with long duration and large spatial range,which account for 10% of the total RELTE,there is a significant turning point in the late 1980s.A change to a much more steady state after the late 1990s is identified.In addition,the integrated indices of RELTE are classified and analyzed.
文摘光伏电池板所处环境的非线性变化使得光伏电池的功率保持在最大功率点(maximum power point,MPP)非常困难。传统的最大功率点跟踪(maximum power point tracking,MPPT)方法普遍存在技术缺陷,无法满足当前需求。针对光伏发电MPPT问题,该文提出了一种基于麻雀搜索算法优化的极限学习机(sparrow search algorithm-extreme learning machine,SSA-ELM)神经网络控制器的MPPT方法。与传统技术相比,该MPPT方法在稳定性、速度、超调和MPP的振荡等方面的效果均较好。使用MATLAB/Simulink平台进行仿真实验,验证了所提控制策略及理论分析的正确性。
基金supported by the National Natural Science Foundation of China(12271344)the Natural Science Foundation of Shanghai(23ZR1425800)。
文摘In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
