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Weak KKM theorems in generalized finitely continuous space with applications 认领 引用
1
作者 方勉 王磊 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第10期1291-1296,共6页
Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax i... Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures. 展开更多
关键词 weak Knaster-Kuratouski-Mazurkiewicz （KKM） mapping generalized finitely continuous space （GFC-space） minimax inequality GFC-quasicovex
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An adaptive ant colony system algorithm for continuous-space optimization problems 认领 引用 被引量：20
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作者 李艳君 吴铁军 《Journal of Zhejiang University Science》 2003年第1期40-46,共7页
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is pr... Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates.Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved. 展开更多
关键词 Ant colony algorithm Continuous space optimization Pheromone update strategy
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Complex genetic algorithm in continuous space 认领 引用 被引量：1
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作者 LI Qiang ZHOU Ji 《Chinese Science Bulletin》 1999年第10期954-960,共7页
A new artificial intelligent optimization method,complex genetic algorithm,is presented,and the theoretical analysis for the effective optima-seeking mechanism of the algorithm is finished.The example calculation prov... A new artificial intelligent optimization method,complex genetic algorithm,is presented,and the theoretical analysis for the effective optima-seeking mechanism of the algorithm is finished.The example calculation proves that it is a successful and simple optimization method. 展开更多
关键词 continuous space complex genetic algorithm artificial intelligent optimization
Research on error performance of underwater OAM multiplexing optical communication assisted by deep learning 认领 引用
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作者 Aiping HUANG Yi CAO +1 位作者 Honglin WANG Linwei TAO 《Optoelectronics Letters》 EI 2026年第5期261-267,共7页
In this paper,a novel convolutional neural network(CNN)assisted decoding method is proposed to recover information directly for underwater orbital angular momentum(OAM)multiplexing optical communication.The effects of... In this paper,a novel convolutional neural network(CNN)assisted decoding method is proposed to recover information directly for underwater orbital angular momentum(OAM)multiplexing optical communication.The effects of various attenuations and ocean water types,such as absorption,scattering,turbulence fading,noise and diffraction,are considered comprehensively in our analysis.A regularly spaced continuous phase screen is used to represent ocean turbulence.And the angular diffraction function is exploited for simulating the propagation of the OAM beams.In order to minimize the bit error rate(BER)and simplify the receiver design,a CNN assisted decoding method is used to compensate the distorted OAM light and decode the transmission data directly without channel estimation and equalization.The CNN is trained to learn the multiplexed OAM light intensity map generated under various water environments.The bit error performance of CNN OAM system is also compared with that of traditional Gerchberg-Saxton(GS)algorithm.Our numerical simulation results indicate that the CNN assisted method combats the impairing effects of fading and improves the underwater OAM system performance obviously.Furthermore,it outperforms GS algorithm in almost all the turbulence environments at the same water environment.And the BER of the CNN assisted system still decreases effectively by increasing signal-to-noise ratio(SNR)even in moderate and strong turbulence situations while at the same time requiring less computation complexity. 展开更多
关键词 angular diffraction function underwater orbital angular recover information directly regularly spaced continuous phase screen Convolutional Neural Network CNN Deep Learning convolutional neural network cnn assisted Underwater Optical Communication
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Some New Fixed Point Theorems in Probabilistic Metric Spaces 认领 引用 被引量：15
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作者 朱传喜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第2期179-185,共7页
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac... In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space. 展开更多
关键词 topological degree. probabilistic metric spaces. operator.compact continuous operator. Z-M-PN space
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Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces 认领 引用
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作者 张红玲 范翠丽 《Journal of Southwest Jiaotong University(English Edition)》 2008年第3期303-307,共5页
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t... The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value. 展开更多
关键词 Generalized S-KKM type theorem Finitely continuous topological space FC-closed value Minimax inequalities
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NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE MODIFIED CAMASSA-HOLM EQUATION ON THE LINE 认领 引用 被引量：3
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作者 傅仰耿 刘正荣 唐昊 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1781-1794,共14页
In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt ＋ umx ＋ 2ux m = 0, m =（1- δx^2）^2u,u（x, 0） = u0（x） ∈ H^s（R）, x ∈ R, t 〉 0,and show that the solution map is not unifor... In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt ＋ umx ＋ 2ux m = 0, m =（1- δx^2）^2u,u（x, 0） = u0（x） ∈ H^s（R）, x ∈ R, t 〉 0,and show that the solution map is not uniformly continuous in Sobolev spaces H^s（R） for s 〉 7/2. Compared with the periodic problem, the non-periodic problem is more difficult,e.g., it depends on the conservation law. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part. 展开更多
关键词 modified Camassa-Holm equation Cauchy problem non-uniform continuity Sobolev spaces
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Preliminary Study of Reconstruction of a Dynamic System Using an One-Dimensional Time Series 认领 引用 被引量：1
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作者 彭永清 朱育峰 严绍瑾 《Advances in Atmospheric Sciences》 SCIE CAS 1994年第3期277-284,共8页
This paper concerns the reconstruction of a dynamic system based on phase space continuation of monthly meantemperature iD time series and the assumption that the equation for the time-varying evolution of phase space... This paper concerns the reconstruction of a dynamic system based on phase space continuation of monthly meantemperature iD time series and the assumption that the equation for the time-varying evolution of phase space statevariables contains linear and nonlinear quadratic terms. followed by the fitting of the dataset subjected to continuation so as to get, by the least square method. the coefficients of the terms, of which those of greater variance contribution are retained for use. Results show that the obtained low-order system may be used to describe nonlinear properties of the short range climate variation shown by monthly mean temperature series. 展开更多
关键词 Monthly mean temperature Time series Phase space continuation Dynamic system
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A Nonlinear Time-lag Differential Equation Mdel for Predicting Monthly Precipitation 认领 引用
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作者 彭永清 严绍谨 王同美 《Advances in Atmospheric Sciences》 SCIE CAS 1995年第3期319-324,共6页
This paper investigates the nonlinear prediction of monthly rainfall time series which consists of phase space continuation of one-dimensional sequence, followed by least-square determination of the coefficients for t... This paper investigates the nonlinear prediction of monthly rainfall time series which consists of phase space continuation of one-dimensional sequence, followed by least-square determination of the coefficients for the terms ofthe time-lag differential equation model and then fitting of the prognostic expression is made to 1951-1980 monthlyrainfall datasets from Changsha station. Results show that the model is likely to describe the nonlinearity of the allnual cycle of precipitation on a monthly basis and to provide a basis for flood prevention and drought combating forthe wet season. 展开更多
关键词 Monthly rainfall Phase space continuation Time-lag differential equation
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Optimal confrontation position selecting games model and its application to one-on-one air combat 认领 引用 被引量：2
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作者 Zekun Duan Genjiu Xu +2 位作者 Xin Liu Jiayuan Ma Liying Wang 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2024年第1期417-428,共12页
In the air combat process,confrontation position is the critical factor to determine the confrontation situation,attack effect and escape probability of UAVs.Therefore,selecting the optimal confrontation position beco... In the air combat process,confrontation position is the critical factor to determine the confrontation situation,attack effect and escape probability of UAVs.Therefore,selecting the optimal confrontation position becomes the primary goal of maneuver decision-making.By taking the position as the UAV’s maneuver strategy,this paper constructs the optimal confrontation position selecting games(OCPSGs)model.In the OCPSGs model,the payoff function of each UAV is defined by the difference between the comprehensive advantages of both sides,and the strategy space of each UAV at every step is defined by its accessible space determined by the maneuverability.Then we design the limit approximation of mixed strategy Nash equilibrium(LAMSNQ)algorithm,which provides a method to determine the optimal probability distribution of positions in the strategy space.In the simulation phase,we assume the motions on three directions are independent and the strategy space is a cuboid to simplify the model.Several simulations are performed to verify the feasibility,effectiveness and stability of the algorithm. 展开更多
关键词 Unmanned aerial vehicles(UAVs) Air combat Continuous strategy space Mixed strategy Nash equilibrium
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Stochastic differential equation software reliability growth model with change-point 认领 引用 被引量：1
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作者 张楠 Cui Gang +1 位作者 Shu Yanjun Liu Hongwei 《High Technology Letters》 EI CAS 2014年第4期383-389,共7页
This paper presents software reliability growth models(SRGMs) with change-point based on the stochastic differential equation(SDE).Although SRGMs based on SDE have been developed in a large scale software system,consi... This paper presents software reliability growth models(SRGMs) with change-point based on the stochastic differential equation(SDE).Although SRGMs based on SDE have been developed in a large scale software system,considering the variation of failure distribution in the existing models during testing time is limited.These SDE SRGMs assume that failures have the same distribution.However,in practice,the fault detection rate can be affected by some factors and may be changed at certain point as time proceeds.With respect to this issue,in this paper,SDE SRGMs with changepoint are proposed to precisely reflect the variations of the failure distribution.A real data set is used to evaluate the new models.The experimental results show that the proposed models have a fairly accurate prediction capability. 展开更多
关键词 software reliability continuous state space stochastic differential equation （SDE） change-point
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Well-posedness of degenerate differential equations in Hiilder continuous function spaces 认领 引用 被引量：1
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作者 Shangquan BU 《Frontiers of Mathematics in China》 SCIE CSCD 2015年第2期239-248,共10页
Using known operator-valued Fourier multiplier results on vectorvalued HSlder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations （Mu）＇（t） = Au（t） ... Using known operator-valued Fourier multiplier results on vectorvalued HSlder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations （Mu）＇（t） = Au（t） ＋ f（t） for t ∈ R in HSlder continuous function spaces C^α（R; X） by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D（A） D（M）. 展开更多
关键词 Well-posedness degenerate differential equation Ca-multiplier,HSlder continuous function space
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Continuous selections for pseudo-lower semicontinuous set-valued mappings on convex structure spaces and hyperspace contractibility 认领 引用
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作者 Li, L Wu, CX 《Chinese Science Bulletin》 1997年第14期1230-1231,共2页
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is... SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This 展开更多
关键词 Continuous selections for pseudo-lower semicontinuous set-valued mappings on convex structure spaces and hyperspace contractibility
A parallel scheduling algorithm for reinforcement learning in large state space 认领 引用
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作者 Quan LIU Xudong YANG +2 位作者 Ling JING Jin LI Jiao LI 《Frontiers of Computer Science》 SCIE CSCD 2012年第6期631-646,共16页
The main challenge in the area of reinforcement learning is scaling up to larger and more complex problems. Aiming at the scaling problem of reinforcement learning, a scalable reinforcement learning method, DCS-SRL, i... The main challenge in the area of reinforcement learning is scaling up to larger and more complex problems. Aiming at the scaling problem of reinforcement learning, a scalable reinforcement learning method, DCS-SRL, is proposed on the basis of divide-and-conquer strategy, and its convergence is proved. In this method, the learning problem in large state space or continuous state space is decomposed into multiple smaller subproblems. Given a specific learning algorithm, each subproblem can be solved independently with limited available resources. In the end, component solutions can be recombined to obtain the desired result. To ad- dress the question of prioritizing subproblems in the scheduler, a weighted priority scheduling algorithm is proposed. This scheduling algorithm ensures that computation is focused on regions of the problem space which are expected to be maximally productive. To expedite the learning process, a new parallel method, called DCS-SPRL, is derived from combining DCS-SRL with a parallel scheduling architecture. In the DCS-SPRL method, the subproblems will be distributed among processors that have the capacity to work in parallel. The experimental results show that learning based on DCS-SPRL has fast convergence speed and good scalability. 展开更多
关键词 divide-and-conquer strategy parallel schedule scalability large state space continuous state space
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A STUDY OF DYNAMIC SYSTEM ESTABLISHMENT IN EOF-CONTINUATION PHASE SPACE 认领 引用
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作者 朱育峰 彭永清 +1 位作者 严绍瑾 张勤 《Acta meteorologica Sinica》 1996年第1期52-60,共9页
For the EOF decomposition continuation phase space, the least square method is applied under the condition of orthogonal basis to find coefficients of all quadratic nonlinear terms of a state evo- lution equation such... For the EOF decomposition continuation phase space, the least square method is applied under the condition of orthogonal basis to find coefficients of all quadratic nonlinear terms of a state evo- lution equation such that a dynamic system that indicates the evolution features of a weather/cli- mate system in a limited area can be formulated. The scheme is compared with that for phase space continuation by time series drift. Results show that the dynamic system established in terms of the present method is likely to give more precise and realistic description of evolution of the weather/ climate system. 展开更多
关键词 empirical orthogonal function (EOF) decomposition phase space continuation dynamic system reconstruction
On Ideal Convergence of Double Sequences in Probabilistic Normed Spaces 认领 引用
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作者 Vijay KUMAR Bernardo LAFUERZA-GUILLÉN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第8期1689-1700,共12页
The notion of ideal convergence is a generalization of statistical convecgence which has been intensively investigated in last few years. For an admissible ideal ∮ C N × N, the aim of the present paper is to int... The notion of ideal convergence is a generalization of statistical convecgence which has been intensively investigated in last few years. For an admissible ideal ∮ C N × N, the aim of the present paper is to introduce the concepts of ∮-convergence and ：∮＊-convergence for double sequences on probabilistic normed spaces （PN spaces for short）. We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide. We also define ∮-Cauchy and ：∮＊- Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces. We establish example which shows that our method of convergence for double sequences on PN spaces is more general. 展开更多
关键词 Ideal convergence double sequence statistical convergence continuous t-norm and prob- abilistic normed spaces
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The Fine Spectra of the Difference Operator △ Over the Sequence Space bv_p,(1≤p<∞) 认领 引用 被引量：3
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作者 Ali M.AKHMEDOV Feyzi BASAR 《Acta Mathematica Sinica,English Series》 SCIE 2007年第10期1757-1768,共12页
The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ... The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞. 展开更多
关键词 spectrum of an operator difference operator the continuous dual and f-dual of a sequence space the AD-property and the sequence space bvp
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A Novel Framework for Lim-inf Convergence in Posets 认领 引用 被引量：1
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作者 Bin ZHAO Jing LU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2022年第5期953-962,共10页
In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T0 enriched closure spaces.More precisely,we define and study Enr-convergence in T0 enriched closure spaces.Especi... In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T0 enriched closure spaces.More precisely,we define and study Enr-convergence in T0 enriched closure spaces.Especially,we give a sufficient and necessary condition for Enr-convergence in T0 enriched closure spaces to be topological. 展开更多
关键词 Closure opeartor lim-inf convergence Enr-convergence enriched continuous space
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GRIP: A Group Recommender Based on Interactive Preference Model 认领 引用 被引量：1
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作者 Bo-Han Li An-Man Zhangi +4 位作者 Wei Zheng Shuo Wani Xiao-Lin Qin Xue Li Hai-Lian Yin 《Journal of Computer Science & Technology》 SCIE EI CSCD 2018年第5期1039-1055,共17页
Numerous applications of recommender systems can provide us a tool to understand users. A group recommender reflects the analysis of multiple users＇ behavior, and aims to provide each user of the group with the thing... Numerous applications of recommender systems can provide us a tool to understand users. A group recommender reflects the analysis of multiple users＇ behavior, and aims to provide each user of the group with the things they involve according to users＇ preferences. Currently, most of the existing group recommenders ignore the interaction among the users. However, in the course of group activities, the interactive preferences will dramatically affect the success of recommenders. The problem becomes even more challenging when some unknown preferences of users are partly influenced by other users in the group. An interaction-based method named GRIP （Group Recommender Based on Interactive Preference） is presented which can use group activity history information and recommender post-rating feedback mechanism to generate interactive preference parameters. To evaluate the performance of the proposed method, it is compared with traditional collaborative filtering on the MovieLens dataset. The results indicate the superiority of the GRIP recommender for multi-users regarding both validity and accuracy. 展开更多
关键词 attribute space continuity collaborative filtering group recommender interactive preference
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Design Methodology of the Structure of Postal Express Mail Networks of Aviation Channels in China 认领 引用
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作者 XU Shun dou 《The Journal of China Universities of Posts and Telecommunications》 2002年第2期25-29,44,共5页
On the basis of the postal area center office system, the continuous space approximation is used to study the structure of postal express mail networks of aviation channels in China. Tradeoffs among sorting, handling,... On the basis of the postal area center office system, the continuous space approximation is used to study the structure of postal express mail networks of aviation channels in China. Tradeoffs among sorting, handling, transportation, administrative and facilities costs are examined. The optimizing design methodology proposed in this paper can be used to analyze and design the postal express mail network. The objective is to minimize the total system cost. 展开更多
关键词 continuous space approximation express mail network system of postal area center office
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