Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
This paper deals with the problem of robust stabilization for uncertain Takagi-Sugeno(T-S)fuzzy neutral systems with input delays and distributed delays.The purpose is to design a state feedback fuzzy controller with ...This paper deals with the problem of robust stabilization for uncertain Takagi-Sugeno(T-S)fuzzy neutral systems with input delays and distributed delays.The purpose is to design a state feedback fuzzy controller with a H∞performance such that the resulting closed-loop system is robustly stable.Sufficient conditions for the solvability of the problem are obtained by utilizing proper Lyapunov functional together with the linear matrix inequality(LMI)approach,especially two different improved results on robust H∞controller design with relaxed conditions are obtained.Finally,we provide two examples to verify the effectiveness of our design method and give some principle for choosing the proper controller under certain circumstances.展开更多
In this paper,we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.Our results...In this paper,we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.Our results include the previous results as special cases extend and improve the main results obtained by many others.展开更多
Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitut...Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitution rates of Gnetales （Ephedra, Gnetum, and Welwitschia） has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species （and 7736 aligned nucleotides） to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil-based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long-distance dispersal, but finer-scale studies are needed to test this hypothesis.展开更多
In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve t...In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.展开更多
In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to ...In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.展开更多
Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for so...Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for solving large-size consistent linear systems. The RGBK algorithm extends the greedy block Kaczmarz algorithm (GBK) presented by Niu and Zheng in <a href="#ref1">[1]</a> by introducing a relaxation parameter to the iteration formulation of GBK, and the AGBK algorithm uses different iterative update rules to minimize the running time. The convergence of the RGBK is proved and a method to determine an optimal parameter is provided. Several examples are presented to show the effectiveness of the proposed methods for overdetermined and underdetermined consistent linear systems with dense and sparse coefficient matrix.展开更多
It is shown that for laser technologies it was necessary to create a new branch of physics: Relaxed Optics (synthesis of methods of the physical optics, quantum electronics, physical chemistry, physics of irreversible...It is shown that for laser technologies it was necessary to create a new branch of physics: Relaxed Optics (synthesis of methods of the physical optics, quantum electronics, physical chemistry, physics of irreversible phenomena in unitary system). It is allowed to explain complex chain processes of interaction light and matter. Possible applications of Relaxed Optical methods for the modeling of the laser-induced processes phenomena, including laser implantation (surface and subsurface processes), laser-induced optical breakdown (volume processes) and laser annealing of radiation and other defects in solid, are discussed. Perspectives of using these methods for the creation of new laser technologies, including creation new types of optoelectronic devices (heterostructures, diffraction lattices, etc.), resolution the problems of metallurgy, material science, painting, architecture and a building, are analyzed.展开更多
Some ways of multilevel relaxed preconditioning matrices for the stiffness matrix in the discretization of selfad joint second order elliptic boundary value problems are proposed. For reason-able assumptions of the re...Some ways of multilevel relaxed preconditioning matrices for the stiffness matrix in the discretization of selfad joint second order elliptic boundary value problems are proposed. For reason-able assumptions of the relaxed factor ω, smaller relative condition numbers are given. The optimal relaxed factor ω is derived, too.展开更多
The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent m...The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.展开更多
An indium-rich InGaN p-n junction is grown on a strain-relaxed InGaN buffer layer.The results show that the n-InGaN is grown coherently on the buffer layer but the p-InGaN layer exhibits a partial strain relaxation.Th...An indium-rich InGaN p-n junction is grown on a strain-relaxed InGaN buffer layer.The results show that the n-InGaN is grown coherently on the buffer layer but the p-InGaN layer exhibits a partial strain relaxation.The fabricated InGaN p-n junction has a low reverse leakage current density on the order of 10^(-8)A/cm^(2)within the measured voltage range,and exhibits a wide spectral response due to the presence of band tail states or deep level states which origin from indium composition fluctuation or various defects.The measured peak responsivity at 438 nm is 31 mA/W at zero bias and reaches 118 mA/W at 3 V reverse bias.In addition,the Raman spectra of the p-and n-type InGaN alloys are also analyzed.展开更多
Germanium-tin(Ge_(1-x)Sn_(x))p-type metal-oxide-semiconductor field effect transistors(pMOSFETs)were fabricated using a strained Ge_(0.985)Sn_(0.015) thin film that was epitaxially grown on a silicon-on-insulator subs...Germanium-tin(Ge_(1-x)Sn_(x))p-type metal-oxide-semiconductor field effect transistors(pMOSFETs)were fabricated using a strained Ge_(0.985)Sn_(0.015) thin film that was epitaxially grown on a silicon-on-insulator substrate with a relaxed Ge buffer layer.The Ge buffer was deposited using a two-step chemical vapor deposition growth technique.The high quality Ge_(0.985)Sn_(0.015) layer was grown by solid source molecular beam epitaxy.Ge_(0.985)Sn_(0.015) pMOSFETs with Si surface passivation,TaN/HfO_(2) gate stack,and nickel stanogermanide[Ni(Ge_(1-x)Sn_(x))]source/drain were fabricated on the grown substrate.The device achieves an effective hole mobility of 182 cm^(2)/V·s at an inversion carrier density of 1×10^(13) cm^(-2).展开更多
Blind signature has a wide range of applications in the fields of E-commerce and block-chain because it can effectively prevent the blind signer from getting the original message with its blindness.Owing to the potent...Blind signature has a wide range of applications in the fields of E-commerce and block-chain because it can effectively prevent the blind signer from getting the original message with its blindness.Owing to the potential unconditional security,quantum blind signature(QBS)is more advantageous than the classical ones.In this paper,an efficient and practical quantum blind signature scheme relaxed security model is presented,where quantum superposition,decoy qubits and hash function are used for the purpose of blindness.Compared with previous QBS scheme,the presented scheme is more efficient and practical with a relaxed security model,in which the signer’s dishonest behavior can be detected other than being prevented as in other QBS schemes.展开更多
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of ...The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.展开更多
A new system for relaxed cocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection methods.Our results generalize and improve the co...A new system for relaxed cocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection methods.Our results generalize and improve the corresponding results of recent works.展开更多
In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-P...In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-Picard contraction.As applications,we derive the linear convergence of the generalized proximal point algorithm and the relaxed forward-backward splitting method in a simple and elegant way.展开更多
Relaxed Lasso method is used for variable selection to 15 main economic factors affecting foreign investment. While Relaxed Lasso method, method of least squares and regression are compared, the result further reveals...Relaxed Lasso method is used for variable selection to 15 main economic factors affecting foreign investment. While Relaxed Lasso method, method of least squares and regression are compared, the result further reveals the main problem facing foreign investment at the present stage.展开更多
A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this ...A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.展开更多
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
基金Research Project of Huzhou University under Grunt KYL21223。
文摘This paper deals with the problem of robust stabilization for uncertain Takagi-Sugeno(T-S)fuzzy neutral systems with input delays and distributed delays.The purpose is to design a state feedback fuzzy controller with a H∞performance such that the resulting closed-loop system is robustly stable.Sufficient conditions for the solvability of the problem are obtained by utilizing proper Lyapunov functional together with the linear matrix inequality(LMI)approach,especially two different improved results on robust H∞controller design with relaxed conditions are obtained.Finally,we provide two examples to verify the effectiveness of our design method and give some principle for choosing the proper controller under certain circumstances.
基金Supported by the NSF of Henan Province(092300410150)Supported by the NSF of Department Education of Henan Province(2009C110002)Supported by the Key Teacher Foundation of Huanghuai University
文摘In this paper,we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.Our results include the previous results as special cases extend and improve the main results obtained by many others.
基金supported,in part,by the National Science Foundation (USA)-Emerging Frontiers,Assembling the Tree of Life,Collaborative Research:Gymnosperms on the Tree of Life:Resolving the Phylogeny of Seed Plants (Grant No. EF-0629657 to SMI-B)supported by the Swedish Research Council (grants to CR)
文摘Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitution rates of Gnetales （Ephedra, Gnetum, and Welwitschia） has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species （and 7736 aligned nucleotides） to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil-based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long-distance dispersal, but finer-scale studies are needed to test this hypothesis.
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
基金Supported by National Natural Science Foundation of China(50977008,60904017,60774048,60728307),the Funds for Creative Research Groups of China(60521003),the Program for Cheung Kong Scholars and Innovative Research Team in University(IRT0421),and the 111 Project(B08015),National High Technology Research and Development Program of China(863 Program)(2006AA04Z183)
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
文摘In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.
文摘In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.
文摘Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for solving large-size consistent linear systems. The RGBK algorithm extends the greedy block Kaczmarz algorithm (GBK) presented by Niu and Zheng in <a href="#ref1">[1]</a> by introducing a relaxation parameter to the iteration formulation of GBK, and the AGBK algorithm uses different iterative update rules to minimize the running time. The convergence of the RGBK is proved and a method to determine an optimal parameter is provided. Several examples are presented to show the effectiveness of the proposed methods for overdetermined and underdetermined consistent linear systems with dense and sparse coefficient matrix.
文摘It is shown that for laser technologies it was necessary to create a new branch of physics: Relaxed Optics (synthesis of methods of the physical optics, quantum electronics, physical chemistry, physics of irreversible phenomena in unitary system). It is allowed to explain complex chain processes of interaction light and matter. Possible applications of Relaxed Optical methods for the modeling of the laser-induced processes phenomena, including laser implantation (surface and subsurface processes), laser-induced optical breakdown (volume processes) and laser annealing of radiation and other defects in solid, are discussed. Perspectives of using these methods for the creation of new laser technologies, including creation new types of optoelectronic devices (heterostructures, diffraction lattices, etc.), resolution the problems of metallurgy, material science, painting, architecture and a building, are analyzed.
文摘Some ways of multilevel relaxed preconditioning matrices for the stiffness matrix in the discretization of selfad joint second order elliptic boundary value problems are proposed. For reason-able assumptions of the relaxed factor ω, smaller relative condition numbers are given. The optimal relaxed factor ω is derived, too.
基金Project supported by the Key Science Foundation of Education Department of Sichuan Province of China (No.2003A081)Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.
基金the Opening Project of Xinjiang Laboratory of Phase Transitions and Microstructures of Condensed Matters(Nos XJDX0912-2012-03,XJDX0912-2012-02)the Project of Changji Collge(Nos 2011YJYB001,2011YJYB006).
文摘An indium-rich InGaN p-n junction is grown on a strain-relaxed InGaN buffer layer.The results show that the n-InGaN is grown coherently on the buffer layer but the p-InGaN layer exhibits a partial strain relaxation.The fabricated InGaN p-n junction has a low reverse leakage current density on the order of 10^(-8)A/cm^(2)within the measured voltage range,and exhibits a wide spectral response due to the presence of band tail states or deep level states which origin from indium composition fluctuation or various defects.The measured peak responsivity at 438 nm is 31 mA/W at zero bias and reaches 118 mA/W at 3 V reverse bias.In addition,the Raman spectra of the p-and n-type InGaN alloys are also analyzed.
基金Supported by the National Basic Research Program of China under Grant Nos 2013CB632103 and 2011CBA00608the National Natural Science Foundation of China under Grant Nos 61036003,61177038 and 61176013the Science Research Foundation of Huaqiao University under Grant 12BS221.
文摘Germanium-tin(Ge_(1-x)Sn_(x))p-type metal-oxide-semiconductor field effect transistors(pMOSFETs)were fabricated using a strained Ge_(0.985)Sn_(0.015) thin film that was epitaxially grown on a silicon-on-insulator substrate with a relaxed Ge buffer layer.The Ge buffer was deposited using a two-step chemical vapor deposition growth technique.The high quality Ge_(0.985)Sn_(0.015) layer was grown by solid source molecular beam epitaxy.Ge_(0.985)Sn_(0.015) pMOSFETs with Si surface passivation,TaN/HfO_(2) gate stack,and nickel stanogermanide[Ni(Ge_(1-x)Sn_(x))]source/drain were fabricated on the grown substrate.The device achieves an effective hole mobility of 182 cm^(2)/V·s at an inversion carrier density of 1×10^(13) cm^(-2).
基金This work was supported by 2018 Provincial Key Research and Development Program(Social Development)Project of Jiangsu Province(No.BF2018719)2018 Provincial Key Research and Development Program(Modern Agriculture)Project of Jiangsu Province(No.2018301).
文摘Blind signature has a wide range of applications in the fields of E-commerce and block-chain because it can effectively prevent the blind signer from getting the original message with its blindness.Owing to the potential unconditional security,quantum blind signature(QBS)is more advantageous than the classical ones.In this paper,an efficient and practical quantum blind signature scheme relaxed security model is presented,where quantum superposition,decoy qubits and hash function are used for the purpose of blindness.Compared with previous QBS scheme,the presented scheme is more efficient and practical with a relaxed security model,in which the signer’s dishonest behavior can be detected other than being prevented as in other QBS schemes.
基金Supported by King Mongkut's University of Technology Thonburi.KMUTT,(CSEC Project No.E01008)supported by the Faculty of Applied Liberal Arts RMUTR Research Fund and King Mongkut's Diamond scholarship for fostering special academic skills by KMUTT
文摘The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.
基金Funded by the Natural Science Foundation of Chongqing(No.CSTC 2009BB8240)
文摘A new system for relaxed cocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection methods.Our results generalize and improve the corresponding results of recent works.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1180145511871059+4 种基金11971238)China Postdoctoral Science Foundation(Grant Nos.2019M6634592020T130081)the Applied Basic Project of Sichuan Province(Grant No.2020YJ0111)the Open Project of Key Laboratory of School of Mathematical Sciences,Chongqing Normal University(Grant No.CSSXKFKTM202004)。
文摘In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-Picard contraction.As applications,we derive the linear convergence of the generalized proximal point algorithm and the relaxed forward-backward splitting method in a simple and elegant way.
文摘Relaxed Lasso method is used for variable selection to 15 main economic factors affecting foreign investment. While Relaxed Lasso method, method of least squares and regression are compared, the result further reveals the main problem facing foreign investment at the present stage.
文摘A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.
