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Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology 被引量:1
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作者 Muhammad Farman Ali Akgül +2 位作者 Mir Sajjad Hashemi Liliana Guran Amelia Bucur 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1385-1403,共19页
New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model arei... New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation. 展开更多
关键词 COVID-19 model fractal-fractional operator Ulam-Hyers stability existence and uniqueness numerical simulation
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GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N) 被引量:1
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作者 Xuejun ZHANG Yuting GUO +1 位作者 Hongxin CHEN Pengcheng TANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1301-1326,共26页
In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t... In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals. 展开更多
关键词 Forelli-Rudin type operator L^(p q s k)(B_(n))space BOUNDEDNESS unit ball
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Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel 被引量:1
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作者 Saima Rashid Fahd Jarad 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第6期2289-2327,共39页
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p... Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated. 展开更多
关键词 Measles epidemic model Atangana-Baleanu Caputo-Fabrizio differential operators existence and uniqueness qualitative analysis Newton interpolating polynomial
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AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS
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作者 Jiangen LIU Fazhan GENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1271-1279,共9页
Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new f... Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators. 展开更多
关键词 k-Prabhakar fractional operator Caputo-Fabrizio operator Atangana-Baleanu operator Sun-Hao-Zhang-Baleanu operator generalized Caputo type operator
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An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets
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作者 Rana Muhammad Zulqarnain Wen-Xiu Ma +2 位作者 Imran Siddique Hijaz Ahmad Sameh Askar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1829-1862,共34页
Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and stra... Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented. 展开更多
关键词 Interval-valued Pythagorean fuzzy soft set IVPFSIWA operator IVPFSIWG operator MCGDM SCM
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Appropriate Combination of Crossover Operator and Mutation Operator in Genetic Algorithms for the Travelling Salesman Problem
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作者 Zakir Hussain Ahmed Habibollah Haron Abdullah Al-Tameem 《Computers, Materials & Continua》 SCIE EI 2024年第5期2399-2425,共27页
Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes... Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes.It uses a crossover operator to create better offspring chromosomes and thus,converges the population.Also,it uses a mutation operator to explore the unexplored areas by the crossover operator,and thus,diversifies the GA search space.A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution.However,appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem.In this present paper,we aim to study the benchmark traveling salesman problem(TSP).We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances.The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem.The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances. 展开更多
关键词 Travelling salesman problem genetic algorithms crossover operator mutation operator comprehensive sequential constructive crossover insertion mutation
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Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation
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作者 张科 李兰兰 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期205-210,共6页
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t... To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion. 展开更多
关键词 Wigner function optical cumulant operator dissipation evolution thermo-entangled state representation integration within ordered product of operators
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Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces
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作者 MA Teng ZHOU Jiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期554-570,共17页
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and... In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given. 展开更多
关键词 Morrey-Herz spaces weighted multilinear p-adic Hardy operator COMMUTATORS operator norms
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Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media
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作者 Pan Huang Yifei Leng +1 位作者 Cheng Lian Honglai Liu 《Engineering》 SCIE EI CAS CSCD 2024年第8期94-103,共10页
Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varyi... Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media. 展开更多
关键词 Porous media Reactive transport Solution operator DeepONet Neural network
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ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
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作者 陈洁玲 刘名生 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期295-310,共16页
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,... In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors. 展开更多
关键词 Bloch-Landau type theorem Bloch constant linear complex operator harmonic mapping biharmonic mapping UNIVALENT
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PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES
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作者 Zuoling LIU Hasi WULAN 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1327-1336,共10页
For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f... For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight. 展开更多
关键词 COMPACTNESS BOUNDEDNESS Bloch type space product type operator weighted Bergman space
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BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS
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作者 陈伯勇 江良英 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期789-809,共21页
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a... In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains. 展开更多
关键词 Hankel operator Hardy space Bergman space pseudoconvex domain
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Maximal operators of pseudo-differential operators with rough symbols
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作者 Ramla Benhamoud ZHU Xiang-rong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期174-180,共7页
Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and ... Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant. 展开更多
关键词 pseudo-differential operator rough Hormander class H-L maximal operator
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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrodinger equation with sextic operator under non-zero boundary conditions
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作者 Luyao Zhang Xiyang Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期268-280,共13页
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main... We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons. 展开更多
关键词 double-pole solitons double-pole breathers Riemann-Hilbert problem non-zero boundary con-ditions nonlinear Schrodinger equation with sextic operator
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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS
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作者 Zhenhai LIU Nikolaos S.PAPAGEORGIOU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1280-1300,共21页
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con... We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems. 展开更多
关键词 periodic boundary condition time-dependent maximal monotone operator convex and nonconvex problems extremal solutions strong relaxation
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THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART
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作者 马文贤 杨四辈 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期532-550,共19页
Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted... Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given. 展开更多
关键词 elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality
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MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES
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作者 林孝盛 杨大春 +1 位作者 杨四辈 袁文 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期484-514,共31页
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som... Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new. 展开更多
关键词 Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function
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A Coupled Thermomechanical Crack Propagation Behavior of Brittle Materials by Peridynamic Differential Operator
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作者 Tianyi Li Xin Gu Qing Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期339-361,共23页
This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic... This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials. 展开更多
关键词 Peridynamic differential operator thermomechanical coupling HETEROGENEITY numerical simulation
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Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection
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作者 Fei Ming Wenyin Gong +1 位作者 Ling Wang Yaochu Jin 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期919-931,共13页
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev... Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs. 展开更多
关键词 Constrained multi-objective optimization deep Qlearning deep reinforcement learning(DRL) evolutionary algorithms evolutionary operator selection
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THE SCHUR TEST OF COMPACT OPERATORS
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作者 Qijian KANG Maofa WANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期2041-2050,共10页
Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of t... Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q). 展开更多
关键词 Schur test compact operator infinite matrix
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