This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective to...Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference...Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.展开更多
Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the ...In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the stability of property(ω),and investigate the relationship between the stability of property(ω)and the(ω)-property of operator functions.展开更多
In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,...In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.展开更多
Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametr...Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.展开更多
Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.展开更多
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovsk...In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.展开更多
In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which ...In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.展开更多
In oceanic and atmospheric science,finer resolutions have become a prevailing trend in all aspects of development.For high-resolution fluid flow simulations,the computational costs of widely used numerical models incr...In oceanic and atmospheric science,finer resolutions have become a prevailing trend in all aspects of development.For high-resolution fluid flow simulations,the computational costs of widely used numerical models increase significantly with the resolution.Artificial intelligence methods have attracted increasing attention because of their high precision and fast computing speeds compared with traditional numerical model methods.The resolution-independent Fourier neural operator(FNO)presents a promising solution to the still challenging problem of high-resolution fluid flow simulations based on low-resolution data.Accordingly,we assess the potential of FNO for high-resolution fluid flow simulations using the vorticity equation as an example.We assess and compare the performance of FNO in multiple high-resolution tests varying the amounts of data and the evolution durations.When assessed with finer resolution data(even up to number of grid points with 1280×1280),the FNO model,trained at low resolution(number of grid points with 64×64)and with limited data,exhibits a stable overall error and good accuracy.Additionally,our work demonstrates that the FNO model takes less time than the traditional numerical method for high-resolution simulations.This suggests that FNO has the prospect of becoming a cost-effective and highly precise model for high-resolution simulations in the future.Moreover,FNO can make longer high-resolution predictions while training with less data by superimposing vorticity fields from previous time steps as input.A suitable initial learning rate can be set according to the frequency principle,and the time intervals of the dataset need to be adjusted according to the spatial resolution of the input when training the FNO model.Our findings can help optimize FNO for future fluid flow simulations.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2...Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
文摘Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
基金supported by National Science Foundations of China(Grant No.11771340,12171373).
文摘Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
基金supported by the National Natural Science Foundation of China(No.11501419)the Nature Science Basic Research Plan in Shaanxi Province of China(No.2021JM-519)。
文摘In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the stability of property(ω),and investigate the relationship between the stability of property(ω)and the(ω)-property of operator functions.
基金Supported by by Natural Science Foundation of Henan(202300410184 and242300421387)。
文摘In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.
基金supported in part by the National Defense Basic Scientific Research Program of China(No.JCKY2021603B030)the Shenzhen Fundamental Research Program,China(No.JCYJ20220818102601004)the Science Center Program of National Natural Science Foundation of China(No.62188101)。
文摘Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
基金Supported by Fujian Provincial Natural Science Foundation of China(2024J01792)。
文摘In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.
基金supported by the National Natural Science Foundation of China(12171075)the Science and Technology Research Project of Education Department of Jilin Province(JJKH20241406KJ)Zhan’s research was supported by the Doctoral Startup Fund of Liaoning University of Technology(XB2024029).
文摘In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.
基金The National Natural Science Foundation of China under contract No.42425606the Basic Scientific Fund for the National Public Research Institute of China(Shu-Xingbei Young Talent Program)under contract No.2023S01+1 种基金the Ocean Decade International Cooperation Center Scientific and Technological Cooperation Project under contract No.GHKJ2024005China-Korea Joint Ocean Research Center Project under contract Nos PI-20240101(China)and 20220407(Korea).
文摘In oceanic and atmospheric science,finer resolutions have become a prevailing trend in all aspects of development.For high-resolution fluid flow simulations,the computational costs of widely used numerical models increase significantly with the resolution.Artificial intelligence methods have attracted increasing attention because of their high precision and fast computing speeds compared with traditional numerical model methods.The resolution-independent Fourier neural operator(FNO)presents a promising solution to the still challenging problem of high-resolution fluid flow simulations based on low-resolution data.Accordingly,we assess the potential of FNO for high-resolution fluid flow simulations using the vorticity equation as an example.We assess and compare the performance of FNO in multiple high-resolution tests varying the amounts of data and the evolution durations.When assessed with finer resolution data(even up to number of grid points with 1280×1280),the FNO model,trained at low resolution(number of grid points with 64×64)and with limited data,exhibits a stable overall error and good accuracy.Additionally,our work demonstrates that the FNO model takes less time than the traditional numerical method for high-resolution simulations.This suggests that FNO has the prospect of becoming a cost-effective and highly precise model for high-resolution simulations in the future.Moreover,FNO can make longer high-resolution predictions while training with less data by superimposing vorticity fields from previous time steps as input.A suitable initial learning rate can be set according to the frequency principle,and the time intervals of the dataset need to be adjusted according to the spatial resolution of the input when training the FNO model.Our findings can help optimize FNO for future fluid flow simulations.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金supported by the National Key Research and Development Program of China(22YFA10057001)the National Science Foundation of Guangdong Province(2023A1515012034)the National Natural Science Foundation of China(12371105,11971295).
文摘Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
