In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
We present a novel approach for calculating the energy budget components during the progressive failure process in cohesive-frictional geomaterials.The energy supplied through external loading can be either stored as ...We present a novel approach for calculating the energy budget components during the progressive failure process in cohesive-frictional geomaterials.The energy supplied through external loading can be either stored as elastic strain energy and plastic energy storage or dissipated through damage growth and irreversible plastic deformation mechanisms.Analytical functions describing energy budget components are derived based on a thermodynamic formulation in geomaterials fracture.The thermodynamically consistent derivation leads to a non-local ductile damage model,which is solved numerically in a non-linear finite element framework.The proposed model captures geomaterial fractures in three benchmark examples,including tensile and biaxial-compressive shear scenarios and slope stability analysis.The aspects of shear fracture propagation and energy budget mechanisms are elaborately investigated,considering different material properties and stochastic distributions.The numerical results are validated against existing experimental data and other analytical methods.The model provides a physics-based understanding of energy budget in geomaterials fracture,leading to advances in ground improvement and other geotechnical supporting systems.展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study ...In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.展开更多
In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations...In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma（J Differential Equations,2001,171：294-314. ）.展开更多
We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probabil...We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probability by using a maximally entangled GHZ state as controlled quantum channel. Then, we put forward two schemes for conclusively implementing the non-local operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The feature of these schemes is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled,the third one can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to implement the same non-local operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.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
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
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
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
In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and effici...In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and efficient method for vortex beam generation by leveraging the intrinsic singularities of dipole scatterers and enhancing their performance through non-local coupling.We demonstrate that the intrinsic singularities—amplitude-zero points in the scattering patterns of electric dipole(ED)and magnetic dipole(MD)resonances–enable the conversion of spin angular momentum(SAM)into orbital angular momentum(OAM),generating a vortex electric field distribution.By arranging these dipolar units into a periodic array,we establish a dual-resonance non-local metasurface that improves directivity and efficiency via non-local collective interactions and the generalized Kerker effect.This configuration significantly enhances forward scattering,producing highly directional vortex beams.Our experimental results show that the non-local metasurface achieves a vortex conversion efficiency approximately 2.2 times higher than that of a reference structure around 40 GHz.This alignment-free,high-efficiency solution offers great potential for expanding millimeter-wave communication capacity and advancing photonic applications.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
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
Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I...Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).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 remote sensing imagery,approximately 67%of the data are affected by cloud cover,significantly increasing the difficulty of image classification,recognition,and other downstream interpretation tasks.To effectively a...In remote sensing imagery,approximately 67%of the data are affected by cloud cover,significantly increasing the difficulty of image classification,recognition,and other downstream interpretation tasks.To effectively address the randomness of cloud distribution and the non-uniformity of cloud thickness,we propose a coarse-to-fine thin cloud removal architecture based on the observations of the random distribution and uneven thickness of cloud.In the coarse-level declouding network,we innovatively introduce a multi-scale attention mechanism,i.e.,pyramid nonlocal attention(PNA).By integrating global context with local detail information,it specifically addresses image quality degradation caused by the uncertainty in cloud distribution.During the fine-level declouding stage,we focus on the impact of cloud thickness on declouding results(primarily manifested as insufficient detail information).Through a carefully designed residual dense module,we significantly enhance the extraction and utilization of feature details.Thus,our approach precisely restores lost local texture features on top of coarse-level results,achieving a substantial leap in declouding quality.To evaluate the effectiveness of our cloud removal technology and attention mechanism,we conducted comprehensive analyses on publicly available datasets.Results demonstrate that our method achieves state-of-the-art performance across a wide range of techniques.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,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras w...In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.展开更多
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金supported by the National Natural Science Foundation of China(Grant No.52179128)the Sand Hazards and Opportunities for Resilience,Energy,and Sustainability(SHORES)Center,funded by Tamkeen under the NYUAD Research Institute Award CG013.
文摘We present a novel approach for calculating the energy budget components during the progressive failure process in cohesive-frictional geomaterials.The energy supplied through external loading can be either stored as elastic strain energy and plastic energy storage or dissipated through damage growth and irreversible plastic deformation mechanisms.Analytical functions describing energy budget components are derived based on a thermodynamic formulation in geomaterials fracture.The thermodynamically consistent derivation leads to a non-local ductile damage model,which is solved numerically in a non-linear finite element framework.The proposed model captures geomaterial fractures in three benchmark examples,including tensile and biaxial-compressive shear scenarios and slope stability analysis.The aspects of shear fracture propagation and energy budget mechanisms are elaborately investigated,considering different material properties and stochastic distributions.The numerical results are validated against existing experimental data and other analytical methods.The model provides a physics-based understanding of energy budget in geomaterials fracture,leading to advances in ground improvement and other geotechnical supporting systems.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金supported by NSF grant DMS-1509505a postdoctoral fellowship of the National Science Foundation(No.DMS-1103786)
文摘In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.
文摘In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma（J Differential Equations,2001,171：294-314. ）.
文摘We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probability by using a maximally entangled GHZ state as controlled quantum channel. Then, we put forward two schemes for conclusively implementing the non-local operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The feature of these schemes is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled,the third one can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to implement the same non-local operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.
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.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 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.
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 National Key R&D Program of China(No.2023YFA1406900 and No.2022YFA1404800)the National Natural Science Foundation of China(U22A2008,12404484)+2 种基金the Opening Funding of National Key Laboratory of Electromagnetic Space Security,and Laoshan Laboratory Science and Technology Innovation Project(No.LSKJ202200801)National Natural Science Foundation of China(No.12234007,No.12321161645)Sichuan Province Science and Technology Support Program(2025ZNSFSC0846).
文摘In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and efficient method for vortex beam generation by leveraging the intrinsic singularities of dipole scatterers and enhancing their performance through non-local coupling.We demonstrate that the intrinsic singularities—amplitude-zero points in the scattering patterns of electric dipole(ED)and magnetic dipole(MD)resonances–enable the conversion of spin angular momentum(SAM)into orbital angular momentum(OAM),generating a vortex electric field distribution.By arranging these dipolar units into a periodic array,we establish a dual-resonance non-local metasurface that improves directivity and efficiency via non-local collective interactions and the generalized Kerker effect.This configuration significantly enhances forward scattering,producing highly directional vortex beams.Our experimental results show that the non-local metasurface achieves a vortex conversion efficiency approximately 2.2 times higher than that of a reference structure around 40 GHz.This alignment-free,high-efficiency solution offers great potential for expanding millimeter-wave communication capacity and advancing photonic applications.
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 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 by the National Natural Science Foundation of China(12071076)the Scientific Research Start-up Foundation of Fujian University of Technology(GY-Z23238)the Program for Education and Scientific Research of Young and Middle-Aged Teachers in Fujian Province(JAT191128,JT180818)。
文摘Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).
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 Fundamental Research Funds for the Central Universities(No.2572025BR14)the China Energy Digital Intelligence Technology Development(Beijing)Co.,Ltd.Science and Technology Innovation Project(No.YA2024001500).
文摘In remote sensing imagery,approximately 67%of the data are affected by cloud cover,significantly increasing the difficulty of image classification,recognition,and other downstream interpretation tasks.To effectively address the randomness of cloud distribution and the non-uniformity of cloud thickness,we propose a coarse-to-fine thin cloud removal architecture based on the observations of the random distribution and uneven thickness of cloud.In the coarse-level declouding network,we innovatively introduce a multi-scale attention mechanism,i.e.,pyramid nonlocal attention(PNA).By integrating global context with local detail information,it specifically addresses image quality degradation caused by the uncertainty in cloud distribution.During the fine-level declouding stage,we focus on the impact of cloud thickness on declouding results(primarily manifested as insufficient detail information).Through a carefully designed residual dense module,we significantly enhance the extraction and utilization of feature details.Thus,our approach precisely restores lost local texture features on top of coarse-level results,achieving a substantial leap in declouding quality.To evaluate the effectiveness of our cloud removal technology and attention mechanism,we conducted comprehensive analyses on publicly available datasets.Results demonstrate that our method achieves state-of-the-art performance across a wide range of techniques.
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(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY231)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.
