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
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper...Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.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
A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator tech...A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.展开更多
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ...We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.展开更多
A way to extend operators in spaces of continuous functions to spaces of continuous set_valued functions is proposed. This extension is developed through the Steiner selections of the set_valued functions. Their prope...A way to extend operators in spaces of continuous functions to spaces of continuous set_valued functions is proposed. This extension is developed through the Steiner selections of the set_valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In Part Ⅱ of this series some applications to approximation theory will be shown.展开更多
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).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
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
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
This paper investigates set-valued state estimation of nonlinear systems with unknown-but-bounded(UBB)noises based on constrained polynomial zonotopes which is utilized to characterize non-convex sets.First,properties...This paper investigates set-valued state estimation of nonlinear systems with unknown-but-bounded(UBB)noises based on constrained polynomial zonotopes which is utilized to characterize non-convex sets.First,properties of constrained polynomial zonotopes are provided and the order reduction method is given to reduce the computational complexity.Then,the corresponding improved prediction-update algorithm is proposed so that it can be adapted to non-convex sets.Based on generalized intersection,the utilization of set-based estimation for attack detection is analyzed.Finally,an example is given to show the efficiency of our results.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
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
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 Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the National Natural Science Foundation of China(Grant No.52475543)Natural Science Foundation of Henan(Grant No.252300421101)+1 种基金Henan Province University Science and Technology Innovation Talent Support Plan(Grant No.24HASTIT048)Science and Technology Innovation Team Project of Zhengzhou University of Light Industry(Grant No.23XNKJTD0101).
文摘Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.
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Project supported by the Natural Science Foundation of Education Department of Sichuan Province ofChina (No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.
文摘We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.
文摘A way to extend operators in spaces of continuous functions to spaces of continuous set_valued functions is proposed. This extension is developed through the Steiner selections of the set_valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In Part Ⅱ of this series some applications to approximation theory will be shown.
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
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 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.
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 the National Natural Science Foundation of China(61703286,62394342,61890924,61991404)。
文摘This paper investigates set-valued state estimation of nonlinear systems with unknown-but-bounded(UBB)noises based on constrained polynomial zonotopes which is utilized to characterize non-convex sets.First,properties of constrained polynomial zonotopes are provided and the order reduction method is given to reduce the computational complexity.Then,the corresponding improved prediction-update algorithm is proposed so that it can be adapted to non-convex sets.Based on generalized intersection,the utilization of set-based estimation for attack detection is analyzed.Finally,an example is given to show the efficiency of our results.
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 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).
