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Neural Operators with Adaptive Spectral and Low-Rank Representations 认领 引用
1
作者 Nikita Sakovich Dmitry Aksenov +1 位作者 Ekaterina Pleshakova Sergey Gataullin 《Computers, Materials & Continua》 SCIE EI 2026年第9期2204-2222,共19页
Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling.Existing architectures,however,typically ... Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling.Existing architectures,however,typically rely on a single representation of the input function—either purely pointwise,as in DeepONet,or purely spectral,as in Fourier Neural Operators—which limits their ability to simultaneously capture local variability and global structure.In this work,we propose NOASLRR,a neural operator that integrates three complementary branches within a unified DeepONet-style formulation:a pointwise MLP embedding,a spectral branch based on Chebyshev polynomial coefficients,and a low-rank linear embedding.The three representations are fused through two learnable sigmoid gating mechanisms that adaptively balance structured inductive biases against unstructured expressivity in an input-dependent manner.We provide a theoretical guarantee showing that the proposed architecture can uniformly approximate any continuous operator admitting a decomposable structure,and we validate the method on three canonical PDE benchmarks:the heat equation,the viscous Burgers equation,and the Laplace equation with Dirichlet boundary conditions.On all three benchmarks NOASLRR converges faster and reaches substantially lower mean squared error than DeepONet and FNO baselines—for the heat equation the final MSE is reduced from 1.1×10⁻³(DeepONet)and 2.9×10⁻²(FNO)to 3.4×10⁻⁴,with comparable improvements on the Burgers and Laplace equations.Ablation experiments further confirm that each of the three branches contributes to the accuracy gains,while the parameter overhead relative to DeepONet remains moderate thanks to the low-rank factorization. 展开更多
关键词 Neural operators operator learning DeepONet spectral representation Chebyshev polynomials low-rank approximation adaptive gating partial differential equations
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Lp→LqEstimates for Stein’s Spherical Maximal Operators 认领 引用
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作者 Naijia Liu Minxing Shen +1 位作者 Liang Song Lixin Yan 《Analysis in Theory and Applications》 CSCD 2026年第1期90-108,共19页
In this article we consider a modification of the Stein’s spherical maximal operator of complex order a on Rn:■We show that when n≥,suppose||mα[1,2]f||Lq(Rn)≤C||f||Lp(Rn)holds for someα∈C,... In this article we consider a modification of the Stein’s spherical maximal operator of complex order a on Rn:■We show that when n≥,suppose||mα[1,2]f||Lq(Rn)≤C||f||Lp(Rn)holds for someα∈C,p,q≥,then we must have that q≥p and Reα≥σn(p,q):=max{1/p-n/q,n+1/2p-n-1/2(1/q+1),n/p-n+1}.Conversely,we show that Mα[1,2]is bounded from Lp(Rn)to Lq(Rn)provided that q≥p and Reα>σ2(p,q)for n=2;and Reα>max{σn(p,q),1/(2p)-(n-2)/(2q)-(n-1)/4}for n>2.The range ofα,p and q is almost optimal in the case when either n=2,or a=0,or(p,q)lies in certain regions for n>2. 展开更多
关键词 spherical maximal operators Lp-improving estimates wave equation local smoothing estimates
Approximation properties by Bézier-Baskakov-Schurer-Szász operators based on Gould-Hopper polynomials 认领 引用
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作者 Naim L.Braha Shagufta Rahman Mohammad Mursaleen 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第2期299-313,共15页
In this study,we introduce a Gould-Hopper polynomial based Bézier variation of the Baskakov-Schurer-Szàsz operators.First,we examine the uniform convergence and error bound using the Ditzian-Totik modulus of... In this study,we introduce a Gould-Hopper polynomial based Bézier variation of the Baskakov-Schurer-Szàsz operators.First,we examine the uniform convergence and error bound using the Ditzian-Totik modulus of smoothness.Next,we obtain the quantitative Voronovskaya and Grüss-Voronovskaya type theorems.Furthermore,we investigate the rate of convergence by using weighted modulus of continuity and for a class of Lipschitz function. 展开更多
关键词 Bézier operators Gould-Hopper polynomials Korovkin type theorem Voronovskaya type theorem rate of convergence Grüss-Voronovskaya type theorem
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THE STRONGLY SINGULAR CALDERÓN-ZYGMUND OPERATORS AND THEIR COMMUTATORS ON MUSIELAK-ORLICZ HARDY SPACES 认领 引用
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作者 Xiao WANG Wenchang SUN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1643-1658,共16页
In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing... In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing a specific subspace of BMO,we further show that the commutators generated by functions within this subspace and strongly singular Calderón-Zygmund operators remain bounded under the same mapping framework. 展开更多
关键词 strongly singular Calderón-Zygmund operators commutators Musielak-Orlicz Hardy spaces
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ERRATUM TO:LOG-CONCAVITY OF THE FIRST DIRICHLET EIGENFUNCTION OF SOME ELLIPTIC DIFFERENTIAL OPERATORS AND CONVEXITY INEQUALITIES FOR THE RELEVANT EIGENVALUE 认领 引用
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作者 Andrea COLESANTI 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期1036-1036,共1页
This note contains some corrections to the paper:Colesanti A.Log-concavity of the first Dirichlet eigenfunction of some elliptic differential operators and convexity inequalities for the relevant eigenvalue.Acta Mathe... This note contains some corrections to the paper:Colesanti A.Log-concavity of the first Dirichlet eigenfunction of some elliptic differential operators and convexity inequalities for the relevant eigenvalue.Acta Mathematica Scientia,2025,45B(1):143-152. 展开更多
关键词 log concavity dirichlet eigenfunction elliptic differential operators convexity inequalities
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Several New Integral and Discrete Operators Based on Special Function 认领 引用
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作者 Anjali Man Singh Beniwal Mohd Atif Wahid 《Journal of Harbin Institute of Technology(New Series)》 CAS 2026年第3期88-96,共9页
This study uses the classical orthogonal Laguerre polynomials as a foundation for constructing new operators.We present the Laguerre-Pǎltǎnea operator based on the modified Laguerre polynomial that facilitates the a... This study uses the classical orthogonal Laguerre polynomials as a foundation for constructing new operators.We present the Laguerre-Pǎltǎnea operator based on the modified Laguerre polynomial that facilitates the approximation of integrable functions.Furthermore,some new discrete and integral-type operators derived from the combination of the Laguerre operator,Laguerre-Pǎltǎnea operator,and Szász-Mirakyan operator are proposed.We compare the error values of the operators and emphasize which operator provides the best approximation.Ultimately,Mathematica software is utilized to generate graphs and infer the convergence of the stated operators to a function for various parameter values under consideration.Additionally,we compare each specified operator and observe that the proposed Laguerre-Pǎltǎnea operator under discussion offers a better approximation than the other potential compositions. 展开更多
关键词 Laguerre polynomial convergence properties Pǎltǎnea operators errors numerical interpretation geometric comparison
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Deep Reinforcement Learning Based on Search Space Independent Operators for Black-Box Continuous Optimization 认领 引用
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作者 Ye Tian Yisai Liu +1 位作者 Shangshang Yang Xingyi Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第4期913-925,共13页
Deep reinforcement learning(DRL)has demonstrated exceptional capabilities in combinatorial optimization,which automatically devises policies for solution construction and optimizer refinement.DRL is particularly adept... Deep reinforcement learning(DRL)has demonstrated exceptional capabilities in combinatorial optimization,which automatically devises policies for solution construction and optimizer refinement.DRL is particularly adept in generating training samples by itself,thereby providing the flexibility to solve a variety of combinatorial optimization problems without supervision.While DRL takes actions according to states extracted from problem-specific information,it cannot be directly applied to black-box continuous optimization lacking explicit information.To address this issue,this paper proposes a search space independent operator based DRL method for black-box continuous optimization.It conceptualizes the optimization process driven by search space independent operators as a Markov decision process,wherein actions are defined as operators and states are extracted from solutions generated by operators.In contrast to other DRLassisted metaheuristics,the proposed method does not rely on any existing metaheuristic.Instead,it innovates by creating totally new operators,able to surpass the performance boundaries of existing metaheuristics.Compared with state-of-the-art metaheuristics and DRL methods,the proposed method shows significantly faster convergence speed on challenging continuous optimization problems. 展开更多
关键词 Black-box optimization continuous optimization metaheuristic reinforcement learning search operator
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MEAN LI-YORKE CHAOS FOR A SEQUENCE OF OPERATORS ON BANACH SPACES 认领 引用
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作者 Jian LI Xinsheng WANG Jianjie ZHAO 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1187-1207,共21页
In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and ... In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and submultiplicative sequences of bounded linear operators are also studied.Furthermore,several criteria for mean Li-Yorke chaos are established. 展开更多
关键词 linear operator mean Li-Yorke chaos absolutely mean irregular vector mean equicontinuity mean sensitivity submultiplicative sequence
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Boundedness of Pesudo-differential Operators on Besov Spaces 认领 引用
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作者 DAI Jiawei LU Yanfei +1 位作者 ZHENG Ruxiu HUANG Qiang 《数学进展》 CSCD 北大核心 2026年第3期578-588,共11页
In this paper,we investigate the boundedness of pseudo-differential operators Tαon Besov spaces Bp,qswith symbol a∈Sρ,δm,0≤ρ≤δ<1.We obtain that Tαis bounded from Bp,qs+m-mc(p)to ... In this paper,we investigate the boundedness of pseudo-differential operators Tαon Besov spaces Bp,qswith symbol a∈Sρ,δm,0≤ρ≤δ<1.We obtain that Tαis bounded from Bp,qs+m-mc(p)to Bp,qs,where■. 展开更多
关键词 pseudo-differential operator Besov space Hörmander class
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THE BOUNDEDNESS OF INHOMOGENEOUS CALDERÓN-ZYGMUND CONVOLUTION OPERATORS ON LOCAL PRODUCT HARDY SPACES 认领 引用
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作者 Shaoyong HE Jiecheng CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期99-111,共13页
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
关键词 local Hardy space Lipschitz space inhomogeneous Calderón-Zygmund operator discrete Calderón identity
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A Two-Stage,Nested Co-Optimization Framework with Adaptive Evolutionary Operators for Component-Level Constellation Morphology and Mission Planning 认领 引用
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作者 Chao Zhang Yunfeng Dong 《Computers, Materials & Continua》 SCIE EI 2026年第10期760-782,共23页
The missile warning constellation is fundamental to national territorial security and has significant strategic and military value.This study proposes a two-stage,nested co-optimization framework with adaptive evoluti... The missile warning constellation is fundamental to national territorial security and has significant strategic and military value.This study proposes a two-stage,nested co-optimization framework with adaptive evolutionary operators,termed TNC-A,to address challenges in genetic representation,evaluation distortion,the curse of dimensionality,and search inefficiency within the co-optimization of component-level constellation morphology and mission planning.A hybrid encoding scheme combining tree-structured and real-valued vector representations was adopted to encode all optimization variables,including constellation configuration,component-level unified platform information,and mission planning parameters.Second,a multi-stage optimization strategy integrated with a double-nested structure was implemented.This approach mitigates the dimensionality curse and addresses the evaluation distortion inherent in traditional engineering methods.Third,adaptive evolutionary operators based on online contribution learning were designed to dynamically adjust the search focus using historical experience,thereby significantly enhancing search efficiency.The simulation results demonstrate the effectiveness and practical applicability of TNC-A,demonstrating its superiority over comparative algorithms under a constrained function evaluation budget.TNC-A reduced the average and standard deviation of the optimization results by 13.7%and 65.3%,respectively,compared with the baseline of traditional engineering methods. 展开更多
关键词 Co-optimization double-nested optimization structure multi-stage optimization strategy adaptive evolutionary operators component-level missile warning constellation
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Direct and Inverse Approximation Theorems for Linear Combinations of Szász-Mirakjan-Durrmeyer Operators in Orlicz Spaces 认领 引用
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作者 Han Lingxiong 《数学理论与应用》 2026年第2期80-90,共11页
This paper investigates approximation problems in Orlicz spaces generated by Young functions.Utilizing Jensen’s inequality and the equivalence between the K-functional and the modulus of smoothness,we establish both ... This paper investigates approximation problems in Orlicz spaces generated by Young functions.Utilizing Jensen’s inequality and the equivalence between the K-functional and the modulus of smoothness,we establish both direct and inverse theorems for approximation by linear combinations of Szász-Mirakjan-Durrmeyer operators in these spaces. 展开更多
关键词 Direct theorem;Inverse theorem;K-functional;Orlicz space;Szász-Mirakjan-Durrmeyer operator
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TRUNCATED TOEPLITZ OPERATORS ON A CLASS OF QUOTIENT MODULES OVER THE BIDISK 认领 引用
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作者 Hong ZOU Tao YU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1581-1602,共22页
In this paper,we study truncated Toeplitz operators and little truncated Hankel operators on Np,q-type quotient modules over the bidisk.We find a necessary and sufficient condition for a truncated Toeplitz operator to... In this paper,we study truncated Toeplitz operators and little truncated Hankel operators on Np,q-type quotient modules over the bidisk.We find a necessary and sufficient condition for a truncated Toeplitz operator to be zero,as a result,we find a characterization equation for bounded truncated Toeplitz operators.We also find a necessary and sufficient condition for a little truncated Hankel operator to be zero operator.This paper also studies the spectra,joint spectra and the essential spectra of truncated Toeplitz operators with some special symbols. 展开更多
关键词 truncated Toeplitz operator little truncated Hankel operator Hardy space bidisk spectrum
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Approximation by modified Durrmeyer type Jakimovski-Leviatan operators 认领 引用
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作者 Qing-bo Cai Şule Yüksel Güngör +1 位作者 BayramÇekim Mehmet AliÖzarslan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2025年第3期709-724,共16页
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
关键词 modulus of continuity Appell polynomials Durrmeyer operators Jakimovski-Leviatan operators Lipschitz type function space
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Lipschitz Estimates for the Commutators of Fractional Hardy and Hardy-Littlewood-Pólya Operators on Grand p-adic Variable Herz Spaces 认领 引用
15
作者 常云鹏 武江龙 《数学进展》 CSCD 北大核心 2026年第2期419-430,共12页
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.
关键词 p-adic field fractional Hardy operator Hardy-Littlewood-Pólya operator grand variable Herz space commutator
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Rota-Baxter Operators on pre-Lie Coalgebras 认领 引用
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作者 CHENG Yong-sheng CUI Ya-xin +1 位作者 DING Wen-jing WU Lin-li 《Chinese Quarterly Journal of Mathematics》 2026年第2期139-146,共8页
In the present paper, we mainly study Rota-Baxter operators(of weight zero)on pre-Lie coalgebras. In particular, the invertible Rota-Baxter operators on pre-Lie coalgebras is well studied, and some fundamental results... In the present paper, we mainly study Rota-Baxter operators(of weight zero)on pre-Lie coalgebras. In particular, the invertible Rota-Baxter operators on pre-Lie coalgebras is well studied, and some fundamental results of the invertible Rota-Baxter relations and derivations on pre-Lie coalgebras are given. Furthermore, using the RotaBaxter operators on pre-Lie coalgebras, some new pre-Lie coalgebraic structures are obtained. 展开更多
关键词 Pre-Lie coalgebras Rota-Baxter operator Derivations
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A Symmetric Mountain Pass Lemma and Its Application to an Equation for a Class of Quasilinear Elliptic Operators in a Variable Exponent Sobolev Space 认领 引用
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作者 Junichi Aramaki 《Communications in Mathematical Research》 CSCD 2026年第2期136-164,共29页
The purpose of this paper is to solve equation for a class of quasilinear elliptic operators containing the p(·)-Laplacian and the mean curvature operator with mixed boundary conditions.More precisely,we are conc... The purpose of this paper is to solve equation for a class of quasilinear elliptic operators containing the p(·)-Laplacian and the mean curvature operator with mixed boundary conditions.More precisely,we are concerned with the problem that has the Dirichlet condition in one part of the boundary and the Steklov condition in another.Using a symmetric mountain pass lemma and its corollary,we show the existence of infinitely many weak solutions of the equation and the boundedness of the sequence of solutions,or convergence to zero of the sequence of solutions according to the hypotheses about the data functions. 展开更多
关键词 Mountain pass lemma p(·)-Laplacian type equation mean curvature operator mixed boundary value problem
Boundedness of Hausdorff Operators on Amalgam Spaces 认领 引用
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作者 HUAN Wenqing LI Xiang 《数学进展》 CSCD 北大核心 2026年第4期874-884,共11页
In this paper,we study several kinds of Hausdorff operators on amalgam spaces,which include the amalgam Morrey space and the amalgam Campanato space.As a corollary,we give the sharp bound of Hausdorff operators on the... In this paper,we study several kinds of Hausdorff operators on amalgam spaces,which include the amalgam Morrey space and the amalgam Campanato space.As a corollary,we give the sharp bound of Hausdorff operators on the classical Campanato space.Furthermore,we also discuss the boundedness of the multilinear Hausdorff operator on amalgam space.These results substantially generalize some classical results. 展开更多
关键词 Hausdorff operator multilinear Hausdorff operator amalgam Campanato space amalgam Morrey space
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Hyponormal Block Toeplitz Operators on the Weighted Bergman Space with Circulant Symbols 认领 引用
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作者 FU Guangyang ZHOU Jiang 《数学进展》 CSCD 北大核心 2026年第1期183-191,共9页
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)=∑Ni=1 Aiziand... 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)=∑Ni=1 Aiziand G(z)=∑Ni=1 A−izi,Aiae culants. 展开更多
关键词 block Toeplitz operator hyponormal weighted Bergman space circulant commutator
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Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets,Aggregation Operators and Basic Uncertainty Information Granule 认领 引用 被引量：1
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作者 Anastasios Dounis Ioannis Palaiothodoros Anna Panagiotou 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第1期759-811,共53页
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
关键词 Medical diagnosis multi-attribute group decision-making(MAGDM) q-ROFS IVq-ROFS BUI aggregation operators similarity measures inverse score function
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