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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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The Characterization of Self-adjoint Domains of Two-interval Odd Order Differential Operators 认领 引用
2
作者 WANG Linyu HAO Xiaoling LI Kun 《数学进展》 CSCD 北大核心 2025年第4期784-802,共19页
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
关键词 self-adjoint domain odd order differential operator two-interval
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Neural Operators with Adaptive Spectral and Low-Rank Representations 认领 引用
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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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ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS 认领 引用 被引量：3
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作者 杨杰 王宇钊 陈文艺 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期387-393,共7页
It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1... It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc. 展开更多
关键词 Hardy space commutator Pseudo-differential operator LMO space
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LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION 认领 引用 被引量：1
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作者 许跃生 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1984年第3期1359-1364,共6页
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun... In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given. 展开更多
关键词 LEIBNIZ S FUNCTION FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN
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Inverse Differential Operators in Time and Space 认领 引用
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作者 Edwin Eugene Klingman 《Journal of Applied Mathematics and Physics》 2023年第12期3789-3799,共11页
When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to ... When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of  is sought in the form  if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations. 展开更多
关键词 Matrix-Inverse Differential Operators Green’s Functions Dirac’s Equation Wave Equations Inverse Curl Operator
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DIFFERENTIAL OPERATORS OF INFINITE ORDER IN THE SPACE OF RAPIDLY DECREASING SEQUENCES 认领 引用
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作者 M.MALDONADO J.PRADA M.J.SENOSIAIN 《Acta Mathematica Scientia》 SCIE CSCD 2016年第2期325-333,共9页
We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D）... We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D） =^∞∑k=0φkD^k.φk constant numbers an a power of D.Dn, meaning, is there a isomorphism X （from s onto s） such that Xφ（D） = D^nX？. We prove that if φ（D） is equivalent to Dn, then φ（D） is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n = 1. 展开更多
关键词 Ordinary differential operators sequence spaces operators on function spaces
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Spectrum of a class of fourth order left-definite differential operators 认领 引用 被引量：2
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作者 GAO Yun-lan SUN Jiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第1期51-56,共6页
The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-def... The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤… 展开更多
关键词 left-definite differential operator right-definite differential operator Krein space spectrum,eigenvalue.
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Realization of the N(odd)-Dimensional Quantum Euclidean Space by Differential Operators 认领 引用 被引量：1
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作者 LIYun JINGSi-Cong 《Communications in Theoretical Physics》 SCIE CAS 2004年第2期175-178,共4页
The quantum Euclidean space is a kind of noncommutative space that is obtained from ordinary Euclidean space by deformation with parameter q. When N is odd, the structure of this space is similar to . Motivated by rea... The quantum Euclidean space is a kind of noncommutative space that is obtained from ordinary Euclidean space by deformation with parameter q. When N is odd, the structure of this space is similar to . Motivated by realization of by differential operators in , we give such realization for and cases and generalize our results to (N odd) in this paper, that is, we show that the algebra of can be realized by differential operators acting on C&#x221e; functions on undeformed space . 展开更多
关键词 noncommutative quantum space differential operator
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abstract Operators and Higher-order Linear Partial Differential Equation 认领 引用
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作者 毕光庆 毕越凯 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第4期511-515,共5页
We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of par... We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations. 展开更多
关键词 partial differential equations abstract operator symbol laplace transform
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ON APPROXIMATION OF SMOOTH FUNCTIONS FROM NULL SPACES OF OPTIMAL LINEAR DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS 认领 引用
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作者 Vesselin Vatchev 《Analysis in Theory and Applications》 2011年第2期187-200,共14页
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients... For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f. 展开更多
关键词 approximation of analytic function differential operator fundamental set of solutions
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RELATIONS OF DERIVATIVE ALGEBRA AND RING OF DIFFERENTIAL OPERATORS IN CHARACTERISTIC p>0 认领 引用
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作者 ZHANG Jiang-feng 《Journal of Shanghai Jiaotong university(Science)》 2002年第1期110-114,共5页
Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that th... Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that there is a differential operator of order p that does not belong to the derivative algebra. By these results, is follows that the derivative algebra is Morita equivalent to K[x p 1,…,x p n] , and hence its global homological dimension, Krull dimension, K 0 group and some other properties are got. 展开更多
关键词 derivative algebra ring of differential operators Morita equivalence
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Some Properties of First Order Differential Operators 认领 引用
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作者 Servais Cyr Gatse 《Advances in Pure Mathematics》 2019年第11期934-943,共10页
We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give so... We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give some properties on the algebra of smooth functions. The Dirac mass at a point is the best example of first order differential operators at this point. This allows to construct a basis of this set and its dual basis. 展开更多
关键词 Commutative Algebra Differential Operators Module of Differentials
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On the Spectra of General Ordinary Quasi-Differential Operators and Their L2w-Solutions 认领 引用
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作者 Sobhy El-Sayed Ibrahim 《Advances in Pure Mathematics》 2022年第3期186-205,共20页
In this paper, we consider the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ+ on the interval [a,b). We shall show in the case of one singular end-poi... In this paper, we consider the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ+ on the interval [a,b). We shall show in the case of one singular end-point and under suitable conditions that all solutions of a general ordinary quasi-differential equation are in the weighted Hilbert space provided that all solutions of the equations and its adjoint are in . Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions may be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while the others are new. 展开更多
关键词 General Ordinary Quasi-Differential Expressions Regular and Singular End-Points Singular Differential Operators Essential Spectra Point Spectra and Regularity Fields
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F-Multiautomata on Join Spaces Induced by Differential Operators 认领 引用
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作者 Rajab Ali Borzooei Hamid Reza Varasteh Abbas Hasankhani 《Applied Mathematics》 2014年第9期1386-1391,共6页
In this paper, we introduce the notion of fuzzy multiautomata and we investigate the hyperstructures induced by the linear second-order differential operators which can be used for construction of fuzzy multiautomata ... In this paper, we introduce the notion of fuzzy multiautomata and we investigate the hyperstructures induced by the linear second-order differential operators which can be used for construction of fuzzy multiautomata serving as a theoretical background for modeling of processes. 展开更多
关键词 Fuzzy Systems Differential Operators Hyperalgebraic Structures Multiautomata
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ONSOMELINEARISOMORPHICTHEOREMSFORCERTAINNONSYMMETRICDIFFERENTIALOPERATORSOFSIXTHORDERWITHPARAMETER 认领 引用
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作者 Zhang Xingtai Liu Yingfan Science of College, NUAA29 Yudao Street, Nanjing 210016, P. R. China 《Transactions of Nanjing University of Aeronautics and Astronautics》 1996年第1期112-117,共6页
This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large ext... This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large extent, explain and control the stability of some objects in their moving processes. 展开更多
关键词 differential operator regularity stability linear isomorphism Opial inequality interpolating inequality
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Generators of Rings of Differential Operators on a Class of k-algebras 认领 引用
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作者 Liu Haixia Wang Mingsheng 《Chinese Quarterly Journal of Mathematics》 1997年第2期1-4,共4页
In this paper,we find an explicit method to calculate generators of rings of differential operators on a class of k-algebras.
关键词 rings of differential operators singular point
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MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators 认领 引用 被引量：3
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作者 Thabet Abdeljawad Muhammad Bilal Riaz +1 位作者 Syed Tauseef Saeed Nazish Iftikhar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第2期821-841,共21页
The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded ... The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators. 展开更多
关键词 MHD Maxwell fluid fractional differential operator heat generation absorption thermal effect non-singular kernels
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Boundedness for Multilinear Operators of Pseudo-Differential Operators 认领 引用
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作者 Jiasheng Zeng Rongping Chen +2 位作者 Jiangang Liu Xiaojing Wang Chunsheng Liu 《Advances in Pure Mathematics》 2023年第7期449-462,共14页
In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the mu... In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the multilinear operators. 展开更多
关键词 Multilinear Operator Pseudo-Differential Operator Sharp Function Estimate BMO
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Introduction to the Special Issue on Analytical and Numerical Solution of the Fractional Differential Equation 认领 引用
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作者 Ndolane Sene Ameth Ndiaye 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第12期2849-2852,共4页
Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its u... Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions. 展开更多
关键词 mathematical physical sciences numerical solutions fractional diffusion equationsin fractional operators fractional differential equations analytical solutions intelligent artificial systemsamong
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