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Feedback Mechanism-driven Mutation Reptile Search Algorithm for Optimizing Interpolation Developable Surfaces

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Journal of Bionic Engineering 2024年第1期21卷 527-571页

作者： Gang Hu Jiao Wang Xiaoni zhu Muhammad Abbas department of Applied mathematics Xi'an University of TechnologyXi'an 710054China School of Mechanical and Precision Instrument Engineering Xi'an University of TechnologyXi'an 710048China department of mathematics University of SargodhaSargodha 40100Pakistan

Curvature lines are special and important curves on *** is of great significance to construct developable surface interpolated on curvature lines in engineering *** this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search ***,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the ***,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving *** IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is *** last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is *** developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.

关键词： Reptile search algorithm Feedback mechanism Adaptive parameter Mutation strategy SGC-Ball interpolation developable surface Shape optimization

A Second-Order Image Denoising Model for Contrast Preservation

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Communications on Applied mathematics and Computation 2024年第2期6卷 1406-1427页

作者： Wei zhu department of mathematics University of AlabamaBox 870350TuscaloosaAL35487USA

In this work,we propose a second-order model for image denoising by employing a novel potential function recently developed in zhu(J Sci Comput 88:46,2021)for the design of a regularization *** to this new second-order derivative based regularizer,the model is able to alleviate the staircase effect and preserve image *** augmented Lagrangian method(ALM)is utilized to minimize the associated functional and convergence analysis is established for the proposed *** experiments are presented to demonstrate the features of the proposed model.

关键词： Image denoising Variational model Image contrast Augmented Lagrangian method(ALM)

Special Unipotent Representations of Simple Linear Lie Groups of Type A

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Acta Mathematica Sinica,English Series 2024年第3期40卷 707-716页

作者： Dan BARBASCH Jia Jun MA Bin Yong SUN Chen Bo zhu department of mathematics Cornell UniversityIthacaNY 14853USA School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China department of mathematics Xiamen University Malaysia CampusSepangSelangor Darul Ehsan43900Malaysia Institute for Advanced Study in mathematics&New Cornerstone Science Laboratory Zhejiang UniversityHangzhou 310058P.R.China department of mathematics National University of Singapore10 Lower Kent Ridge RoadSingapore 119076

Let G be a special linear group over the real,the complex or the quaternion,or a special unitary *** this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show... 详细信息

关键词： Special unipotent representations unitary representations coherent continuation Weyl group representations

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

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Acta Mathematica Scientia 2024年第1期44卷 386-404页

作者：丁卫汤彦朱月萍 School of Sciences Nantong UniversityNantong226007China department of mathematics Nantong Normal CollegeNantong226010China

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality *** this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

关键词： weighted multi-parameter local Hardy spaces atomic decomposition boundedness inhomogeneous Journéclass

Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen zhu Institute for Advanced Study in mathematics Zhejiang UniversityHangzhou 310058P.R.China Morningside Center of mathematics AMSSChinese Academy of SciencesBeijing 100190P.R.China New Cornerstone Lab Beijing International Center for Mathematical ResearchPeking Ui Beijing 100871P.R.China department of mathematics Massachusetts Institute of TechnologyCambridge MA 02139United States department of mathematics Stanford UniversityStanfordCA 94305United States

In this article,we study deformations of conjugate self-dual Galois *** study is ***,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called ***,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations

Transfer of Highest Weight Modules and Small Unipotent Representations

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Acta Mathematica Sinica,English Series 2024年第3期40卷 772-791页

作者： Hai An HE Jing Song HUANG Kayue Daniel WONG department of mathematics College of SciencesShanghai UniversityShanghai 200444P.R.China Newtouch Center for mathematics of Shanghai University Shanghai 200444P.R.China mathematics Research Center School of Science and EngineeringThe Chinese University of Hong KongShenzhen 518172P.R.China

We study the transfer between small special unipotent representations for all equal rank real forms of type E_(6) and E_(7). As a consequence, one can verify these modules are unitarity using the results of Wallach an... 详细信息

关键词： Unipotent representations Wallach representations Transfer of unitary modules

Distributed order estimation for continuous-time stochastic systems

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Control Theory and Technology 2024年第3期22卷 406-418页

作者： Xinghua zhu Zhixin Liu Xiaoming Hu Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China department of mathematics KTH Royal Institute of TechnologyStockholm 10044Sweden

In this paper,we investigate the distributed estimation problem of continuous-time stochastic dynamic systems over sensor networks when both the system order and parameters are *** propose a local information criterion(LIC)based on the L_(0)penalty *** minimizing LIC at the diffusion time instant and utilizing the continuous-time diffusion least squares algorithm,we obtain a distributed estimation algorithm to simultaneously estimate the unknown order and the parameters of the *** dealing with the effect of the system noises and the coupling relationship between estimation of system orders and parameters,we establish the almost sure convergence results of the proposed distributed estimation ***,we give a simulation example to verify the effectiveness of the distributed algorithm in estimating the system order and parameters.

关键词： Stochastic differential equations Sensor networks Distributed order estimation Cooperative excitation condition.Convergence

Two Applications of the ■■-Hodge Theory

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Chinese Annals of mathematics,Series B 2024年第1期45卷 137-150页

作者： Dingchang WEI Shengmao zhu Center of Mathematical Sciences Zhejiang UniversityHangzhou 310027China department of mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina

Using Hodge theory and Banach fixed point theorem,Liu and zhu developed a global method to deal with various problems in deformation *** this note,the authors generalize Liu-zhu's method to treat two deformation problems for non-Kahler *** apply the ■■-Hodge theory to construct a deformation formula for(p,q)-forms of compact complex manifold under deformations,which can be used to study the Hodge number of complex manifold under *** the second part of this note,by using the ■■-Hodge theory,they provide a simple proof of the unobstructed deformation theorem for the non-Kahler Calabi-Yau ■■-manifolds.

关键词： Complex structures Deformations (p,q)-Forms Non-Kahler Calabi-Yaumanifolds

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

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Communications on Applied mathematics and Computation 2024年第1期6卷 190-217页

作者： Fangyao zhu Juntao Huang Yang Yang department of Mathematical Sciences Michigan Technological UniversityHoughtonMI49931USA department of mathematics and Statistics Texas Tech UniversityLubbockTX79409USA

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive *** are several difficulties in constructing suitable numerical *** of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and ***,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step *** obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG *** traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass *** solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is *** the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and *** time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the *** methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be ***,it is not straightforward to combine the bound-preserving DG methods and the Patankar time *** positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target *** match the degree of freedom,we use polynomials on rectangular meshes for problems in two space *** evolve in time,we first read the polynomials at the Gaussian ***,suitable slope l

关键词： Compressible Euler equations Chemical reacting flows Bound-preserving Discontinuous Galerkin(DG)method Modified Patankar method