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Partial Collapsing Degeneration of Floer Trajectories and Adiabatic Gluing

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Acta Mathematica Sinica,English Series 2024年第1期40卷 161-249页

作者： Yong-Geun OH Ke ZHU Center for geometry and Physics Institute for Basic Science(IBS)79 Jigok-ro 127beon-gilNam-guPohang-siGyeongsangbuk-doKorea 37673&POSTECHGyeongsangbuk doKorea Department of mathematics and Statistics Minnesota State UniversityMankatoMN 56001USA

In the present paper,we study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic ε-family and its reversal adiabatic gluing,as the prototype of the partial collapsing degeneration of 2-dimensional(perturbed)J-holomorphic maps to 1-dimensional gradient *** consider the case when the Floer equations are S^(1)-invariant on parts of their domains whose adiabatic limit has positive length as ε→0,which we call thimble-flow-thimble *** main gluing theorem we prove also applies to the case with Lagrangian boundaries such as in the problem of recovering holomorphic disks out of pearly *** particular,our gluing theorem gives rise to a new direct proof of the chain isomorphism property between the Morse-Bott version of Lagrangian intersection Floer complex of L by Fukaya-Oh-Ohta-Ono and the pearly complex of L Lalonde and *** also provides another proof of the present authors’earlier proof of the isomorphism property of the PSS map without involving the target rescaling and the scale-dependent gluing.

关键词： Floer trajectory equation partial collapsing degeneration thimble-flow-thimble moduli space adiabatic gluing exponential decay estimates three-interval method

A new two-step variational model for multiplicative noise removal with applications to texture images

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Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 486-501页

作者： ZHANG Long-hui YAO Wen-juan SHI Sheng-zhu GUO Zhi-chang ZHANG Da-zhi School of mathematics Harbin Institute of TechnologyHarbin 150001China

Multiplicative noise removal problems have attracted much attention in recent *** additive noise,multiplicative noise destroys almost all information of the original image,especially for texture *** by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this *** the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field *** the isophote directions are constructed,an image is restored to fit the constructed directions in the second *** existence and uniqueness of the solution to the variational problems are *** these two steps,we use the gradient descent method and construct finite difference schemes to solve the ***,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the *** results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

关键词： multiplicative noise removal texture images total variation two-step variational method aug-mented Lagrangian method

A DIRECT DISCONTINUOUS GALERKIN METHOD FOR TIME FRACTIONAL DIFFUSION EQUATIONS WITH FRACTIONAL DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第1期42卷 156-177页

作者： Jingjun Zhao Wenjiao Zhao Yang Xu School of mathematics Harbin Institute of TechnologyHarbin 150001China

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary *** well-posedness for the weak solutions is studied.A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes,together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh,and then the fully discrete scheme is ***,the stability and the error estimate for the full scheme are analyzed in *** experiments are also given to illustrate the effectiveness of the proposed method.

关键词： Time fractional diffusion equation Numerical stability Convergence

On a Formation of Singularities of Solutions to Soliton Equations Represented by L,A,B-triples

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Acta Mathematica Sinica,English Series 2024年第1期40卷 406-416页

作者： Iskander A.TAIMANOV Novosibirsk State University 630090 Novosibirskand Sobolev Institute of Mathematics630090 NovosibirskRussia

We discuss the mechanism of formation of singularities of solutions to the Novikov-Veselov,modified Novikov-Veselov,and Davey-Stewartson II(DSII)equations obtained by the Moutard type *** equations admit the L,A,B-triple presentation,the generalization of the L,Apairs for 2+1-soliton *** relate the blow-up of solutions to the non-conservation of the zero level of discrete spectrum of the *** also present a class of exact solutions,of the DSII system,which depend on two functional parameters,and show that all possible singularities of solutions to DSII equation obtained by the Moutard transformation are indeterminancies,i.e.,points when approaching which in different spatial directions the solution has different limits.

关键词： Soliton equation blow up Davey-Stewartson equation Moutard transformation

Wormhole solutions under the effect of dark matter in f(R,L_(m))gravity

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Communications in Theoretical Physics 2024年第5期76卷 102-113页

作者： Lakhan V Jaybhaye Moreshwar Tayde PK Sahoo Department of mathematics Birla Institute of Technology and Science-PilaniHyderabad CampusHyderabad-500078India

In the background of f(R,L_(m))gravity,this work investigates three distinct dark matter halo profiles to test the possibility of generalised wormhole geometry within the galactic halo *** current study aims to accomplish these goals by examining various dark matter profiles including universal rotation curves(URC),Navarro-Frenk-White(NFW)model-Ⅰ,and NFW model-Ⅱinside two distinct f(R,L_(m))gravity *** to the f(R,L_(m))=R/2+L^(a)_(m)model,the dark matter(DM)halo density profiles produce suitable shape functions that meet all the necessary requirements for exhibiting the wormhole geometries with appropriate choice of free *** addition,to examine DM profiles under the f(R,L_(m))=R/2+(1+λR)L_(m) model,we consider a specific shape ***,we observed that the derived solution from both two models violates the null energy constraints,confirming that the DM supports wormholes to maintain in the galactic halo.

关键词： f(R L_(m))gravity wormhole dark matter(Some figures may appear in colour only in the online journal)

A new quantity in Finsler geometry

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Science China mathematics 2024年第4期67卷 883-890页

作者： Xiaohuan Mo Xiaoyang Wang Key Laboratory of Pure and Applied mathematics School of Mathematical SciencesPeking UniversityBeijing 100871China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study a new Finslerian quantity■defined by the T-curvature and the angular metric *** show that the■-curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature but also has a vanishing *** find that the■-curvature is closely related to the Riemann curvature,the Matsumoto torsion and theΘ-*** solve ***’s open problem in terms of the■-***,we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the■-curvature,generalizing a theorem previously only known in the case of negatively curved Finsler metrics of scalar flag curvature.

关键词： Finsler metric Finslerian quantity T-curvature -curvature Randers metric

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY discrete FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

New black-to-white hole solutions with improved geometry and energy conditions

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Science China(Physics,Mechanics & Astronomy) 2024年第7期67卷 30-43页

作者： Zhongwen Feng Yi Ling Xiaoning Wu Qingquan Jiang School of Physics and Astronomy China West Normal UniversityNanchong 637009China institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China School of Physics University of Chinese Academy of SciencesBeijing 100049China institute of mathematics Academy of Mathematics and System Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China

We construct new black-to-white hole solutions which connect the geometry of spacetime at some gluing surface inside the *** continuity of the metric can be guaranteed up to the arbitrary order which is controlled by the power factor *** sort of black-to-white holes is characterized by the sub-Planckian scalar curvature,independent of the mass of black-to-white *** importantly,we show that the energy condition is only violated within a small region near the gluing *** geodesics of particles within the region from black hole to white hole is also *** turns out that the matter falling into the black hole may pass through the center without singularity and come out from the white *** scenario provides novel ideas for understanding the information loss paradox in traditional black hole physics.

关键词： regular black hole energy condition singularity quantum gravity