检索结果-南通市图书馆

Communications in mathematical Research 2024年第1期40卷 1-29页

作者： Elizabeth Hawkins Leo G.Rebholz Duygu Vargun department of mathematical sciences Clemson UniversityClemsonSC 29634USA

We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.

关键词： Navier-Stokes equations projection method penalty method continuous data assimilation

Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2024年第3期45卷 441-462页

作者： Jingnan JU Shanjian TANG Shanghai Center for mathematical sciences Fudan University department of Finance and Control sciences School of Mathematical Sciences Fudan University

This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short) with bounded terminal conditions. The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z. The existence and uniqueness results are given to these BSDEs. As an application, an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.

关键词： Markovian BSDE Quadratic growth Unbounded sub-quadratic term coefficients Coupled FBSDE 60H10

NSNO:Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2024年第2期37卷 413-440页

作者： CHEN Fukai LIU Ziyang LIN Guochang CHEN Junqing SHI Zuoqiang department of mathematical sciences Tsinghua UniversityBeijing 100084China Yau mathematical sciences Center Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing Institute of mathematical sciences and Applications Beijing 101408China

In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions.Helmholtz equation is a crucial partial differential equation(PDE)with applications in various scientific and engineering fields.However,efficient solver of Helmholtz equation is still a big challenge especially in the case of high wavenumber.Recently,deep learning has shown great potential in solving PDEs especially in learning solution operators.Inspired by Neumann series in Helmholtz equation,the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale feature.Extensive experiments show that the proposed NSNO significantly outperforms the state-of-the-art FNO with at least 60%lower relative L^(2)-error,especially in the large wavenumber case,and has 50%lower computational cost and less data requirement.Moreover,NSNO can be used as the surrogate model in inverse scattering problems.Numerical tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.

关键词： Helmholtz equation inverse problem neumann series neural network solution operator

Equivariant Tautological Integrals on Flag Varieties

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2024年第3期45卷 463-486页

作者： Xiaobo ZHUANG department of mathematical sciences Zhejiang Sci-Tech University

The author apples the Atiyah-Bott-Berline-Vergne formula to the equivariant tautological integrals over flag varieties of types A, B, C, D, and recovers the formulas expressing the integrals as iterated residues at in... 详细信息

关键词： Localization Flag variety Residue 55N91 14M15

A Population Dynamics Approach to the Distribution of Space Debris in Low Earth Orbit

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2024年第1期6卷 340-353页

作者： John Jurkiewicz Peter Hinow department of mathematical sciences University of Wisconsin-MilwaukeeMilwaukeeWI53201USA

The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space.This debris population continues to grow due to ground launches,the loss of external parts from space ships,and uncontrollable collisions between objects.A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical.Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy.We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth.Finally,we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.

关键词： Population dynamics Space debris Kessler syndrome Diffusion Low-Earth orbit

On hypersurfaces of H2×H2

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2024年第2期67卷 339-366页

作者： Dong Gao Hui Ma Zeke Yao School of Science Beijing University of Civil Engineering and Architecture department of mathematical sciences Tsinghua University

In this paper, we study hypersurfaces of H2× H2. We first classify the hypersurfaces with constant principal curvatures and constant product angle functions. Then we classify homogeneous hypersurfaces and isoparametric hypersurfaces, respectively. Finally, we classify the hypersurfaces with at most two distinct constant principal curvatures, as well as those with three distinct constant principal curvatures under some additional conditions.

关键词： constant principal curvature homogeneous hypersurface isoparametric hypersurface 53C42 53B25 53C40

Dilation,discrimination and Uhlmann's theorem of link products of quantum channels

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Chinese Physics B 2024年第3期33卷 201-206页

作者：雷强操刘桁 Asutosh Kumar 武俊德 School of mathematical sciences Harbin Institute of TechnologyHarbin 150001China department of Physics Gaya CollegeMagadh UniversityRampurGaya 823001India School of mathematical sciences Zhejiang UniversityHangzhou 310027China

We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

关键词： quantum channels link products Stinespring dilation theorem Uhlmann's theorem

Emergent Geometry of KP Hierarchy

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第1期40卷 3-25页

作者： Jian ZHOU department of mathematical sciences Tsinghua UniversityBeijng 100084P.R.China

We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of so... 详细信息

关键词： KP hierarchy tau-functions spectral curves

On the Bicanonical Map of Algebraic Threefolds of General Type

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年

作者： Meng CHEN Chen JIANG Jian Shi YAN School of mathematical sciences & Shanghai Center for mathematical sciences Fudan University Shanghai Center for mathematical sciences & School of mathematical sciences Fudan University department of Mathematics Northeastern University

We answer an open problem of the first author and Zhang(see Open Problem 6.4(3) in Math. Z. 258(2008), 565–585) and prove that, for any nonsingular projective 3-fold of general type with the geometric genus greater t...

关键词：

The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第3期40卷 885-934页

作者： Shi Lin YU department of Mathematics School of Mathematical SciencesXiamen UniversityXiamen 361005P.R.China

In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups.Only even quantizations were considered there.In this paper,these results are generalized to the case of general quantizations with arbitrary periods.The key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over X.As an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.

关键词： Coadjoint orbit method deformation quantization Harish-Chandra modules semisimple Liegroups