检索结果-南通市图书馆

Journal of Ocean Engineering and Science 2024年第5期9卷 489-507页

作者： Shailendra Singh S.Saha Ray National Institute of Technology Department of MathematicsRourkela 769008India

In this paper,a new eighth-order(1.1.-dimensional time-dependent extended KdV equation has been *** considered equation is being found completely integrable by using the Painlevéanalysis ***,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant *** auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed *** solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton ***-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered *** the results are being expressed graphically to signify the physical importance of the considered equation.

关键词： Higher-order KdV equation Painlevéanalysis Auto-Bäcklund transformation Simplified Hirota method

Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第2期40卷 595-618页

作者： Xi Yin ZHENG department of {1. Yunnan UniversityKunming 650091P.R.China

This paper first shows that for any p∈(1.2)there exists a continuously differentiable function f on l^(p)(and L^(p))such that the proximal subdifferential of f is empty everywhere,and hence it is not suitable to develop theory on proximal subdifferential in the classical Banach spaces l^(P)and L^(P) with p∈(1.2).On the other hand,this paper establishes variational analysis based on the proximal subdifferential in the framework of smooth Banach spaces of power type 2,which conclude all Hilbert spaces and all the classical spaces l^(P)and L^(P)with p∈(2,+∞).In particular,in such a smooth space,we provide the proximal subdifferential rules for sum functions,product functions,composite functions and supremum functions,which extend the basic results on the proximal subdifferential established in the framework of Hilbert *** of our main results are new even in the Hilbert space *** applications,we provide KKT-like conditions for nonsmooth optimization problems in terms of proximal subdifferential.

关键词： Smooth Banach space proximal subdifferential proximal normal cone KKT condition

维普期刊数据库

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

在线全文

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 501-532页

作者： Juntao Huang Wei Guo Yingda Cheng department of {1. and Statistics Texas Tech UniversityLubbockTX79409USA department of Computational {1. Science and EngineeringMichigan State UniversityEast LansingMI48824USA department of {1. Michigan State UniversityEast LansingMI48824USA

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software *** C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://***/JuntaoHuang/*** package is capable of treating a large class of high dimensional linear and nonlinear *** review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical *** further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

关键词： Adaptive sparse grid Discontinuous Galerkin High dimensional partial differential equation Software development

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied mathematics and Computation 2024年第2期6卷 1369-1405页

作者： Kevin Bui Yifei Lou Fredrick Park Jack Xin department of {1. University of CaliforniaIrvineIrvineCA 92697-3875USA department of {1. University of North CarolinaChapel HillChapel HillNC 27599.USA department of {1. and Computer Science Whittier CollegeWhittierCA 90602USA

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1.-αl_(2) *** convergence of the ADMM algorithm is *** the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation *** experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or *** compare the AITV method with its original convex TV and nonconvex TVP(O1.counterparts,showcasing the qualitative and quantitative advantages of our proposed method.

关键词： Image segmentation Non-convex optimization Mumford-Shah(MS)model Alternating direction method of multipliers(ADMMs) Proximal operator

High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

在线全文

维普期刊数据库

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 325-339页

作者： Zheng Chen Lin Mu department of {1. University of Massachusetts Dartmouth285 Old Westport RoadDartmouth02747MAUSA department of {1. University of GeorgiaAthens30602GAUSA

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random *** tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been ***,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been *** provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

关键词： Stochastic Galerkin scheme linear transport equations generalized polynomial approach stochastic asymptotic-preserving property

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

National Science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data Science Peking University Zuse Institute Berlin department of {1. and Computer Science Freie Universit?t Berlin Laboratory of mathematics and Applied mathematics(LMAM)and School of Mathematical Sciences Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

A new model of flow over stretching(shrinking)and porous sheet with its numerical solutions

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 381-397页

作者： Azhar Ali Dil Nawaz Khan Marwat Saleem Asghar department of {1. Islamia College Peshawar 25120Jamrod roadPeshawarKhyber PakhtunkhwaPakistan department of {1. COMSATS Institute of Information TechnologyPark RoadTarlai KalanIslamabad 45550Pakistan

The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this *** modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a ***,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one *** a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary *** final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and ***,we have recovered the classical results for special and appropriate values of the parameters(δ_(1.,δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special *** is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing *** result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible *** significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet

关键词： permeable stretching(shrinking)sheets sheet of variable thickness heat transfer numerical(dual)solutions stability analysis

维普期刊数据库

Nearest Neighbor Sampling of Point Sets Using Rays

在线全文

学校读者我要写书评

暂无评论

Communications on Applied mathematics and Computation 2024年第2期6卷 1131-1174页

作者： Liangchen Liu Louis Ly Colin B.Macdonald Richard Tsai department of {1. The University of Texas at Austin2515 SpeedwayAustinTX 78712USA Oden Institute for Computational Engineering and Sciences The University of Texas at Austin201 E24th StAustinTX 78712USA department of {1. University of British Columbia1984 Mathematics RdVancouverBCV6T1Z2Canada

We propose a new framework for the sampling,compression,and analysis of distributions of point sets and other geometric objects embedded in Euclidean *** approach involves constructing a tensor called the RaySense sketch,which captures nearest neighbors from the underlying geometry of points along a set of *** explore various operations that can be performed on the RaySense sketch,leading to different properties and potential *** information about the data set can be extracted from the sketch,independent of the ray *** integrals on point sets can be efficiently computed using the *** also present several examples illustrating applications of the proposed strategy in practical scenarios.

关键词： Point clouds Sampling Classification Registration Deep learning Voronoi cell analysis

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2024年第3期44卷 865-886页

作者：韩斌赖宁安 Andrei TARFULEA department of {1. Hangzhou Dianzi UniversityHangzhou310018China School of Mathematical Sciences Zhejiang Normal UniversityJinhua321004China department of {1. Louisiana State UniversityBaton Rouge70803USA

We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational *** first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity *** then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1. by showing that the linearized operator is a contraction mapping under the right circumstances.

关键词： thermal fluid equations energy-variational method well-posedness theory for PDE paraproduct calculus

维普期刊数据库

Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

在线全文

学校读者我要写书评

暂无评论

Communications on Applied mathematics and Computation 2024年第2期6卷 790-810页

作者： Howard Heaton Samy Wu Fung Stanley Osher Typal Research Typal LLCLos AngelesUSA department of Applied {1. and Statistics Colorado School of MinesGoldenUSA department {1. UCLALos AngelesUSA

Computing tasks may often be posed as optimization *** objective functions for real-world scenarios are often nonconvex and/or ***-of-the-art methods for solving these problems typically only guarantee convergence to local *** work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective *** core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing *** of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi *** numerical examples illustrate global convergence.

关键词： Global optimization Moreau envelope Hamilton-Jacobi Hopf-Lax-Cole-Hopf Proximals Zero-order optimization