检索结果-南通市图书馆

The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions:soliton resolution via the mixed■-Riemann-Hilbert problem

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

Communications in Theoretical Physics 2024年第6期76卷 13-25页

作者： Minghe Zhang Zhenya Yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we investigate the Cauchy problem of the Sasa-Satsuma(SS)equation with initial data belonging to the Schwartz *** SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3×3 Lax *** the aid of the■nonlinear steepest descent method of the mixed■-Riemann-Hilbert problem,we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

关键词： Sasa-Satsuma equation inverse scattering ■-Riemann-Hilbert problem ■steepest descent method soliton resolution

Sharp bilinear decomposition for products of both anisotropic Hardy spaces and their dual spaces with its applications to endpoint boundedness of commutators

在线全文

学校读者我要写书评

暂无评论

Science China mathematics 2024年第9期67卷 2091-2152页

作者： Jun Liu Dachun Yang Mingdong Zhang school of mathematics China University of Mining and TechnologyXuzhou 221116China Laboratory of mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

Let a:=(a_(1),...,a_(n))2[1,∞)^(n),p∈(0,1),andα:=1/*** any x∈R^(n)and t∈[0,∞),letΦ_(p)(x,t):={t/1+(t[x]_(a)^(ν))^(1-p)if να■N,t/1+(t[x]_(a)^(ν))^(1-p)[log(e+|x|a)]^(p)if να∈N,let where [·]a:=1+|·|a,|·|a denotes the anisotropic quasi-homogeneous norm with respect to a,and ν:=a_(1)+…+a_(n).Let H_(a)^(p)(R^(n)),L_(a)^(a)(R^(n)),and H_(a)^(Φ_(p))(R^(n))be,respectively,the anisotropic Hardy space,the anisotropic Campanato space,and the anisotropic Musielak-Orlicz Hardy space associated with Φ_(p) on R^(n).In this article,via first establishing the wavelet characterization of anisotropic Campanato spaces,we prove that for any f∈H_(a)^(p)(R^(n))and g∈L_(a)^(a)(R^(n)),the product of f and g can be decomposed into S(f,g)+T(f,g) in the sense of tempered distributions,where S is a bilinear operator bounded from H_(a)^(p)(R^(n))*L_(a)^(a)(R^(Φ_(p))) to L^(1)(R^(n)) and T is a bilinear operator bounded from H_(a)^(p)(R^(n))*L_(a)^(a)(R^(n)) to H_(a)^(Φ_(p))(R^(n)) .Moreover,this bilinear decomposition is sharp in the dual sense that any y■H_(a)^(Φ_(p))(R^(n)) that fits into the above bilinear decomposition should satisfy(L^(1)(R^(n))+y)*=(L^(1)(R^(n)+H_(a)^(Φ_(p))(R^(n))*.As applications,for any non-constant b∈L_(a)^(a)(R^(n)) and any sublinear operator T satisfying some mild bounded assumptions,we find the largest subspace of H_(a)^(p)(R^(n)),denoted by H_(a,b)^(p)(R^(n)),such that the commutator [b,T] is bounded from H_(a,b)^(p)(R^(n))to L^(1)(R^(n)).In addition,when T is an anisotropic CalderónZygmund operator,the boundedness of [b,T] from H_(a,b)^(p)(R^(n))to L^(1)(R^(n))(or to H_(a)^(1)(R^(n)) is also *** key of their proofs is the wavelet characterization of function spaces under consideration.

关键词： anisotropic Euclidean space bilinear decomposition Hardy space Campanato space Musielak-Orlicz Hardy space commutator wavelet

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2024年第1期44卷 189-194页

作者：东瑜昕林和子陆琳根 school of Mathematical sciences Fudan UniversityShanghai20043China school of mathematics and Statistics&Laboratory of Analytical mathematics and Applications(Ministry of Education)&FJKLMAA Fujian Normal UniversityFuzhou350108China

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional *** the Michale-Simon Sobolev inequality,this inequ... 详细信息

关键词： asymptotically nonnegative sectional curvature logarithmic Sobolev inequality ABP method

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2024年第3期37卷 1271-1294页

作者： HE Shitao SHEN Liyong WU Qin YUAN Chunming school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our *** results are presented to show the advantages of the proposed algorithms.

关键词： Cubic B-spline Hausdorff distance interpolation tangential direction

BUBBLING ANALYSIS FOR A NONLINEAR DIRAC EQUATION ON SURFACES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2024年第6期44卷 2073-2082页

作者：陈优民刘磊朱苗苗 Department of mathematics Shantou University school of mathematics and Statistics and Hubei Key Laboratory of Mathematical sciences Central China Normal University school of Mathematical sciences Shanghai Jiao Tong University

In this paper,we apply the three circle type method and a Hardy type inequality to a nonlinear Dirac type equation on surfaces,and provide alternative proofs to the energy quantization results.

关键词： 53C27 58J05 energy identity Hardy inequality nonlinear Dirac equation three circle method

An Encoding-Decoding Framework Based on CNN for circ RNA-RBP Binding Sites Prediction

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 Journal of Electronics 2024年第1期33卷 256-263页

作者： Yajing GUO Xiujuan LEI Yi PAN school of computer Science Shaanxi Normal University Faculty of computer Science and Control Engineering Shenzhen Institute of Advanced TechnologyChinese Academy of Sciences Department of computer Science Georgia State University

Predicting RNA binding protein(RBP) binding sites on circular RNAs(circ RNAs) is a fundamental step to understand their interaction mechanism. Numerous computational methods are developed to solve this problem, but they cannot fully learn the features. Therefore, we propose circ-CNNED, a convolutional neural network(CNN)-based encoding and decoding framework. We first adopt two encoding methods to obtain two original matrices. We preprocess them using CNN before fusion. To capture the feature dependencies, we utilize temporal convolutional network(TCN) and CNN to construct encoding and decoding blocks, respectively. Then we introduce global expectation pooling to learn latent information and enhance the robustness of circ-CNNED. We perform circ-CNNED across 37 datasets to evaluate its effect. The comparison and ablation experiments demonstrate that our method is superior. In addition, motif enrichment analysis on four datasets helps us to explore the reason for performance improvement of circ-CNNED.

关键词： Proteins RNA Neural networks Encoding Robustness Decoding Convolutional neural networks

同方期刊数据库

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2024年第2期44卷 484-514页

作者：林孝盛杨大春杨四辈袁文 Laboratory of mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China school of mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild *** HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by *** this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy *** results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey ***,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

关键词： Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function

Navigation Finsler metrics on a gradient Ricci soliton

在线全文

学校读者我要写书评

暂无评论

Applied mathematics(A Journal of Chinese Universities) 2024年第2期39卷 266-275页

作者： LI Ying MO Xiao-huan WANG Xiao-yang Department of Applied mathematics Zhejiang University of TechnologyHangzhou 310023China 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 class of Finsler metrics defined by a vector field on a gradient Ricci *** obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral *** we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein *** its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

关键词： gradient Ricci soliton navigation Finsler metric isotropic S-curvature Ricci curvature Gaussian shrinking soliton

Pre-Training Physics-Informed Neural Network with Mixed Sampling and Its Application in High-Dimensional Systems

在线全文

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 494-510页

作者： LIU Haiyi ZHANG Yabin WANG Lei school of mathematics and Physics North China Electric Power UniversityBeijing 102206China school of Control and computer Engineering North China Electric Power UniversityBeijing 102206China

Recently,the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential ***,for some cases of high-dimensional systems,such technique may be time-consuming and *** this paper,the authors put forward a pre-training physics-informed neural network with mixed sampling(pPINN)to address these *** based on the initial and boundary conditions,the authors design the pre-training stage to filter out the set of the misfitting points,which is regarded as part of the training points in the next *** authors further take the parameters of the neural network in Stage 1 as the initialization in Stage *** advantage of the proposed approach is that it takes less time to transfer the valuable information from the first stage to the second one to improve the calculation accuracy,especially for the high-dimensional *** verify the performance of the pPINN algorithm,the authors first focus on the growing-and-decaying mode of line rogue wave in the Davey-Stewartson I *** case is the accelerated motion of lump in the inhomogeneous Kadomtsev-Petviashvili equation,which admits a more complex evolution than the uniform *** exact solution provides a perfect sample for data experiments,and can also be used as a reference frame to identify the performance of the *** experiments confirm that the pPINN algorithm can improve the prediction accuracy and training efficiency well,and reduce the training time to a large extent for simulating nonlinear waves of high-dimensional equations.

关键词： High-dimensional systems mixed sampling nonlinear wave pre-training physics-informed neural network