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The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li School of mathematics Jilin UniversityChangchun 130012China institute of mathematics Jilin UniversityChangchun 130012China School of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also *** our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

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A polynomial resultant approach to algebraic constructions of extremal graphs

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Science China mathematics 2024年

作者： Tao Zhang Zixiang Xu Gennian Ge institute of mathematics and interdisciplinary sciences Xidian University School of Mathematical sciences Capital Normal University

The Turan problem asks for the largest number of edges ex（n, H） in an n-vertex graph not containing a fixed forbidden subgraph H, which is one of the most important problems in extremal graph theory. However,the order of magnitude of ex（n, H） for bipartite graphs is known only in a handful of cases. In particular,giving explicit constructions of extremal graphs is very challenging in this field. In this paper, we develop a polynomial resultant approach to the algebraic construction of explicit extremal graphs, which can efficiently decide whether a specified structure exists. A key insight in our approach is the multipolynomial resultant, which is a fundamental tool of computational algebraic geometry. Our main results include the matched lower bounds on the Turan number of 1-subdivision of K3,t1and the linear Turan number of the Berge theta hypergraphΘ3B,t2, where t1= 25 and t2= 217. Moreover, the constant t1 improves the random algebraic construction of Bukh and Conlon（2018） and makes the known estimation better on the smallest value of t1 concerning a problem posed by Conlon et al.（2021） by reducing the value from a magnitude of 1056 to the number 25, while the constant t2improves a result of He and Tait（2019）.

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Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

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Science China mathematics 2024年第11期67卷 2433-2452页

作者： Feng Shao institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

Let X be an irreducible Hermitian symmetric space of compact type(IHSS for short).In this paper,we give the irreducible decomposition of *** a by-product,we give a cohomological characterization of the rank of ***,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

关键词： tangent bundle pseudoeffective threshold irreducible Hermitian symmetric space of compact type (IHSS) multiplicity free action

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Contrasts of bimodal tropical instability waves(TIWs)-induced wind stress perturbations in the Pacific Ocean among observations,ocean models,and coupled climate models

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Journal of Oceanology and Limnology 2024年第1期42卷 1-23页

作者： Kai MA Chuanyu LIU Junli XU Fan WANG School of mathematics and Physics Research Institute for Mathematics and Interdisciplinary SciencesQingdao University of Science and TechnologyQingdao 266100China Key Laboratory of Ocean Circulation and Waves Institute of OceanologyChinese Academy of SciencesQingdao 266071China Pilot National Laboratory for Marine Science and Technology(Qingdao) Qingdao 266237China

The coupling between wind stress perturbations and sea surface temperature(SST)perturbations induced by tropical instability waves(TIWs)in the Pacific Ocean has been revealed previously and proven crucial to both the atmosphere and ***,an overlooked fact by previous studies is that the loosely defined“TIWs”actually consist of two modes,including the Yanai wave-based TIW on the equator(hereafter eTIW)and the Rossby wave-based TIW off the equator(hereafter vTIW).Hence,the individual feedbacks of the wind stress to the bimodal TIWs remain *** this study,individual coupling relationships are established for both eTIW and v TIW,including the relationship between the TIW-induced SST perturbations and two components of wind stress perturbations,and the relationship between the TIW-induced wind stress perturbation divergence(curl)and the downwind(crosswind)TIW-induced SST *** show that,due to different distributions of eTIW and vTIW,the coupling strength induced by the eTIW is stronger on the equator,and that by the vTIW is stronger off the *** results of any of eTIW and vTIW are higher than those of the loosely defined *** further investigated how well the coupling relationships remained in several widely recognized oceanic general circulation models and fully coupled climate ***,the coupling relationships cannot be well represented in most numerical ***,we confirmed that higher resolution usually corresponds to more accurate ***,the coupling models established in this study are complementary to previous research and can be used to refine the oceanic and coupled climate models.

关键词： bimodal tropical instability waves mesoscale air-sea interaction coupled models Yanai wave

2-local unstable homotopy groups of indecomposable A3～2-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A3～*** main technique used is analysing the homotopy property of J（A,X）,defined by Gray（1973） for a CW-pair（X,A）,which is homoto... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

BCCLR:A Skeleton-Based Action Recognition with Graph Convolutional Network Combining Behavior Dependence and Context Clues

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Computers, Materials & Continua 2024年第3期78卷 4489-4507页

作者： Yunhe Wang Yuxin Xia Shuai Liu College of Information Science and Engineering Institute of Interdisciplinary StudiesHunan Normal UniversityChangsha410081China School of Educational sciences Institute of Interdisciplinary StudiesHunan Normal UniversityChangsha410081China

In recent years,skeleton-based action recognition has made great achievements in Computer Vision.A graph convolutional network(GCN)is effective for action recognition,modelling the human skeleton as a spatio-temporal *** GCNs define the graph topology by physical relations of the human ***,this predefined graph ignores the spatial relationship between non-adjacent joint pairs in special actions and the behavior dependence between joint pairs,resulting in a low recognition rate for specific actions with implicit correlation between joint *** addition,existing methods ignore the trend correlation between adjacent frames within an action and context clues,leading to erroneous action recognition with similar ***,this study proposes a learnable GCN based on behavior dependence,which considers implicit joint correlation by constructing a dynamic learnable graph with extraction of specific behavior dependence of joint *** using the weight relationship between the joint pairs,an adaptive model is *** also designs a self-attention module to obtain their inter-frame topological relationship for exploring the context of *** the shared topology and the multi-head self-attention map,the module obtains the context-based clue topology to update the dynamic graph convolution,achieving accurate recognition of different actions with similar *** experiments on public datasets demonstrate that the proposed method achieves better results and realizes higher quality representation of actions under various evaluation protocols compared to state-of-the-art methods.

关键词： Action recognition deep learning GCN behavior dependence context clue self-attention

A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems Science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi Department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate

Q-BioLiP:A Comprehensive Resource for Quaternary Structure-based Protein-ligand Interactions

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Genomics, Proteomics & Bioinformatics 2024年第1期22卷 151-159页

作者： Hong Wei Wenkai Wang Zhenling Peng Jianyi Yang School of Mathematical sciences Nankai UniversityTianjin 300071China MOE Frontiers Science Center for Nonlinear Expectations Research Center for Mathematics and Interdisciplinary SciencesShandong UniversityQingdao 266237China

Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand ***,several known issues occurred with it over the past *** example,the protein-ligand interactions are represented in the form of single chain-based tertiary structures,which may be inappropriate as many interactions involve multiple protein chains(known as quaternary structures).We sought to address these issues,resulting in Q-BioLiP,a comprehensive resource for quaternary structure-based protein-ligand *** major features of Q-BioLiP include:(1)representing protein structures in the form of quaternary structures rather than single chain-based tertiary structures;(2)pairing DNA/RNA chains properly rather than separation;(3)providing both experimental and predicted binding affinities;(4)retaining both biologically relevant and irrelevant interactions to alleviate the wrong justification of ligands’biological relevance;and(5)developing a new quaternary structure-based algorithm for the modelling of protein-ligand complex *** these new features,Q-BioLiP is expected to be a valuable resource for studying biomolecule interactions,including protein-small molecule interaction,protein-metal ion interaction,protein-peptide interaction,protein-protein interaction,protein-DNA/RNA interaction,and RNA-small molecule interaction.Q-BioLiP is freely available at https://***/Q-BioLiP/.

关键词： Protein-ligand interaction Quaternary structure Protein-ligand binding site Protein-protein interaction Binding affinity