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Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds

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Science China mathematics 2024年第7期67卷 1665-1718页

作者： Qi’an Guan Zhitong Mi Zheng Yuan school of Mathematical sciences Peking UniversityBeijing100871China school of mathematics and Statistics Beijing Jiaotong UniversityBeijing100044China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

关键词： minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex K?hler manifold

FNNWV: farthest-nearest neighbor-based weighted voting for class-imbalanced crowdsourcing

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Science China(Information sciences) 2024年第10期67卷 172-188页

作者： Wenjun ZHANG Liangxiao JIANG Ziqi CHEN Chaoqun LI school of computer Science China University of Geosciences Key Laboratory of Artificial Intelligence Ministry of Education school of mathematics and Physics China University of Geosciences

In crowdsourcing scenarios, we can hire crowd workers to label crowdsourced tasks and then use label integration algorithms to infer the integrated label for each instance in the tasks. As more and more label integration algorithms are proposed, the performance of inference based only on the information of the inferred instance gradually converges. Recent algorithms attempt to exploit the information of the inferred instance's nearest neighbors to infer and achieve good performance. However, when crowdsourced tasks are class-imbalanced, negative instances are more easily to occur in the nearest neighbors because negative instances are the majority, and thus recent algorithms are more easily biased toward the negative class. To this end, in this paper, we propose a novel label integration algorithm called farthest-nearest neighbor-based weighted voting(FNNWV) for class-imbalanced crowdsourcing. Specifically, FNNWV considers the nearest neighbors to be more similar to the inferred instance and thus uses them to vote ayes in weighted voting. Yet at the same time, FNNWV considers the farthest neighbors to be more different from the inferred instance and thus uses them to vote nays in weighted voting. Since negative instances are easier to occur in both the nearest neighbors and the farthest neighbors, FNNWV weakens the effect of negative instances by voting ayes and nays. The experimental results on 22 simulated and one real-world crowdsourced datasets show that FNNWV significantly outperforms all the other state-of-the-art competitors.

关键词： crowdsourcing label integration nearest neighbor farthest neighbor weighted voting

THE NYSTROM METHOD FOR ELASTIC WAVE SCATTERINGBY UNBOUNDED ROUGH SURFACES

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Journal of Computational mathematics 2024年第5期42卷 1407-1426页

作者： Jianliang Li Xiaoli Liu Bo Zhang Haiwen Zhang Key Laboratory of Computing and Stochastic mathematics School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China school of Mathematical sciences Beihang UniversityBeijing 100191China LSEC and Academy of mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China Academy of mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China

We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering problem based on the integral equation *** of the Nystr¨om method is established with convergence rate depending on the smoothness of the rough *** doing so,a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral *** experiments are presented to demonstrate the effectiveness of the *** subject classification:35P25,45P05.

关键词： Elastic wave scattering Unbounded rough surface Nystrom method

Joint training with local soft attention and dual cross-neighbor label smoothing for unsupervised person re-identification

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Computational Visual Media 2024年第3期10卷 543-558页

作者： Qing Han Longfei Li Weidong Min Qi Wang Qingpeng Zeng Shimiao Cui Jiongjin Chen school of mathematics and computer sciences Nanchang UniversityNanchang 330031China Institute of Metaverse Nanchang UniversityNanchang 330031China Jiangxi Key Laboratory of Smart City Nanchang 330031China

Existing unsupervised person re-identification approaches fail to fully capture thefine-grained features of local regions,which can result in people with similar appearances and different identities being assigned the same label after *** identity-independent information contained in different local regions leads to different levels of local *** address these challenges,joint training with local soft attention and dual cross-neighbor label smoothing(DCLS)is proposed in this ***,the joint training is divided into global and local parts,whereby a soft attention mechanism is proposed for the local branch to accurately capture the subtle differences in local regions,which improves the ability of the re-identification model in identifying a person’s local significant ***,DCLS is designed to progressively mitigate label noise in different local *** DCLS uses global and local similarity metrics to semantically align the global and local regions of the person and further determines the proximity association between local regions through the cross information of neighboring regions,thereby achieving label smoothing of the global and local regions throughout the training *** extensive experiments,the proposed method outperformed existing methods under unsupervised settings on several standard person re-identification datasets.

关键词： person re-identification(Re-ID) unsupervised learning(USL) local soft attention joint training dual cross-neighbor label smoothing(DCLS)

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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Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

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Science China mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau Mathematical sciences Center Tsinghua UniversityBeijing 100084China school of mathematics Shandong UniversityJinan 250100China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic *** precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关键词： 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy

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

Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants

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Science China(Physics,Mechanics & Astronomy) 2024年第9期67卷 43-50页

作者： Xiao-Bin Liang Bo Li Shao-Ming Fei school of mathematics and computer Science Shangrao Normal UniversityShangrao 334001China Quantum Information Research Center Shangrao Normal UniversityShangrao 334001China school of Mathematical sciences Capital Normal UniversityBeijing 100048China

Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical ***,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement *** any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty *** demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation ***,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this ***,our findings resolve the conjecture posed in[***.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.

关键词： uncertainty relation the tightest uncertainty constants optimal observable sets

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Dynamics of Caputo fractional-order SIRV model:The effects of imperfect vaccination on disease transmission

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International Journal of Biomathematics 2024年第4期17卷 267-285页

作者： Auwal Abdullahi Mohd Hafiz Mohd Department of mathematics and computer Science Federal University Kashere Nigeria school of Mathematical sciences Universiti Sains Malaysia 11800 USMPulau PinangMalaysia

Though vaccination protects individuals against many infectious diseases,such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become *** study,therefore,determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV(Susceptible-Infected-Recovered-Vaccinated)epidemic *** properties of the new model including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation-are thoroughly ***,our simulation results report that an increase in the imperfect vaccination force increases the population of infected *** the memory effect,the higher“memory”the epidemic system has of past states(which corresponds to decreasing values of fractionalorder parameter),the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics.

关键词： Vaccination model fractional-order model Caputo fractional-order derivative Mittag-Leffer function fixed-point theory