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The Hilbert expansion of the Boltzmann equation in the incompressible Euler level in a channel

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Science China Mathematics 2025年第1期68卷 39-88页

作者： Feimin Huang Weiqiang Wang Yong Wang Feng Xiao Academy of Mathematics and Systems Science Chinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) School of Mathematics and StatisticsHunan Normal University

The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary *** this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is *** on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,***,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are *** the help of the L2-L∞framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.

关键词： Boltzmann equation incompressible Euler equations hydrodynamic limit Hilbert expansion specular reflection boundary condition viscous boundary layer Knudsen boundary layer

Twist monomials of binary delta-matroids

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Acta Mathematica Sinica,English Series 2025年

作者： Qi YAN Xian'an JIN school of Mathematics and statistics Lanzhou University school of Mathematical sciences Xiamen University

Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials have only one term and posed a problem:what would happen for odd binary delta-matroids? In this paper, we show that a normal binary deltamatroid whose twist polynomials have only one term if and only if each connected component of the intersection graph of the delta-matroid is either a complete graph of odd order or a single vertex with a loop.

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Aperiodically semi-intermittent-based fixed-time stabilization and synchronization of delayed discontinuous inertial neural networks

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Science China(Information sciences) 2025年第1期68卷 238-254页

作者： Guodong ZHANG Jinde CAO school of Mathematics and statistics South-Central Minzu University school of Mathematics Southeast University

This article concentrates on the fixed-time stabilization(FS) and fixed-time synchronization(FTS) of discontinuous inertial neural networks(DINNs) with distributed delays. Using mathematical induction to a new differential equality, a novel fixed-time stability lemma is constructed. Then, by designing an aperiodically semi-intermittent switching control and combining it with the theory of nonsmooth analysis, some novel criteria on the FS and FTS of DINNs are obtained. Unlike the methods used in most existing studies, the FS and FTS results are structured using the newly proposed fixed-time stability lemma and the nonreduced-order approach, resulting in broader practical applications and strengthening the scientific quality of the derived results. Lastly, numerical simulations and applications proffer the effectiveness of the established FS and FTS criteria.

关键词： inertial neural networks fixed-time synchronization semi-intermittent switching control nonreduced-order approach fixed-time stabilization

New types of singular solutions of conformal Q-curvature equations

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Acta Mathematica Sinica,English Series 2025年

作者： Zongming Guo Zhongyuan Liu Fangshu Wan Department of Mathematics Henan Normal University school of Mathematics and statistics Henan University school of Mathematical sciences Anhui University

We construct radial and non-radial singular solutions u ∈ C4（B{0}） with a non-removable singular point x = 0 for the conformal Q-curvature equation:■where B = {x ∈ R4: |x| D0≥ 0, and satisfying ■Moreover, detailed asymptotic expansions near x = 0 of these radial and non-radial singular solutions can be established. As an application, we can also obtain the existence of two types of solutions u ∈ C4（R4■） to the problem ■ satisfying |x|-2u（x） →-D D0, and satisfying u（x） = o（|x|2） uniformly as |x| → ∞.

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Weak KAM theory for two classes of almost periodic Hamiltonian systems

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Science China Mathematics 2025年

作者： Xun Niu Kaizhi Wang Yong Li school of Mathematics and statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal University school of Mathematical sciences Shanghai Frontier Science Center of Modern Analysis (CMA-Shanghai)Shanghai Jiao Tong University Institute of Mathematics Jilin University

The purpose of this paper is to investigate the dynamics of Bohr almost periodic and Levitan almost periodic Hamiltonian systems via the weak KAM theory. We obtain minimal measures and weak KAM solutions in both cases. The weak KAM solution is a weak solution to the Hamilton-Jacobi equation, which formally transforms the original Hamiltonian systems into an integrable one. Consequently, we get the existence of an invariant torus in the aforementioned weak sense.

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Single-cell technologies: current and near future

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Science China Life sciences 2025年第1期68卷 1-4页

作者： Chenfei Wang Qi Liu Xiaohui Fan Tieliu Shi Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration Ministry of EducationOrthopedics DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Frontier Science Center for Stem Cells School of Life Sciences and TechnologyTongji University Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Research Institute of Intelligent Computing Zhejiang Lab Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang University National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang University Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal University Key Laboratory of Advanced Theory and Application in statistics and Data Science (MOE) School of StatisticsEast China Normal University

Single-cell technologies enable the indepth exploration of multiple biological hierarchies at the scale of individual cells,which have deepened our knowledge of cellular diversity, tissue organization, and overall organism function(Sun et al.,2024). In 2009, single-cell RNA sequencing(sc RNA-seq) was first developed as a powerful tool to dissect gene expression and uncover transcriptional *** the rapid advancement of technology, single-cell approaches have expanded to encompass other omics, such as genomics, epigenomics, proteomics,and metabolomics.

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Exit options sustain altruistic punishment and decrease the second-order free-riders, but it is not a panacea

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Science China(Information sciences) 2025年第1期68卷 278-291页

作者： Chen SHEN Zhao SONG Lei SHI Jun TANIMOTO Zhen WANG Faculty of Engineering sciences Kyushu University school of statistics and Mathematics Yunnan University of Finance and Economics school of Computing Engineering and Digital Technologies Teesside University school of Artificial Intelligence OPtics and Electro Nics (iOPEN) Northwestern Polytechnical University

Why do humans punish free riders at their own expense? This behavior represents an evolutionary puzzle in human societies. This study explores the role of exit strategies in fostering altruistic punishment within evolutionary game theory. We extend the traditional prisoner's dilemma model by incorporating exiters, players who opt out for a small payoff while nullifying their opponent's payoff, and altruistic punishers who cooperate and punish non-cooperators. Our findings indicate that in well-mixed populations, exiters destabilize defection but do not promote altruistic punishment. In social networks, however,exiters enable altruistic punishment via cyclic dominance among altruistic punishers, defectors, and exiters. Notably, this cyclic dominance is sensitive to exit payoffs; adjustments can lead to cyclic dominance of non-punishing cooperators, defectors, and exiters, or to a bi-stable state between these two types of cyclic dominance. These results highlight the nuanced impact of exiters on altruistic punishment, emphasizing the need for careful incentivization of exit behavior. While exiters can support altruistic punishment in networked populations, their effectiveness is not a panacea and is highly sensitive to exit payoffs, indicating limits to the voluntary participation mechanism.

关键词： evolutionary game theory altruistic punishment coexistence cyclic dominance bi-stable

Single-cell omics: experimental workflow, data analyses and applications

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Science China Life sciences 2025年第1期68卷 5-102页

作者： Fengying Sun Haoyan Li Dongqing Sun Shaliu Fu Lei Gu Xin Shao Qinqin Wang Xin Dong Bin Duan Feiyang Xing Jun Wu Minmin Xiao Fangqing Zhao Jing-Dong J.Han Qi Liu Xiaohui Fan Chen Li Chenfei Wang Tieliu Shi Department of Clinical Laboratory the Affiliated Wuhu Hospital of East China Normal University (The Second People's Hospital of Wuhu City) Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang University Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration (Tongji University) Ministry of EducationOrthopaedic DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Frontier Science Center for Stem Cells School of Life Sciences and TechnologyTongji University Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Research Institute of Intelligent Computing Zhejiang Lab Shanghai Research Institute for Intelligent Autonomous Systems Center for Single-cell Omics School of Public HealthShanghai Jiao Tong University School of Medicine National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang University Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal University Beijing Institutes of Life Science Chinese Academy of Sciences Peking-Tsinghua Center for Life sciences Academy for Advanced Interdisciplinary StudiesCenter for Quantitative Biology (CQB)Peking University Zhejiang Key Laboratory of Precision Diagnosis and Therapy for Major Gynecological Diseases Women's HospitalZhejiang University School of Medicine Key Laboratory of Advanced Theory and Application in statistics and Data Science-MOE School of StatisticsEast China Normal University

Cells are the fundamental units of biological systems and exhibit unique development trajectories and molecular features. Our exploration of how the genomes orchestrate the formation and maintenance of each cell, and control the cellular phenotypes of various organismsis, is both captivating and intricate. Since the inception of the first single-cell RNA technology, technologies related to single-cell sequencing have experienced rapid advancements in recent years. These technologies have expanded horizontally to include single-cell genome, epigenome,proteome, and metabolome, while vertically, they have progressed to integrate multiple omics data and incorporate additional information such as spatial sc RNA-seq and CRISPR screening. Single-cell omics represent a groundbreaking advancement in the biomedical field,offering profound insights into the understanding of complex diseases, including cancers. Here, we comprehensively summarize recent advances in single-cell omics technologies, with a specific focus on the methodology section. This overview aims to guide researchers in selecting appropriate methods for single-cell sequencing and related data analysis.

关键词： single-cell sequencing genome epigenome proteomics metabolomics multimodal spatial transcriptomics CRISPR screening

Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

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Science China Mathematics 2025年

作者： Xin Lü Shengli Tan Kang Zuo school of Mathematical sciences Key Laboratory of Mathematics and Engineering Applications(Ministry of Education) Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University school of Mathematics and statistics Wuhan University Institut für Mathematik Universit?t Mainz

We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g≥4. In particular, Shimura curves of Mumford type are not...

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