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Number rigid determinantal point processes induced by generalized Cantor sets

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Acta Mathematica Sinica,English Series 2025年

作者： Zhaofeng LIN Yanqi QIU Kai WANG school of Fundamental Physics and mathematical sciences HIAS University of Chinese Academy of Sciences school of mathematical sciences Fudan University

We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line R, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any givenθ∈(0, 1), there exists a generalized Cantor set with Lebesgue measure θ, such that the corresponding determinantal point process is Ghosh-Peres number rigid.

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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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Soliton Solutions of a Coupled KdV System via Backlund Transformation

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应用数学 2025年第1期38卷 211-216页

作者： CAO Xifang WU Yiheng LU Yi XU Wenjing XIA Yutong school of mathematical sciences Yangzhou UniversityYangzhou 225002China

In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV *** system was first proposed by Wang in *** we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV *** from a trivial seed solution,we construct soliton *** also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.

关键词： KdV equation Coupled KdV system B¨acklund transformation Soliton

An Approximation Method for Singular Trudinger-Moser Inequality

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应用数学 2025年第1期38卷 64-70页

作者： ZHU Maochun XU Wenyan JIANG Rou school of mathematical sciences Jiangsu UniversityZhenjiang 212013China

In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser ***,we obtain the concentration level of the functional and show it converges to the concentrati... 详细信息

关键词： Singular Trudinger-Moser inequality Approximation functional Concentration level

Continuous edge chromatic numbers of abelian group actions

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Science China Mathematics 2025年

作者： Su Gao Ruijun Wang Tianhao Wang school of mathematical sciences and Laboratory of Pure Mathematics and Combinatorics Nankai University

We prove that for any generating set S of Z~n, the continuous edge chromatic number χ′c（G） of the Schreier graph of the Bernoulli shift action G = F(S, 2Z~n) is χ′（G） + 1 = |S| + 1. In particular, for the stan...

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Molecular dynamics simulations of helium transport through inorganic mineral nanopores

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Science China Earth sciences 2025年第1期68卷 237-252页

作者： Dandan SONG Ping GUAN Chi ZHANG Jiahao REN school of Earth and Space sciences Peking University

Helium transport through nanoscale inorganic mineral pores and pore throats is essential for its overall migration. To elucidate helium's transport dynamics within nanopores, we employed equilibrium and non-equilibrium molecular dynamics simulations to investigate helium's static self-diffusion and pressure-driven flow in quartz slit-shaped nanopores. We also introduced water and various gases, including hydrogen, methane, ethane, nitrogen, and carbon dioxide, into the nanopores to assess their influence on helium transport. Our findings indicate minimal helium adsorption on quartz pore surfaces. Under conditions where the pore size is less than 5 nm and the pressure under 10 MPa, environmental factors markedly influence helium diffusion. Large pore sizes, high temperatures, and low gas pressures enhance helium desorption and facilitate faster diffusion. We observed a positive correlation between helium flow velocity and factors such as pore size, pressure gradient, and surface smoothness of the pores. Notably, the presence of pore water and carrier gases in quartz nanopores, which diffuse more slowly than helium, tends to reduce helium surface adsorption and slow its diffusion. Among the carrier gases studied, nitrogen showed similar adsorption capacity, diffusivity, and stability to helium, while carbon dioxide displayed the highest adsorption capacity and the slowest diffusion rate, markedly differing from helium. Based on the simulation results, we concluded that water and carrier gases primarily function as transport mediums in helium migration, moving together with helium. Nitrogen, which shares similar properties with helium, effectively assists in this co-migration process. Conversely, carbon dioxide, due to its high adsorption capacity and slow diffusion, tends to be lost during co-migration. As a result, gas reservoirs with high nitrogen levels and low carbon dioxide levels are more likely to have higher helium concentrations. Additionally, the smaller por

关键词： Helium transport Slit nanopores Molecular dynamics simulations Diffusion Flow carriers

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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An equivariant index theorem on R~n in the context of continuous fields of C*-algebras

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Science China Mathematics 2025年

作者： Baiying Ren Hang Wang Zijing Wang Research Center for Operator Algebras School of Mathematical SciencesEast China Normal University

We prove an equivariant index theorem on the Euclidean space using a continuous field of C*-algebras. This generalizes the work of Elliott et al.（1996）, which is a special case of the algebraic index theorem by Nest and Tsygan （1995）. Using our formula, we see that the equivariant index of the Bott-Dirac operator on R2ncan be explicitly calculated.

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