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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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Practical approach for detecting k-nonseparability of multipartite quantum states

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 32-48页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of mathematics Taiyuan University of Technology school of mathematics and Statistics Shanxi University Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi University

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information, and there are no practical methods or tools to complete this task satisfactorily so far. We propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems, 2 ≤ k ≤ n. This criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipartite finite-dimensional systems. To exemplify the application of our scheme, we have developed a software tool that facilitates swift and precise identification of entanglement, k-nonseparability, and genuine entanglement within n-qubit systems, specifically tailored for systems with 2 ≤ n ≤ 4.

关键词： multipartite systems entanglement states entanglement witnesses ${\bm~k}$-nonseparability

Regression analysis of squeezing-induced hybrid nanofluid flow in Darcy-Forchheimer porous medium

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Applied mathematics and Mechanics(English Edition) 2025年第1期46卷 193-208页

作者： K.MUHAMMAD M.SARFRAZ Department of Humanities and sciences School of Electrical Engineering and Computer Science National University of Sciences and Technology Department of mathematics Quaid-i-Azam University

This article presents a mathematical model addressing a scenario involving a hybrid nanofluid flow between two infinite parallel plates. One plate remains stationary, while the other moves downward at a squeezing velocity. The space between these plates contains a Darcy-Forchheimer porous medium. A mixture of water-based fluid with gold(Au) and silicon dioxide(Si O2) nanoparticles is formulated. In contrast to the conventional Fourier's heat flux equation, this study employs the Cattaneo-Christov heat flux equation. A uniform magnetic field is applied perpendicular to the flow direction, invoking magnetohydrodynamic(MHD) effects. Further, the model accounts for Joule heating, which is the heat generated when an electric current passes through the fluid. The problem is solved via NDSolve in MATHEMATICA. Numerical and statistical analyses are conducted to provide insights into the behavior of the nanomaterials between the parallel plates with respect to the flow, energy transport, and skin *** findings of this study have potential applications in enhancing cooling systems and optimizing thermal management strategies. It is observed that the squeezing motion generates additional pressure gradients within the fluid, which enhances the flow rate but reduces the frictional drag. Consequently, the fluid is pushed more vigorously between the plates, increasing the flow velocity. As the fluid experiences higher flow rates due to the increased squeezing effect, it spends less time in the region between the plates. The thermal relaxation, however, abruptly changes the temperature, leading to a decrease in the temperature fluctuations.

关键词： convective boundary condition Darcy-Forchheimer medium hybrid nanofluid Joule heating magnetohydrodynamic (MHD) numerical solution squeezing flow regression analysis O361 O175.2

Limit theorems of the 2D stochastic Navier-Stokes equation driven by a time-periodic force and a degenerate noise

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Science China mathematics 2025年

作者： Rongchang Liu Kening Lu Department of mathematics University of Arizona school of mathematics Sichuan University

The periodically forced 2D Navier-Stokes equation with a degenerate noise is studied. For the Markov chain obtained by restricting the solution process to the Poincarésection, we prove a quantitative version of the strong law of large numbers and the central limit theorem with explicit convergence rates. A law of the iterated logarithm is also obtained. The proof is based on a martingale approximation procedure.

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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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Dynamical complexity of Anosov systems driven by a quasi-periodic force

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Science China mathematics 2025年第1期 89-136页

作者： Wen Huang Zeng Lian Kening Lu Department of mathematics University of Science and Technology of China school of mathematics Sichuan University

Consider C2Anosov systems on a compact manifold driven by a quasi-periodic *** study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic *** that these systems are non-wandering（i.e.,every point in the phase space is nonwandering）,we prove a set of results:（1） the existence of abundance of random periodic points;（2） a random Liv?ic theorem;（3） a random Ma?é-Bousch-Conze-Guivarc'h lemma;（4） the existence of strong random ***,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.

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Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China mathematics 2025年第1期 223-252页

作者： Weidong Liu Dennis Leung Qi-Man Shao school of Mathematical sciences Shanghai Jiao Tong University school of mathematics and Statistics University of Melbourne Department of Statistics and Data Science SICMSouthern University of Science and Technology

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

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Silk damping in scalar-induced gravitational waves: a novel probe for new physics

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 79-85页

作者： Yan-Heng Yu Sai Wang Theoretical Physics Division Institute of High Energy Physics Chinese Academy of Sciences school of Physics University of Chinese Academy of Sciences

Silk damping is well known in the study of cosmic microwave background（CMB） and accounts for suppression of the angular power spectrum of CMB on large angular multipoles. In this article, we study the effect of Silk damping on the scalar-induced gravitational waves（SIGWs）. Resulting from the dissipation of cosmic fluid, the Silk damping notably suppresses the energydensity spectrum of SIGWs on scales comparable to a diffusion scale at the decoupling time of weakly-interacting particles. The effect offers a novel observable for probing the underlying particle interaction, especially for those mediated by heavy gauge bosons beyond the standard model of particles. We anticipate that pulsar timing arrays are sensitive to gauge bosons with mass ～10～3-10～4 GeV, while space-and ground-based interferometers to those with mass ～10～7-1012GeV, leading to essential complements to on-going and future experiments of high-energy physics.

关键词： scalar-induced gravitational waves Silk damping new physics

Distance two Heegaard splittings, JSJ decompositions and ranks of 3-manifolds

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Science China mathematics 2025年

作者： Wenjie Diao Yanqing Zou school of Mathematical sciences East China Normal University Shanghai Key Laboratory of Pure mathematics and Mathematical Practice East China Normal University

For any pair of integers g and n with g ≥ 3 and 1 ≤ n ≤ g, we build a 3-manifold with a distance-2,genus-g Heegaard splitting so that(1) it contains n pairwise disjoint and nonisotopic essential tori;(2) after it is cut open along these tori, one resulting piece is hyperbolic while the others are small Seifert fibered spaces;(3) it provides a substantial result to the rank versus genus problem. These generalize a result in Qiu and Zou(2019).

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