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Essentially Commuting Dual Truncated Toeplitz Operators

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Chinese Annals of mathematics,Series B 2024年第4期45卷 597-636页

作者： Chongchao WANG Xianfeng ZHAO Dechao ZHENG College of mathematics and Physics Wenzhou University College of mathematics and Statistics Chongqing University Center of mathematics Chongqing University department of mathematics Vanderbilt University

In this paper, the authors completely characterize when two dual truncated Toeplitz operators ar e essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Their main idea... 详细信息

关键词： 47B32 47B35 Dual truncated Toeplitz operator Essentially commuting Hardy space

Evolution of light deflection and shadow from a gauge-potential-like AdS black hole under the influence of a non-magnetic plasma medium

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Communications in Theoretical Physics 2024年第9期76卷 85-96页

作者： Riasat Ali Xia Tiecheng Muhammad Awais Rimsha Babar department of mathematics Shanghai University and Newtouch Center for Mathematics of Shanghai University department of mathematics University of Engineering and Technology department of mathematics GC University Faisalabad Layyah Campus

We investigate the light deflection in the weak field approximation from the accelerating charged AdS black hole. For this purpose, we apply the Gauss–Bonnet theorem to calculate the light deflection in the weak field area and use the Gibbons–Werner approach to analyze the optical geometry of the accelerating charged AdS black hole in the non-magnetic plasma absence/presence of a non-magnetic medium. We also represent the graphical behavior of the light deflection angle w.r.t. the impact parameter. We also compute the light deflection angle using Keeton and Petters approximations under the impact of accelerating charged AdS black hole geometry. Furthermore, by using the ray-tracing approach, we determine the shadow in the nonmagnetic plasma presence and also demonstrate that graphical shadow has an impact on the gauge potential, non-magnetic plasma frequencies and charge.

关键词： accelerating charged AdS black hole deflection angle Gibbons-Werner approach ray-tracing approach shadow

Centered Waves for the Two-dimensional Pseudo-Steady van der Waals Gas Satisfied Maxwell's Law Around a Sharp Corner

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Chinese Annals of mathematics,Series B 2024年第04期45卷 537-554页

作者： Shuangrong LI Wancheng SHENG department of mathematics Shanghai University Shanghai 200444 China department of mathematics Zhejiang University of Science and Technology department of mathematics Newtouch Center for Mathematics of Shanghai University Shanghai University

In this paper, the authors study the centered waves for the two-dimensional(2D for short) pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner. In view of the initial value of the specific volume and the properties of van der Waals gas, the centered waves at the sharp corner are constructed by classification. It is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan, fan-jump or fan-jump-fan), or a combination of waves and constant state. Moreover, the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.

关键词： Centered simple wave Composite wave Two-dimensional Euler equations Van der Waals gas

Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct

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Chinese Annals of mathematics,Series B 2024年第2期45卷 279-296页

作者： Fenglun WEI Jianli LIU department of mathematics Shanghai University Newtouch Center for mathematics of Shanghai University

Heat exchange plays an important role in hydrodynamical systems,which is an interesting topic in theory and *** this paper,the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange,under the small perturbations of initial and boundary conditions in a finite rectilinear duct.

关键词： Compressible Euler equations Heat exchange Supersonic Rayleigh fow Steady solution Classical solution

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of Systems Science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu School of mathematics Statistics and Mechanics Beijing University of Technology Academy of mathematics and Systems Science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

∞-Tilting Subcategories in Extriangulated Categories

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Chinese Annals of mathematics,Series B 2024年第1期45卷 151-160页

作者： Zhen ZHANG Jiaqun WEI Shance WANG department of mathematics Qilu Normal UniversityJinan 250200China Institution of mathematics School of Mathematics ScienceNanjing Normal UniversityNanjing 210023China

In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.

关键词： Extriangulated category ∞-Tilting subcategory Auslander-Reiten correspondence Bazzoni characterization

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

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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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