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Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng Department of mathematics and Statistics Fuyang Normal University School of mathematics Sichuan University

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of A from the category CZ/t（A） of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra. Moreover, we describe the semiderived Ringel-Hall algebra by the generators and defining relations. In particular, if t is an odd integer, we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of $\mathbb{Z}/t$-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers

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Science China mathematics 2024年第8期67卷 1807-1826页

作者： Meryem Akboudj Yong Jiao Adam Os?kowski School of mathematics and Statistics Hunan Key Laboratory of Analytical Mathematics and ApplicationsCentral South University Faculty of mathematics Informatics and MechanicsUniversity of Warsaw

Let p>2 be a given exponent. In this paper, we prove, with the best constant, the weak-type(p, p)inequality ■ for a large class of non-symmetric Fourier multipliers Tm obtained via modulation of jumps of certain Lévy processes. In particular, the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane. The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle. Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.

关键词： weak-type bound Fourier multiplier martingale differential subordination laminate

Parametric “non-nested” discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang Department of mathematics North Carolina State University SMS–HCIC–School of mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu University

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained using repeated parametric greatest common divisors. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminant that is not based on repeated greatest common divisors. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

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Science China mathematics 2024年第8期67卷 1865-1880页

作者： Xiequan Fan Haijuan Hu Lihu Xu Center for Applied mathematics Tianjin University School of mathematics and Statistics Northeastern University at Qinhuangdao Department of mathematics Faculty of Science and TechnologyUniversity of Macau

In this paper, we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE. Due to our results, Berry-Esseen's bounds and moderate deviation principles are also o... 详细信息

关键词： Euler-Maruyama scheme Cramér-type moderate deviations self-normalized sequences Berry-Esseen's bounds

∞-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 considered.To 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

2-local unstable homotopy groups of indecomposable A32-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 A32-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is ho... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Study of bending angle and shadow in a new Schwarzschild-like black hole affected by plasma and non-plasma mediums

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Chinese Physics C 2024年第5期48卷 309-318页

作者： Riasat Ali Tiecheng Xia Muhammad Awais Rimsha Babar Department of mathematics Newtouch Center for Mathematics of Shanghai UniversityShanghai 200444China Department of mathematics University of Engineering and Technology Lahore-54890Pakistan Department of mathematics GC University Faisalabad Layyah CampusLayyah-31200Pakistan

In this study,we analyze the models of the deflection angle of a new Schwarzschild-like black hole(BH)and employ the optical metric of the BH.To achieve this,we use the Gaussian curvature of the optical metric and the Gauss-Bonnet theorem,known as the Gibbons-Werner technique,to determine the deflection angle.Furthermore,we examine the deflection angle in the presence of a plasma medium and the effect of the plasma medium on the deflection angle.The deflection angle of the BH solution in the gauged super-gravity is computed using the Keeton-Petters approach.Utilizing the ray-tracing technique,we investigate the shadow of the corresponding BH and analyze the plots of the deflection angle and shadow to verify the influence of the plasma and algebraic thermodynamic parameters on the deflection angle and shadow.

关键词： new Schwarzschild-like black hole Gibbons-Werner and Keeton-Petters techniques deflection angle ray-tracing approach shadow