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Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1697-1726页

作者： Timilehin Opeyemi Alakoya Oluwatosin Temitope Mewomo school of mathematics Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

In this paper,we study the concept of split monotone variational inclusion problem with multiple output *** propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert *** proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued ***,some parameters are relaxed to accommodate a larger range of values for the step *** some mild conditions on the control parameters and without prior knowledge of the operator norms,we obtain strong convergence result for the proposed ***,we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed *** of the existing results in the literature could be viewed as special cases of our result in this paper.

关键词： Split inverse problems non-Lipschitz operators inertial technique self-adaptive step sizes

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

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Acta Mathematica Scientia 2024年第2期44卷 445-454页

作者：张子厚周晶 school of mathematics Physics and StatisticsShanghai University of Engineering ScienceShanghai201620China

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym *** introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a *** are the generalizations of the weak^(*)denting point of a set in a dual Banach *** use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach ***,we also characterize an approximatively weak compact Chebyshev set in dual Banach ***,we define the nearly weak dentability in Banach spaces,which is a generalization of near *** prove the necessary and sufficient conditions of the reflexivity by nearly weak *** also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

关键词： weak^(*)-weak denting point nearly weak dentability very smooth space point of weak^(*)-weak continuity extreme point approximatively weak compactness w-strong proximinality reflexivity

The twisted conical Kahler-Ricci solitons on Fano manifolds

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Science China mathematics 2024年第5期67卷 1085-1102页

作者： Xishen Jin Jiawei Liu school of mathematics Renmin University of ChinaBeijing 100872China school of mathematics and statistics Nanjing University of Science&TechnologyNanjing 210094China

In this paper,we show the relation between the existence of twisted conical K?hler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano *** is based on our proofs of some openness theorems on the existence of twisted conical Kahler-Ricci solitons,which generalize Donaldson’s existence conjecture and the openness theorem of the conical K?hler-Einstein metrics to the conical soliton case.

关键词： greatest log Bakry-Emery-Ricci lower bound twisted conical Kahler-Ricci soliton twisted Kahler-Ricci soliton

Testing high-dimensional covariance structures using double-normalized observations Dedicated to the Memory of Professor Xiru Chen on the Twentieth Anniversary of His Passing

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Science China mathematics 2024年

作者： Yanqing Yin Huiqin Li Zhidong Bai school of mathematics and statistics Chongqing University school of mathematics and statistics Northeast Normal University

In this paper, we focus on the test for high-dimensional covariance structures using doublenormalized observations for an elliptical population. By investigating the limiting spectral properties of the sample covariance matrix of double-normalized observations, we propose test statistics applicable for testing the diagonality of the population covariance matrix. Extensive simulations are conducted to investigate the performances of the proposed test in various situations.

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Multicolored Bipartite Ramsey Numbers of Large Cycles

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 347-357页

作者： Shao-qiang LIU Yue-jian PENG College of mathematics and statistics Hanshan Normal UniversityChaozhou 521041China school of mathematics Hunan UniversityChangsha 410082China

For an integer r≥2 and bipartite graphs Hi,where 1≤i≤r,the bipartite Ramsey number br(H1,H2,…,Hr)is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN;N contains a monochromatic subgraph isomorphic to Hi in color i for some 1≤i≤*** show that if r≥3;α1,α2>0,αj+2≥[(j+2)!-1]Σi=1^(j+1)α1 for j=1,2…r-2,then br(C2[α1n],C2[α2n],…,C2[αrn]=(Σ=j=1^(r)a j+o(1))n.

关键词： ramsey number bipartite ramsey number regularity lemma

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 UniversityFuyang 236037China school of mathematics Sichuan UniversityChengdu 610064China

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness *** define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall ***,we describe the semiderived Ringel-Hall algebra by the generators and defining *** 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 Z/t-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

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A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

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Acta Mathematica Scientia 2024年第4期44卷 1337-1346页

作者： Xiaosong LIU Taishun LIU school of mathematics and statistics Lingnan Normal UniversityZhanjiang 524048China Department of mathematics Huzhou UniversityHuzhou 313000China

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of *** next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of *** results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

关键词： refined Schwarz-Pick estimate bounded holomorphic mapping Carathéodory metric first order Fréchet derivative higher order Fréchet derivatives

Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system

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Chinese Physics B 2024年第6期33卷 309-322页

作者：徐玲姜磊 school of Mathematical Sciences Sichuan Normal UniversityChengdu 610066China school of mathematics and statistics Linyi UniversityLinyi 276000China

This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined ***, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.

关键词： asymmetric coupled confined space synchronization stochastic resonance stability

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2024年第1期44卷 103-114页

作者：刘慧芳毛志强 school of mathematics and statistics Jiangxi Normal UniversityNanchang330022China school of mathematics and Computer Jiangxi Science and Technology Normal UniversityNanchang330038China

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

关键词： Nevanlinna theory nonlinear differential equations meromorphic functions entire functions