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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 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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On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition

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Science China mathematics 2024年第4期67卷 819-854页

作者： Zijin Li Xinghong Pan Jiaqi Yang school of mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China school of mathematics and Key Laboratory of Ministry of Industry and Information Technology Nanjing University of Aeronautics and AstronauticsNanjing 211106China school of mathematics and statistics Northwestern Polytechnical UniversityXi'an 710129China

The original Leray’s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary condition at spatial *** this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is *** to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary ***,the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced,which will serve as the asymptotic profile of the solution to the generalized Leray’s problem at spatial ***,a solenoidal vector function defined in the whole pipe,satisfying the Navierslip boundary condition,having the designated flux and equalling the Poiseuille flow at a large distance,will be carefully *** plays an important role in reformulating our ***,the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity.

关键词： stationary Navier-Stokes system Navier-slip boundary condition Leray's problem

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A unified pre-training and adaptation framework for combinatorial optimization on graphs

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Science China mathematics 2024年第6期67卷 1439-1456页

作者： Ruibin Zeng Minglong Lei Lingfeng Niu Lan Cheng school of Computer Science and Technology University of Chinese Academy of SciencesBeijing100049China Faculty of Information Technology Beijing University of TechnologyBeijing100124China school of Economics and Management University of Chinese Academy of SciencesBeijing100190China school of mathematics and statistics Central South UniversityChangsha410075China

Combinatorial optimization(CO)on graphs is a classic topic that has been extensively studied across many scientific and industrial ***,solving CO problems on graphs through learning methods has attracted great *** deep learning methods,e.g.,graph neural networks(GNNs),have been used to effectively assist the process of solving ***,current frameworks based on GNNs are mainly designed for certain CO problems,thereby failing to consider their transferable and generalizable abilities among different COs on ***,simply using original graphs to model COs only captures the direct correlations among objects,which does not consider the mathematical logicality and properties of *** this paper,we propose a unified pre-training and adaptation framework for COs on graphs with the help of the maximum satisfiability(Max-SAT)*** first use Max-SAT to bridge different COs on graphs since they can be converted to Max-SAT problems represented by standard formulas and clauses with logical *** we further design a pre-training and domain adaptation framework to extract the transferable and generalizable features so that different COs can benefit from *** the pre-training stage,Max-SAT instances are generated to initialize the parameters of the *** the fine-tuning stage,instances from CO and Max-SAT problems are used for adaptation so that the transferable ability can be further *** experiments on several datasets show that features extracted by our framework exhibit superior transferability and Max-SAT can boost the ability to solve COs on graphs.

关键词： combinatorial optimization graph neural networks domain adaptation maximum satisfiability problem

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Event-triggered distributed cross-dimensional formation control for heterogeneous multi-agent systems

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Frontiers of Information Technology & Electronic Engineering 2024年第8期25卷 1123-1133页

作者： Huimin WEI Chen PENG Min ZHAO school of Mechatronic Engineering and Automation Shanghai UniversityShanghai 200444China school of mathematics and statistics Nantong UniversityNantong 226019China

This paper concerns the event-triggered distributed cross-dimensional formation control problem of heterogeneous multi-agent systems(HMASs)subject to limited network *** central aim is to design an effective distributed formation control scheme that will achieve the desired formation control objectives even in the presence of restricted ***,a multi-dimensional HMAS is first developed,where a group of agents are assigned to several subgroups based on their ***,to mitigate the excessive consumption of communication resources,a cross-dimensional event-triggered communication mechanism is designed to reduce the information interaction among agents with different *** the proposed event-based communication mechanism,the problem of HMAS cross-dimensional formation control is transformed into the asymptotic stability problem of a closed-loop error ***,several stability criteria for designing a cross-dimensional formation control protocol and communication schedule are presented in an environment where there is no information interaction among follower ***,a simulation case study is provided to validate the effectiveness of the proposed formation control protocol.

关键词： Heterogeneous multi-agent systems Formation control Cross-dimensional event-triggered mechanism

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

Distributed Heterogeneous Multi-Agent Optimization with Stochastic Sub-Gradient

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Journal of Systems Science & Complexity 2024年第4期37卷 1470-1487页

作者： HU Haokun MO Lipo CAO Xianbing school of mathematics and statistics Central South UniversityChangsha 410083China school of mathematics and statistics Beijing Technology and Business UniversityBeijing 100048China Research Centre for Agri-Product Quality Traceability Beijing Technology and Business UniversityBeijing 100048China school of Computer and Artificial Intelligence Beijing Technology and Business UniversityBeijing 100048China China Food Flavor and Nutrition Health Innovation Center Beijing Technology and Business UniversityBeijing 100048China

This paper studies the optimization problem of heterogeneous networks under a timevarying *** agent only accesses to one local objective function,which is *** improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all *** weaken the effect of these noises,two step sizes are introduced in the control *** graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost *** last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.

关键词： Communication noises distributed stochastic optimization heterogeneous networks subgradient measurement noises

Trace formula of the integro-differential operator on a quantum graph

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Applied mathematics(A Journal of Chinese Universities) 2024年第2期39卷 311-318页

作者： WEI Li-xiao YANG Chuan-fu school of mathematics and statistics Nanjing University of Science and TechnologyNanjing 210094China.

In this paper we study the eigenvalue problem for integro-differential operators on a lasso *** trace formula of the operator is established by applying the residual technique in complex analysis.

关键词： integro-differential operators eigenvalue trace formula

On the Proper Holomorphic Mappings between Equidimensional Hartogs Domains over Hermitian Symmetric Manifolds

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1215-1228页

作者： En Chao BI school of mathematics and statistics Qingdao UniversityQingdao 266071P.R.China

In this paper,we study a family of Hartogs domains fibred over Hermitian symmetric manifolds being a unit ball in C^(m).The aim of the present study is to establish the rigidity results about proper holomorphic mappings between two equidimensional Hartogs domains over Hermitian symmetric *** particular,we can fully determine its biholomorphic equivalence and automorphism group.

关键词： Proper holomorphic mapping Hartogs domains Hermitian symmetric manifolds

Equivalence between the internal observability and equation

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Applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 89-97页

作者： LIU Wen-jun TU Zhi-yu school of mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave *** by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

关键词： Moore-Gibson-Thompson equation internal observability exponential stability