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Acta Mathematica Scientia 2024年第1期44卷 247-274页

作者：郭真华张学耀 school of mathematics and CNS Northwest UniversityXi’an710127China school of mathematics and information Science Guangxi UniversityNanning530004China

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

关键词： decay rates interface Navier-Stokes equations vacuum

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

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Acta Mathematica Scientia 2024年第2期44卷 650-670页

作者：司智勇 school of mathematics and information Science Henan Polytechnic UniversityJiaozuo454003China

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

关键词： time-dependent Ginzburg-Landau equation generalized scalar auxiliary variable algorithm maximum bound principle energy stability

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

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Journal of Systems Science & Complexity 2024年第3期37卷 924-946页

作者： YANG Anqing MA Shuping school of information Engineering Shandong Management UniversityJinan 250357China school of mathematics Shandong UniversityJinan 250100China

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

关键词： Impulsive switched singular systems input-to-state stability UDE-based control

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 infinity.In this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is addressed.Due to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary terms.First,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 infinity.Second,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 constructed.This plays an important role in reformulating our problem.Third,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

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 program.Influenced 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

The stable Auslander-Reiten components of certain monomorphism categories

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Science China mathematics 2024年第3期67卷 505-526页

作者： Rasool Hafezi Yi Zhang school of mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China

Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj. In particular, for the finite components, we show that under certain mild conditions,their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.

关键词： monomorphism category almost split sequence Auslander-Reiten quiver Gorenstein projective module

UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS

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Journal of Computational mathematics 2024年第2期42卷 415-431页

作者： Yanmi Wu Dongyang Shi PLA information Engineering University Zhengzhou 450001China school of mathematics and information Sciences Yantai UniversityYantai 264005China

In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.

关键词： Time-dependent Bi-wave problem Two-grid mixed finite element method Uniform superclose and superconvergent estimates

Approximate Synchronization of Multi-Agent Systems over Finite Fields

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Journal of Systems Science & Complexity 2024年第4期37卷 1561-1580页

作者： YU Miao FENG Jun-e XIA Jianwei FU Shihua SHEN Hao school of Mathematical Sciences Liaocheng University school of mathematics Shandong University school of Electrical and information Engineering Anhui University of Technology

In this paper, the approximate synchronization of leader-follower multiagent systems(MASs) over finite fields is studied in regard to local and global synchronization. First, the approximately synchronous state set(ASSS) is obtained. Second, combined with ASSS and transient periods, some criteria for the local and global approximate synchronization of systems are given. Moreover, the algorithms for calculating the maximum approximately synchronous basin(MASB) and the maximum control invariant set(MCIS) are presented. Third, the global approximate synchronization of the system is achieved by designing the state feedback control, and a design algorithm of the controller using the truth matrix method is proposed. Moreover, the results of approximate synchronization are degenerated to complete synchronization. Last, two examples are shown to demonstrate the results of this paper.

关键词： Approximate synchronization finite field multiagent system semi-tensor product state feedback control

A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao Xia Liu Xiaoli Huang school of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China school of mathematics and information Science North Minzu UniversityYinchuan 750021China Ningxia Province Key Laboratory of Intelligent information and Data Processing Yinchuan 750021China school of mathematics and Statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming

Recent Advances on Deep Learning for Sign Language Recognition

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Computer Modeling in Engineering & Sciences 2024年第6期139卷 2399-2450页

作者： Yanqiong Zhang Xianwei Jiang school of mathematics and information Science Nanjing Normal University of Special EducationNanjing210038China

Sign language,a visual-gestural language used by the deaf and hard-of-hearing community,plays a crucial role in facilitating communication and promoting inclusivity.Sign language recognition(SLR),the process of automatically recognizing and interpreting sign language gestures,has gained significant attention in recent years due to its potential to bridge the communication gap between the hearing impaired and the hearing world.The emergence and continuous development of deep learning techniques have provided inspiration and momentum for advancing SLR.This paper presents a comprehensive and up-to-date analysis of the advancements,challenges,and opportunities in deep learning-based sign language recognition,focusing on the past five years of research.We explore various aspects of SLR,including sign data acquisition technologies,sign language datasets,evaluation methods,and different types of neural networks.Convolutional Neural Networks(CNN)and Recurrent Neural Networks(RNN)have shown promising results in fingerspelling and isolated sign recognition.However,the continuous nature of sign language poses challenges,leading to the exploration of advanced neural network models such as the Transformer model for continuous sign language recognition(CSLR).Despite significant advancements,several challenges remain in the field of SLR.These challenges include expanding sign language datasets,achieving user independence in recognition systems,exploring different input modalities,effectively fusing features,modeling co-articulation,and improving semantic and syntactic understanding.Additionally,developing lightweight network architectures for mobile applications is crucial for practical implementation.By addressing these challenges,we can further advance the field of deep learning for sign language recognition and improve communication for the hearing-impaired community.

关键词： Sign language recognition deep learning artificial intelligence computer vision gesture recognition