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science China(Information sciences) 2024年第6期67卷 328-341页

作者： Xian-Ming ZHANG Qing-Long HAN Bao-Lin ZHANG Xiaohua GE Dawei ZHANG School of science Computingand Engineering TechnologiesSwinburne University of Technology college of Automation and Electronic Engineering Qingdao University of Science & Technology School of mathematics Shandong University

This paper is concerned with event-triggered H∞control of sampled-data systems. Its novelties lie in three aspects:（i） A novel accumulated-state-error-based event-triggered scheme is introduced by comparing the integral of the state error from tk to t with the system state sampled at tk. This condition works well due to the fact that the so-called Zeno behaviour does not occur.（ii） A novel Lyapunov functional is constructed to establish a criterion to ensure some certain H∞performance of the closed-loop system. This Lyapunov functional is dependent on the integral of the state error involved in the event-triggered scheme.（iii） Under the event-triggered sampling scheme, suitable state-feedback controllers can be designed rather than be given a priori. Moreover, a self-triggered implementation of the proposed event-triggered sampling scheme is presented as well. Finally, a batch reactor model and an inverted pendulum system are given to demonstrate the effectiveness of the proposed method.

关键词： event-triggered sampling self-triggered implementation $H_\infty$ control looped-functional

Nodal Solutions with a Prescribed Number of Nodes for Quasilinear Schr?dinger Equations with a Cubic Term

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Journal of Mathematical Research with Applications 2024年第5期 681-696页

作者： Jing LAI Na LIU Tao WANG college of mathematics and computing science Hunan University of Science and Technology

This paper is concerned with the existence of nodal solutions for the following quasilinear Schr?dinger equation with a cubic term ■ where N ≥ 3, λ > 0, the function V（|x|） is a radially symmetric and positive potential. By using the variational method and energy comparison method, for any given integer k ≥ 1, the above equation admits a radial nodal solution Uk,4λhaving exactly k nodes via a limit ***, the energy of Uk,4λis monotonically increasing in k and for any sequence {λ_n}, up to a subsequence,■ converges strongly to some ■ as λ_n→+∞, which is a radial nodal solution with exactly k nodes of the classical Schr¨dinger equation ■ Our results extend the existing ones in the literature from the super-cubic case to the cubic case.

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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of Systems science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun DONG Huanhe FANG Yong college of mathematics and Systems science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Quantum control based on three forms of Lyapunov functions

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Chinese Physics B 2024年第4期33卷 216-222页

作者：俞国慧杨洪礼 college of mathematics and Systems science Shandong University of Science and TechnologyQingdao 266590China

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state *** this paper, the specific control laws under the three forms are *** is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test *** calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing ***, a unified form of the control laws under the three forms is given.

关键词： quantum system Lyapunov function particle swarm optimization simulated annealing algorithms quantum control

DCVAE-adv:A Universal Adversarial Example Generation Method for White and Black Box Attacks

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Tsinghua science and Technology 2024年第2期29卷 430-446页

作者： Lei Xu Junhai Zhai college of mathematics and Information science Hebei UniversityBaoding 071002China

Deep neural network(DNN)has strong representation learning ability,but it is vulnerable and easy to be fooled by adversarial *** order to handle the vulnerability of DNN,many methods have been *** general idea of existing methods is to reduce the chance of DNN models being fooled by observing some designed adversarial examples,which are generated by adding perturbations to the original *** this paper,we propose a novel adversarial example generation method,called *** from the existing methods,DCVAE-adv constructs adversarial examples by mixing both explicit and implicit perturbations without using original ***,the proposed method can be applied to both white box and black box *** addition,in the inference stage,the adversarial examples can be generated without loading the original images into memory,which greatly reduces the memory *** compared DCVAE-adv with three most advanced adversarial attack algorithms:FGSM,AdvGAN,and AdvGAN++.The experimental results demonstrate that DCVAE-adv is superior to these state-of-the-art methods in terms of attack success rate and transfer ability for targeted *** code is available at https://***/xzforeverlove/DCVAE-adv.

关键词： deep neural network adversarial examples white box attack black box attack robustness

Global Solvability for a Predator-Prey Model with Prey-Taxis and Rotational Flux Terms

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Chinese Annals of mathematics,Series B 2024年第2期45卷 297-318页

作者： Guoqiang REN Bin LIU School of mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific computing Huazhong Universityof Science and Technology

In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model... 详细信息

关键词： Predator-prey Prey-taxis Giopal existence Kotational flnux

Physical informed memory networks for solving PDEs:implementation and applications

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Communications in Theoretical Physics 2024年第2期76卷 51-61页

作者： Jiuyun Sun Huanhe Dong Yong Fang college of mathematics and Systems science Shandong University of Science and TechnologyQingdao 266590China

With the advent of physics informed neural networks(PINNs),deep learning has gained interest for solving nonlinear partial differential equations(PDEs)in recent *** this paper,physics informed memory networks(PIMNs)are proposed as a new approach to solving PDEs by using physical laws and dynamic behavior of *** the fully connected structure of the PINNs,the PIMNs construct the long-term dependence of the dynamics behavior with the help of the long short-term memory ***,the PDEs residuals are approximated using difference schemes in the form of convolution filter,which avoids information loss at the neighborhood of the sampling ***,the performance of the PIMNs is assessed by solving the Kd V equation and the nonlinear Schr?dinger equation,and the effects of difference schemes,boundary conditions,network structure and mesh size on the solutions are *** show that the PIMNs are insensitive to boundary conditions and have excellent solution accuracy even with only the initial conditions.

关键词： nonlinear partial differential equations physics informed memory networks physics informed neural networks numerical solution

New Results on Equivalence of Multivariate Polynomial Matrices

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Journal of Systems science & Complexity 2024年

作者： GUAN Jiancheng LIU Jinwang ZHENG Licui WU Tao LIU Jie School of mathematics and computing science Hunan University of science and Technology

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible *** authors give a necessary and sufficient condition for this *** the authors present an algorithm to reduce a class of multivariate polynomial matrices to their Smith forms.

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Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 665-694页

作者： Aihemaitijiang YUMAIER Ehmet KASIM college of mathematics and Systems science Xinjiang UniversityUrumqi 830046China

This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for ***,we investigate the well-posedenss of the system by applying the operator semigroup ***,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.

关键词： multi-state system C0-semigroup Dirichlet operator well-posedness asymptotic behavior

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels