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A Domain Decomposition Method for Nonconforming Finite Element Approximations of Eigenvalue Problems

Communications on Applied Mathematics and Computation 2025年第2期7卷 606-636页

作者： Qigang Liang Wei Wang Xuejun Xu School of Mathematical Science Tongji UniversityShanghai200092China Key Laboratory of Intelligent Computing and Applications(Tongji University) Ministry of EducationShanghai200092China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

Since the nonconforming finite elements(NFEs)play a significant role in approximating PDE eigenvalues from below,this paper develops a new and parallel two-level preconditioned Jacobi-Davidson(PJD)method for solving the large scale discrete eigenvalue problems resulting from NFE discretization of 2mth(m=1.2)order elliptic eigenvalue *** a spectral projection on the coarse space and an overlapping domain decomposition(DD),a parallel preconditioned system can be solved in each iteration.A rigorous analysis reveals that the convergence rate of our two-level PJD method is optimal and *** results supporting our theory are given.

关键词： PDE eigenvalue problems Nonconforming finite elements(NFEs) Preconditioned Jacobi-Davidson(PJD)method Overlapping domain decomposition(DD)

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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

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Communications on Applied Mathematics and Computation 2023年第1期5卷 3-30页

作者： Kunlei Zhao Yulong Du Li Yuan State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beihang UniversityBeijing 100191China

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词： Global smoothness indicator Linear weights Sixth-order accuracy WENO

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Few-shot image recognition based on multi-scale features prototypical network

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High Technology Letters 2024年第3期30卷 280-289页

作者： LIU Jiatong DUAN Yong School of Information Science Engineering Shenyang University of TechnologyShenyang 110870P.R.China Shenyang Key Laboratory of Advanced Computing and Application Innovation Shenyang 110870P.R.China

In order to improve the model􀆳s capability in expressing features during few-shot learning,a multi-scale features prototypical network(MS-PN)algorithm is *** metric learning algo-rithm is employed to extract image features and project them into a feature space,thus evaluating the similarity between samples based on their relative distances within the metric *** sufficiently extract feature information from limited sample data and mitigate the impact of constrained data vol-ume,a multi-scale feature extraction network is presented to capture data features at various scales during the process of image feature ***,the position of the prototype is fine-tuned by assigning weights to data points to mitigate the influence of outliers on the *** loss function integrates contrastive loss and label-smoothing to bring similar data points closer and separate dissimilar data points within the metric *** evaluations are conducted on small-sample datasets mini-ImageNet and *** method in this paper can achieve higher classification ***,in the 5-way 1-shot experiment,classification accuracy reaches 50.13%and 66.79%respectively on these two ***,in the 5-way 5-shot ex-periment,accuracy of 66.79%and 85.91%are observed,respectively.

关键词： few-shot learning multi-scale feature prototypical network channel attention label-smoothing

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A Further Understanding of Differential-Linear Cryptanalysis

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Chinese Journal of Electronics 2020年第4期29卷 660-666页

作者： REN Jiongjiong CHEN Shaozhen State Key Laboratory of Mathematical Engineering and Advanced Computing State Key Laboratory of Cryptology

Differential-linear cryptanalysis has attracted much attention since proposed to attack DES in 1994, and then some generalized theories are developed to complement and unify the ***, the links between differential-linear cryptanalysis and other important cryptanalysis methods have been still *** motivation is to fix the *** establishing some boolean equations, we propose the mathematical links among differential, linear and differential-linear *** then generalise the definition of capacity and present some properties of the capacity of differential *** links and properties are employed to explore the relationships between multidimensional differential-linear hulls and integral *** show that a multidimensional differential-linear hull of certain correlation always implies the existence of an integral distinguisher and a zero-correlation linear hull, while a special integral distinguisher indicates the existence of a multidimensional differential-linear hull.

关键词： Block cipher Differential cryptanalysis Linear cryptanalysis Differential-linear cryptanalysis Integral distinguisher Zero-correlation

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The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation

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Science China Mathematics 2024年第5期67卷 975-1010页

作者： Qi Qiao Xiang Zhang School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Ministry of Education) and Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai)Shanghai Jiao Tong UniversityShanghai 200240China

For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusionmechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve *** and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the ***,we characterize both the nonlinear and spectral stability of this travelling pulse.

关键词： coupled FitzHugh-Nagumo equation singular perturbation travelling pulse spectrum nonlinear stability spectral stability

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An Encoded Double Auxiliary Pilot Channel Estimation Method for Intrinsic Interference Cancellation in FBMC/OQAM Systems 6

An Encoded Double Auxiliary Pilot Channel Estimation Method ...

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6th IEEE International Conference on Artificial Intelligence in engineering and Technology, IICAIET 2024

作者： Xing, Sixuan Xiang, Jianhong Wang, Ying Qi, Liangang Zhong, Yu College of Information and Communication Engineering Harbin Engineering University Harbin China Harbin Engineering University Key Laboratory of Advanced Ship Communication and Information Technology Harbin China Agile and Intelligent Computing Key Laboratory Chengdu China

ISBN: (纸本)9798350389692

Filter bank multicarrier technique (FBMC) is considered as a promising modulation technique suitable for future communications. However, the presence of intrinsic interference prevents the efficient implementation of techniques such as channel estimation. This paper presents a encode double auxiliary pilot channel estimation method (EDAP) for filter bank multicarrier offset quadrature amplitude modulation (FBMC/OQAM) systems. In order to eliminate the intrinsic interference, we add auxiliary symbols around the pilot, and at the same time perform a precoding process to minimize the auxiliary pilot energy loss and computational complexity. In order to validate the above method, the OQAM/FBMC system is modeled. Theoretical analysis and numerical results show that the method improves the channel estimation accuracy by 2.15-3.22 dB in double selective channels while maintaining low power consumption and low complexity. © 2024 IEEE.

关键词： Quadrature amplitude modulation

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Stepwise DOA Estimation for Coherent and Uncorrelated Mixed Signals on Coprime Array 5

Stepwise DOA Estimation for Coherent and Uncorrelated Mixed ...

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5th IEEE advanced Information Management, Communicates, Electronic and Automation Control Conference, IMCEC 2022

作者： Jiang, Heng Li, Lichun Zhang, Hailong Pan, Hongyi Li, Xue College of Information System Engineering Information Engineering University Zhengzhou China State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou China

ISBN: (纸本)9781665479677

The coprime array constructs virtual array to obtain higher degrees of freedom (DOF), but the premise of doing so is that the signals are independent of each other. Once there are coherent signals, the signal model of virtual array is destroyed and the method fails. To solve these problems, we propose the stepwise estimation of the Direction of Arrival (DOA) for a mixture of coherent and uncorrelated signals. Firstly, the symmetry of the two coprime subarrays is used to eliminate the uncorrelated signals, and combined with the properties of prime numbers, the coherent source DOA is jointly estimated. The obtained coherent source DOA was combined with the optimization algorithm to remove the coherent signal in the mixed signal. Finally, the virtual domain signal processing method was used to estimate the independent source DOA. This method can effectively reduce the influence of coherent signals on the accuracy of DOA estimation without loss of degrees of freedom. In this paper, the feasibility of the proposed method is proved by theoretical derivation, and the effectiveness of the method is also verified by experimental simulations. © 2022 IEEE.

关键词： Direction of arrival

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A Modeling Method of Cyberspace Security Structure Based on Layer-Level Division 5

A Modeling Method of Cyberspace Security Structure Based on ...

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5th IEEE International Conference on Computer and Communication engineering Technology, CCET 2022

作者： Zhu, Yuwen Yu, Lei State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou China Information Security Institute of Information Engineering Beijing100000 China

ISBN: (数字)9781665467353

ISBN: (纸本)9781665467353

As the cyberspace structure becomes more and more complex, the problems of dynamic network space topology, complex composition structure, large spanning space scale, and a high degree of self-organization are becoming more and more important. In this paper, we model the cyberspace elements and their dependencies by combining the knowledge of graph theory. Layer adopts a network space modeling method combining virtual and real, and level adopts a spatial iteration method. Combining the layer-level models into one, this paper proposes a fast modeling method for cyberspace security structure model with network connection relationship, hierarchical relationship, and vulnerability information as input. This method can not only clearly express the individual vulnerability constraints in the network space, but also clearly express the hierarchical relationship of the complex dependencies of network individuals. For independent network elements or independent network element groups, it has flexibility and can greatly reduce the computational complexity in later applications. © 2022 IEEE.

关键词： Graph theory

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Zokfuzz: Detection of Web Vulnerabilities via Fuzzing 2

Zokfuzz: Detection of Web Vulnerabilities via Fuzzing

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2nd International Conference on Consumer Electronics and Computer engineering, ICCECE 2022

作者： Zhang, Hao Dong, Weiyu Jiang, Liehui School of Cyber Science and Engineering Zhengzhou University Zhengzhou China State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou China

ISBN: (纸本)9781665408868

Fuzzing is one of the mainstream web application automated vulnerability detection methods. Because of its black box characteristics, it can be used to detect vulnerabilities without knowing the source code of the target application, so it is widely used. However, traditional web application fuzzing methods have the disadvantages of limited test cases, slow execution process, and low efficiency. In order to solve these problems, some scholars introduced genetic algorithms in the fuzzing process. However, after the test cases are entered, it is difficult to automatically detect the state of the web application, which will lead to deviations in the evolution direction of the population and the high aggressiveness of the test cases. This paper proposes a web application fuzzing script, which can realize automatic monitoring of web application status changes, and at the same time more accurately judge whether the test case is offensive. On this basis, an improved mutation method is proposed to enable the population to quickly evolve more aggressive test cases. Experimental results show that ZokFuzz can detect more web vulnerabilities compared to X-Ray and Burp Suite. © 2022 IEEE.

关键词： Genetic algorithms

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Programmable logic controller memory management vulnerability analysis 3

Programmable logic controller memory management vulnerabilit...

引用

2022 3rd International Conference on Signal Processing and Computer Science, SPCS 2022

作者： Geng, Yangyang Ma, Rongkuan Wei, Qiang Wang, Wenhai State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou China State Key Laboratory of Industrial Control Technology Zhejiang University Hangzhou310000 China

Programmable logic controller (PLC) is omnipresent in industrial control system (ICS), which plays an imperative part in critical infrastructures. However, once a PLC is compromised by an attacker, it will create destructive effects on critical infrastructures. The memory systems in PLCs are considered significant targets for attackers to disrupt real-world physical processes. In this paper, we proposed five types of attacks on the PLC memory management mechanism. Furthermore, we evaluated the feasibility of our memory attack generation approach on six PLCs from three leading controller vendors. A total of 22 memory attack payloads are implemented with several vulnerabilities on the target PLCs. © Published under licence by IOP Publishing Ltd.

关键词： Programmable logic controllers

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