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On Isodual Double Toeplitz Codes

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Journal of Systems Science & Complexity 2024年第5期37卷 2196-2206页

作者： SHI Minjia XU Li SOLé Patrick Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University State Key Laboratory of information Security Institute of Information Engineering Chinese Academy of Sciences CNRS University of Aix Marseille Centrale Marseille

Double Toeplitz（shortly DT） codes are introduced here as a generalization of double circulant codes. The authors show that such a code is isodual, hence formally self-dual（FSD）. FSD codes form a far-reaching generalization of self-dual codes, the most important class of codes of rate one-half. Self-dual DT codes are characterized as double circulant or double negacirculant. Likewise, even binary DT codes are characterized as double circulant. Numerical examples obtained by exhaustive search show that the codes constructed have best-known minimum distance, up to one unit, amongst formally self-dual codes, and sometimes improve on the known values. For q = 2, the authors find four improvements on the best-known values of the minimum distance of FSD codes. Over F4an explicit construction of DT codes, based on quadratic residues in a prime field, performs equally well. The authors show that DT codes are asymptotically good over Fq. Specifically, the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.

关键词： Double circulant codes double Toeplitz codes formally self-dual codes isodual codes

A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row-column confusion and closed-loop bi-directional diffusion

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Chinese Physics B 2024年第2期33卷 228-237页

作者：张哲祎牟俊 Santo Banerjee 曹颖鸿 School of information Science and Engineering Dalian Polytechnic UniversityDalian 116034China Department of mathematical sciences Politecnico di TorinoTorino 10129Italy

Security during remote transmission has been an important concern for researchers in recent *** this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the *** ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic *** highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark *** experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.

关键词： chaotic hierarchical encryption multi-medical image encryption differentiated visual effects row-column confusion closed-loop bi-directional diffusion transform domain watermark embedding

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

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Chinese Physics B 2024年第7期33卷 137-145页

作者：张晓娇吴祥 School of Mathematics and information Science Nanchang Normal UniversityNanchang 330032China School of mathematical sciences Guizhou Normal UniversityGuiyang 550001China

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

关键词： contraction theory virtual system bipartite consensus Lurie multi-agent systems

Chimera states of phase oscillator populations with nonlocal higher-order couplings

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Chinese Physics B 2024年第4期33卷 402-407页

作者：伍勇刚余华健郑志刚徐灿 School of mathematical sciences Huaqiao UniversityQuanzhou 362021China Institute of Systems Science and College of information Science and Engineering Huaqiao UniversityXiamen 361021China

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical ***, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial *** works have shown that higher-order interactions promote coherent ***, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent ***, we identify that the chimera states arise as a result of multi-attractors in dynamic ***, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera *** the observed results can be well described in terms of the dimension reduction *** study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

关键词： synchronization complex system coupled oscillators phase transition

Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1767-1777页

作者： Yan Yue SHI Bo ZHANG Xu TANG Yu Feng LU School of mathematical sciences Ocean University of ChinaQingdao 266100P.R.China School of Mathematics and information sciences Yantai UniversityYantai 264005P.R.China School of mathematical sciences Space Engineering UniversityBeijing 101416P.R.China School of mathematical sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a ***,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)*** also give some interesting examples.

关键词： Reducing subspace operator-weighted shifts Toeplitz operator von Neumann algebra

A SCHWARZ LEMMA FOR TRANSVERSALLY V-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

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Acta Mathematica Scientia 2024年第6期44卷 2509-2526页

作者：黄昕 School of mathematical sciences Fudan University School of Mathematics and Statistics Nanjing University of Information Science and Technology

In this paper,we prove a transversal V-Laplacian comparison theorem under a transversal Bakry-Emery Ricci *** establish a Schwarz type lemma for transversally V-harmonic maps of bounded generalized transversal dilatat... 详细信息

关键词： Schwarz lemma transversal V-Laplacian comparison theorem transversally V-harmonic map

Density peak clustering using tensor network

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Science China(information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHI Yun SHANG Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of mathematical sciences University of Chinese Academy of Sciences National Center for Mathematics and Interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

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Chinese Physics B 2024年第10期33卷 176-189页

作者： Xuan Wang Santo Banerjee Yinghong Cao Jun Mou School of information Science and Engineering Dalian Polytechnic UniversityDalian 116034China Department of mathematical sciences Giuseppe Luigi LagrangePolitecnico di TorinoCorso Duca degli Abruzzi 24TorinoItaly

Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for *** this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron *** simulations show that the neuronal models in different scenarios have multiple burst firing *** introduction of the memristor makes the neuronal model exhibit complex dynamical ***,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.

关键词： memristor multistability Hamilton energy firing pattern Neuron model hardware implementation

Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces

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Acta Mathematica Sinica,English Series 2024年第8期40卷 1967-1988页

作者： Jian Xiang DONG Chun Xu XU Yu Feng LU School of mathematical sciences Dalian University of TechnologyDalian 116024P.R.China School of Mathematics and information Science Guangzhou UniversityGuangzhou 510006P.R.China

In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz oper... 详细信息

关键词： Block dual Toeplitz operators boundedness compactness Fock space (semi)-commutator