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Burning Numbers of Barbells

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 526-538页

作者： Hui-qing LIU Rui-ting ZHANG Xiao-lan HU hubei key laboratory of Applied mathematics&Faculty of mathematics and Statistic Hubei UniversityWuhan 430062China hubei key laboratory of mathematical sciences&school of mathematics and statistics Central China Normal UniversityWuhan 430079China

Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk su... 详细信息

关键词： burning number short/long barbell isometric subtree cycle

BUBBLING ANALYSIS FOR A NONLINEAR DIRAC EQUATION ON SURFACES

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Acta Mathematica Scientia 2024年第6期44卷 2073-2082页

作者：陈优民刘磊朱苗苗 Department of mathematics Shantou University school of mathematics and statistics and hubei key laboratory of mathematical sciences Central China Normal University school of mathematical sciences Shanghai Jiao Tong University

In this paper,we apply the three circle type method and a Hardy type inequality to a nonlinear Dirac type equation on surfaces,and provide alternative proofs to the energy quantization results.

关键词： 53C27 58J05 energy identity Hardy inequality nonlinear Dirac equation three circle method

Polynomial-Time key-Recovery Attacks Against NTRURe Encrypt from ASIACCS'15

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Journal of Systems Science & Complexity 2024年第3期37卷 1308-1325页

作者： LIU Zhen PAN Yanbin ZHENG Jinwei school of Cyber Science and Technology Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhan 430062China key laboratory of mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of mathematical sciences University of Chinese Academy of SciencesBeijing 100190China

In ASIACCS 2015, Nu nez, et al. proposed a proxy re-encryption scheme, named NTRURe Encrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator’s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee’s private key. Because of the potential resistance to quantum algorithm, high efficiency and various applications in real life,NTRURe Encrypt has drawn lots of attention and its security has been widely discussed and *** PQCrypto2019, Liu, et al. proposed two key recovery attacks against it. However, their first attack heavily relies on a weaken decryption oracle, and the second attack needs to collect about 260ciphertexts from the same message by theoretical analysis, which makes both of the attacks unrealistic. In this paper, inspired by the broadcast attack against NTRU, the authors find out that for NTRURe Encrypt the delegator and the delegatee can efficiently recover each other’s private key in polynomial time without any unrealistic assumptions. In addition, the authors also show how to fix NTRURe Encrypt to resist the proposed attacks. As a by-product, the authors also show how to commit broadcast attacks against NTRU 2001 with even dg, which was thought infeasible before.

关键词： Broadcast attack key recovery NTRU NTRUReEncrypt

Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds

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Science China mathematics 2024年

作者： Wanjun Ai Lei Liu Miaomiao Zhu school of mathematics and statistics Southwest University school of mathematics and statistics and hubei key laboratory of mathematical sciences Central China Normal University school of mathematical sciences Shanghai Jiao Tong University

For a sequence of approximate Dirac-harmonic maps from a Riemannian surface with a smooth boundary into a stationary Lorentzian manifold,we study the boundary blow-up analysis and prove the positive energy identity for spinors and the Lorentzian energy identity for ***,the positive energy identity for maps holds when the target is a static Lorentzian manifold.

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A new quantity in Finsler geometry

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Science China mathematics 2024年第4期67卷 883-890页

作者： Xiaohuan Mo Xiaoyang Wang key laboratory of Pure and Applied mathematics School of Mathematical SciencesPeking UniversityBeijing 100871China school of mathematics and statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study a new Finslerian quantity■defined by the T-curvature and the angular metric *** show that the■-curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature but also has a vanishing *** find that the■-curvature is closely related to the Riemann curvature,the Matsumoto torsion and theΘ-*** solve ***’s open problem in terms of the■-***,we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the■-curvature,generalizing a theorem previously only known in the case of negatively curved Finsler metrics of scalar flag curvature.

关键词： Finsler metric Finslerian quantity T-curvature -curvature Randers metric

Gorenstein projective modules over rings of Morita contexts

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Science China mathematics 2024年第11期67卷 2453-2484页

作者： Qianqian Guo Changchang Xi school of mathematical sciences Capital Normal University school of mathematical sciences Laboratory of Mathematics and Complex Systems(Ministry of Education of China)Beijing Normal University school of mathematics and statistics Shaanxi Normal University

Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism *** extends greatly the results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature,where only sufficient conditions are given under a strong assumption of compatibility of *** application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita *** results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.

关键词： Gorenstein-projective module noetherian ring noncommutative tensor product totally exact complex weakly compatible bimodule

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

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Acta Mathematica Scientia 2024年第2期44卷 484-514页

作者：林孝盛杨大春杨四辈袁文 laboratory of mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China school of mathematics and statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild *** HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by *** this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy *** results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey ***,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

关键词： Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function

The Non-inclusion Diagnosability of Hypercubes Under the PMC Model

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Journal of the Operations Research Society of China 2024年第2期12卷 478-484页

作者： Mei-Jie Ma Min Xu Tong-Tong Ding Xiang-Jun Li Qiang Zhu school of mathematics and statistics Qilu University of Technology(Shandong Academy of Sciences)Jinan 250353ShandongChina school of mathematical sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China school of Information and mathematics Yangtze UniversityJingzhou 434023HubeiChina school of mathematics and statistics XiDian UniversityXi'an 710071ShaanXiChina

Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection ***-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor *** on a sound assumption proposed by Zhu et ***,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability t_(N)(Q_(n))of the hypercube under the PMC model is *** is,assume that if two vertex sets F_(1) and F_(2) are both consistent with a syndrome and F_(1)C F_(2),then F_(2) is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Q_(n) under the PMC model.

关键词： Interconnection network Diagnosability Hypercube PMC model

Aubry-Mather theory for contact Hamiltonian systems Ⅲ

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Science China mathematics 2024年第11期67卷 2541-2570页

作者： Panrui Ni Lin Wang Shanghai Center for mathematical sciences Fudan University school of mathematics and statistics Beijing Institute of Technology

By exploiting the contact Hamiltonian dynamics（T*M × R,Φ_t） around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φ_t-recurrent set,the strongly static set,the Aubry set,the Ma?é set,and the Φ_t-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser（KAM） solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-Mather theory weak KAM theory contact Hamiltonian systems Hamilton-Jacobi equations