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GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

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Acta Mathematica Scientia 2024年第3期44卷 909-924页

作者：王晓闪王忠谦贾哲 Department of mathematics Luoyang Normal UniversityLuoyang471934China school of mathematics science Jiangsu Second Normal UniversityNanjing210013China school of mathematics and Statistics Linyi UniversityLinyi276005China

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> *** addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> *** is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

关键词： global weak solutions attraction-repulsion p-Laplacian logistic source

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

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1594-1608页

作者： Lulu FANG Jihua MA Kunkun SONG Xin YANG school of mathematics and Statistics Nanjing University of Science and TechnologyNanjing210094China school of mathematics and Statistics Wuhan UniversityWuhan 430072China Key Laboratory of Computing and Stochastic mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction *** study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial *** a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

关键词： continued fractions product of partial quotients Hausdorff dimension

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

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IEEE/CAA Journal of Automatica Sinica 2024年第5期11卷 1304-1306页

作者： Meng-Meng Jiang Kemei Zhang Xue-Jun Xie school of mathematics science Liaocheng UniversityLiaocheng 252059China school of mathematics science Qufu Normal UniversityQufu 273165China Institute of Automation Qufu Normal UniversityQufu 273165China

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order *** constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

关键词： Nonlinear stabilization guarantee

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of Systems science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu school of mathematics Statistics and MechanicsBeijing University of TechnologyBeijing 100124China Academy of mathematics and Systems science Chinese Academy of SciencesBeijing 100190China

In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer *** a result,research on this model has *** this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model *** authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed ***,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these *** effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION

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Journal of Computational mathematics 2024年第4期42卷 1124-1144页

作者： Hanzhang Hu Yanping Chen Jianwei Zhou school of mathematics Jiaying UniversityMeizhou 514015China school of Mathematical science South China Normal UniversityGuangzhou 510631China school of mathematics and Statistics Linyi UniversityLinyi 276005China

A two-grid finite element method with L1 scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger *** finite element solution in the L-norm are proved bounded without any time-step size conditions(dependent on spatial-step size).The classical L1 scheme is considered in the time direction,and the two-grid finite element method is applied in spatial *** optimal order error estimations of the two-grid solution in the LP-norm is proved without any time-step size *** is shown,both theoretically and numerically,that the coarse space can be extremely coarse,with no loss in the order of accuracy.

关键词： Time-fractional nonlinear Schrodinger equation Two-grid finite element me-thod The L1 scheme

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data science Peking University Zuse Institute Berlin Department of mathematics and Computer science Freie Universit?t Berlin Laboratory of mathematics and Applied mathematics(LMAM)and school of Mathematical {3.s Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

APPROXIMATELY ARTINIAN （NOETHERIAN） C*-ALGEBRAS

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Acta Mathematica Scientia 2024年第6期44卷 2485-2497页

作者： Mohammad ROUZBEHANI Massoud AMINI Mohammad B.ASADI school of mathematics Statistics and Computer ScienceCollege of ScienceUniversity of Tehran Department of mathematics Faculty of Mathematical SciencesTarbiat Modares University school of mathematics Institute for Research in Fundamental Sciences (IPM)

In this article,we introduce and study the class of approximately Artinian（Noetherian） C*-algebras,called AR-algebras（AN-algebras）,which is a simultaneous generalization of Artinian（Noetherian） C*-algebras and *** study properties such as the ideal property and topological dimension zero for *** particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely *** extends the Kirchberg's O∞-absorption theorem,and implies that a weakly purely infinite C*-algebra is Noetherian iff every its ideal has a full projection.

关键词： (weakly) purely infinite 46L05 46L80 Artinian C*-algebra graph C*-algebra ideal property inductive limit Noetherian

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

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Acta Mathematica Scientia 2024年第3期44卷 1145-1164页

作者：冯立超张春艳曹进德武志辉 College of science North China University of Science and TechnologyTangshan063210China school of mathematics Southeast UniversityNanjing210096China Department of mathematics Harbin University of Science and TechnologyHarbin150080China

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential ***,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential *** comparison with autonomous cases,non-autonomous systems are of great interest and represent an important ***,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are *** should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

关键词： hybrid neutral stochastic differential delay system discrete feedback control general stabilization polynomial stabilization