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A Criterion for Elliptic Curves with Second Lowest 2-Power in L(1)(Ⅱ)

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Acta Mathematica Sinica,English Series 2005年第5期21卷 961-976页

作者： chun Lai zhao LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

Let D = p1p2 …pm, where p1,p2, ……,pm are distinct rational primes with p1 ≡p2 ≡3（mod 8）, pi =1（mod 8）（3 ≤ i ≤ m）, and m is any positive integer. In this paper, we give a simple combinatorial criterion for the value of the complex L-function of the congruent elliptic curve ED2 ： y^2 = x^3- D^2x at s = 1, divided by the period ω defined below, to be exactly divisible by 2^2m-2, the second lowest 2-power with respect to the number of the Gaussian prime factors of D. As a corollary, we obtain a new series of non-congruent numbers whose prime factors can be arbitrarily many. Our result is in accord with the predictions of the conjecture of Birch and Swinnerton-Dyer.

关键词： Elliptic curve L-function Congruent number BSD conjecture

Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion

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Acta Mechanica Sinica 2012年第5期28卷 1424-1435页

作者： Xue-Liang Zhang Bang-chun Wen chun-Yu zhao School of Mechanical Engineering and Automation Northeastern University

In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.

关键词： Synchronization Vibrating system Stability Coupling dynamic - Vibratory synchronization transmission

Two-Particle Boltzmann H-theorem

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Acta Mathematicae Applicatae Sinica 2015年第3期31卷 747-756页

作者： Burenmandula Ying-chun zhao AQILALTU School of Mathematics and Statistics Chifeng University Primary Education College Chifeng University School of Mathematical Sciences Inner Mongolia University

The celebrated H-theorem of Boltzmann has important physical significance. The H-theorem states that entropy cannot diminish, and that the distribution function f（z, t） must tend towards its equilibrium *** this paper, using the relationship between solutions of Boltzmann equation and the two-particle Boltzmann equation system, we obtain three forms of Two-Particle Boltzmann H-theorem from the two-particle Boltzmann equation system of BBGGKY hierarchy, and give an application example for the Two-Particle Boltzmann H-theorem. Also, the relation between entropy and the Two-Particle Boltzmann H-theorem is obtained.

关键词： two-particle Boltzmann system two-Particle Boltzmann H-theorem Boltzmnnn H-theorem entropy

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1115-1126页

作者： chun Xiang zhao Feng Juan MENG Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013P.R.China School of Mathematics and Physics Jiangsu University of TechnologyChangzhou 213001P.R.China

In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at *** the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed *** results obtained essentially improve and complete some previous works.

关键词： Time-dependent attractor extensible beams equation nonlocal weak damping

Modeling for heterogeneous objects based on X language: A modeling method of algorithm-hardware

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第2期13卷 125-147页

作者： Liu Yue zhao chun School of Computer Beijing Information Science and Technology University Beijing 100101P.R.China

With the development of system engineering and related technology,modeling and sim-ulation of complex systems need to include many disciplines,modeling languages,sim-ulation environments,*** using unified modeling language to build models,barriers among different fields can be broken;the efficiency of model integration can be ***,a complex system contains some integrated circuit modules,which can be used for control or calculation of the *** with system model,integrated circuit model is more fine-grained and lower-level and contains logic for control and ***,a method that modeling integrated circuit by unified modeling language is *** this paper,a unified modeling language is introduced,called X language,and a modeling method of algorithm-hardware based on the X language is *** of all,the hardware characteristics of the Kalman filter algorithm are extracted by analyzing the ***,X language models are built to describe the ***,the X language models are converted to Very-High-Speed Integrated Circuit Hardware Description Language(VHDL).Finally,the algorithm-hardware mod-els are simulated and *** results show that the algorithm-hardware modeling method based on X language is feasible.

关键词： Model integration X language VHDL

A residual-based message passing algorithm for constraint satisfaction problems

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Communications in Theoretical Physics 2022年第3期74卷 77-86页

作者： chun-Yan zhao Yan-Rong Fu Jin-Hua zhao College of Science University of Shanghai for Science and TechnologyShanghai 200093China Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum MatterSouth China Normal UniversityGuangzhou 510006China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing CenterSouth China Normal UniversityGuangzhou 510006China

Message passing algorithms,whose iterative nature captures complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages,provide a powerful toolkit in tackling hard computational tasks in optimization,inference,and learning *** the context of constraint satisfaction problems(CSPs),when a control parameter(such as constraint density)is tuned,multiple threshold phenomena emerge,signaling fundamental structural transitions in their solution *** solutions around these transition points is exceedingly challenging for algorithm design,where message passing algorithms suffer from a large message fiuctuation far from *** we introduce a residual-based updating step into message passing algorithms,in which messages with large variation between consecutive steps are given high priority in the updating *** the specific example of model RB(revised B),a typical prototype of random CSPs with growing domains,we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational *** approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.

关键词： constraint satisfaction problems model RB message passing algorithms residuals of messages

FPGA-based edge computing: Task modeling for cloud-edge collaboration

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第2期13卷 148-167页

作者： Chuan Xiao chun zhao School of Computer Beijing Information Science and Technology University Beijing 100101 China

With the development of the Internet of Things and devices continuing to scale,using cloud computing resources to process data in real-time is *** computing technologies can improve real-time performance in processing *** introducing the FPGA into the computing node and using the dynamic reconfigurability of the FPGA,the FPGA-based edge node can increase the edge node *** this paper,a task-based collaborative method for an FPGA-based edge computing system is proposed in order to meet the collaboration among FPGA-based edge nodes,edge nodes,and the *** modeling of the task includes two parts,task information and task-dependent *** information is used to describe the running information and dependency infor-mation required for the task ***-dependent file contains the configuration bit-stream of FPGA in running of the *** analyzing the task behavior,this paper builds four basic behaviors,analyzes the critical attributes of each behavior,and summa-rizes the task model suitable for FPGA-based edge *** with specific functions can be created by modifying different attributes of model ***,the availability of the model and the task-based collaborative method are verified by simulation *** experimental results that the task model proposed in this paper can meet cloud-edge collaboration in the FPGA-based edge computing environment.

关键词： Task modeling edge computing cloud-edge collaboration

Synthesis and in vitro-Anti-hepatitis B Virus Activities of Several Ethyl 5-Hydroxy-1H-indole-3-carboxylates

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Chemical Research in Chinese Universities 2006年第5期22卷 577-583页

作者： zhao chun-shen zhao Yan-fang CHAI Hui-fang GONG Ping Liaoning Province Key Laboratory of Innovative Medicine Research and Design Shenyang Pharmaceutical University Shenyang 110016 P. R. China

A series of ethyl 5-hydroxyindole-3-earboxylates 6a-10r was designed and synthesized. The structures of all the compounds were confirmed by IR, ^1H NMR, and MS and their anti-hepatitis B virus （HBV） activities were evaluated in 2.2.15 cells. Among them, compound 7g { ethyl 5-hydroxy-2- [ （ 3-methoxyphenylsulfinyl ） methyl ] -1-methyl-4- [ （4-methylpiperazin-1-yl） methyl ]-1H-indole-3-carboxylate} displays a significant anti-HBV activity, which is more potent than the positive control lamivudine.

关键词： Ethyl 5-hydroxy-1H-indole-3-carboxylates Synthesis Anti-hepatitis B virus activity

Bi-f-harmonic map equations on singly warped product manifolds

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Applied Mathematics(A Journal of Chinese Universities) 2015年第1期30卷 111-126页

作者： zhao chun-li LU Wei-jun Center of Mathematical Sciences Zhejiang University College of Sciences Guangxi University for Nationalities

Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps. In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensionM manifolds and some special maps from or into a warped product manifold.

关键词： f-tension field bi-f-tension field bi-f-harmonic map f-bi-harmonic map singly warped productmanifold.