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Uniform and Semi-uniform Convergence for Discontinuous Skew-product Transformation and Observation

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Acta Mathematica Sinica,English Series 2021年第2期37卷 333-344页

作者： Xia PAN zuo huan zheng Zhe ZHOU College of Liberal Arts and Sciences National University of Defense TechnologyChangsha 410073P.R.China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049P.R.China ollege of Mathematics and Statistics Hainan Normal UniversityHaikou 571158P.R.China

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.

关键词： Skew-product transformation uniform ergodicity semi-uniform ergodicity

A Note on Equilibrium of Eventually Strongly Monotone Skew-product Semiflows

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Acta Mathematicae Applicatae Sinica 2010年第2期26卷 307-310页

作者： Xi-liang Li zuo-huan zheng Shandong Institute of Business and Technology Yantai 264005 China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China

In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.

关键词： continuous equilibrium eventually strongly monotone skew-product semiflow

Almost Periodic Solutions by the Harmonic Balance Method

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 943-954页

作者： Ji-feng CHU zuo-huan zheng Zhe ZHOU Department of Mathematics Shanghai Normal UniversityShanghai 200234China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China College of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China

We consider non-autonomous ordinary differential equations in two *** is the one-dimensional case that admits a condition of hyperbolicity,and the other one is the higher-dimensional case that admits an exponential *** differential equations of this kind,we give a rigorous treatment of the Harmonic Balance Method to look for almost periodic solutions.

关键词： almost periodic solution Harmonic balance method exponential dichotomy

A Mathematical Model of the Photosynthetic Carbon Metabolism Has Multiple Steady States Under the Same Parameter Conditions

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 591-604页

作者： Jin-ling ZHOU zuo-huan zheng Xin-guang ZHU Institute of Science and Technology Zhejiang International Studies University. Hangzhou 310012 China Institute of Applied Mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences. Beijing 100080 China CAS-MPG Partner Institute for Computational Biology and Key Laboratory for Computational Biology Shanghai Institutes for Biological Sciences Chinese Academy of Sciences Shanghai 200031 China

This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also another two important metabolic pathways： starch synthesis and photorespiratory pathway. Theoretically, the paper shows the existence of steady states, stability and instability of the steady states, the effects of CO2 concentration on steady states. Especially, a critical point is found, the system has only one steady state with C02 concentration in the left neighborhood of the critical point, but has two with C02 concentration in the right neighborhood. In addition, the paper also explores the influence of C02 concentration on the efficiency of photosynthesis. These theoretical results not only provide insight to the kinetic behaviors of the photosynthetic carbon metabolism, but also can be used to help improving the efficiency of photosynthesis in plants.

关键词： photosynthesis the efficiency of photosynthesis multiple steady states stability critical point

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 695-707页

作者： Song-bai GUO Yu-ling XUE Xi-liang LI zuo-huan zheng School of Science Beijing University of Civil Engineering and ArchitectureBeijing 102616China School of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Information Science Shandong Technology and Business UniversityYantai 264005China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>*** approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using *** addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)1.

关键词： uniform persistence epidemic model control reproduction number quarantine standard incidence rate

Efficient Task Decomposition for Sequential Crowdsourced Task Solving

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Chinese Journal of Electronics 2020年第3期29卷 468-475页

作者： JIANG huan zuo Min MATSUBARA Shigeo National Engineering Laboratory for Agri-product Quality Traceability School of Computer and Information EngineeringBeijing Technology and Business University

In order to facilitate crowdsourcing-based task solving, complex tasks are decomposed into smaller subtasks that can be executed by individual *** task into sequential subtasks attracts a plenty of empirical explorations. The absence of formal studies makes it difficult to provide task requesters with explicit guidelines on task decomposition *** formally present the vertical task decomposition model by specifying the positive quality dependencies among sequential subtasks. Our focus is on addressing solutions of low quality intentionally provided by selfinterested workers who are paid equally or based on their contributions. By combining the theoretical analysis on workers’ strategic behaviors and experimental exploration on the efficiency of task decomposition, our study demonstrates the relationship between the incentive and the worker’s performance, and gives the explicit instructions on vertical task decomposition, which show promise on improving the quality of the final outcome.

关键词： Crowdsourcing Task decomposition Subtask dependence Solution quality Revenue sharing

Investigation of wake-induced vibration interference between two staggered wave-cone cylinders at subcritical Reynolds number

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Journal of Hydrodynamics 2024年第2期36卷 378-393页

作者： Lin Zou Di-wei Liu Jian Liu Hong-cheng zuo Yin-huan zheng Hao Xia School of Mechanical and Electronic Engineering Wuhan University of TechnologyWuhan430070China Department of Aeronautical and Automotive Engineering Loughborough UniversityLoughboroughUK

The wake induced vibration(WIV)of a one-and two-degree-of-freedom(1DOF,2DOF)downstream wave-cone cylinder(WCC)behind a stationary equal-size upstream wave-cone cylinder in the staggered arrangement is numerically investigated at subcritical Reynolds number of 3900 by using shear stressed transfer(SST)k-ωturbulence *** streamwise pitch ratios(P/Dm)vary from 4 to 6 with a fixed incident angleα=8°.Experimental measurements were also performed for the validation of the present numerical *** is found that the largest vibration amplitude in crossflow direction occurred at P/Dm=4,Ur=8 with small difference of streamwise vibration at P/Dm=4,*** from single wavy-cone cylinder(SWCC),the downstream flexible one of a pair staggered WCCs got larger vibration amplitude during phase switching stage instead of in-phase *** upstream wake will suppress the triple frequency of main frequency in the power spectra density(PSD)functions of Cl but stimulate the double one of *** intriguing vibration mechanism happened in all 2DOF cases where the trajectory of downstream WCC is a significant ellipse rather than a figure of *** transformation of phase switching and the variation of the main frequency of drag coefficient(Cd)can be explained by the vortex-shedding modes of downstream WCC.

关键词： Two wave-cone cylinders staggered arrangement wake induced vibration phase switching vortex shedding

Case Study on the γ-algorithm: Possible Tests from the Luminosity versus Displacement Correlation of High Mass X-Ray Binaries

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Research in Astronomy and Astrophysics 2022年第1期22卷 1-13页

作者： Zhao-Yu zuo huan Zhang Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter School of PhysicsXi'an Jiaotong UniversityXi'an 710049China

Using the apparent correlation of luminosity(L;) versus displacement(R) of high mass X-ray binaries(HMXBs),we aim to constrain the common envelope(CE) mechanism, which is vital in the formation and evolution of compact binaries. We find that under the assumption of the γ-algorithm, the apparent correlation can also be reconstructed generally within a reasonable range of key parameters adopted, though the population of HMXBs is distinct with that in the canonical αCE-formalism. We compare the spatial distribution of HMXBs under the two CE mechanisms, and suggest the difference in L;versus R distribution may provide an additional clue for the study of the CE phase and to discriminate between CE models.

关键词： (stars:)binaries(including multiple):close galaxies:starburst stars:evolution X-rays:binaries

MDP-Based Budget Allocation for Efficient Cooperative Task Solving

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Chinese Journal of Electronics 2017年第5期26卷 966-972页

作者： JIANG huan zuo Min MATSUBARA Shigeo School of Computer and Information Engineering Beijing Technology and Business University

In order to facilitate crowdsourcing-based task solving,complex tasks are decomposed into interdependent subtasks that can be executed cooperatively by individual *** to maximize the quality of the final solution subject to the self-interested worker’s utility maximization,a key challenge is to allocate the limited budget among the subtasks as the rewards for workers having various levels of *** study is the first attempt to show the value of Markov decision processes(MDPs)for the problem of optimizing the quality of the final solution by dynamically determining the budget allocation on sequentially dependent subtasks under the budget constraints and the uncertainty of the workers’ *** simulation-based approach verifies that compared to some offline methods where workers’ abilities are fully known,our proposed MDP-based payment planning is more efficient at optimizing the final quality under the same limited budget.

关键词： Budget allocation Markov decision processes(MDPs) Cooperative task solving Task quality optimization Crowdsourcing