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Stability of nonlinear impulsive stochastic systems with Markovian switching under generalized average dwell time condition

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Science China(Information Sciences) 2018年第11期61卷 208-222页

作者： Xiaozheng FU quanxin zhu Key Laboratory of HPC-SIP(MOE) College of Mathematics and Statistics Hunan Normal University School of Mathematical Sciences and Institute of Finance and Statistics Nanjing Normal University

This paper examines the p-th moment globally asymptotic stability in probability and p-th moment stochastic input-to-state stability for a type of impulsive stochastic system with Markovian *** applying the generalized average dwell time approach, some novel sufficient conditions are obtained to ensure these stability properties. Furthermore, the coefficient of the Lyapunov function is allowed to be time-varying, which generalizes and improves the existing results. As corollaries, nonlinear restrictions on the drift and diffusion coefficients are used as substitutes for some previous conditions. Two examples are provided to illustrate the effectiveness of the theoretical results.

关键词： generalized average dwell time condition impulsive stochastic system Markovian switching time-varying coefficient input-to-state stability nonlinear restrictions

STRONG N-DISCOUNT AND FINITE-HORIZON OPTIMALITY FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES

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Journal of Systems Science & Complexity 2014年第5期27卷 1045-1063页

作者： zhu quanxin GUO Xianping School of Mathematical Sciences and Institute of Finance and Statistics Nanjing Normal University School of Mathematics and Computational Science Zhongshan University

This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish *** corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower *** mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount *** authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.

关键词： Continuous-time Markov decision process expected average reward criterion finite-horizon optimality Polish space strong n-discount optimality

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Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

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International Journal of Biomathematics 2021年第1期14卷 31-50页

作者： Luyao Xin Yingxin Guo quanxin zhu School of Mathematical Sciences Qufu Normal UniversityQufu 273165ShandongP.R.China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081HunanP.R.China

In this paper,we propose a new mathematical model based on the association between susceptible and recovered ***,we study the stability of this model with the deterministic case and obtain the conditions for the extinction of ***,in view of the association between susceptible and recovered individual perturbed by white noise,we also give sufficient conditions for the extinction and the permanence in mean of disease with the white ***,we have numerical simulations to demonstrate the correctness of obtained theoretical results.

关键词： Extinction permanence in mean stability stochastic epidemic model

Dynamical study of a predator-prey system with Michaelis-Menten type predator-harvesting

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生物数学学报:英文版 2023年第8期16卷 121-153页

作者： Ankur Jyoti Kashyap quanxin zhu Hemanta Kumar Sarmah Debasish Bhattacharjee Department of Mathematics Gauhati University AssamIndia Department of Mathematics Assam Royal Global University GuwahatiIndia School of Mathematical Sciences and Statistics Hunan Normal University Changsha410081P.R.China Sajkashyap.maths@***

The predation process plays a significant role in advancing life evolution and the maintenance of ecological balance and *** cooperation in predators is one of the most remarkable features of the predation process,which benefits the predators by developing fear upon their *** study investigates the dynamical behavior of a modified LV-type predator-prey system with Michaelis-Menten-type harvesting of predators where predators adopt cooperation strategy during *** ecologically feasible steady states of the system and their asymptotic stabilities are *** local codimension one bifurcations,***,saddle-node and Hopf bifurcations,that emerge in the system are *** approach is utilized to show the appearance of transcritical bifurcation and saddle-node bifurcation.A backward Hopfbifurcation is detected when the harvesting effort is increased,which destabilizes the system by generating periodic *** stability nature of the Hopf-bifurcating periodic orbits is determined by computing the first Lyapunov *** analyses revealed that above a threshold value of the harvesting effort promotes the coexistence of both *** periodic solutions of the system are also observed when the conversion efficiency rate or the hunting cooperation rate is *** have also explored codimension two bifurcations *** generalized Hopf and the Bogdanov-Takens bifurcation exhibit by the *** visualize the dynamical behavior of the system,numerical simulations are conducted using an ecologically plausible parameter *** existence of the bionomic equilibrium of the model is ***,an optimal harvesting policy for the proposed model is derived by considering harvesting effort as a control parameter with the help of Pontryagins maximum principle.

关键词： Hunting cooperation Michaelis-Menten-type harvesting transcritical and saddle-node bifurcation Hopf bifurcation optimal harvesting policy

PROBING A STOCHASTIC EPIDEMIC HEPATITIS C VIRUS MODEL WITH A CHRONICALLY INFECTED TREATED POPULATION

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Acta Mathematica Scientia 2022年第5期42卷 2087-2112页

作者： S.P.RAJASEKAR M.PITCHAIMANI quanxin zhu Ramanujan Institute for Advanced Study in Mathematics Universityof MadrasChennai-600005Tamil NaduIndia Department of Mathematics Government Arts College for WomenNilakottai-624202Tamil NaduIndia CHP-LCOCS School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

The hepatitis C virus is hitherto a tremendous threat to human beings,but many researchers have analyzed mathematical models for hepatitis C virus transmission dynamics only in the deterministic *** plays an immense role in pathology and ***,the main theme of this article is to investigate a stochastic epidemic hepatitis C virus model with five states of epidemiological classification:susceptible,acutely infected,chronically infected,recovered or removed and chronically infected,and *** stochastic hepatitis C virus model in epidemiology is established based on the environmental influence on individuals,is manifested by stochastic perturbations,and is proportional to each *** assert that the stochastic HCV model has a unique global positive solution and attains sufficient conditions for the extinction of the hepatotropic RNA ***,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of an ergodic stationary distribution of the solutions to the stochastic HCV ***,this article confirms that using numerical simulations,the six parameters of the stochastic HCV model can have a high impact over the disease transmission dynamics,specifically the disease transmission rate,the rate of chronically infected population,the rate of progression to chronic infection,the treatment failure rate of chronically infected population,the recovery rate from chronic infection and the treatment rate of the chronically infected ***,numerical simulations validate the effectiveness of our theoretical conclusions.

关键词： infeted chroniclly infeted treated hepatitis Cextinction stationary distributior

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The Microwave Synthesis and Photocatalytic Activity of W⁶⁺-Doped TiO₂ Nanocomposite

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Modern Research in Catalysis 2016年第2期5卷 45-49页

作者： Yulin Tang Shuibin Yang quanxin zhu Xuehong Liao Hubei Key Laboratory for Processing and Application of Catalytic Materials College of Chemical Engineering Huanggang Normal University Huanggang China

W6+-doped TiO2 was prepared by sodium tungsten (VI) and titanium sulfate with sodium dodecyl sulfate as surfactant under microwave irradiation. The samples were characterized by X-ray diffraction (XRD) and Scanning electron micrograph (SEM). The results showed that the as-prepared nanocomposite of inventory molar ratio of 2% calcined at 500°C for 2 h was anatase. The SEM showed that the majority of the catalyst was a relatively flake structure, and some fine particles attached to it. We also studied the photocatalytic activity of the as-prepared samples by using degradation of methyl orange. The factors including inventory molar ratio and concentration of W6+-doped, calcined temperature, amount of hydrogen peroxide and acidity of solution were investigated. When the catalyst was 1.0 g/L, pH was 2, C(H2O2) was 3 mL/L, the degradation rate of TiO2 for methyl orange of 20 mg/L reached 79.63% in 40 min.

关键词： W6+-Doping Titanium Dioxide Microwave Synthesis Photocatalysis Methyl Orange

Efficacy of rapid antigen self-testing for SARS-CoV-2 screening:Real-world evidence from a prospective cohort study

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Genes & Diseases 2024年第5期11卷 88-90页

作者： Yaoyue Hu Bin Peng Jie Fan zhu Yang Jianjiang Xue quanxin Long Jie Xia Yuan Hu Xuefei Cai Li Zhou Ailong Huang School of Public Health Chongqing Medical UniversityChongqing 400016China The Second Affiliated Hospital of Chongqing Medical University Chongqing 400016China Clinical Laboratory University-Town Hospital of Chongqing Medical UniversityChongqing 401331China Key Laboratory of Molecular Biology on Infectious Diseases Designated by the Chinese Ministry of Education Chongqing Medical UniversityChongqing 400016China

Antigen rapid diagnostic tests(Ag-RDTs)have been considered and implemented as an important diagnostic and screening tool to identify SARS-CoV-2 infections in community settings.1 Ag-RDTs are less sensitive,particularly in asymptomatic populations,compared with laboratorybased viral nucleic acid amplification tests(NAATs)such as reverse transcription polymerase chain reaction(RT-PCR).2 However,taking into account the facts that Ag-RDTs are effective for identifying most contagious individuals,they are faster and less expensive than RT-PCR,as well as that RT-PCR could produce positive results for weeks to months after the infection,2 WHO recommends Ag-RDTs be offered as COVID-19 self-testing for screening purposes in addition to professionally administered testing services regardless of the community transmission level.

关键词： testing faster rapid

Average Optimality for Markov Decision Processes in Borel Spaces:New Conditions and Approaches

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Average Optimality for Markov Decision Processes in Borel Sp...

以0为反射壁和拟飞射壁的生灭过程爆发前的向下性质

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作者： Xianping Guo, quanxin zhu (The school of Mathematics and Computational Science Zhongshan University,Guangzhou 510275)

In this paper we study discrete-time Markov decision processes (MDPs) with Borel state and action spaces. The criterion to be minimized is expected average costs, and the costs may have neither upper nor lower bounds. We first provide two optimality inequalities with opposed directions, and also give conditions for the existence of solutions to two inequalities. Then, from the two inequalities we ensure the existence of average optimal (deterministic) stationary policies under additional continuity-compactness assumptions. Our conditions are weaker than those in the previous literature. In particular, some new sufficient conditions for the existence of average optimal stationary policies are imposed on the primitive subjects of models. Moreover, our approach is slightly different from the "optimality inequality approach" widely used in MDPs. Finally, we apply our results to a controlled queueing system and the generalized Potlach processes with control.

关键词： Discrete-time Markov decision processes average expected criterion average cost optimality inequality optimal stationary policy.

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应用概率统计 2005年第2期21卷 188-196页

作者：朱全新杨向群华南师范大学数学系广州510631 湖南师范大学数学系长沙410081

本文研究以0为反射壁和以0为拟飞射壁的两种生灭过程爆发前的向下性质,通过首次引入含一个边界的无穷维线性方程组,得到了多种情况下过程在爆发前从状态k(k≥i)运动到状态i-1的平均时间的精确表达式;同时,我们还定义了特征数eia,并表明... 详细信息

本文研究以0为反射壁和以0为拟飞射壁的两种生灭过程爆发前的向下性质,通过首次引入含一个边界的无穷维线性方程组,得到了多种情况下过程在爆发前从状态k(k≥i)运动到状态i-1的平均时间的精确表达式;同时,我们还定义了特征数eia,并表明了它的概率意义.

关键词： Q^a过程,生灭过程反射壁拟飞射壁爆发前

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