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mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 508-525页

作者： Li-li LIU Hong-gang WANG Ya-zhi LI Shanxi Key Laboratory of mathematical Techniques and Big Data Analysis on Disease Control and Prevention Complex Systems Research CenterShanxi UniversityTaiyuan 030006China School of Mathematics and Statistics Qiannan Normal University for NationalitiesDuyun 558000China

Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a *** this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are *** to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the *** illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.

关键词： delayed HBV model capsids general incidence function two infection routes global stability

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The Coarse l^(p)-Novikov Conjecture and Banach Spaces with Property(H)

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 193-220页

作者： Huan WANG Qin WANG Research center for Operator Algebras School of Mathematical SciencesEast China Normal UniversityShanghai 200241China Key Laboratory of MEA Ministry of Educationand Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghai 200241China

In this paper,for 1

关键词： The coarse l^(p)-Novikov conjecture Banach spaces with Property(H) Coarse geometry K-Theory

Existence of multi-hump generalized homoclinic solutions for a class of reversible systems

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Science China Mathematics 2024年

作者： Shengfu Deng Yan Zhou Jinsen Zhuang School of mathematical Sciences Huaqiao University

In this paper, we investigate a class of reversible dynamical systems in four dimensions. The spectrums of their linear operators at the equilibria are assumed to have a pair of positive and negative real eigenvalues and a pair of purely imaginary eigenvalues for the small parameterμ> 0, where these two real eigenvalues bifurcate from a double eigenvalue 0 forμ=0. It has been shown that this class of systems owns a generalized homoclinic solution with one hump at the center （a homoclinic solution exponentially approaching a periodic solution with a small amplitude）. This paper gives a rigorous existence proof of two-hump *** two humps are far away and are glued by the small oscillations in the middle if some appropriate free constants are activated. The obtained results are also applied to some classical systems. The ideas here may be used to study the existence of 2k-hump solutions.

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A class of natural pinus koraiensis population system with time delay and diffusion term

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International Journal of Biomathematics 2024年第2期17卷 233-262页

作者： Guo-Feng Feng Jiaqi Chen Bin Ge School of mathematical Sciences Harbin Engineering University Harbin 150001 P.R.China

In this paper,we consider the long-term sustainability of the northeast Korean *** propose a class of natural Korean pine population system with time delay and diffusion ***,by analyzing the roots distribution of the characteristic equation,we study the stability of the model system with diffusion terms and prove the occurrence of Hopf ***,we introduce lactation time delay into a population model with a diffusion term,based on stability theory of ordinary differential equation,norm form methods and center manifold theorem,the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are ***,some numerical simulations are given.

关键词： Pinus koraiensis populations delay diffusion term Hopf bifurcation periodic solution

Space-time estimates of the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

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Science China Mathematics 2024年第5期67卷 1059-1084页

作者： Zhigang Wu Weike Wang Department of Mathematics Donghua UniversityShanghai 201620China School of mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Shanghai Frontier Science center of Modern Analysis(CMA-Shanghai) Shanghai Jiao Tong UniversityShanghai 200240China

The space-time behavior for the Cauchy problem of the 3D compressible bipolar Navier-Stokes-Poisson(BNSP)system with unequal viscosities is *** space-time estimate of the electric field▽φ=▽(-△)^(-1)(n-Zρ)is the most important in deducing generalized Huygens’principle for the BNSP system and it requires proving that the space-time estimate of n-Zρonly contains the diffusion wave due to the singularity of the operator▽(-△)^(-1).A suitable linear combination of unknowns reformulating the original system into two small subsystems for the special case(with equal viscosities)in Wu and Wang(2017)is crucial for both linear analysis and nonlinear estimates,especially for the space-time estimate of▽φ.However,the benefits from this reformulation will no longer exist in general ***,we study an 8×8 Green’s matrix *** importantly,each entry in Green’s matrix contains wave operators in the low-frequency part,which will generally produce Huygens’wave;as a result,one cannot achieve the space-time estimate of n-Zρthat only contains the diffusion wave as *** overcome this difficulty by taking a more detailed spectral analysis and developing new estimates arising from subtle cancellations in Green’s function.

关键词： Green's function bipolar Navier-Stokes-Poisson system unequal viscosities

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The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation

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Science China Mathematics 2024年第5期67卷 975-1010页

作者： Qi Qiao Xiang Zhang School of mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Ministry of Education) and Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai)Shanghai Jiao Tong UniversityShanghai 200240China

For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusionmechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve *** and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the ***,we characterize both the nonlinear and spectral stability of this travelling pulse.

关键词： coupled FitzHugh-Nagumo equation singular perturbation travelling pulse spectrum nonlinear stability spectral stability

A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem

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Annals of Applied Mathematics 2024年第1期40卷 71-104页

作者： Dawei Wu Zhennan Zhou School of mathematical Sciences Peking UniversityBeijing 100871China Beijing International center for mathematical Research Peking UniversityBeijing 100871China

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov *** simulations of this stochastic process and its invariant measure are of *** this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error *** a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.

关键词： Growth-fragmentation model Markov chain numerical approximation space discretization convergence rate

Incidence and warning signs for complications of human brucellosis: a multi-center observational study from China

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Infectious Diseases of Poverty 2024年第1期13卷 53-62页

作者： Qing-Nan Shi Hui-Jie Qin Qiao-Shan Lu hu Li Zhong-Fa Tao Meng-Guang Fan Mu-Heta Aishan Zeng-Qiang Kou Qiu-Lan Chen Wen-Wu Yin Yan-Ping Zhang National Key Laboratory of Intelligent Tracking and Forecasting for Infectious Diseases Chinese Center for Disease Control and PreventionChangbai RoadChangping DistrictBejing 102206China School of Public Health Guangxi Medical UniversityNanningChina Nanning center for Disease Control and Prevention NanningChina Guizhou center for Disease Control and Prevention GuiyangChina Inner Mongolia center for Disease Control and Prevention HohhotChina Xinjiang Uighur Autonomous Region center for Disease Control and Prevention UrumqiChina Shandong center for Disease Control and Prevention JinanChina

Background Brucellosis is a severe zoonotic disease that is often overlooked, particularly in impoverished countries. Timely identification of focal complications in brucellosis is crucial for improving treatment outcomes. However, there is currently a lack of established indicators or biomarkers for diagnosing these complications. Therefore, this study aimed to investigate potential warning signs of focal complications in human brucellosis, with the goal of providing practical parameters for clinicians to aid in the diagnosis and management of *** A multi-center cross-sectional study was conducted in China from December 2019 to August 2021. The study aimed to investigate the clinical characteristics and complications of patients with brucellosis using a questionnaire survey and medical record system. The presence of warning signs for complications was assessed using univariate and multivariate logistic regression models. Receiver operating characteristic (ROC) curves and the area under the curve (AUC) were used for variable screening and model *** A total of 880 participants diagnosed with human brucellosis were enrolled. The median age of the patients was 50 years [interquartile range (IQR): 41.5-58.0], and 54.8% had complications. The most common organ system affected by complications was the osteoarticular system (43.1%), with peripheral arthritis (30.0%), spondylitis (16.6%), paravertebral abscess (5.0%), and sacroiliitis (2.7%) being the most prevalent. Complications in other organ systems included the genitourinary system (4.7%), respiratory system (4.7%), and hematologic system (4.6%). Several factors were found to be associated with focal brucellosis. These factors included a long delay in diagnosis [odds ratio (OR) = 3.963, 95% confidence interval(CI): 1.906-8.238 for > 90 days], the presence of underlying disease (OR = 1.675, 95%CI: 1.176-2.384), arthralgia (OR = 3.197, 95%CI: 1.986-5.148), eye bulging pain (OR = 3.482, 95%CI:

关键词： Brucellosis Complications Clinical spectrum Warning signs

The pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black hole

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Science China(Physics,Mechanics & Astronomy) 2024年

作者： Li-Ming Cao Jia-Ning Chen Liang-Bi Wu Li-Bo Xie Yu-Sen Zhou Peng Huanwu center for Fundamental Theory Interdisciplinary center for Theoretical Study and Department of Modern Physics University of Science and Technology of China School of Fundamental Physics and mathematical Sciences Hangzhou Institute for Advanced StudyUCAS

In this study,we investigate the pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black ***,we use the hyperboloidal framework to cast the quasinormal mode (QNM) problem into an eigenvalue problem associated with a non-selfadjoint operator,and then the spectrum and pseudospectrum are ***,the invariant subspace method is exploited to improve the computational efficiency for *** investigation into the spectrum(in)stability entails two main *** the one hand,we calculate the spectra of the quantum corrected black hole,then by the means of the migration ratio,the impact of the quantum correction effect on the Schwarzschild black hole has been *** results indicate that the so-called“migration ratio instability”will occur for small black holes with small angular momentum number *** the eikonal limit,the migration ratios remain the same for each *** the other hand,we study the spectrum(in)stability of the quantum corrected black hole by directly adding some particular perturbations into the effective potential,where perturbations are located at the event horizon and null infinity,*** are two interesting observations under the same perturbation energy ***,perturbations at infinity are more capable of generating spectrum instability than those at the event ***,we find that the peak distribution can lead to the instability of QNM spectrum more efficiently than the average distribution.

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