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Modeling and investigating malaria *** and *** infections:Application to Djibouti data

Infectious Disease Modelling 2024年第4期9卷 1095-1116页

作者： Yahyeh Souleiman Liban Ismail Raluca Eftimie Centre de Recherche en mathematiques et Numerique(CRMN) University of the DjiboutiCampus BalbalaDjibouti Laboratoire mathematiques de Besançon(LMB) University of Bourgogne Franche-ComteBesanconFrance

Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium *** are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plasmodium Vivax,are the most *** Djibouti,the two species of Plasmodium are present in different proportions in the infected population:77%of *** and 33%of *** this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax *** focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model(i.e.,existence and stability of various eqiuilibria).Then we use computational approaches to:(a)identify model parameters using real data on malaria infections in Djibouti;(b)illustrate the influence of different estimated parameters on the basic reproduction numbers;(c)perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans,for infections with each of the Plasmodium *** originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of *** addition,sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction ***,the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.

关键词： Falciparum and vivax models Reproduction number Stability analysis Sensitivity analysis FAST method LHS method Djibouti data

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Guillaume Broux-Quemerais,Sarah Kaakai, Anis Matoussi,Wissal Sabbagh

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Probability, Uncertainty and Quantitative Risk 2024年第2期9卷 149-180页

作者： Guillaume Broux-Quemerais Sarah Kaakarl Anis Matoussi Wissal Sabbagh Laboratoire Manceau de mathematiques&FR CNRS No 2962 Institut du Risque et de I'AssuranceLeMansUniversityFrance Centre de Mathématiques Appliquees(CMAP) CNRSEcole polytechniqueInstitut Polytechnique de Paris91120 PalaiseauFrance

In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor *** this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic *** viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the *** particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo *** also propose two new deep learning numerical schemes for ***,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.

关键词： Deep leaming scheme Forward utilities Ergodic BSDEs Markovian solution Deep learning algorithm

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再论相似于Mobius函数的可乘函数

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中国科学：数学 2024年第9期54卷 1313-1324页

作者：刘青阳吴杰中国人民大学数学学院北京100872 CNRS LAMA 8050 Laboratoire d'Analyse et de Mathematiques AppliqueesUniversite Paris-Est Creteil94010 Crteil CedexFrance

设k≥2是一个正整数,f(n)是一个可乘算术函数,其Dirichlet级数F(s)具有如下形式:F(s)={L(s,χ)H(s)ζ(ks)−1,若k为偶数,L(s,χ)H(s)L(ks,χ)−1,若k为奇数,其中,ζ是Riemannζ-函数,χ是一个模q>3的非主Dirichlet特征,L(s,χ)是相应的Dirichlet L-函数,且H(s)=Σ∞n=1 h(n)n^(−s)是在半平面ℜe s>0上绝对收敛的Dirichlet级数,对σ>0及某个常数A≥0满足Σ∞n=1|h(n)|n−σ≪σ^(−A).本文得到f(n)的部分和函数的上界估计及Ω-结果,这些结果改进并推广了Aymone等(2022)的最新结果.

关键词：可乘函数 Mobius函数 Dirichlet级数

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WAVE COMPUTATION ON THE HYPERBOLIC DOUBLE DOUGHNUT

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Journal of Computational Mathematics 2010年第6期28卷 790-806页

作者： Agnes Bachelot-Motet Universite de Bordeaux Institut de Mathematiques

We compute the waves propagating on the compact surface of constant negative curvature and genus 2 that is a toy model in quantum chaos theory and cosmic topology. We adopt a variational approach using finite elements. We have to implement the action of the fuchsian group by suitable boundary conditions of periodic type. Despite the ergodicity of the dynamics that is quantum weak mixing, the computation is very accurate. A spectral analysis of the transient waves allows to compute the spectrum and the eigenfunctions of the Laplace-Beltrami operator. We test the exponential decay due to a localized dumping satisfying the assumption of geometric control.

关键词： Wave equation Hyperbolic manifold Finite elements Quantum chaos.

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QMLE for Periodic Time-Varying Asymmetric log GARCH Models

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Communications in Mathematics and Statistics 2021年第3期9卷 273-297页

作者： Ahmed Ghezal Departement de mathematiques Universite Constantine 1ConstantineAlgeria

This paper establishes probabilistic and statistical properties of the extension of timeinvariant coefficients asymmetric log GARCH processes to periodically time-varying coefficients(P logGARCH)*** thesemodels,the parameters of log−volatility are allowed to switch periodically between different *** main motivations of this newmodel are able to capture the asymmetry and hence leverage effect,in addition,the volatility coefficients are not a subject to positivity ***,some probabilistic properties of asymmetric P log GARCH models have been obtained,especially,sufficient conditions ensuring the existence of stationary,causal,ergodic(in periodic sense)solution and moments properties are ***,we establish the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator(QMLE)under extremely strong ***,we carry out a simulation study of the performance of the QML and the P log GARCH is applied to model the crude oil prices of Algerian Saharan Blend.

关键词： QML Periodicity Asymmetric log GARCH EGARCH Stationarity Asymptotic properties

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A Stein deficit for the logarithmic Sobolev inequality

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Science China Mathematics 2017年第7期60卷 1163-1180页

作者： LEDOUX Michel NOURDIN Ivan PECCATI Giovanni Institut de mathematiques de Toulouse Universite de Toulouse-Paul-Sabatier Toulouse F-31062 France Institut Universitaire de France UR en mathematiques-FSTC Luxembourg University Luxembourg City L-1359 Luxembourg

We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian *** techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.

关键词： deficit logarithmic Sobolev inequality Ornstein-Uhlenbeck semigroup minimum mean-square error Stein kernel

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Degenerate Anisotropic Elliptic Problems and Magnetized Plasma Simulations

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Communications in Computational Physics 2012年第1期11卷 147-178页

作者： Stephane Brull Pierre Degond Fabrice Deluzet Institut de mathematiques de Bordeaux UMR 5251 Equipe Mathematiques Appliquees de Bordeaux(MAB)Universite Bordeaux 1351cours de la Liberation-33405 TALENCE cedexFrance Universite de Toulouse UPSINSAUT1UTMInstitut de Mathematiques de ToulouseF-31062 ToulouseFrance CNRS Institut de Mathematiques de Toulouse UMR 5219F-31062 ToulouseFrance

This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic *** numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate *** is also designed to be equally accurate in the strongly and the mildly anisotropic *** method is applied to the Euler-Lorentz system,in the drift-fluid *** system provides a model for magnetized plasmas.

关键词： Anisotropic elliptic problem asymptotic-preserving scheme Lorentz force large magnetic field low-Mach number drift-fluid limit

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Existence, Uniqueness and Functoriality of the Perfect Locality over a Frobenius P-Category

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Algebra Colloquium 2016年第4期23卷 541-622页

作者： Lluis Puig CNRS Institut de Mathematiques de Jussieu 6 Av Bizet 94340 Joinville-le-Pont France

Let p be a prime, P a finite p-group and F- a Frobenius P-category. The question on the existence of a suitable category L^scextending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category L^sc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient condition for the vanishing of these n-cohomology groups. Recently, Andrew Chermak has proved the existence and the uniqueness of L^sc via his objective partial groups, and Bob Oliver, following some of Chermak＇s methods, has also proved the vanishing of those n-cohomology groups for n 〉1, both applying the Classification of the finite simple groups. Here we give direct proofs of the existence and the uniqueness of L^sc; moreover, in [11] we already show that L^sc can be completed in a suitable category L extending F and we also prove some functoriality of this correspondence.

关键词： group Frobenius P-category locality

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A Correction to the Uniqueness of a Partial Perfect Locality over a Frobenius P-Category

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Algebra Colloquium 2019年第4期26卷 541-559页

作者： Lluis Puig Jiping Zhang CNRS Institut de Mathematiques de Jussieu 6 Av Bizet94340 Joinville-le-PontFrance 不详

Let p be a prime,P a finite p-group and F a Frobenius ***[Existcnee,uniqueness and functoriality of the perfect locality over a Frobenius P-category,Algebra Colloq.23(2016)541-622],we claimed the uniqueness of the partial perfect locality over any up-closed set X of J--selfcentralizing subgroups of P,but recently Bob Oliver exhibits some counter-cxamplcs,demanding some revision of our *** this note we show that,up to replacing the perfect localities by the extendable perfect localities over any up-closed set X of J7-selfcentralizing subgroups of P,our arguments are correct,still proving the existence and the uniqueness of the perfect J730-locality,since it is *** take advantage of this revision to simplify some of our arguments.

关键词： group P-category local structure

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On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river

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International Journal of Biomathematics 2017年第6期10卷 25-49页

作者： Imene Meriem Mostefaoui Ali Moussaoui Laboratoire de mathematiques Image et Applications Universite de La Rochelle Pdle Sciences et Technologies Avenue Michel Crepeau 17000 La Rochelle France Laboratoire D'Analyse Non Lineaire et mathematiques Appliquees Universite de Tlemcen Tlemcen Algeria Laboratoire D'Analyse Non Lineaire et mathematiques Appliquees Departement de Mathematique Faculte des Sciences Universite de Tlemcen Tlemcen Algeria

In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are：（i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.

关键词： Reaction-diffusion systems steady states problems degree theory semi-groups.

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