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On the density of shifted primes with large prime factors

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Science China Mathematics 2018年第1期61卷 83-94页

作者： Bin Feng Jie Wu School of Mathematics and Statistics Yangtze Normal University CNRS Institut lie Cartan de Lorraine

As usual, denote by P(n) the largest prime factor of the integer n 1 with the convention P(1) = *** 0 < θ < 1, define Tθ(x) := |{p x : P(p-1) ≥ p~θ}|.In this paper, we obtain a new lower bound for Tθ(x) as x →∞... 详细信息

As usual, denote by P(n) the largest prime factor of the integer n 1 with the convention P(1) = *** 0 define Tθ(x) := |{p x : P(p-1) ≥ p~θ}|.In this paper, we obtain a new lower bound for Tθ(x) as x →∞, which improves some recent results of Luca et al.(2015) and Chen and Chen(2017). As a corollary, we partially prove a conjecture of Chen and Chen(2017)about the size of Tθ(x).

关键词： shifted prime friable integer sieve

An Ohsawa-Takegoshi theorem on compact Khler manifolds

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Science China Mathematics 2014年第1期57卷 9-30页

作者： YI Li Institut Elie cartan Universit de LorraineVandoeuvre-lès-nancy 54506France

We prove two extension theorems of Ohsawa-Takegoshi type on compact Khler *** our proof,there are many complications arising from the regularization process of quasi-psh functions on compact Khler manifolds,and unfortunately we only obtain particular cases of the expected *** remark that the two special cases we proved are natural,since they occur in many *** hope that the new techniques we develop here will allow us to obtain the general extension result of Ohsawa-Takegoshi type on compact Khler manifolds in a near future.

关键词： Ohsawa-Takegoshi theorem compact Khler manifolds quasi-psh functions

A GENERAL deCAY AND OPTIMAL deCAY RESULT IN A HEAT SYSTEM WITH A VISCOELASTIC TERM

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Acta Mathematica Scientia 2019年第2期39卷 618-626页

作者： Abderrahmane YOUKANA Salim A.MESSAOUDI Aissa GUESMIA department of Mathematics University of Batna department of Mathematics and Statistics KFUPM Elie cartan Institute of lorraine Universite de Lorraine department of Mathematics and Statistics King Fahd University of Petroleum and Minerals

We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature.

关键词： heat equation viscoelastic general decay optimal

Two upper bounds for the Erdos-Hooley delta-function

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Science China Mathematics 2023年第12期66卷 2683-2692页

作者： Regis de la Breteche Gerald Tenenbaum Institut de Mathematiques Universite Paris CiteSorbonne UniversiteCNRSParis F-75013France Institut Elie cartan Universite de LorraineVandoeuvre-les-NancyBP 70239France

For integer n≥1 and real u,let Δ(n,u):=|{d:d] n,e^(u)deltafunction is then defined by Δ(n):=Max_(u∈R)Δ(n,u).We improve the current upper bounds for the average and normal orders of ... 详细信息

关键词： concentration of divisors average order normal order Waring’s problem

SOME STABILITY RESULTS FOR TIMOSHENKO SYSTEMS WITH COOPERATIVE FRICTIONAL AND INFINITE-MEMORY DAMPINGS IN THE DISPLACEMENT

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Acta Mathematica Scientia 2016年第1期36卷 1-33页

作者： Aissa GUESMIA Salim MESSA O UDI department of Mathematics and Statistics College of Sciences King Fahd University of Petroleum and Minerals P.O. Box 5005 Dhahran 31261 Saudi Arabia Institut Elie cartan de lorraine UMR 7502 Universitd de Lorraine Bat. A Ile du Saulcy 57045 Metz Cedex 01 France

In this paper, we consider a vibrating system of Timoshenko-type in a one- dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initiM data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.

关键词： well-posedness decay damping Timoshenko thermoelasticity

Modeling the Environmental and Seasonal Influence on Canopy Dynamic and Litterfall of Even-Aged Forest Ecosystems by a Model Coupling Growth & Yield and Process-Based Approaches

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Modeling the Environmental and Seasonal Influence on Canopy ...

Methodology for Constructing a Short-Term Event Risk Score in Heart Failure Patients

2012 IEEE 4th International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA 2012)

作者： Sainte-Marie J. Henrot A. Barrandon M. Nouvellon Y. Roupsard O. Laclau J.-P. Saint-Andr L. Institut Elie cartan Universit de lorraine Vandoeuvre-lès-Nancy France Eco & Sols CIRAD Montpellier France Biogeochim Ecosystem Forestier INRA Champenoux France

ISBN: (纸本)9781467300681

The aim is to propose a dynamic model of forest growth and biomass suitable to varied ecosystems with different species,soil types,climate conditions and forest *** model is combining different approaches(growth & yield,process-based and biogeochemical cycles) to take into account carbon,water and nutrient cycles and to include several processes such as wood production,transpiration,litterfall,litter decomposition or losses of nutrients by *** a model is necessary to anticipate and adapt forest management under different environmental and management scenarii(global changes).Considering the whole forest ecosystem,the seasonality of canopy dynamics and litterfall production is involved in key processes:photosynthesis and carbon production,stand transpiration and water cycle,litter decomposition and nutrient cycling.A dynamical probabilistic model for leaves demography has been *** model is strongly constrained by environmental factors and is able to rank their *** adjustment can highlight relationships between different scales of processes involved,from cellular-scale to *** aim is to provide:i) a predicting model suitable to a large range of ecosystems,ii) hierarchical analyses of the environmental processes driving canopy dynamics.

关键词： AdaptationtoClimateChange CropModels DynamicModel ForestGrowthModels ForestManagement LeafEcology Process-BasedModel(PBM) StochasticModel

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Applied Mathematics 2018年第8期9卷 954-974页

作者： Kévin Duarte Jean-Marie Monnez Eliane Albuisson CNRS INRIA Institut Elie Cartan de Lorraine Université de Lorraine Nancy France CHRU Nancy INSERM Université de Lorraine CIC Plurithématique Nancy France IUT Nancy-Charlemagne Université de Lorraine Nancy France Institut Elie cartan de lorraine Université de Lorraine CNRS Nancy France CHRU Nancy BIOBASE P&ocirc le S2R Université de Lorraine Nancy France Faculté de Médecine InSciDenS Université de Lorraine Nancy France

We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.

关键词： Ensemble Predictor Linear Discriminant Analysis Logistic Regression Mixed Data Scoring Supervised Classification

Implied fractional hazard rates and default risk distributions

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 21-34页

作者： Charles S.Tapiero Pierre Vallois Topfer Chair Distinguished Professor of Financial Engineering and Technology Management Department of Finance and Risk EngineeringNew York University Tandon School of Engineering6 Metro Tech22201 BrooklynNew YorkUSA Universite de lorraine Institut de Mathematiques Elie Cartan de LorraineINRIA.BIGSCNRS UMR 7502 BP 239F-54506Vandoeuvre-Les-NancyFrance

default probability distributions are often defined in terms of their conditional default probability distribution,or their hazard *** their definition,they imply a unique probability density *** applications of default probability distributions are varied,including the risk premium model used to price default bonds,reliability measurement models,insurance,*** probability density functions(FPD),however,are not in general conventional probability density functions(Tapiero and Vallois,Physica A,.***.462:1161–1177,2016).As a result,a fractional FPD does not define a fractional hazard ***,a fractional hazard rate implies a unique and conventional *** example,an exponential distribution fractional hazard rate implies a Weibull probability density function while,a fractional exponential probability distribution is not a conventional distribution and therefore does not define a fractional hazard *** purpose of this paper consists of defining fractional hazard rates implied fractional distributions and to highlight their usefulness to granular default risk *** of such an approach are *** example,pricing default bonds,pricing complex insurance contracts,as well as complex network risks of various granularity,that have well defined and quantitative definitions of their hazard rates.

关键词： function. fractional bonds

Efficient Numerical Computation of Time-Fractional Nonlinear Schrodinger Equations in Unbounded Domain

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Communications in Computational Physics 2019年第1期25卷 218-243页

作者： Jiwei Zhang Dongfang Li Xavier Antoine Beijing Computational Science Research Center Beijing 100193P.R.China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Institut Elie cartan de lorraine UMR CNRS 7502Universit́e de LorraineInria Nancy-Grand EstSPHINX TeamF-54506 Vandoeuvre-l`es-Nancy CedexFrance

The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded *** first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization ***,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is *** accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional *** resulting algorithm is highly efficient for long time ***,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.

关键词： Time-fractional nonlinear Schrodinger equation absorbing boundary condition sta-bility analysis convergence analysis sum-of-exponentials approximation