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American Journal of Computational mathematics 2023年第1期13卷 82-90页

作者： Prosper Kouadio Kimou département mathématiques et Informatiques Institut Polytechnique Félix Houphou&#235t-Boigny Yamoussoukro C&#244te d’Ivoire

denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible to express a,b and c as function of the Fermat principal divisors. denote by the set of possible non-trivial solutions of the diophantine equation . And, let (p prime). We prove that, in the first case of Fermat’s theorem, one has . In the second case of Fermat’s theorem, we show that , ,. Furthermore, we have implemented a python program to calculate the Fermat divisors of Pythagoreans triples. The results of this program, confirm the model used. We now have an effective tool to directly process diophantine equations and that of Fermat. .

关键词： Fermat’s Last Theorem Fermat divisors Barlow’s Relations Greatest Common divisor

Stochastic differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

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Acta mathematicae Applicatae Sinica 2011年第4期27卷 647-678页

作者： Rainer BUCKdAHN département de mathématiques Université de Bretagne Occidentale6avenue Victor-le-GorgeuB.P.80929285 Brest cedexFrance Institute for Advanced Study Shangdong UniversityJinan 250100China

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic differential Equations （RBSdes）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSdes being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSdes by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.

关键词： stochastic differential games value function reflected backward stochastic differential equations,dynamic programming principle Isaacs equations with obstacles viscosity solution

Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System

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Communications on Applied mathematics and Computation 2022年第1期4卷 34-59页

作者： Francis Filbet Tao Xiong Institut de mathématiques de Toulouse UniversitéPaul SabatierToulouse 31062France School of mathematical Sciences and Fujian Provincial Key Laboratory of mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005Fujian ProvinceChina

We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity *** schemes are designed to be systematically as accurate as one wants with prov-able conservation of mass and possibly total *** properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson *** proposed scheme employs the discontinuous Galerkin discretization for both the Vlasov and the Poisson equations,resulting in a consistent description of the distribu-tion function and the electric *** simulations are performed to verify the order of the accuracy and conservation properties.

关键词： Energy conserving discontinuous Galerkin method Hermite spectral method Vlasov-Poisson

Preclinical and clinical evidence of the association of colibactinproducing Escherichia coli with anxiety and depression in colon cancer

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World Journal of Gastroenterology 2024年第21期30卷 2817-2826页

作者： Fabien Rondepierre Maëva Meynier Johan Gagniere Vincent deneuvy Anissa deneuvy Gwenaelle Roche Elodie Baudu Bruno Pereira Richard Bonnet Nicolas Barnich Frédéric Antonio Carvalho denis Pezet mathilde Bonnet Isabelle Jalenques Service de Psychiatrie de l’Adulte A et Psychologie Médicale CHU Clermont-FerrandClermont-Ferrand 63000France M2iSH UMR 1071INSERMUniversity of Clermont AuvergneINRAE USC 1382Clermont-Ferrand 63001France Neurodol UMR 1107INSERMUniversity of Clermont AuvergneClermont-Ferrand 63001France department of digestive Surgery CHU de Clermont-FerrandClermont-Ferrand 63001France Biostatistics Unit Department of Clinical Research and InnovationCHU Clermont-FerrandClermont-Ferrand 63000France department of Bacteriology CHU de Clermont-FerrandClermont-Ferrand 63001France UniversitéClermont Auvergne INPCNRSClermont Auvergne Institut PascalClermont-Ferrand 63000France

BACKGROUNd The association between the intestinal microbiota and psychiatric disorders is becoming increasingly *** gut microbiota contributes to colorectal carcinogenesis(CRC),as demonstrated with colibactin-producing Escherichia coli(CoPEC).AIM To evaluate the association between CoPEC prevalence and anxiety-and depressive-like behaviors with both preclinical and clinical *** Patients followed after a CRC surgery and for whom the prevalence of CoPEC has been investigated underwent a psychiatric *** were compared according to the CoPEC *** parallel C57BL6/J wild type mice and mice with a CRC susceptibility were chronically infected with a CoPEC *** behavior was assessed using the Elevated Plus Maze test,the Forced Swimming Test and the Behavior recognition system PhenoTyper®.RESULTS In a limited cohort,all patients with CoPEC colonization presented with psychiatric disorders several years before cancer diagnosis,whereas only one patient(17%)without CoPEC *** result was confirmed in C57BL6/J wildtype mice and in a CRC susceptibility mouse model(adenomatous polyposis colimultiple intestinal neoplasia/+).Mice exhibited a significant increase in anxiety-and depressive-like behaviors after chronic infection with a CoPEC *** This finding provides the first evidence that CoPEC infection can induce microbiota-gut-brain axis disturbances in addition to its procarcinogenic properties.

关键词： Colorectal cancer Colibactin Escherichia coli Colibactin-producing Escherichia coli Inflammation Anxiety depression Behavior

EXISTENCE ANd BOUNdedNESS OF SOLUTIONS FOR SYSTEMS OF QUASILINEAR ELLIPTIC EQUATIONS

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Acta mathematica Scientia 2021年第2期41卷 397-412页

作者： Abdelkrim MOUSSA OUI Jean VELIN Applied mathematics Laboratory Faculty of Exact SciencesA.Mira Bejaia UniversityAlgeria département de mathématiques et Informatique Laboratoire LAMIAUniversitédes AntillesCampus de Fouillole 97159 Pointe-à-PitreGuadeloupe(FWI)

This article sets forth results on the existence and boundedness of solutions for quasilinear elliptic systems involving p-Laplacian and q-Laplacian *** approach combines Schaefer's fixed point as well as Moser's iter... 详细信息

关键词： p-Laplacian Schaefer's fixed point Besov and Sobolev spaces boundedness regularity

INVARIANCE ANd STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS

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Acta mathematica Scientia 2011年第6期31卷 2141-2158页

作者： Guy Mtivier Jeffrey Rauch Institut de mathmatiques de Bordeaux Universit de Bordeaux department of mathematics University of Michigan

The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.

关键词： geometric optics profile equation localisation vector bundles propagation cones

Some Uniqueness Results for Functional damped Semilinear differential Equations in Fréchet Spaces

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Acta mathematica Sinica,English Series 2008年第1期24卷 95-106页

作者： Abdelghani OUAHAB Laboratoire de mathématiques Universitéde Sidi Bel Abbès BP 89

A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. math. Quebec 22, （2）, 161-168 （1998））, combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space.

关键词： differential equations damped semigroup family cosinus mild solution fixed point uniqueness Frechet spaces contraction

ASYMPTOTIC BEHAVIOR OF THE TE ANd TM APPROXIMATIONS TO SECONd HARMONIC GENERATION

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Journal of Computational mathematics 2007年第1期25卷 49-66页

作者： Na■ma A■ssa Faculté de mathématiques USTHBBP32El AliaBab Ezzouar16111Alger Centre de mathématiques Appliquées CNRS UMR 7641■Ecole PolytechniquePalaiseau 91128 CedexFrance

We consider a Second Harmonic Generation （SHG） problem of an optical signal wave with an optical pump in a medium represented by a smooth bounded domain Ω→∩ IR^d which is assumed to contain a heterogeneous material： a compactly imbedded subdomain B^r →∩∩ in the shape of a small ball contains a nonlinear material, while Ω／ B^r is filled with a linear material. We begin by proving existence and uniqueness of the solution to the TE approximation of SHG for arbitrary bounded susceptibilities, thus improving the result obtained by Bao and dobson （ Eur. J. Appl. math. 6 （1995）, 573-590） under small enough susceptibilities assuption. We then establish an existence and uniqueness result of a solution to the TM approximation problem. In both parts we study the asymptotic behavior of the system as the size of the nonlinear material vanishes： error estimates and asymptotic expansion of the solution are derived for both TE and TM approximations.

关键词： Second harmonic generation TE Approximation TM Approximation.

Hyperverse, 5-dimensional Gravity and Multiverses as Nested Gogberashvili Shells

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Journal of High Energy Physics, Gravitation and Cosmology 2022年第4期8卷 983-989页

作者： Igor Yu. Potemine Institut de mathématiques Université Paul Sabatier Toulouse France

We consider the Hyperverse as a collection of multiverses in 5-dimensional spacetime with gravitational constant G. Each multiverse in our simplified model is a bouquet of nested spherical Gogberashvili shells. If gk is the gravitational constant of a thin shell Sk and εk, its thickness then G ~ εkgk. The physical universe is supposed to be one of those shells inside the local nested bouquet called Local Multiverse. We relate this construction to Robinson-Trautman metrics describing expanding spacetimes with spherical gravitational waves. Supermassive astronomical black holes, located at cores of elliptic/spiral galaxies, are also conjecturally described within this theory. Our constructions are equally consistent with the modern theory of cosmological coupling.

关键词： 5-dimensional Gravity Black Hole Multiverse Spherical Shell

SIMPLE PROOFS OF THE CAUCHY-SCHWARTZ INEQUALITY ANd THE NEGATIVE dISCRIMINANT PROPERTY IN ARCHIMEdeAN ALMOST f-ALGEBRAS

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Analysis in Theory and Applications 2009年第2期25卷 117-124页

作者： Adel Toumi Mohamed Ali Toumi Nedra Toumi Laboratoire de Physique des Liquides Critiques Département de Physique Faculté des Sciences de Bizerte 7021 Zarzouna Bizerte Tunisia département des mathématiques Faculté des Sciences de Bizerte 7021 Zarzouna Bizerte Tunisia

The paper presents simple proofs of the Cauchy-Schwartz inequality and the negative discriminant property in archimedean almost f-algebras^[5], based on a sequence approximation.

关键词： Cauchy-Schwartz inequality f-algebra almost f-algebra positive square g-algebra