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Long-wave instabilities

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Science China mathematics 2024年第8期67卷 1761-1776页

作者： Dongfen Bian Emmanuel Grenier School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Unité de mathématiques Pures et Appliquées CNRS UMR 5669Ecole Normale Supérieure de LyonLyon 69007France

This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its *** these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.

关键词： Navier-Stokes equations boundary layers Prandtl equations

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

Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations

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Chinese Annals of mathematics,Series B 2024年第4期45卷 573-596页

作者： Xinghong PAN Chaojiang XU School of mathematics and Key Laboratory of MIIT Nanjing University of Aeronautics and AstronauticsNanjing 211106China School of mathematics and Key Laboratory of MIIT Nanjing University of Aeronautics and AstronauticsNanjing 211106Chinaand Laboratoire de Mathématiques Raphaël SalemUMR 6085 CNRSUniversitéde Rouen Normandie76801 Saint-Étienne-du-RouvrayFrance.

In this paper,the authors will prove the global existence of solutions to the three dimensional axially symmetric Prandtl boundary layer equations with small initial data,which lies in H1Sobolev space with respect to the normal variable and is analytical with respect to the tangential *** main novelty of this paper relies on careful constructions of a tangentially weighted analytic energy functional and a specially designed good unknown for the reformulated *** result extends that of Paicu-Zhang in[Paicu,*** Zhang,P.,Global existence and the decay of solutions to the Prandtl system with small analytic data,***.,241(1),2021,403–446].from the two dimensional case to the three dimensional axially symmetric case,but the method used here is a direct energy estimates rather than Fourier analysis techniques applied there.

关键词： Global existence Tangentially analytical solutions Axially symmetric Prandtl equations

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

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Journal of Applied mathematics and Physics 2024年第3期12卷 897-911页

作者： Kumwimba Seya Didier Kasongo Ntambwe Dany Panga Lutanda Grégoire Mayuke Katshongo Jean Paul Lunda Ngoy Jean Pierre Département de mathématiques et Informatique Faculté des Sciences Université de Lubumbashi Lubumbashi Democratic Republic of the Congo

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

关键词： Fuzzy-Valued Function Hausdorff Distance Quasi-Fuzzy Parallelipiped Henstock Integral

The Dual of the Two-Variable Exponent Amalgam Spaces (L^q(),l^p())(Ω)

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Journal of Applied mathematics and Physics 2024年第2期12卷 383-431页

作者： Sambourou Massinanke Sékou Coulibaly Mamadou Traore departement d’Etudes et de Recherches de mathématiques et d’Informatique Université des Sciences des Techniques et des Technolo-gies de Bamako Bamako Mali

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

关键词： Amalgam Spaces Variable Exponent Lebesgue Spaces Dual of a Vector Space

Fermat and Pythagoras Divisors for a New Explicit Proof of Fermat’s Theorem:a⁴ + b⁴ = c⁴. Part I

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Advances in Pure mathematics 2024年第4期14卷 303-319页

作者： Prosper Kouadio Kimou François Emmanuel Tanoé Kouassi Vincent Kouakou Laboratoire d’ Informatique et de Math&#233matiques appliqu&#233es Institut Polytechnique F&#233lix Houphou&#235t BOIGNY Yamoussoukro Cote d&#8217Ivoire ufr mathé matiques et Informatique Universit&#233 F&#233lix Houphouet BOIGNY Abidjan Cote d&#8217Ivoire ufr Sciences Fondamentales Appliqué es Universit&#233 NANGUI ABROGOUA Abidjan Cote d&#8217Ivoire

In this paper we prove in a new way, the well known result, that Fermat’s equation a4 + b4 = c4, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F0) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−10) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F0): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=

关键词： Factorisation in ℤ Greatest Common Divisor Pythagoras Equation Pythagorician Triplets Fermat's Equations Pythagorician Divisors Fermat's Divisors Diophantine Equations of degree 2 4-Integral Closure of ℤ in ℚ

Bearing Capacity Analysis of Spread Footing on Massif in the “Corniche Ouest” of the Dakar Peninsula (Senegal, West Africa)

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Open Journal of Civil Engineering 2024年第3期14卷 421-434页

作者： Moussa Sawadogo Déthie Sarr Oustasse A. Sall Dpartement de Gotechnique L2M UFR Sciences de lIngnieur Universit Iba Der THIAM de This This Sngal Dpartement de Gnie-Civil UFR Sciences de lIngnieur Universit Iba Der THIAM de This This Sngal

This study presents various approaches to calculating the bearing capacity of spread footings applied to the rock mass of the western corniche at the tip of the Dakar peninsula. The bearing capacity was estimated using empirical, analytical and numerical approaches based on the parameters of the rock mass and the foundation. Laboratory tests were carried out on basanite, as well as on the other facies detected. The results of these studies give a range of allowable bearing capacity values varying between 1.92 and 11.39 MPa for the empirical methods and from 7.13 to 25.50 MPa for the analytical methods. A wide dispersion of results was observed according to the different approaches. This dispersion of results is explained by the use of different rock parameters depending on the method used. The allowable bearing capacity results obtained with varying approaches of calculation remain admissible to support the loads. On the other hand, the foundation calculations show acceptable settlement of the order of a millimeter for all the layers, especially in the thin clay layers resting on the bedrock at shallow depths, where the rigidity of the rock reduces settlement.

关键词： Peninsula of Dakar Bearing Capacity Basanites Rock Mass Spread Footings

Comparative Study between Dielectric Properties and Compaction Parameters: Case Study on Three Laterite Quarries

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Open Journal of Geology 2024年第8期14卷 746-759页

作者： Cheikh Diallo Diene Sabou Sarr Abdoulaye Cissé Mapathé Ndiaye Laboratoire de Gophysique UFR Sciences de lIngnieur University Iba Der Thiam Thies Senegal Laboratoire de Modlisation et de Mcanique des Sols UFR Sciences de lIngnieur University Iba Der Thiam Thies Senegal

This work studies the variability of the relationship between relative permittivity and compaction parameters as a function of certain geotechnical properties for different laterite types. This study allows to purpose the dielectric permittivity as a third compaction parameter allowing to obtain a non destructive control méthod. Preliminary studies on Diack laterite had shown a good correlation. Additional investigations are carried out to verify the possibility of generalizing this correlation to three new laterite careers: Ngoudiane, Yéba and Fandene. To proceed, particle size analysis, Atterberg limits, specific weight tests and compaction according to the modified Proctor test were performed on laterite samples. Using the radar method, experimental permittivities are determined for laterite samples by the point method of propagation times and confirmed by the diffraction hyperbole method. The geotechnical and radar data obtained allowed correlations between permittivity and water content on the one hand and between permittivity and dry density on the other. The results show that the maximum dry density as a function of permittivity corresponds with the optimum Proctor, which confirms the results previously obtained on Diack laterite.

关键词： Radar Laterite Moisture Content Dry density Permittivity Geotechnical Properties

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Continuous Coefficients

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Acta mathematica Sinica,English Series 2012年第10期28卷 2011-2020页

作者： Auguste AMAN Jean Marc OWO ufr de mathématiques et Informatique Université de Cocody

A new class of generalized backward doubly stochastic differential equations （GBDSdes in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which al... 详细信息

关键词： Backward doubly stochastic differential equations L@vy processes Teugels martingales comparison theorem continuous and linear growth conditions