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Rigidity of non-renormalizable Newton maps

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Science China mathematics 2024年第4期67卷 855-872页

作者： Pascale Roesch Yongcheng Yin Jinsong Zeng Institut de mathématiques de Toulouse Universite Paul SabatierToulouse 31062France School of mathematical Sciences Zhejiang UniversityHangzhou 310027China College of mathematics and Statistics Shenzhen UniversityShenzhen 518061China

Non-renormalizable Newton maps are *** precisely,we prove that their Julia sets carry no invariant line fields and that a topological conjugacy between them is equivalent to a quasiconformal conjugacy.

关键词： Newton map non-renormalizable rigidity invariant line field

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 Astronautics Laboratoire de mathématiques Rapha?l Salem UMR 6085 CNRSUniversité de Rouen Normandie

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： Axially symmetric Global existence Prandtl equations Tangentially analytical solutions

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

New Fusion Approach of Spatial and Channel Attention for Semantic Segmentation of Very High Spatial Resolution Remote Sensing Images

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Open Journal of Applied Sciences 2024年第2期14卷 288-319页

作者： Armand Kodjo Atiampo Gokou Hervé Fabrice diédié Unité de Recherche et d’Expertise du Numerique (UREN) Université Virtuelle de Céte d’Ivoire Abidjan Ivory Coast Laboratoire de mathématiques et Informatique Université Peleforo Gon Coulibaly Korhogo Ivory Coast

The semantic segmentation of very high spatial resolution remote sensing images is difficult due to the complexity of interpreting the interactions between the objects in the scene. Indeed, effective segmentation requires considering spatial local context and long-term dependencies. To address this problem, the proposed approach is inspired by the MAC-UNet network which is an extension of U-Net, densely connected combined with channel attention. The advantages of this solution are as follows: 4) The new model introduces a new attention called propagate attention to build an attention-based encoder. 2) The fusion of multi-scale information is achieved by a weighted linear combination of the attentions whose coefficients are learned during the training phase. 3) Introducing in the decoder, the Spatial-Channel-Global-Local block which is an attention layer that uniquely combines channel attention and spatial attention locally and globally. The performances of the model are evaluated on 2 datasets WHdLd and dLRSd and show results of mean intersection over union (mIoU) index in progress between 1.54% and 10.47% for dLRSd and between 1.04% and 4.37% for WHdLd compared with the most efficient algorithms with attention mechanisms like MAU-Net and transformers like TMNet.

关键词： Spatial-Channel Attention Super-Token Segmentation Self-Attention Vision Transformer

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再论相似于M?bius函数的可乘函数

中国科学:数学 2024年

作者：刘青阳吴杰 CNRS LAMA 8050 Laboratoire d’Analyse et de Mathématiques AppliquéesUniversité Paris-Est Créteil 中国人民大学数学学院

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:■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)=∑n=1∞h(n)n-s是在半平面Res>0上绝对收敛的dirichlet级数,对σ>0及某个常数A≥0满足∑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 M?bius函数 dirichlet级数

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−1d. To reach such a result, we suppose first that (F0) 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

New Characterizations of the dual Spaces of Hardy-amalgam Spaces

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Acta mathematica Sinica,English Series 2022年第3期38卷 519-546页

作者： Zobo Vincent de Paul ABLE Justin FEUTO Laboratoire de mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.582Abidjan 22Côte d’Ivoire Laboratoire de mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.1194Abidjan 22Côte d’Ivoire

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0dual spaces whenever 0d q≤p<∞.Moreover,when 0 详细信息

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0dual spaces whenever 0d q≤pde with those obtained in our earlier papers.

关键词： Amalgam spaces Hardy-amalgam spaces duality Pseudo-differential operators

EXISTENCE OF SOLUTIONS FOR GRAdIENT SYSTEMS WITH APPLICATION TO dIFFUSION PROBLEMS INVOLVING NONCONVEX ENERGIES

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Acta mathematica Scientia 2018年第6期38卷 1767-1778页

作者： Sahbi BOUSSANdeL dpartement de mathmatiques Facult des Sciences de Bizerte

In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations... 详细信息

关键词： gradient systems existence of solutions Galerkin method type (M) condition semi-coerciveness diffusion equations

ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

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Acta mathematica Scientia 2013年第4期33卷 1187-1201页

作者： Souhir ELLEUCH Maher MNIF département de mathématiques Université de Sfax Faculté des Sciences de SfaxLaboratoire de Physiques Mathématiques

When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and sufficient conditionson A and B for wh{ch Mc is upper semi-Fredholm with negative index or Weyl for some C C ∈LR（K, H）.

关键词： linear relation Fredholm and semi-Fredholm relation essential approximatepoint spectra for linear relation