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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 H1.obolev 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

Fermat and Pythagoras Divisors for a New Explicit Proof of FermatR1.;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 dR1. 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−1.s , witch is absurd. 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

Black hole shadows in Einstein-Bel-Robinson gravity

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Chinese Physics C 2024年第5期48卷 272-283页

作者： B.Hamil B.C.Lütfüoğlu laboratoire de Physique {1.ématique et Subatomique Facultédes Sciences ExactesUniversitéConstantine 1ConstantineAlgeria department of Physics University of Hradec KrálovéRokitanského 6250003 Hradec KrálovéCzechia

Gravity models given by higher-order scalar curvature corrections are believed to bear important consequences. Einstein-Bel-Robinson (EBR) gravity with quartic curvature modification motivated Sajadi et al. to explore static spherically symmetric black hole solutions using perturbative methods. In this study, inspired by their work, we investigate AdS black hole shadows in EBR gravity and demonstrate how the gravity parameter alters the energy emission rate. Finally, we address the same problem in the presence of plasma, because the black holes are thought to be surrounded by a medium that changes the geodesic of photons.

关键词： black hole shadows Einstein-Bel-Robinson gravity plasma

Evaluation of Water Losses by Evaporation in the Nakanbe Basin

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Atmospheric and Climate Sciences 2024年第1期14卷 29-41页

作者： Bayala Alfred Kabre Sayouba Yonli Hamma Fabien Chesneau Xavier Thierry Sikoudouin Maurice Ky Zeghmati Belkacem Kieno P. Florent Kam Sié Unité de Formation et de Recherche en Sciences Exactes et appliquées (UFR/SEA) Laboratoire d’Energies Thermiques Renouvelables (LETRE) Université Joseph KI-ZERBO Ouagadougou Burkina Faso Unité de Formation et de recherche en Science Exactes et appliquées Centre Universitaire de Kaya (CU-K) Perpignan France laboratoire de Modélisation Pluridisciplinaire et Simulation Université de Perpignan Via Domitia Perpignan France Unité de Formation et de Recherche en Sciences Exactes et appliquées (UFR/SEA) Laboratoire de Matériaux et Environnement Uni-versité Joseph KI-ZERBO Ouagadougou Burkina Faso laboratoire de Physique et Chimie de l’ Environnement (LPCE) Université Joseph KI-ZERBO Ouagadougou Burkina Faso

A numerical approach to heat and mass transfer in a large water reservoir is presented. This water reservoir is likened to a parallelepiped reservoir whose vertical and lower walls are adiabatic and impermeable. The equations that govern natural convection in water are solved by the finite volume method and Thomas’salgorithm. The adequacy between the velocity and pressure fields is ensured by the SIMPLE algorithm. We are going to evaluate the water losses by evaporation from three dams in the Nakanbé basin in Burkina Faso for a period of thirty years, that is to say from January 1. 1.91. to March 1., 2020. The three dams have a rate of evaporation greater than 40% of the volume of water stored. Indeed the rate of evaporation in each dam increases with the water filling rate in the reservoir: we have observed the following results for each dam in the Nakanbé basin;for the date of 02/27/1.88 to 03/1./2020., the Loumbila dam received a total volume of stored water of 22.02 Mm3 and 1..57 Mm3 as the total volume of water evaporated at the same date. At the Ouaga dam (2 + 3), it stored a water volume of 4.06 Mm3 and evaporated 2.03 Mm3 of its storage volume from 01.01.1.88 to 05/07/201.. Finally, with regard to the Bagré dam, it stored 745.1. Mm3 of water and 365.1. Mm3 as the volume of water evaporated from 01.01.1.93 to 03/31.2020.

关键词： Numerical Study Evaporation Meteorological Data Natural Convection Basins Dams

Optimization of Tin-Doped Hybrid Perovskite Solar Cells

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Open Journal of Applied Sciences 2024年第3期14卷 687-706页

作者： Bakary Coulibaly Abou Ahou Florentine Kokora desiré Meledje Boko Aka Bernabé Mari Soucase IREN (Institut de Recherche sur les Energies Nouvelles Abidjan Cote d’Ivoire Unité de Formation et de Recherche des Sciences Fondamentales appliquées (UFRSFA) Universite Nangui Abrogoua Abidjan Cote d’Ivoire laboratoire de Physiques Fondamentales {1.ées (LPFA) Université Nangui Abrogoua Abidjan Cote d’Ivoire Institut de Disseny i Fabricació Universitat Politècnica. València Spain

Perovskites are a category of materials with a unique crystal structure that allows them to absorb sunlight efficiently. This efficiency is particularly high in the case of CH3NH3Pb1.xSnxI3 mixed perovskites. The combination of lead (Pb) and tin (Sn) in this matrix provides a broad spectrum of sunlight absorption, enabling the generation of a larger voltage and, subsequently, increased power. The primary objective in solar cell development is to maximize the conversion of sunlight into electricity. Mixed perovskites like CH3NH3Pb1.xSnxI3 have demonstrated significant potential in this regard. Their tunable bandgap, courtesy of varying the Pb: Sn ratio, allows for the optimization of sunlight absorption. The result is solar cells that surpass many conventional counterparts in terms of energy efficiency. Another significant advantage of these mixed perovskite solar cells is their cost-effectiveness. They can be manufactured using solution-based processes, which are less expensive than the high-vacuum methods required for traditional silicon solar cells. While the prospects for mixed perovskite solar cells are undeniably promising, there are concerns about the toxicity of lead, a key component of these cells. Lead is known to have harmful effects on the environment and health. The aim of our work is to reduce or eliminate lead toxicity in the perovskite cell while maintaining its efficiency. Thus, in a theoretical and experimental approach, we obtained following efficiencies of samples: CH3NH3PbI3 (22.49%) CH3NH3Pb0.75Sn0.25I3 (22.72%), CH3NH3Pb0.5Sn0.5I3 (23.00%) CH3NH3Pb0.25Sn0.75I3 (22.61.), CH3NH3SnI3 (22.38%). Doping with 50% tin

关键词： Cost Efficiency Lead/Tin Perovskite Toxicity

Microbial Quality and Molecular Identification of Enterotoxigenic Staphylococcus Strains Isolated from Dried, Smoked, and Braised Fish Sold in Ouagadougou Markets

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Advances in Microbiology 2024年第1期14卷 59-76页

作者： Arouna Ouédraogo Ganamé Abasse Ouédraogo Henri Sidabéwindin Ouédraogo François Tchoumbougnang Cheikna Zongo Aly Savadogo laboratoire de Biochimie et d’Immunologie {1.é es (LABIA) Universit&eacute Joseph Ki-Zerbo Ouagadougou Burkina Faso laboratoire de Valorisation et Contrô le de Qualit&eacute Institut des Sciences Halieutiques Universit&eacute de Douala Douala Cameroon

Background: The investigation of toxin genes in strains involved in staphylococcal food poisoning contributes to food safety. The aim of this study was to isolate and identify enterotoxigenic Staphylococcus strains from dried, smoked, and braised fish sold in Ouagadougou markets. Methodology: Staphylococci were isolated using standard microbiology methods. Staphylococcus strains were identified using API Staph kit (Reference # 20500, BioMerieux S.A., Marcy l'Etoile, France). The molecular identification of isolated Staphylococcus aureus strains was specifically confirmed by PCR using the Staur4 and Staur6 primers. The genes encoding enterotoxins, enterotoxin-like toxins, exfoliative toxins, and TSST-1.toxin were detected by multiplex PCR using specific primers from Inquaba Biotec West Africa Ltd, Africa's Genomics Company. Results: The results of the microbiological quality assessment indicated that most of the samples analyzed were found to be of unsatisfactory microbiological quality according to the Staphylococcus aureus microbiological criteria (m = 1.2). Overall, only 1..55% of samples were satisfactory, while 97.45% were unsatisfactory. The STAPH API gallery allowed the identification of the following species: Staphylococcus aureus, Staphylococcus xylosus, Staphylococcus lugdunensis, Staphylococcus hominis, Staphylococcus haemolyticus, Staphylococcus lentus, Staphylococcus sciuri and Staphylococcus capitis. Of the 1.8 Staphylococcus isolates, 81.(75%) showed at least one (1. toxin gene. Among the 21.toxin genes tested in this study, 20 genes were detected in all strains analyzed. The staphylococcal toxin genes detected were present in both Staphylococcus aureus and the other coagulase-negative strains isolated in this study. In addition, these genes are found individually or in association in certain strains. The most frequent genes detected in toxin gene-positive strains were: the tsst-1.gene in 45 isolated strains (41.7%), sei (1./1..8%), seg (1./1.%), ser (

关键词： Fish Stapholocuccus Toxin Genes Ouagadougou

Numerical Simulation of Turbulent Diffusion Flames of a Biogas Enriched with Hydrogen

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Fluid Dynamics & Materials Processing 2024年第1期20卷 79-96页

作者： Naima Krarraz Amina Sabeur Khadidja Safer Ahmed Ouadha laboratoire des Science et Ingénierie Maritimes Facultéde Génie MécaniqueUniversitédes Sciences et de la Technologie d’Oran Mohamed BoudiafOranAlgérie laboratoire des Carburants Gazeux et de l’Environnement Facultéde Génie MécaniqueUniversitédes Sciences et de la Laboratoire des Carburants Gazeux et de l’Environneme

Any biogas produced by the anaerobic fermentation of organic materials has the advantage of being an environmentally friendly ***,the relatively low calorific value of such gases makes their effective utilization in practical applications relatively *** present study considers the addition of hydrogen as a potential solution to mitigate this *** particular,the properties of turbulent diffusion jet flames and the related pollutant emissions are investigated numerically for different operating *** related numerical simulations are conducted by solving the RANS equations in the frame of the Reynolds Stress Model in combination with the flamelet *** effects are also taken into account and the combustion kinetics are described via the GRI-Mech 3.0 reaction *** considered hydrogen fuel enrichment spans the range from 0%to 50%in terms of *** varies between 1.and 1. *** results show that both hydrogen addition and pressure increase lead to an improvement in terms of mixing quality and have a significant effect on flame temperature and *** also reduce CO_(2) emissions but increase NOx *** NO is shown to be the predominant NO formation mechanism.

关键词： Biogas hydrogen diffusion flame turbulence NO formation route pressure

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 mathé{1. 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

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 {1.ématiques 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 1..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