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New Asymptotic Results on Fermat-Wiles Theorem

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Advances in Pure Mathematics 2024年第6期14卷 421-441页

作者： Kimou Kouadio Prosper Kouakou kouassi Vincent tanoé François UMRI MSN Felix Houphouet-Boigny National Polytechnic Institute Yamoussoukro Ivory Coast Nangui Abrogoua University Applied Fundamental Sciences Department Abidjan Ivory Coast UFRMI Flix Houphout-Boigny University Abidjan Ivory Coast

We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.

关键词： Fermat’s Last Theorem Fermat-Wiles Theorem Kimou’s Divisors Diophantine Quotient Diophantine Remainders Balzano Weierstrass Analysis Theorem

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

Physical and Chemical Characterizations of Rubber Latex Cup Bottom Oil

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Advances in Bioscience and Biotechnology 2024年第9期15卷 511-521页

作者： kouassi Konan Edmond Abolle Abollé Aketchi tanoé Lucien Konan Affoué Tindo Sylvie Boa David Yao kouassi Benjamin Laboratoire de Thermodynamique et Physico-Chimie du Milieu (LTPCM) Unit de Formation et de Recherche Sciences Fondamentales et Appliques Universit Nangui Abrogoua Abidjan Cte dIvoire Laboratoire des Procds Industriels de synthse de lEnvironnement et des Energies Nouvelles (LAPISEN) de lInstitut National Polytechnique Flix Houphout Boigny de Yamoussoukro Yamoussoukro Cte dIvoire

Rubber latex is an important economic resource. However, the residues from its harvesting are thrown away, even though they contain lipids that can be recycled. This recovery of the residues from the bottom of the cup requires first and foremost their characterization. The aim of this study is therefore to determine the main physical and chemical characteristics of rubber latex cup bottom oil. Oil’s physical parameters determination shows that it has a density of 951 kg∙m−3, a kinematic viscosity of 48.57 cSt and a water content of 0.0845%. Chemical parameters, meanwhile, indicate that this cup bottom residue has a fat content of 95.96%, an acid number of 2.805 mg KOH/g and an iodine number of 92.42 g I2/100g. Therefore, rubber latex cup bottom oil can be used in the formulation of biofuels, biolubricants, paints, varnishes, alkyd resins, polishing oils, soaps, and insecticides.

关键词： Rubber Latex Cup Bottoms Oil Density Viscosity Characterizations

Epidemiology of Overweight and Childhood Obesity in Abidjan:Cases Collected by the Nutrition Department of the National Institute of Public Health in Abidjan(Côte d’Ivoire)

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Journal of Pharmacy and Pharmacology 2021年第12期9卷 438-443页

作者： Assi Kaudhis KRH N’Guessan Blao AR kouassi E.S. kouassi KF Ake-tano O. Tiahou G Anin A.L Firmin kouassi Institut National de SantéPublique(INSP)d'Abidjan Côte d'Ivoire UniversitéNangui Abrogoua(Abidjan) Côte d'Ivoire SociétéIvoirienne de Nutrition(SIN) Côte d'Ivoire Laboratoire de biologie et de recherche médicale Institut National de SantéPublique(INSP)d'AbidjanCôte d'Ivoire Institut des Sciences Anthropologiques de Développement(ISAD-UniversitéFélix-Houphouët-Boigny d'Abidjan Côte d'Ivoire Laboratoire de Biomorphologie et d'Anthropologie Physique Côte d'Ivoire 不详

Objective:The objective of this work is to describe the epidemiological profile of overweight or obese children monitored at the nutrition service of the National Institute of Public Health(INSP)of ***:This is a retrospective and cross-sectional study that took place from April 28,2017 to December 28,2018 at the Nutrition Department of the *** concerned 181 children or adolescents of both sexes aged 5 to 19 years monitored for their excess weight in the said *** was collected using a summary sheet of medical records over the study ***:The results obtained indicate that out of all 181 young patients,130(71.8%)were girls,of which 122(67.4%)were obese.49.2%of these patients were between 10 and 14 years old with a mean age of 12.24 *** biochemical assessment showed that the disturbance was always greater in obese patients except for the proportion of biochemical results disturbed in uric acid level which was higher in overweight *** subjects developed eating disorders such as overeating for 87.8%and snacking in 55.2%of ***:The epidemiological profile of overweight children and adolescents requires a rapid fight against this pathology.

关键词： Overweight obesity overweight children adolescents.

Modeling and Optimization of Two Clays Acidic Activation for Phosphate Ions Removal in Aqueous Solution by Response Surface Methodology

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Journal of Water Resource and Protection 2019年第2期11卷 200-216页

作者： Yao joseph Adjoumani Pierre Jean Marie Richard Dablé Konan Edmond kouassi Soumahoro Gueu Alain Stéphane Assémian kouassi Benjamin Yao Laboratoire Thermodynamique Traitement et Sciences des Surfaces et Interfaces Ingénierie et Physicochimie des Procédés et de Mécaniques des Matériaux (L2TSIPM) Institut National Polytechnique Félix Houphou&euml t Boigny INP H-B Yamoussoukro C&ocirc te d’Ivoire Laboratoire des Procédés Industriels de Synthèse et de l’Environnement (LAPISEN) Institut National Polytechnique Félix Houphou&euml t Boigny INP H-B Yamoussoukro C&ocirc te d’Ivoire

This work deals with phosphate ions removal in aqueous solution by adsorption carried out using two clays, both in activated form. One, non-swelling clay, rich in kaolinite, is associated with illite and quartz. The other, swelling, richer in montmorillonite, is associated with kaolinite, illite and quartz. Seven factors including these two clays were taken into account in a series of experimental designs in order to model and optimize the acidic activation process favoring a better phosphate removal. In addition to the choice of clay nature, the study was also interested in the identification of the mineral acid, between hydrochloric acid and sulfuric acid, which would promote this acidic activation. Response Surface Methodology (RSM) was used for this purpose by sequentially applying Plackett and Burman Design and Full Factorial Design (FD) for screening. Then, a central composite design (CCD) was used for modeling the activation process. A mathematical surface model has been successfully established. Thus, the best acidic activation conditions were obtained by activating the montmorillonite clay with a 2N sulfuric acid solution, in an acid/clay mass ratio of 7.5 at 100°C for 16H. The phosphate removal maximum rate obtained was estimated at 89.32% ± 0.86%.

关键词： Clay Acidic Activation Modeling Optimization Phosphate Removal Response Surface Methodology

Application of the Dempster-Shafer Theory to the Classification of Pixels from Aster Satellite Images and Spectral Indices

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Journal of Applied Mathematics and Physics 2017年第7期5卷 1462-1477页

作者： Jean-Claude Okaingni Sié Ouattara Adles Francis kouassi Adama Koné Wognin joseph Vangah Alain Clement Laboratory of Signals and Electrical Systems (L2SE)) Institut National Polytechnique Houphou&eumlt Boigny Yamoussoukro Cote D’Ivoire Institut National Polytechnique Houphouët Boigny (INPHB) Yamoussoukro Cote D’Ivoire Ecole Supérieure des Technologies de l’Information et de la Communication (ESATIC) Abidjan Cote D’Ivoire Institut Universitaire de Technologie d’Angers (IUT) Angers France

In this paper, it is proposed to apply the Dempster-Shafer Theory (DST) or the theory of evidence to map vegetation, aquatic and mineral surfaces with a view to detecting potential areas of observation of outcrops of geological formations (rocks, breastplates, regolith, etc.). The proposed approach consists in aggregating information by using the DST. From pretreated Aster satellite images (geo-referencing, geometric correction and resampling at 15 m), new channels were produced by determining the spectral indices NDVI, MNDWI and NDBaI. Then, the DST formalism was modeled and generated under the MATLAB software, an image segmented into six classes including three absolute classes (E,V,M) and three classes of confusion ({E,V}, {M,V}, {E,M}). The control on the land, based on geographic coordinates of pixels of different classes on said image, has made it possible to make a concordant interpretation thereof. Our contribution lies in taking into account imperfections (inaccuracies and uncertainties) related to source information by using mass functions based on a simple support model (two focal elements: the discernment framework and the potential set of belonging of the pixel to be classified) with a normal law for the good management of these.

关键词： Dempster-Shafer Theory Belief Functions Source Modeling Aster Satellite Images Spectral Indices Classification

Surgical Treatment of Chronic Constrictive Pericarditis in a Developing Country

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World Journal of Cardiovascular Surgery 2022年第11期12卷 281-191页

作者： kouassi Antonin Souaga Eric Koutoua Katché Yoboua Aimé Kirioua-Kamenan Jean Calaire Degré Kwadjau Anderson Amani Gnamien Randolph Niava joseph Kouamé Paul Yapo Yapo kouassi Flavien Kendja Cardiovascular Surgery Department The Abidjan Heart Institute Abidjan C&#244te d’Ivoire Anesthesia and Intensive Care Department The Abidjan Heart Institute Abidjan C&#244te d’Ivoire

Background: Chronic constrictive pericarditis is a rare but serious clinical entity with a poor prognosis in the absence of surgical treatment. The purpose of this study was to report on our experience of subtotal anterior pericardectomy and analyze our surgical results. Results: We included 74 patients operated on for chronic constrictive pericarditis in our institution during the period from January 1985 to December 2020. There were 29 female and 45 male patients, with an average age of 28 years (range: 8 - 64 years). 36.5% of patients were in NYHA class III or IV. Physical signs were dominated by peripheral signs of right heart failure in 93.2% of cases. The surgical procedure was a subtotal anterior pericardectomy from the left to the right phrenic nerve, freeing the heart chambers and the large vessels. The surgical results were marked by a functional improvement in 82.4% of the cases. The postoperative complications were marked by a low cardiac output in 8.1% of the cases, a atrial fibrillation in 4.1% of the cases, a haemorrhage in 1.4% of the cases, a haemothorax in 2.7% of the cases. Perioperative mortality was 5.4% patients. The causes of death were low cardiac output in 50% of cases, hemorrhage in 25% of cases, and hepatocellular insufficiency in 25% of cases. We observed a mortality of 2.9% after an average follow-up of 5.17 years ± 4.76 years. All other survivors were asymptomatic and no re-intervention for recurrence was performed. Conclusions: Subtotal anterior pericardectomy was the technique we used for the treatment of chronic constrictive pericarditis. It allowed having satisfactory surgical results with a functional improvement and an acceptable morbidity.

关键词： Constrictive Pericarditis Subtotal Pericardectomy Result

Surgical Myocardial Revascularization in a Sub-Saharan African Country: Indications and Results

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World Journal of Cardiovascular Surgery 2021年第11期11卷 95-103页

作者： kouassi Antonin Souaga Gnamien Randolph Niava Eric Koutoua Katché Kwadjau Anderson Amani Yoboua Aimé Kirioua-Kamenan Jean Calaire Degré Arnau Ekou Aka Roland N’guetta joseph Kouamé Landry Kohou-Koné Yapo Paul Yapo kouassi Flavien Kendja kouassi Michel Kangah Cardiovascular Surgery Department of the Abidjan Heart Institute Abidjan C&#244te d’Ivoire Hemodynamics Department of the Abidjan Heart Institute Abidjan C&#244te d’Ivoire Anesthesia and Intensive Care Department of the Abidjan Heart Institute Abidjan C&#244te d’Ivoire

Introduction: Despite the advances of interventional catheterization, surgery remains the treatment of choice for some coronary lesions. Objective: To report the indications and results of surgical revascularization of the myocardium at the Abidjan Heart Institute. Patient and Methods: This is a retrospective study of patients with coronary insufficiency who underwent surgical myocardial revascularization between March 2014 and May 2020 in the Cardiovascular Surgery Department of the Abidjan Heart Institute. There were 17 patients, 11 of whom were men (64.7%) and 6 women (35.3%), The mean age of the patients was 57.5 years ± 8.8. All patients were symptomatic with disabling angina in class III of the Canadian Cardiac Society (CCS). This sym- ptomatology had been evolving on average for 5 years and 6 patients had a history of acute coronary syndrome, 2 of whom had undergone prior angioplasty. Coronary angiography revealed mono-truncated (17.6%), bi-truncated (23.5%) and tri-truncated (58.8%) lesions. Results: The patients were operated under cardiopulmonary bypass (CPB) 15 cases (88.2%) and off pump in 2 cases (11.8%). They underwent a single bypass in 23.5% of cases, a double bypass in 47.1% of cases and a triple bypass in 29.4% of cases. We observed 3 cases of complications (17.6%), namely transient acute renal failure, mediastinitis and postoperative bleeding. The operative and hospital mortality was nil. After a mean follow-up of 3 ± 1.8 years, all patients were

关键词： Myocardial Revascularization Coronary Surgery Bypass

Nutrient Intake and Impact of the Consumption of Two Street Foods (Garba and Rice Eggplant Sauce) in Humans

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Food and Nutrition Sciences 2022年第3期13卷 195-210页

作者： N’Gbésso Amos Ekissi Yadé Réné Soro Gnogbo Alexis Bahi Ahou Bénédicte Nina kouassi N’Guessan Jean-Eugène Parfait Kouadio kouassi Benjamin Yao Allico joseph Djaman Laboratory of Biotechnology Agriculture and Valorization of Biological Resources Department Biosciences University Félix Hou-phouet-Boigny Abidjan C&#244 te d’Ivoire Department of Clinical and Fundamental Biochemistry Institute Pasteur in C&#244 te d’Ivoire Abidjan C&#244 te d’Ivoire Laboratory of Biochemistry Microbiology and Valorization of Agricultural Resources Institute of Agropastoral Management Univer-sity Péléforo Gon Coulibaly Korhogo C&#244 te d’Ivoire Department Communication Environment and Society University Alassane Ouattara Bouake C&#244 te d’Ivoire Laboratory of Biocatalysis and Bioprocessing Department of Food Science and Technology University Nangui Abrogoua Abidjan C&#244 te d’Ivoire Laboratory of Industrial Processes Synthesis Environment and New Energies Institute National Polytechnique Felix Houphouet-Boigny Yamoussoukro C&#244 te d’Ivoire

Many lifestyle factors can affect health, but nutrition is an important, modifiable, and powerful factor in promoting health, preventing and treating disease, and improving quality of life. Inadequate dietary intake, regardless of the cause, can have negative effects on human growth and development. Analysis of tuna “Garba” and rice with eggplant sauce consumed in Abidjan (Côte d’Ivoire) revealed low levels of water-soluble B vitamins. Also, the analysis of these dishes observed the presence of histidine, leucine, valine, glutamine, arginine, cysteine and alanine. The tuna “Garba” (Gab) dish showed levels in amino acids ranging from 69.8 ± 1.33 to 764 ± 2.08 mg/kg and 77.1 ± 1.95 to 754.67 ± 2.8 mg/kg in the eggplant sauce rice (Risa) dish. During 15 days of consumption of these dishes by the wistar rats, anthropometric parameters, namely body length and abdominal circumference, showed a significant increase in the rats consuming the rice eggplant sauce. The rats showed BMI, Lee’s Index and Adipocyte Index ranged from 0.27 ± 0.01 to 0.31 ± 0.01 g/cm2;0.25 ± 0.01 to 0.26 ± 0.00 cm and 1.67% ± 0.25% to 1.96% ± 0.21% respectively. The nutritional profiling of these two street foods by LIM and SAIN score presented poor profiles.

关键词： Nutritional Values Tuna Garba Rice Eggplant Sauce Nutritional Profiling Abidjan (Côte d’Ivoire)