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Origin of Sexy Prime Numbers, Origin of Cousin Prime Numbers, Equations from Supposedly Prime Numbers, Origin of the Mersenne Number, Origin of the Fermat Number

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Advances in Pure Mathematics 2024年第5期14卷 321-332页

作者： Mady ndiaye Middle School Badara Mbaye Kaba Dakar Academy Inspection Ministry of National Education of Senegal Dakar Senegal

We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.

关键词： Cousin Prime Numbers Sexy Prime Numbers Real Sexy Prime Numbers Equations from Supposed Prime Numbers Mersenne Number Fermat Number Supposed Prime Numbers Prime Numbers

Matrix Riccati Equations in Optimal Control

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Applied Mathematics 2024年第3期15卷 199-213页

作者： Malick ndiaye School of Computer Sciences and Mathematics Marist College Poughkeepsie USA

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

关键词： Optimal Control Matrix Riccati Equation Change of Variable

Preliminary Identification of a Prime Number Other Than 2 and 3, the Origin of Twin Prime Numbers, the Structure of the Chain of Prime Numbers and the Set of Prime Numbers Less Than a Given Integer

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Advances in Pure Mathematics 2024年第1期14卷 30-48页

作者： Mady ndiaye Middle School Badara Mbaye Kaba Dakar Academy Inspection Ministry of National Education of Senegal Dakar Senegal

The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it Esp. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted Enp. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted Ep. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.

关键词： Supposedly Prime Numbers Non-Prime Numbers Prime Numbers Prime Numbers Less Than a Given Integer Prime Numbers between Two Given Integers

Effects of Prandtl and Jacob Numbers and Dimensionless Thermal Conductivity on Velocity Profiles in Media (Porous and Liquid)

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Journal of Modern Physics 2024年第10期15卷 1603-1614页

作者： Momath ndiaye Madialène Sene Goumbo ndiaye Department of Hydraulics Rural Engineering Machinery and Renewable Energy UFR Fundamental and Engineering Sciences University of Sine Saloum El Hadj Ibrahima NIASS Kaolack Senegal

In this present study, we analyzed the effects of Prandtl and Jacob numbers and dimensionless thermal conductivity on the velocity profiles in media (porous and liquid). The transfers in the porous medium and the liquid film are described respectively by the improved Wooding model and the classical boundary layer equations. The mesh of the digital domain is considered uniform in the transverse and longitudinal directions. The advection and diffusion terms are discretized with a back-centered and centered scheme respectively. The coupled systems of algebraic equations thus obtained are solved numerically using an iterative line-by-line relaxation method of the Gauss-Seidel type. The results show that the parameters relating to the thermal problem (the dimensionless thermal conductivity, the Prandtl (Pr) and Jacob (Ja) numbers) have no influence on the dimensionless speed, although the thermal and hydrodynamic problems are coupled. Via the heat balance equation. The results obtained show that the parameters relating to the thermal problem have no influence on the dimensionless speed, although the thermal and hydrodynamic problems are coupled via the heat balance equation. So, at first approximation with the chosen constants, we can solve the hydrodynamic problem independently of the thermal problem.

关键词： Condensation Implicit Finite Difference Thin Film Porous Material Model Wooding Vertical Wall

Hydrological Modelling of the Casamance River in Its Upstream Section (Basin at Kolda Level) to Predict Its Future States as a Function of Different Stresses

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Open Journal of Geology 2024年第2期14卷 143-154页

作者： Coumba ndiaye Saïdou Ndao Laboratory of Water and Environment Sciences and Technologies (LaSTEE) Polytechnic School of Thies (EPT) Thies Senegal UFR Sciences and Technologies (SET) University Iba Der Thiam of Thies (UIDT) Thies Senegal

Flow records for stations in the Casamance basin are incomplete. Several gaps were noted over the 1980-2021 study period, making this study tedious. The aim of this study is to assess the potential impact of climate change on the flow of the Casamance watershed at Kolda. To this end, hydrological series are simulated and then extended using the GR2M rainfall-runoff model, with a monthly time step. Projected climate data are derived from a multi-model ensemble under scenarios SSP2-4.5 (scenario with additional radiative forcing of 4.5 W/m2 by 2099) and SSP5-8.5 (scenario with additional radiative forcing of 8.5 W/m2 by 2099). An analysis of the homogeneity of the rainfall data series from the Kolda station was carried out using KhronoStat software. The Casamance watershed was then delimited using ArcGIS to determine the morphometric parameters of the basin, which will be decisive for the rest of the work. Next, monthly evapotranspiration was calculated using the formula proposed by Oudin et al. This, together with rainfall and runoff, forms the input data for the model. The GR2M model was then calibrated and cross-validated using various simulations to assess its performance and robustness in the Casamance watershed. The version of the model with the calibrated parameters will make it possible to extend Casamance river flows to 2099. This simulation of future flows with GR2M shows a decrease in the flow of the Casamance at Kolda with the two scenarios SSP2-4.5 and SSP5-8.5 during the rainy period, and almost zero flows during the dry season from the period 2040-2059.

关键词： Casamance Watershed Climate Change GR2M Climate Models

Obstructive Tumor of the Palate in the Old Person: A Case Report

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Open Journal of Stomatology 2024年第5期14卷 199-205页

作者： Silly Toure Mouhamadou Makhtar ndiaye Abibou ndiaye Mamadou Coume Mame Sanou Diouf Baye Karim Diallo Maxillofacial Surgery and Stomatology Department Aristide Le Dantec University Hospital of Dakar Dakar Senegal Geriatrics Department Aristide Le Dantec University Hospital of Dakar Dakar Senegal ENT and Head and Neck Surgery Department FANN University Hospital of Dakar Dakar Senegal

Introduction: Pleomorphic adenoma or mixed salivary gland tumor is a heterogeneous benign tumor of the salivary glands. The most common site is the parotid gland. Its extra-parotid locations, particularly in the accessory salivary glands, are rarer. We report a case of a pleomorphic adenoma of the posterior palate which posed management problems. Observation: This is an 85-year-old patient who consulted for a tumor of the posterior palate that had been evolving for 3 years. The examination revealed a globular tumor of the posterior palate extending beyond the midline by approximately 7 cm in long axis, shooting towards the oropharynx and hindering breathing, speech and eating, indicating a life-saving tracheotomy. A CT scan of the facial area revealed a well-circumscribed tumor at the expense of the soft palate, with multiple sites of bone lysis. The biopsy performed was in favor of a pleomorphic adenoma. The patient underwent total surgical excision of a huge tumor on the palate. The aftermath of the operation was marked by a loosening of the sutures with an oronasal fistula requiring the creation of an obturator plate due to the patient’s refusal to have another operation. Conclusion: Large pleomorphic adenoma of the posterior palate is a rare entity that can cause respiratory problems and surgical difficulties. His prognosis is generally good.

关键词： Pleomorphic Adenoma Posterior Palate Respiratory Disorders Prognosis Obturator Plaque

Sinonasal Polyposis: About 60 Cases at Fann University Hospital Center, Senegal

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International Journal of Otolaryngology and Head & Neck Surgery 2024年第1期13卷 53-61页

作者： Mame Sanou Diouf Moustapha ndiaye Ahmadou Dembele Evelyne Siga Diom Ciré ndiaye Amadou Thiam Richard E. A. Deguenonvo Abdou Sy Malick ndiaye Abdourahmane Tall Issa Cheikh ndiaye Raymond Diouf HOGIP Hospital Center Dakar Senegal Fann University Hospital Center Dakar Senegal Ourossogui Hospital Center Matam Senegal La Paix Hospital Center Ziguinchor Senegal Children Hospital Center of Diamniadio Dakar Senegal

Introduction: Sinonasal polyposis (SNP) is a chronic inflammatory disease of the mucosa of the nasal cavities and facial sinuses. It is characterized by an oedematous, multifocal and bilateral degeneration of the nasosinus mucosa, which originates in the lateral masses of the ethmoid, where it causes the formation of smooth, gelatinous, translucent and pyriform polyp lesions. The objective of this study was to review epidemiological, clinical, paraclinical data and evaluate the results of endoscopic surgical treatment. Patients and Methods: This is a retrospective study on 60 patients followed at the ENT department of the Fann National University Hospital Center, from January 2010 to December 2015. All patients with sinonasal polyposis were included in the study. Results: The average age of our patients was 38 years and the sex ratio (M/F) was 0.8. In the patients’ histories, we found 18% asthma and 10% Widal’s disease. The average consultation time was 8.5 years. All patients had consulted for nasal obstruction;rhinorrhea was bilateral and found in 67.7% of cases, with olfactory disorders accounting for 50%. The CT scan performed in 58% of cases made it possible to specify the extent of the lesions;the involvement of the ethmoidal sinus was constant and extended to the other sinuses except in 2 cases. All patients had received medical treatment with local corticosteroids. Endoscopic surgical treatment was initiated in 43% of cases after failure of corticosteroid-based medical treatment. The evolution under treatment marked by the reappearance of symptoms that increased each month. At one month postoperatively, all clinical symptomatology had improved with the exception of olfactory disorders, which persisted in 3 patients. At 12 months we noted 12 cases of reappearance of nasal obstruction. Conclusion: SNP is a disease of little known etiology. The diagnosis is almost always clinical. Endoscopic surgery remains a recourse to medical treatment. For good local contro

关键词： Sinonasal Polyposis Endonasal Endoscopic Surgery CHNU Fann

Characterization of Wastewater in School Environments for an Ecological Treatment Solution: A Case Study of Ndiebene Gandiol 1 School

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Journal of Water Resource and Protection 2024年第1期16卷 27-40页

作者： Falilou Coundoul Abdou Khafor ndiaye Abdoulaye Deme Polytechnic Institute of Saint-Louis Gaston Berger University Saint-Louis Sénégal Applied Sciences and Technologies Training and Research Unit Gaston Berger University Saint-Louis Sénégal

The study conducted at Ndiebene Gandiol 1 school in Senegal has unveiled serious environmental and public health challenges. The wastewater analysis revealed high levels of Biochemical Oxygen Demand (BOD5), Chemical Oxygen Demand (COD), and fecal coliforms, signaling potential risks to the well-being of students and staff. This situation mirrors a wider issue in rural educational settings, where inadequate sanitation persists. Intensive wastewater treatment options are known for their effectiveness against high pollutant loads but are resource-intensive in both energy and cost. Conversely, extensive treatment systems, while requiring more land, provide a sustainable alternative by harnessing natural processes for pollutant removal. The research suggests a hybrid treatment approach could serve the school’s needs, balancing the robust capabilities of intensive methods with the ecological benefits of extensive systems. Such a solution would need to be tailored to the specific environmental, financial, and logistical context of the school, based on comprehensive feasibility studies and stakeholder engagement. This study’s findings underscore the urgency of addressing sanitation in schools, as it is intrinsically linked to the health and academic success of students. Quick, effective, and long-term strategies are vital to secure a healthier and more prosperous future for the youth. With proper implementation, the school can transform its sanitation facilities, setting a precedent for rural educational institutions in Senegal and similar contexts globally.

关键词： Wastewater Characterization Ecological Treatment School Sanitation Phytoremediation Rural Infrastructure Environmental Health

Management of Square Carcinoma of the Lower Lip Using Camille-Bernard Flap under Local Anesthesia: When Constraints Dictate Our Attitude

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Open Journal of Stomatology 2024年第4期14卷 191-197页

作者： Silly Toure Mouhamadou Makhtar ndiaye Abibou ndiaye Mame Sanou Diouf Birame Loum Baye Karim Diallo Department of Maxillofacial Surgery and Stomatology CHU Aristide Le Dantec of Dakar Dakar Senegal ENT Department Fann University Hospital Dakar Senegal

Introduction: Squamous cell carcinomas of the lip essentially pose a therapeutic management problem. In the West, their treatment is done under general anesthesia and follows the classic rules of oncology. In our context of exercise, we sometimes have a different attitude dictated by various constraints. Observation: 55-year-old patient with no notable history, seen in consultation for a very large ulcerative-budding lesion on the right 2/3 of the lower lip with mucocutaneous involvement without lymph node findings found on examination. Faced with this suspicious lesion and the patient’s financial difficulties, we decided to operate under local anesthesia to remove this tumor. The oncological excision was followed by immediate plasty using a Camille-Bernard flap with a good immediate aesthetic and functional result and postoperative day 7. The patient was unable to take his surgical specimen to anatomy-pathology and was lost to follow-up due to lack of financial resources. On anatomo-pathological analysis of the surgical specimen, the margins were healthy with confirmation of squamous cell carcinoma (anapathological reading made for scientific interest). Discussion: The particular mentality of certain patients and their difficult financial conditions push us to have an unconventional therapeutic attitude in oncology, but which nevertheless makes it possible to resolve certain problems that we often face. Local anesthesia is possible and realistic in cases like ours and the results can be acceptable and life-saving.

关键词： Squamous Cell Carcinoma Lower Lip Camille Bernard Flap Local Anesthesia