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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

The Riccati Equation, Differential Transform, Rational Solutions and Applications

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Applied Mathematics 2022年第9期13卷 774-792页

作者： malick ndiaye Department of Mathematics and Computer Sciences Marist College Poughkeepsie NY USA

In this article, the Riccati Equation is considered. Various techniques of finding analytical solutions are explored. Those techniques consist mainly of making a change of variable or the use of Differential Transform. It is shown that the nonconstant rational functions whose numerator and denominator are of degree 1, cannot be solutions to the Riccati equation. Two applications of the Riccati equation are discussed. The first one deals with Quantum Mechanics and the second one deal with Physics.

关键词： Riccati Equation Differential Transform Rational Solutions

Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

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Journal of Quantum Computing 2022年第3期4卷 135-146页

作者： Augusto Gonzalez Bonorino malick ndiaye Casimer DeCusatis Claremont Graduate University Claremont91711USA Marist College Poughkeepsie12601USA

The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical *** systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and *** this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian *** implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum *** with classical results and areas for future research are discussed.

关键词： Quantum computing matrix ricatti equations differential equations qiskit hybrid algorithm HHL algorithm

Maize Crop N Uptake from Organic Material of <i>Gliricidia sepium </i>Coinoculated with <i>Rhizobium</i>and Arbuscular Mycorrhizal Fungus in Sub-Saharian Africa Sandy Soil

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American Journal of Plant Sciences 2017年第3期8卷 428-440页

作者： Adama Diouf malick ndiaye Mame Arama Fall-ndiaye Tahir Abdoulaye Diop Laboratoire de Biotechnologies des Champignons Département de Biologie Végétale Faculté des Sciences et Techniques Université Cheikh Anta Diop Dakar Sénégal Laboratoire Commun de Microbiologie IRD/ISRA/UCAD Centre de Recherche de Bel Air Dakar Sénégal

The effect of green manure of gliricidia (Gliricidia sepium (Jacq.) Walp) leguminous plants applied for cereal maize cultivation and N uptake by cereal were investigated and analyzed in relation to influence of dual inoculation of gliricidia with microbial symbionts. Two pot experiments were conducted in greenhouse. The first trial was set up to enhance growth of gliricidia with exotic and indigenous rhizobial strains and arbuscular mycorrhizal fungus and the second to determine the effect of gliricidia organic material on maize growth. Direct 15N-labelling techniques were used to estimate N-fixed by gliricidia plant and N uptake of maize cereal crop from green manuring was calculated. Growth of gliricidia trees estimated by aboveground biomass production and N fixed were positively affected by dual inoculations. This study showed that shoot dry weight and N accumulation of maize cultivated under gliricidia green manure were influenced by its application and indirectly by microbial treatments. The N recovery by the maize accounted 17.32% to 26.52% of N applied as gliricidia organic material. Gliricidia green manure N accumulation and release, and afterward microbial inoculations were substantially determining on maize crop N uptake and growth in sandy soil of Sub-Saharian Africa.

关键词： Arbuscular Mycorrhizal Fungus Green Manure Maize Nitrogen Rhizobium

Linear and Nonlinear Stokes Waves Theory: Numerical Hydrodynamic and Energy Studies

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Open Journal of Fluid Dynamics 2023年第1期13卷 61-79页

作者： Alpha malick ndiaye Fadel Diop Samba Dia Cheikh Mbow Laboratoire de Mécanique des Fluides et Transferts Département de Physique Faculté des Sciences et Techniques Université Cheikh Anta Diop (UCAD) Dakar Sénégal

The increase of wave energy in electricity production is an objective shared by many countries to meet growing demand and global warming. To analyze devices capable of converting the energy of sea waves into electrical energy, it is important to master the various theories of gravity waves and generation. We will in our work consider a numerical waves tank for an amplitude A=0.5, a wavelength λ=0.25 , an average height He=10 and a Froude number fixed at 1 × 105. Numerical wave channel analysis is used to reproduce the natural phenomenon of wave propagation in an experimental model. Wave makers are usually used to generate waves in the channel. In theory, the influence of an incident wave can be considered, as in the case of our study. In this study, the evolution of the hydrodynamic parameters and the energy transported in one wavelength can be determined by calculation. A change of variable will be done in this work to facilitate the writing of the boundary conditions at the free surface and at the bottom. The nonlinear Stokes theory will be studied in this case in order to provide hydrodynamic solutions through the Navier-Stokes equations to finally deduce the energetic results. To do this, the finite difference method will be used for the hydrodynamic results such as the velocity potential and the free surface elevation and the trapezium method of Newton for the energetic results. Thus, we will determine the energetic potential according to the decrease in the slope of the tank. To do this, we will take as values of beta representing the inverse of the slope of the tank, β=100, β=105, β=110 and β=105. .

关键词： Waves Tank Energy Waves Gravity Waves Navier-Stokes Numerical Nonlinear Stokes Theory

Sensitivity Analysis of the Penman-Monteith Reference Evapotranspiration to Climatic Variables: Case of Burkina Faso

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Journal of Water Resource and Protection 2017年第12期9卷 1364-1376页

作者： Papa malick ndiaye Ansoumana Bodian Lamine Diop Koffi Djaman Laboratoire Leï di “Dynamique des Territoires et Développement” Université Gaston Berger (UGB) Saint Louis Senegal UFR S2ATA Sciences Agronomiques de l’Aquaculture et des Technologies Alimentaires Université Gaston Berger Saint-Louis Senegal NMSU: Agricultural Science Center at Farmington Department of Plant and Environmental Sciences New Mexico State University Farmington USA

Sensitivity analysis is important in understanding the effect of each climatic input variable on the variation of the evapotranspiration which is a significant element for hydrological modelling, irrigation programs, and water resources management. This study investigates the responses of evapotranspiration to the variation of maximum and minimum temperature, solar radiation, wind speed and maximum and minimum relative humidity. Daily data from 1998 to 2012 of eight stations are used. For each climatic variable, a variation of 5% up to ±25% was performed in order to evaluate the sensitivity of the evapotranspiration to the input variables. Results show that evapotranspiration is more sensitive to the variation of solar radiation, maximal temperature and wind speed, respectively.

关键词： Evapotranspiration Penman-Monteith Sensitivity Coefficient Burkina Faso

Darier-Ferrand Dermofibrosarcoma: A Case Report of a Cervical Localization

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International Journal of Otolaryngology and Head & Neck Surgery 2023年第5期12卷 317-325页

作者： Aminata Mbaye Ndiassé ndiaye Ndeye Fatou Thiam Ousmane Sano Rachid Vitamine Mouhamed Salem Ould Abderrahmane Maïmouna Diagne malick ndiaye ENT Department Thiès Regional Hospital Thies Senegal ENT Department Ouakam Military Hospital Dakar Senegal Radiology Department Thies Regional Hospital Thies Senegal ENT Department Diamniadio Children’s Hospital Dakar Senegal

Darier-Ferrand dermatofibrosarcoma (DFS) is a cutaneous mesenchymal tumor of intermediate malignancy. It is a rare but not exceptional tumor, accounting for 0.1% of malignant skin tumors. Histological examination is essential for diagnosis. Wide surgical excision is the standard treatment. DFS is a tumor whose prognosis and evolutionary risk are mainly linked to the delay in diagnosis and the quality of the first excision. Late diagnosis makes excision and reconstruction surgery difficult. The chances of recovery in the case of well-performed primary surgery are significantly greater than in the case of salvage surgery. To improve prognosis, early, codified, multidisciplinary management is essential. In our African context, and especially in the case of patients living in rural areas, errant diagnoses are often found hence the importance of raising awareness and providing information to healthcare personnel. We report a case of an enlarged left supraclavicular Darier-Ferrand dermatofibrosarcoma. The patient had come for a late consultation at a stage when the tumour was large. The CT scan was a great help in the pre-operative phase. The patient underwent complete surgical excision, the postoperative course was straightforward and the histology of the surgical specimen confirmed the diagnosis. The resection margins were healthy. The patient is alive at one year with no recurrence or metastasis.

关键词： Cervical Localization Dermatofibrosarcoma Skin Tumor Wide Surgery

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

Assessment of Radiofrequency in Otorhinolaryngology at the Military Hospital of Ouakam (MHO)

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International Journal of Otolaryngology and Head & Neck Surgery 2021年第5期10卷 433-440页

作者： Abdou Sy Ahmadou Cheikhou Sall Mamadou Oury Barry Ndè ye Fatou Thiam Pape Yakhya Ba malick ndiaye ENT Department Diamniadio Children Hospital Dakar Senegal ENT and Cervicofacial Surgery Department of the Military Hospital of Ouakam (MHO) Hyderabad India

Introduction: Coblation® is a low temperature-controlled tissue ablation technique widely used in human surgery. Its development in otorhinolaryngology has allowed a spectacular advance in the management of diseases of the nasal and oral cavities. The objective of our work was to study the indications for radiofrequency in ENT, to describe the technical aspects and to evaluate the results of his practice at the HMO. Patients and Methods: This is a retrospective study carried out in the ENT and Head and Neck Surgery department of the Ouakam Military Hospital (MHO) over a period of 3 years (from January 2015 to the end of December 2017), involving 37 patients who received radiofrequency treatment in the ENT sphere. Results: The study was carried out on 37 patients. The sex ratio of 0.19. The mean age of the patients was 33.3 years. The indications were dominated by chronic caseous cryptic tonsillitis with or without halitosis with 24 cases (64.9%) followed by recurrent tonsillitis in 5 cases (13.5%) then we have obstructive hypertrophy of the palatal tonsils with syndrome sleep apnea (OSAS) in 4 cases (10.8%) followed by nasal obstruction (hypertrophy of the inferior turbinates) and hypertrophy of the soft palate and uvula in 2 cases (5.4%). The complication rate was 8.1% and dominated by transient dysgeusia in 1 case or 2.7%, uvula edema in 1 case or 2.7% and bleeding in 1 case or 2.7%. The postoperative follow-up was done one week, 1 month, 3 months, 6 months and 12 months after radiofrequency. Volumetric reduction begins to set in from 1 month (62.5%) and becomes maximum in 3 months (74.3%). Conclusion: Coblation® is a controlled tissue ablation technique at low temperature, patented by ArthroCare® Corporation in 1997. Very widespread in human surgery. Its development in otorhinolaryngology was later, but allowed a spectacular advance in the management of diseases o

关键词： Radiofrequency Evaluation Coblation Indications Techniques Complication