Papers by Norbert Hounkonnou
Modelling COVID-19 dynamics in the sixteen West African countries
De Gruyter eBooks, Jun 19, 2023
COVID-19 and intensive medicine in developing countries: critical cares management during a sanitary crisis
De Gruyter eBooks, Jun 19, 2023
Quantum mechanics : a self-contained course
This book is the first in a series of three volumes devoted to quantum mechanics and to quantum f... more This book is the first in a series of three volumes devoted to quantum mechanics and to quantum field theory. It is self-contained, and the only prerequisites are knowledge of integral calculus and partial differential equations, as well as Newton's mechanics of point masses. New subjects are developed in requisite detail at the various points where they are required. The mathematics is at the same time explicit but kept in check, so that the reader does not get bogged down in annoying generalizations that might distract him or her from the physics. Each chapter is complemented by ten problems, and the student is strongly advised to try them all by himself or herself before looking at our full solutions in the third volume.
Properties of acoustic polaron in free-standing slab
Physica B-condensed Matter, Oct 1, 2022
Journal of Mathematical Physics, Oct 1, 2010
From the realization of q-oscillator algebra in terms of generalized derivative, we compute the m... more From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szegő polynomials as well as their relevant properties. We also compute the matrix elements associated to the (p, q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.
Renormalized Gaussian approach to size effects and exchange interactions: Application to localized ferromagnets and amorphous magnets
Journal of Magnetism and Magnetic Materials, Nov 1, 2018
Abstract This paper gives a model field-theoretic description of thermodynamic magnetization fluc... more Abstract This paper gives a model field-theoretic description of thermodynamic magnetization fluctuations and exchange interactions in localized ferromagnets and amorphous magnets. A local Ginzburg-Landau type Hamiltonian is used to describe the properties observed in the transition region. The approach provides another method of tackling interacting spin systems dominated by size effects, fluctuations and correlations, which lead to a dimensional phenomenology of critical behavior. It is also found that the competition between long- and short-range interactions gives rise to the redistribution of the density of spins and causes the anisotropy of the electron spectrum. Above the upper-critical dimension, the approach behaves like mean-field theory with however, thermodynamic quantities modified by intrinsic critical fluctuations, whereas it predicts correctly the universal quantities for dimension 4 and below. At all temperatures, the model matches the magnetic observables, thus providing a unified picture for both the Gaussian and critical regimes.
Pseudo-Solution of Weight Equations in Neural Networks: Application for Statistical Parameters Estimation
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 2018
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural... more An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is implemented for the approximation of smooth batch data containing input–output of the hidden neurons and the final neural output of the network. The training set is associated with the adjustable parameters of the network by weight equations that may be compatible or incompatible.Then we have obtained the exact input weight of the nonlinear equations and the approximated output weight of the linear equations using the conjugate gradient method with an adaptive learning rate. Using the multi-agent system as the different rates of traders of five regions in the Republic of Benin smuggling the fuel from the Federal Republic of Nigeria and the computational neural networks, one can predict the average rates of fuel smuggling traders thinking of this activity in terms of its dangerous character and those susceptible to give up this activity, respectively. This information enables the planner or the decision-maker to compare alternative actions, to select the best one for ensuring the retraining of these traders.
Quantum Mechanics: A Self-Contained Course, Volume 1
$W_{(\alpha,\beta)}^{\nu,\gamma}(p, q)$-deformed Witt algebra: induced deformed oscillator, associated hypergeometric functions, deformed states and matrix elements
arXiv (Cornell University), Oct 26, 2012
This work addresses a generalization of the Witt algebra, called $W_{(\alpha,\beta)}^{\nu,\gamma}... more This work addresses a generalization of the Witt algebra, called $W_{(\alpha,\beta)}^{\nu,\gamma} (p, q)-$ deformed Witt algebra. The time-independent Schrödinger equation for the induced deformed harmonic oscillator is solved; explicitanalytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed for both negative and nonnegative integers, engendering new classes of hypergeometric functions. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.
Proceedings of the third International Workshop on Contemporary Problems in Mathematical Physics, Cotonou, Republic of Benin, 1 - 7 November 2003
WORLD SCIENTIFIC eBooks, 2004
Thermodynamic Properties and Optical Absorption of Polaron in Monolayer Graphene Under Laser Field
Journal of Low Temperature Physics, Mar 18, 2021
In this work, we use the variational method to investigate thermal properties and optical absorpt... more In this work, we use the variational method to investigate thermal properties and optical absorption of polaron in monolayer graphene under laser field. We have shown that the energies and the optical absorption of the system strongly depend on laser parameters and graphene characteristics. We found that the simple model adopted to calculate the optical absorption is enough accurate and interesting to investigate the optical absorption coefficient of the polarons in graphene. We observe that the laser assists the polaron in the optical absoprtion phenomenon. We observe that temperature, the coupling between electron and quantum of lattice vibration, laser parameters and wave number affect the disorder in the system. Contrary to temperature, the laser increases the disorder in the system. At low temperature, the polaronic system becomes decoherent for low values of wave number and gains coherency for high values of wave number. In addition, the coherence of the system is not significantly affected by the laser field but there is a considerable change at higher temperatures. We also observed that laser increases the capacity of system to store energy.
Spin–orbit interaction on the thermodynamics of three-dimensional impurity magnetopolaron under strong parabolic potential
European Physical Journal Plus, May 1, 2020
In the present paper, the thermodynamics of three-dimensional impurity magnetopolaron under stron... more In the present paper, the thermodynamics of three-dimensional impurity magnetopolaron under strong parabolic potential is investigated. To this aim, we first analytically solved the Schrodinger equation to have the complete energy spectrum in the presence of spin–orbit interaction. We equally use the canonical ensemble approach to obtain the partition function before calculating the thermodynamic parameters. Afterward, we found a great dependence of those thermodynamic parameters such as entropy and heat capacity on spin–orbit interaction (SOI). From this investigation, we found that there are some particular values of SOI for which we have a minimum values reached by the entropy as well as in the presence of magnetic field than temperature. This study allows us to conclude that SOI is a very useful parameter in order to build stable quantum system.
Dynamics of COVID-19 pandemic – control problem and equilibrium stability characterization
De Gruyter eBooks, Jun 19, 2023
arXiv (Cornell University), Apr 4, 2023
This chapter aims to provide a clear and understandable picture of constructive semigroups with a... more This chapter aims to provide a clear and understandable picture of constructive semigroups with apartness in Bishop's style of constructive mathematics, BISH. Our theory is partly inspired by the classical case, but it is distinguished from it in two significant aspects: we use intuitionistic logic rather than classical throughout; our work is based on the notion of apartness (between elements of the set, and, later, between elements and its subsets). Following Heyting, at least initially, classical semigroup theory is seen as a guide that helps us to develop the constructive theory of semigroups with apartness. To have a structure, we need a set, a relation, and rules establishing how we will put them together. Working within classical or intuitionistic logic, in order to analyze algebraic structures, it is necessary to start with study on sets and ordered sets, relational systems, etc. A comparative analysis between presented classical and constructive results is also a part of this chapter. All proofs can be found in the Appendix.
Laguerre–Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two
ABSTRACT In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discr... more ABSTRACT In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.
Problematic of Mathematics, Social Sciences, and Arts: A Ubiquitous Constructive Interaction in Algebraic Modeling
Mathematics in mind, 2023
Thermodynamique des interfaces et mécanique des fluides =, Dec 31, 2022
relatons comment à la fin du 18 ème siècle, une découverte liée à la combustion, a pu remettre en... more relatons comment à la fin du 18 ème siècle, une découverte liée à la combustion, a pu remettre en cause l'idée que l'on avait des constituant de la matière et conduire à révolutionner la chimie. Il a fallu que soit trouvée une interprétation correcte de cette découverte et pour cela revisiter en cause les théories et les dogmes existants. On mena ensuite une réflexion fondamentale sur le travail expérimental et l'importance des mesures quantitatives, inventer une manière scientifique d'opérer. Les innovations et les progrès réalisés durant les deux siècles suivants en physique et en chimie, mais aussi en thermodynamique et en mécanique, ont amené à la situation actuelle où la combustion a trouvé sa place en tant que science à part entière. ABSTRACT. We relate how at the end of the 18th century, a discovery linked to combustion, could challenge the idea that we had about constituents of matter and lead to revolutionize chemistry. A correct interpretation of this discovery had to be found and for that to question existing theories and dogmas. It then took a fundamental reflection on experimental work and the importance of quantitative measurements, to invent a scientific way of operating. The innovations and the progress made during the following two centuries in physics and chemistry, but also in thermodynamics and mechanics, brought to the current situation where combustion has found its place as a science in its own right. MOTS-CLÉS. chimie, révolution, combustion, flamme, interface.
(Hom-)(co)associative Ternary (Co)algebras and Infinitesimal Ternary (Hom-)bialgebras
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Dec 31, 2022
International Journal of Applied Mechanics and Engineering, May 24, 2017
A wide range of applications is based nowadays on analytical developments which allow a precise a... more A wide range of applications is based nowadays on analytical developments which allow a precise and effective approach and short time of computations compared with the time required for numerical methods; in this way these developments are suitable for calculations in real time. This work proposes an approach for solving a two-dimensional harmonic problem of a rectangular plate under local surface loading using Vlasov's symbolic method of initial functions and a general solution of the harmonic equation for a rectangle. Substituting the harmonic functions in symbolic form for the corresponding solutions allows us to give the exact solution of the problem in trigonometric form.
arXiv (Cornell University), Aug 6, 2020
Semigroups aren't a barren, sterile flower on the tree of algebra, they are a natural algebraic a... more Semigroups aren't a barren, sterile flower on the tree of algebra, they are a natural algebraic approach to some of the most fundamental concepts of algebra (and mathematics in general), this is why they have been in existence for more then half a century, and this is why they are here to stay.
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Papers by Norbert Hounkonnou