# Mahouton Norbert HounkonnouUniversity of Abomey-Calavi | UAC · Research Laboratory of Mathematics and Mathematical Physics (LRMPM)

Mahouton Norbert Hounkonnou

DSc., Full Professor

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325

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Introduction

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January 2006 - present

## Publications

Publications (325)

The partially and totally (co)associative ternary (co) algebras, and infinitesimal bialgebras are constructed and discussed. Their trimodules and matched pairs are defined and completely characterized. Main structural properties and relations are also deduced and analyzed. In addition, the partially and totally hom-coassociative ternary coalgebras...

We define new velocity and acceleration having dimension of (Length)^{\alpha}/(Time) ( L e n g t h ) α / ( T i m e ) and (Length)^{\alpha}/(Time)^2, ( L e n g t h ) α / ( T i m e ) 2 , respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the sam...

We gave some applications of the $p-$adic R($\rho,q) beta and gamma functions and it connections with $p-$adic amplitude and string theory

Constructions of n-ary bialgebras and n-ary infinitesimal bialgebras of associative type and their hom-analogs, generalizing the hom-bialgebras and infinitesimal hom-bialgebras are investigated. Main algebraic characteristics of n-ary totally, n-ary weak totally, n-ary partially and n-ary alternate partially associative algebras and bialgebras, and...

This paper addresses a Hom-associative algebra built as a direct sum of a given Hom-associative algebra \((\mathcal {A}, \cdot , \alpha )\) and its dual \((\mathcal {A}^{*}, \circ , \alpha ^{*}),\) endowed with a non-degenerate symmetric bilinear form \(\mathcal {B},\) where \(\cdot \) and \(\circ \) are the products defined on \(\mathcal {A}\) and...

2023 The International Conference on Mathematical Analysis, Applications and Computational Simulation (ICMAACS 2023) is aimed to provide a high-level platform where mathematicians and scientists exchange recent developments, discoveries, and progress in Pure and Applied Mathematics and Their Applications in real-world problems. Its aim is to create...

We showed that fermion Spin Lie groups are p−adic, and demonstarted the connection of the spin(1/2) with Iwasawa algebras. We have also defined the p−adic zeta function for
spin(1/2) and extended the p−adic integral (Fermionic and Bosonic due to T. Kim)
quantum calculus to R(p, q)−deformation and we also did an application to p−adic R(ρ, q)−gamma...

This paper addresses the construction of Cauchy operators and related identities from R( p,q )-deformed quantum algebras. The generating function, Mehler and Rogers formulae, and their extended identities for the homogeneous Rogers-Szegö polynomials are computed and discussed. Relevant particular identities extracted from known quantum algebras are...

In this work, we address the $p$-adic analogues of the fermion spin Lie algebras and Lie groups. We consider the extension of the fermion spin Lie groups and Lie algebras to the $p-$adic Lie groups and investigate the way to extend their integral to the zeta function as well. We show that their groups are ghost friendly. In addition, we develop the...

The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law. Conformable momentum and Laplace-Runge-Lenz vectors are considered, generating $SO(3), SO(4),$ and $SO(1, 3)$ dyna...

In this paper, we provide a novel generalization of quantum orthogonal polynomials from [Formula: see text]-deformed quantum algebras introduced in earlier works. We construct related quantum Jacobi polynomials and their probability distribution, factorial moments, recurrence relation, and governing difference equation. Surprisingly, these polynomi...

In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties, namely ($\mathcal{R}(p,q)$-mean, $\mathcal{R}(p,q)$-variance and $\mathcal{R}(p,q)$-covariance) are computed and di...

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 base...

In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365 (2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172 (2018), we investigate a class of generalized coherent states for associated Jacobi polynomials and hypergeometric functions, satisfying the resolution of the identity with respect to a weight functio...

This work is one of the analytical approaches to evaluate the evaporation frequency response
of injected droplets, using the Heidmann analogy of a single droplet that is continuously fed with the
same liquid fuel. Based on a linear analysis using the Rayleigh criterion, a dimensionless response factor
is determined. The effects due to the variation...

In this paper, we prove the first Heine’s transformation formula using
q-difference equations. Main relevant identities such as q-Binomial theorem and $q$-Difference operator are also considered.

Motivated by our recent work published in [23], we achieve, in this paper, a matrix formulation of the density operator to construct a two-component vector coherent state representation for a supersymmetric harmonic oscillator. We investigate and discuss the main relevant statistical properties. We use the completeness relation to perform the therm...

This work addresses an extension of Fourier-Stieltjes transform of a vector measure defined on compact groups to locally compact groups, by using a group representation induced by a representation of one of its compact subgroups.

In this paper, we focus on the characterization of Lie algebras of fermionic, bosonic and parastatistic operators of spin particles. We provide a method to construct a Lie group structure for the quantum spin particles. We show the semi-simplicity of the Lie algebra for a quantum spin particle, and extend the results to the Lie group level. Besides...

Изучается гамильтонова динамика космического аппарата на фоне метрик Алькубьерре и Гeделя. Получены гамильтоновы векторные поля, управляющие эволюцией системы, построены и обсуждаются операторы рекурсии, порождающие константы движения. Кроме того, описаны соответствующие мастер-симметрии.

Background: Stunting is a public health issue in many low and middle income countries. The role played by exclusive breastfeeding practice (EBF) and water source (WS) used by the mothers in stunting reduction needs to be more clarified. Objective: To test whether EBF and WS are moderators or mediators of participation in Nutrition at Centre (N@C) p...

We study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and Gödel metrics. We derive the Hamiltonian vector fields governing the system evolution, construct and discuss related recursion operators generating the constants of motion. Besides, we characterize relevant master symmetries.

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides,...

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides,...

In this chapter, the authors examine the oscillatory temperature field of a spherical drop in evaporation. The motionless drop is fed continuously at the center so that it maintains a constant volume during the process. It is known that evaporation may amplify high‐frequency acoustic perturbations arising from the rocket engine and damage the rocke...

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science...

In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the Fourier-Stieltjes t...

We study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and G\"odel metrics. We derive the Hamiltonian vector fields governing the system evolution, construct and discuss related recursion operators generating the constants of motion. Besides, we characterize relevant master symmetries.

In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837--851.] to construct q-difference equations with seven variables, which generalize recent works of Jia et al [Symmetry 2021, 13, 1222.]. In addition, we derive Rogers formulas, extended Rogers f...

We investigate the dynamics and decoherence of the exciton polaron in a 2D transition metal dichalcogenides modulated by a magnetic field barrier. Using the Huybrechts method and an approximate diagonalization of exciton-phonon operators is performed to derive the fundamental energy, the first excited state energy, the effective mass and the mobili...

The density operator representation in the context of multi-matrix vector coherent states basis is performed and applied to Landau levels of an electron in an electromagnetic field coupled to an isotropic harmonic potential. Main relevant statistical properties such as the Mandel Q-parameter and the signal-to-quantum-noise ratio are derived and dis...

The vaporisation frequency response due to pressure oscillations is analysed for a spray of repetitively injected drops into a combustion chamber. In the Heidmann analogy, this vaporizing spray is represented by the so-called ‘mean droplet’, which is a continuously fed spherical droplet at rest inside the combustion chamber. Only radial thermal con...

The Bollobás–Riordan (BR) polynomial [(2002), Math. Ann. 323 81] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects, called rank 3 weakly coloured stranded graphs. Stranded graphs arise in the study of tensor models for quantum gravity in physics, and gener...

A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function $\mathcal{H}_{nc}$ describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form $\omega_{nc}$ is defined. A re...

This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation is performed with the introduction of the Laplace-Runge-Lenz vector. The existence of quasi-bi-Hamiltonian stru...

Integrals of motion are constructed from noncommutative (NC) Kepler dynamics, generating $SO(3),$ $SO(4),$ and $SO(1,3)$ dynamical symmetry groups. The Hamiltonian vector field is derived in action-angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is comp...

Particularly cool sea surface temperatures (SSTs) were observed in 2012 along the Northern Gulf of Guinea (NGoG) coast. This strong cooling event was seen from February to June and reached maxima in the coastal upwelling areas: SST anomalies of -1°C were observed in Sassandra Upwelling area in Côte d’Ivoire (SUC, situated east of Cape Palmas) and S...

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang–Baxter equation in an anti-flexible algebra which is...

The history of nonassociative algebraic structures can be traced at least to the middle of the 19th century. Today, the theory of nonassociative algebraic structures is an enormously broad and greatly advanced area. Interesting new algebraic ideas arise, with challenging opportunities to discover connections to other areas of mathematics, natural s...

So if you asked me: why do mathematics? I would say: mathematics helps people flourish. Mathematics is for human flourishing. Because we are not mathematical machines. We live, we breathe, we feel, we bleed. Why should anyone care about mathematics if it doesn't connect deeply to some human desire: to play, seek truth, pursue beauty, fight for just...

Построены интегралы движения из некоммутативной кеплеровой динамики, порождающие динамические группы симметрий $SO(3)$, $SO(4)$ и $SO(1,3)$. Получено гамильтоново векторное поле в переменных действие-угол и показано существование иерархии бигамильтоновых структур. Вычислено и обсуждается семейство рекурсивных операторов Нейенхейса.

Integrals of motion are constructed from noncommutative (NC) Kepler dynamics, generating SO(3),
SO(4), and SO(1, 3) dynamical symmetry groups. The Hamiltonian vector field is derived in action-angle
coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family
of Nijenhuis recursion operators is computed...

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 op...

In this work, we are studying thermodynamics properties and optical absorption of bipolaron in graphene under a laser field using the variational method. We obtain the ground and first excited states of the bipolaron which strongly depend on laser parameter and graphene characteristics. It is seen that the optical absorption of a bipolaron in graph...

This work investigates the cumulative effects of fluctuations of order parameters and magnetoelectric coupling on the two-dimensional RMnO3 (R = Tb, Lu and Y). The study is carried out through a modified Landau model resulting from microscopic considerations. It is shown that during the transition from the paramagnetic (paraelectric) to ferromagnet...

In this work, the density operator diagonal representation in the coherent states basis, known as the Glauber–Sudarshan-P representation, is used to study harmonic oscillator quantum systems and models of spinless electrons moving in a two-dimensional noncommutative space, subject to a magnetic field background coupled with a harmonic oscillator. R...

This work treats entropy and heat capacity of a monolayer transition metal dichalcogenide quantum dot under magnetic field using the canonical ensemble approach. We consider four following TMDs: MoSe2, MoS2, WSe2 and WS2. At low temperature heat capacity increases steadily, shows a shoulder and thereafter becomes constant for high temperatures. MoS...

We perform generalizations of Witt and Virasoro algebras, and derive the corresponding Korteweg–de Vries equations from known [Formula: see text]-deformed quantum algebras previously introduced in J. Math. Phys. 51 (2010) 063518. Related relevant properties are investigated and discussed. Besides, we construct the [Formula: see text]-deformed Witt...

WEBINAR camfmen.masfak.ni.ac.rs www.cipma.net "So if you asked me: why do mathematics? I would say: mathematics helps people flourish. Mathematics is for human flourishing. Because we are not mathematical machines. We live, we breathe, we feel, we bleed. Why should anyone care about mathematics if it doesn't connect deeply to some human desire: to...

From the definition and properties of unital hom-associative algebras, and the use of the Kaplansky’s construction, we develop algebraic structures called 2-hom-associative bialgebras, 2-hom-bialgebras, and 2-2-hom-bialgebras. Besides, we define and characterize the hom-associative dialgebras, hom-Leibniz algebra and hom-left symmetric dialgebras,...

This paper addresses a Hom-associative algebra built as a direct sum of a given Hom-associative algebra $(\mathcal{A}, \cdot, \alpha)$ and its dual $(\mathcal{A}^{\ast}, \circ, \alpha^{\ast}),$ endowed with a non-degenerate symmetric bilinear form $\mathcal{B},$ where $\cdot$ and $\circ$ are the products defined on $\mathcal{A}$ and $\mathcal{A}^{\...

We perform generalizations of Witt and Virasoro algebras, and derive the corresponding Korteweg-de Vries equations from known R(p,q)-deformed quantum algebras previously introduced in J. Math. Phys. 51, 063518, (2010). Related relevant properties are investigated and discussed. Besides, we construct the R(p,q)-deformed Witt n- algebra, and determin...

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science...

(1) If spin (n) is a double cover of SO (n) group, what is the cover of spin (2) and what is also the cover for spin (1/2) are they both related?
(2) Is it possible to construct the Iwasawa decomposition at both the Lie algebra and Lie group levels of the spin particles ?

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 partit...

In this paper, we focus on the characterization of Lie algebras of fermionic, bosonic and parastatistic operators of spin particles. We provide a method to construct a Lie group structure for the quantum spin particles. We show the semi-simplicity of a quantum spin particle Lie algebra, and extend the results to the Lie group level. Besides, we per...

In this paper, we define a new velocity having a dimension of $(Length)^{\alpha}/(Time)$ and a new acceleration having a dimension of $(Length)^{\alpha}/(Time)^2$, based on the fractional addition rule. We then discuss the fractional mechanics in one dimension. We show the conservation of fractional energy, and formulate the Hamiltonian formalism f...

This work is devoted to a theoretical analysis of mass frequency response to pressure oscillations of a spray of repetitively injected drops into a combustion chamber. A single stationary spherical droplet continuously fed with the same liquid fuel so that its volume remains constant despite the evaporation, the so-called 'mean droplet' in the Heid...

This work is devoted to a theoretical analysis of mass frequency response to pressure oscillations of a spray of repetitively injected drops into a combustion chamber. A single stationary spherical droplet continuously fed with the same liquid fuel so that its volume remains constant despite the evaporation, the so-called 'mean droplet' in the Heid...

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang-Baxter equation in an anti-flexible algebra which is...

Deformed quantum algebras, namely the q-deformed algebras and their extensions to (p, q)-deformed algebras, continue to attract much attention. One of the main reasons is that these topics represent a meeting point of nowadays fast developing areas in mathematics and physics like the theory of quantum orthogonal polynomials and special functions, q...

The oscillatory temperature field of a spherical drop in evaporation is examined. The motionless drop is fed continuously at the centre so that it keeps a constant volume during the process. The feeding with the same liquid is carried out by assuming an adiabatic centre regime. Effects of heat conduction and that of the variation of the Peclet numb...

This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation is performed with the introduction of the Laplace{ Runge{Lenz vector. The existence of quasi-bi-Hamiltonian str...

The multifractal structure of daily temperature and relative humidity is investigated in this study. Multifractal Detrended Fluctuation Analysis (MFDFA) method has been applied on data observed from 1967 to 2012 at the six synoptic stations of Benin (Cotonou, Bohicon, Parakou, Save, Natitingou and Kandi). We estimate the generalized Hurst exponent,...

In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance mat...

This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial formulae, factorial and binomial moments, and Stirling numbers. Moreover, the R(p,q)-Stirling numbers of the second ki...

The tropical Atlantic is home to multiple coupled climate variations covering a wide range of timescales and impacting societally relevant phenomena such as continental rainfall, Atlantic hurricane activity, oceanic biological productivity, and atmospheric circulation in the equatorial Pacific. The tropical Atlantic also connects the southern and n...

We study the higher-order nonlinear Schrödinger equation which takes care of the second as well as third order dispersion effects, cubic and quintic self phase modulations, self steepening and nonlinear dispersion effects. Taking advantage of the initial condition, we transform theprevious equation into a nonlinear functional equation to which we a...

Mobile peer-to-peer networking (MP2P) is a relatively new paradigm compared to other wireless network technologies. In the last 10–15 years, it has gained tremendous popularity because of its usefulness in applications such as file sharing over the Internet in a decentralized manner. Security of mobile P2P networks represents an open research topic...

A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form ωnc is defined. A related NC Poisson bracket is o...

This paper addresses an R(p,q)-deformed conformal Virasoro algebra with an arbitrary conformal dimension ?. Well-known deformations constructed in the literature are deduced as particular cases. Then, the special case of the conformal dimension ? = 1 is elucidated for its interesting properties. The R(p,q)- KdV equation, associated with the deforme...

This paper addresses an R(p,q)-deformation of basic univariate discrete distributions of the probability theory, focusing on uniform, binomial, logarithmic, Euler, hypergeometric,contagious, and P\'olya distributions. Relevant R(p,q-deformed factorial moments of a random variable are investigated. The generalized q- Quesne distributions are derived...

This work gives value to the importance of Hilbert-Schmidt operators in the formulation of noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.

This work provides a characterization of left and right Zinbiel algebras.Basic identities are established and discussed, showing that Zinbiel algebras are center-symmetric, and therefore Lie-admissible algebras. Their bimodules are given, and used to build a Zinbiel algebra structure on the direct sum of the underlying vector space and a finite-dim...

In this work, we study thermal conduction and convection combined effects on frequency response to pressure oscillations of a spray of repetitively injected drops in a combustion chamber. The theoretical model is based on Heidmann analogy of the so called “mean droplet”which is a single spherical vaporizing droplet with constant average radius, giv...

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 s...

In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are elucidated.

In this work, we describe the geometric and probabilistic properties of a noncommutative 2- torus in a magnetic field. We study the volume invariance, integrated scalar curvature and volume form by using the method of perturbation by inner derivation of the magnetic Laplacian in the noncommutative 2-torus. Then, we analyze the magnetic stochastic p...

This paper addresses an R(p,q)-deformed conformal Virasoro algebra with an arbitrary conformal dimension Delta. Wellknown deformations constructed in the literature are deduced as particular cases. Then, the special case of the conformal dimension Delta=1 is elucidated for its interesting properties. The R(p,q)-KdV equation, associated with the def...

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually adjoint first order difference operators. These classes encompass equations of hypergeometric type describing class...