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Thomas Bouetou Bouetou

Publications and source records attributed to Thomas Bouetou Bouetou.

At least 19 recordsLinked to original sources
arXiv2026

Diffeomorphism Group Actions on Para-Kähler Structures: Lifts and Induced Dynamics on 3-Webs

Let $M$ be a smooth manifold equipped with a para-Kähler structure. We define an action of the diffeomorphism group $\operatorname{Diff}(M)$ on the space of para-Kähler structures and prove that this action preserves the associated affine structures. Although this result is well known, we provide a proof based on this action, showing in particular that an isometry commutes with the Levi--Civita connection. We then construct several natural liftings of this action to the tangent bundle $TM$, the cotangent bundle $T^*M$, and the Whitney sum $E=TM\oplus T^*M$. In certain cases, these lifted actions induce natural dynamical systems on a distinguished class of $3$-webs.

math.DS↗
arXiv2026

Thermodynamics, Joule-Thomson Expansion and Ruppeiner Geometry of a Dyonic NED-AdS Black Hole Surrounded by Quintessence

We investigate the thermodynamic properties, Joule-Thomson expansion, and microscopic structure of a dyonic Reissner-Nordström-AdS black hole in nonlinear electrodynamics surrounded by quintessence. Within the extended phase-space formalism, analytical expressions for the mass, Hawking temperature, equation of state, heat capacity, Gibbs free energy, Joule-Thomson coefficient, and Ruppeiner curvature are derived. The effects of the nonlinear-electrodynamics parameter $ω$, the quintessence parameters $(c,ε)$, the dyonic charge $Q$, and the pressure $P$ are systematically investigated. The temperature profiles and equation of state exhibit a Van der Waals--like phase structure, with critical points strongly modified by the quintessence and nonlinear electrodynamivs contributions. The heat capacity and Gibbs free energy further reveal the corresponding thermodynamic stability and phase-transition behaviour. The Joule-Thomson analysis shows distinct cooling and heating regions separated by inversion points. In particular, quintessence generally lowers the critical and inversion temperatures, while increasing the charge and varying the nonlinear parameter significantly deform the inversion structure. The Ruppeiner curvature exhibits pronounced peaks and sign changes near critical regions, indicating strong thermodynamic correlations and alternating attractive and repulsive effective microscopic interactions. The limiting cases $ω\sim 1$, $c\sim 0$, and $Q\sim 0$ consistently recover the corresponding Maxwell, no-quintessence, and neutral black hole behaviours. These results demonstrate that the combined effects of nonlinear electrodynamics, dyonic charge, quintessence, and AdS pressure substantially reshape both the macroscopic phase structure and the effective microscopic interactions of the black hole.

gr-qc↗
arXiv2026

Hawking Radiation and Second-Order Quantum Corrected Thermodynamics with Black Hole Remnant Formation in a Vaidya-Bonnor Black Hole Surrounded by Quintessence

In this work, we investigate Hawking radiation and second order quantum corrected thermodynamics of a Vaidya-Bonnor black hole surrounded by quintessence. Within the Hamilton-Jacobi tunneling formalism, analytical expressions for the event horizons, tunneling probability, and Hawking temperature are derived by treating the quintessence field as a perturbative contribution. The classical thermodynamic quantities, including entropy, heat capacity, enthalpy, Helmholtz free energy, and Gibbs free energy, are then obtained and analyzed. Quantum thermal fluctuations are incorporated through logarithmic and inverse-entropy corrections to the Bekenstein-Hawking entropy, leading to second-order corrected thermodynamic quantities. Their effects on thermal stability and phase transitions are examined in detail. Furthermore, analytical expressions for the quantum-corrected remnant radius and remnant mass are derived, showing that the combined effects of quintessence and quantum corrections can prevent complete black hole evaporation and lead to the formation of a stable remnant. Our results show that both quintessence and higher-order quantum corrections enhance thermodynamdymic stability and significantly favor the formation of stable black hole remnants.

gr-qc↗
arXiv2026

On examples of duals Saito's basis of some inhomogeneous divisors, and application

We investigate a class of non-quasi-homogeneous free divisors in the sense of Saito. These divisors are defined by equations of the form $D:= \{h=0\}$ on $\mathbb{C}^p$, where the polynomial $h$ is specific linear combination of monomials involving the product of coordinates. For this class, we explicitly construct a Saito basis for the module of logarithmic vector fields $Der(logD)$. This construction is then applied to the setting of logarithmic Poisson geometry. Focusing on the example defined by $h=xy+x^{2}y^{2}+x^3y^3$ on the Poisson algebra $(\mathcal{A}=\mathbb{C}[x,y], \{-,-\}_{h})$, where the Poisson bracket is induced by the bivector $π= h\partial x\wedge\partial y$. We define the associated Koszul bracket on the module of logarithmic 1-forms. This enables us to prove that $π$ endows the sheaf of logarithmic 1-forms $Ω^{1}(log D )$ with a Lie-Rinehart algebra structure. Furthermore, we introduce and provide explicit descriptions for the resulting cohomology theory, which we term the logarithmic Poisson cohomology $H_{log}^{\bullet} $ of $\{-,-\}_{h}$. As a related and foundational computation, we also calculate the corresponding logarithmic De Rham cohomology $H^{\bullet}_{DR}$ for the divisor $D$ and we make a generalization in dimension 2.

math.DG↗
arXiv2025

On Logit Weibull Manifold

In this work, it is shown that there is no potential function on the Weilbull statistical manifold. However, from the two-parameter Weibull model we can extract a model with a potential function called the logit model. On this logit model, there is a completely integrable Hamiltonian gradient system.

math.ST↗
arXiv2025

Riemannian curvature of gaussian distribution in dual coordinate system

In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this new coordinate system, which allows us to characterize existing geometric invariants, such as the dual potential function and the Fisher metric.

math.DG↗
arXiv2025

Completely Integrable Gradient System on the bivariate beta statistical manifold

This paper investigates the geometry of a completely integrable gradient system defined on the three parameter bivariate beta statistical manifold of the first kind. We prove that the associated vector field is Hamiltonian and admits a Lax pair representation implying complete integrability. We show that the potential function derived from exponential family structure defines a Riemannian metric equivalent to the Fisher information metric. By applying Stirling's approximation to the gamma functions involved in the potential, we obtain an explicit expression that facilitates the study of the pseudo-riemannian geometry of the manifold. Furthermore, we demonstrate that the gradient flow is linearizable in dual affine coordinates, and we identify the Hamiltonian function whose gradient defines the flow. These results highlight the deep interplay between information geometry, dynamical systems, and asymptotic analysis.

math.DG↗
arXiv2025

A Kahlerian approche to the Schrodinger equation in Siegel jacobi Space of the lognormal distribution

In this paper, we describe the evolution of spectral curves in the Siegel Jacobi space through the Schrodinger equation constructed from a Kahler geometry induced on the lognormal statistical manifold via Dombrowski's construction. We introduce new holomorphic structures and show that the Hamiltonian vector field coincides with the fundamental vector field generated by holomorphic isometries. We construct the time dependent Schrodinger equation from this geometric setting and show that the associated energy is not constant, but varies with time. This work establishes a bridge between Kahler geometry, statistical models, and the formalism of quantum mechanics.

math.DG↗
arXiv2025

Schouten like metrics on five dimensional nilpotents Lie groups

The prescribed Ricci curvature problem involves finding a Riemannian metric g that satisfies the equation ric(g) = T, where T is a fixed symmetric (0, 2)-tensor field on a differential manifold M. In this paper, we introduce the concept of Schouten-like metrics as particular solutions to the prescribed Ricci curvature problem. We classify these metrics on five-dimensional nilpotent Lie groups by establishing a connection with algebraic Schouten solitons. This approach also enables us to classify five-dimensional nilsolitons, providing a comprehensive understanding of their geometric structures and properties.

math.DG↗
arXiv2024

The prescribed Ricci curvature problem on 5-dimensional nilpotent Lie groups

In this paper, using the Milnor-type theorem technique, we provide on each nilpotent five dimensional Lie group, some global existence result of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) =cT, where Ric(g) is the Ricci curvature of g and T a given left-invariant symmetric (0, 2)-tensor field.

math.DG↗
arXiv2023

Thermodynamics of Non-linear magnetic-charged AdS black hole surrounded by quintessence, in the background of perfect fluid dark matter

In this paper, we study the thermodynamic features of a non-linear magnetic-charged AdS black hole surrounded by quintessence, in the background of perfect fluid dark matter(PFDM). After having constructed the corresponding metric, we analyse the structure of the horizon. We find that the existence of inner or outer horizon are constrained by the presence of dark matter. Afterwards, we put out the mass and the temperature of the black hole, in order to get its entropy. Subsequently, we find the expression of the pressure which leads us to get the table of critical values and the isothermal diagram. Especially, we find that the critical values of the temperature and the pressure increase as the dark matter parameter increases. Also, analysing the isothermal diagram, we observe a van der Waals-like behaviour remarked by the presence of a first-order phase transition when we cross the critical temperature. Additionally, we compute and plot the heat capacity and the Hessian matrix of the black hole mass. For the heat capacity, we find that a second-order phase transition occurs, leading the black hole to move from stable phase to unstable one. Furthermore, it comes out that this phase transition point is shifted towards higher values of the horizon radius, as we decrease the dark matter density and increase the quintessence density.

gr-qc↗
arXiv2021

Large scale deduplication based on fingerprints

In fingerprint-based systems, the size of databases increases considerably with population growth. In developing countries, because of the difficulty in using a central system when enlisting voters, it often happens that several regional voter databases are created and then merged to form a central database. A process is used to remove duplicates and ensure uniqueness by voter. Until now, companies specializing in biometrics use several costly computing servers with algorithms to perform large-scale deduplication based on fingerprints. These algorithms take a considerable time because of their complexity in O (n2), where n is the size of the database. This article presents an algorithm that can perform this operation in O (2n), with just a computer. It is based on the development of an index obtained using a 5 * 5 matrix performed on each fingerprint. This index makes it possible to build clusters of O (1) in size in order to compare fingerprints. This approach has been evaluated using close to 11 4000 fingerprints, and the results obtained show that this approach allows a penetration rate of less than 1%, an almost O (1) identification, and an O (n) deduplication. A base of 10 000 000 fingerprints can be deduplicated with a just computer in less than two hours, contrary to several days and servers for the usual tools. Keywords: fingerprint, cluster, index, deduplication.

cs.CV↗
arXiv2019

Thermodynamic of a rotating and Non-linear magnetic-charged black hole in the quintessence field

We purpose an approach for the thermodynamic analysis of rotating and non-linear magnetic-charged black hole with quintessence. Accordingly, we compute various thermodynamics quantities of the black hole, such as mass, temperature, potential provided from the magnetic charge, and the heat capacity. Moreover, we study phase transitions of this black hole, analyzing the plot of its heat capacity. Then, we have shown that the black hole mass would have a phase of decrease, while the temperature increases from negative absolute temperatures. From the behavior of the heat capacity, we point out that the black hole undergoes to a second-order phase transition, which is shifted towards the higher values of entropy as we increase the rotating parameter $a$ or the magnetic parameter $Q$.

gr-qc↗
arXiv2016

Occupation time statistics of the random acceleration model

The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time $T_+$ of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of $T_+$ analytically and also study the statistics of $T_+$ with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time $T_+$ and the time $T_m$ at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$ coincide and are given by Lévy's arcsine law. We show that for randomly accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.

cond-mat.stat-mech↗
arXiv2016

On representations of Bol algebras

In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical Engel's theorem and the ex- tension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations of Bol algebras and show that it is a tensor category. In the case of regular representations of Bol algebras, we give a complete classification of them for all two-dimensional Bol algebras.

math.AG↗
arXiv2014

On the geometry of three-dimensional Bol algebras with solvable enveloping Lie algebras of small dimension

We give the description of three-dimensional Lie triple systems and their corresponding Lie algebras with invomorphisme, The description of three-dimensional Bol algebras linked with the distinguished Lie triple systems above is given. The construction of the object describing the isotopy of Bol algebras. The description of Bol 3-Webs, connected with the selected Bol algebras.

math.RA↗