# Abstracts

The abstracts booklet is here.

1. AHMED Jamil
National University of Technology
Black Hole Chemistry
The subject of black hole chemistry will be introduced in this talk.

2. AREMUA Isiaka
Université de Lomé
Coherent states construction using the density operator method: a case study
In this work, the density operator diagonal representation in the coherent states basis, known as the Glauber-Sudarshan (GS)-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 backgroud coupled with a harmonic oscillator. Relevant statistical properties like the Q-Husimi distribution and the Wehrl entropy are investigated.

3. ARJIKA Sama
Another homogeneous $q$-difference operators and their applications
In this talk, we define two homogeneous operators $\\\\mathbb{E}(y,z;D_{q})$ and $K(u,v; \\\\theta_{xy})$ which turn out to be suitable for dealing with the trivariate Cauchy polynomials $\\\\tilde{p}_n(x,y,z)$ and the generalized Hahn polynomials S_n(x,y,u,v;q)$. By using these operators, we derive: generating functions, extended generating functions, Mehler\\\'s formula and Roger\\\'s formula for the polynomials$\\\\tilde{p}_n(x,y,z)$and$S_n(x,y,u,v;q)$. 4. ATCHADE Mintodê Nicodème INTERNATIONAL CHAIR IN MATHEMATICAL PHYSICS AND APPLICATIONS (ICMPA)/ ENSGMM (UNSTIM) Agricultural production and economic growth: an analysis by a statistical approach The purpose of this paper is to construct a theoretical framework for analyzing the connection between economic growth, land health care, and agricultural production. In this work, the economy is composed of two sectors, one of agricultural goods and the other of non agricultural goods. Equilibrium is defined when capital per-capita in period t is equal to that of period t+1. The importance of the paper is in its ability to analyze the change in agricultural land health along the growth path of the economy. An example and a simulation are presented in order to confirm the theoretical results and demonstrate that the model can be used for empirical analysis. The paper constructs a connection between economic growth and agricultural sector economic development. Keywords: Economic growth, agriculture, land health care 5. ATINDOGBE Cyriaque FAST-UAC To be completed To be completed 6. BAI Chengming Chern Institute of Mathematics, Nankai University TBA TBA 7. BAKARE Emmanuel Afolabi Federal University Oye Ekiti, Ekiti State Optimal control analysis of cholera dynamics in the presence of asymptotic transmission In this paper, a non-linear ordinary differential mathematical model of cholera disease exhibiting the impact of multiple control strategies on the transmission dynamics of cholera was formulated and analyzed. Stability of the disease free equilibrium with that of the endemic equilibrium and the reproduction number were determined. If the reproduction number is less than one then the cholera eventually will disappear from the population but if it is greater than one the disease will persist in the population and more people will die. The influence of asymptotic transmission on the dynamics of cholera transmission was investigated and detailed sensitivity analysis and qualitative optimal control analysis of the cholera model were carried out. The necessary conditions for the optimal control of the cholera disease using Pontryagin\\\'s Maximum Principle in order to determine optimal strategies for controlling the spread of the disease was determined. Finally the effect of the control strategies on the dynamical behaviour of the system using numerical simulation to illustrate was established. 8. BALOGOUN Momboladji ICMPA Unesco Chair To be announced To be announced 9. BELFAKIR Abdessamad Faculty of sciences-Mohammed V University Generalized Heisenberg Algebras: periodicity and finite representation We consider the Generalized Heisenberg Algebra( GHA) and the deformed GHA with fi nite representations. We provide the necessary restriction on the characteristic function of the periodic GHA and of the periodic deformed GHA and study particular examples. Then, we give a deformation of GHA raising operator of the Morse system and conclude that this system can be described by a periodic deformed GHA as it can be deduced from a nilpotent GHA. 10. BEN GELOUN Joseph Laboratoire d\'Informatique de Paris Nord, Univ. Paris 13 TBA TBA 11. BIKORIMANA Pierre Célestin Institut de Mathématiques et Sciences Physiques IMSP Introduction of cosymplectique Geometry We will give Basic of cosymplectique Geometry 12. DJIBIBE Moussa Zakari Université de Lomé A NEW NUMERICAL METHOD FOR THIRD PSEUDO-PARABOLIC FRACTIONAL EQUATION WITH PURELY NONLOCAL CONDITIONS The aims of this work are to present a numerical technique for solving the one- dimensional pseudo-parabolic fractional differential equation that combine classical and integral conditions A Laplace transform technique is introduced for solving considered equation, definite integrals are approximated by higth-precision quadrature schemes. To invert the equation numerically back into the time domain, we apply the Stehfest inversion algorithm. The accuracy and computational effeciency of the proposed method are verified by numerical examples. 13. DOUHADJI Abalo Université de Lome Decomposition d\'une mesure vectorielle Considérant une mesure vectorielle m de K(G,E) Ou G est un groupe compact et E un espace de banach, on se propose de la décomposer en deux mesures ma absolument continue par rapport à la mesure de Haar et me étrangère à la mesure de haar 14. DOUMATE Jonas Faculté des Sciences et Techniques (FAST)/Université d\'Abomey-Calavi (UAC) TBA TBA 15. ESSOH Modeste Université Nangui Abrogoua Norm comparison of the maximum operator and its truncateds We show in this work that the maximal operator of Hardy Littlewood and its truncated have the same norm in Morrey spaces 16. FOLLY-GBETOULA Mensah University of the Witwatersrand On some difference equations Group theory is applied to obtain generators of the Lie algebra for a class of difference equations of higher order. This is followed by deriving solutions via some linear recurrences and with the introduction of some number-theoretic arithmetical functions. Furthermore, sufficient conditions for existence of periodic solutions are provided in some special cases. 17. GADJAGBOUI Bourgeois University of the Witwatersrand Symmetry and Invariance Methods for Difference and Differential Equations: Applications to Stochastic Problems in Mathematics of Finance To be announced. 18. GAZEAU Jean Pierre Université Paris Diderot Signal analysis and quantum formalism: A quantization with no Planck constant Signal analysis is built on various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets ... Constructions of Gabor or wavelet families rest upon group representation theory, Weyl-Heisenberg, affine group, etc., like many standard or generalised coherent state families. The same resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or time-scale quantum formalism and revealing interesting or unexpected features. Some promising extensions to classical electromagnetism viewed as a quantum theory for waves and not for photons will be mentioned. 19. GBEMOU koami Université de Lomé An involution on the space of bounded vector measures We consider the space of bounded vector measures defined on a locally compact group G with values in a C*-agebra A (named M^1(G,A)). We construct an involution on the space of such measures, define their Fourier-Stieltjes transform. And then we prove a *-Banach algebra structure on this space. 20. HALIYA Essossolim Cyrille International Chair in Mathematical Physics and Applications (UNESCO-CHAIR) To be announced To be completed 21. KARA Abdul Hamid University of the Witwatersrand The relationship between the invariance and conservation laws of differential equations We highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of conservation laws that whilst the former establishes the role of multipliers, the latter presents a formal procedure to determine the flows. Secondly, we show that there is an underlying relationship between the symmetries and conservation laws in a general setting, extending the results of Kara &Mahomed. The results take apparently differently forms for point symmetry generators and higher-order symmetries. Similarities exist, to some extent, with a previously established result relating symmetries andmultipliers of a differential equation. A number of examples are presented. 22. KEUMO TSIAZE Roger Magloire University of Yaoundé I A statistical approach to zero-dimensional Ginzburg-Landau fields The physical properties of low-dimensional systems have recently become one of the primary centers of interest in condensed matter research. This point of view was based on the observation that \"in one and zero dimensions ferromagnets do not magnetize, bosons do not condense and electrons do not superconduct\". Understanding these phenomena might provide the key to understanding several of the main problems of modern condensed matter physics. As is well known, the size of the critical region becomes larger as the dimensions of the system decrease below the coherence length. We perform Hartree–Fock calculations which typically result from the coarse-graining of a microscopic Ginzburg-Landau Hamiltonian taking into account the geometry, the strongly fluctuating and correlated nature of zero-dimensional systems. Without applying a magnetic field, we explain the zero-temperature phase transition of zero-dimensional systems in accordance with the Mermin–Wagner–Hohenberg theorem. Results for the specific heat and the zero-field diamagnetic inverse susceptibility per unit volume are presented. Granular superconductors are provided in support of the analysis so as to demonstrate the usefulness of the method. 23. MASSAMBA Fortuné University of KwaZulu-Natal On locally conformal almost cosymplectic manifolds In this talk, we present a class of almost contact manifolds, namely locally conformal (l.c.) almost contact manifolds. We prove that there exist subclasses which contain the class of bundle-like metric structures. Under some conditions, we show that the class of conformal changes of almost cosymplectic structures is a subclass of (almost)- cosymplectic structures, and that the leaves of the contact distribution of an l.c. almost cosymplectic manifold are Kahler. 24. MENSAH Yaogan University of Lomé Aspects of the Fourier analysis on groups and general uniform spaces The aim of this talk is to discuss a generalization of the Fourier analysis for measures on uniform spaces. 25. MISHRA Satyendra Kumar Indian Statistical Institute Bangalore TBA To Be Announced. 26. MWAKILAMA Elias PAUSTI at Jomo Kenyatta University of Agriculture and Technology Characteristics of MHD Nanofluid flow through expanding or contracting channel with permeable walls in the presence of slip conditions and viscous dissipation We investigate the presence of both the slip condition and viscous dissipation effects on characteristics of MHD Nanofluid flow for the problem studied by Rahman, Alam, and Khan (2017) where water was considered as a base fluid on Cu, and Ag nanoparticles. 27. NAWA Victor Mooto University of Zambia A weighted score interval for a binomial proportion An alternative method of constructing a confidence interval for a binomial proportion is proposed. The proposed method, known as the weighted score interval, is obtained by applying some weights on the score interval leading to shortening or widening of the score interval depending on the choice of the weights. The weighted score interval is a general form of the score interval and is equivalent to the score interval when the weight is taken to be one. When appropriate weights are chosen, simulation results indicate that the proposed interval performs better than the standard, Agresti-Coull and score intervals in terms of mean coverage probability and mean absolute error. 28. N\\\'DOLO Emanonfi Elias International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair) Emanonfi Elias N\'Dolo In this talk, we will present the probalility density of fermions in generalized anisotropic universe. We introduce the space variable in the anisotropic Bianchi I universe. Using the Bogoliubov transformation, we relate the positive and negative frequency functions which allows us to compute the Bogoliubov coefficents. We show that the probability density of fermions created is independance of the space variable. 29. OGIUGO Mike Yaba College of Technology The number of chains of subgroups in certain finite symmetric groups In this paper, we follow the notion of natural equivalence relation defined on the subgroup lattice to enumerates the number of chains of subgroups of$G$that end in$G\$. Moreover, this counting problem in fuzzy group theory as been naturally extended to non-abelian groups such as symmetric groups. The number of rooted chains of subgroups of certain finite symmetric groups is also same as the distinct number of fuzzy subgroups.

Federal University Oye Ekiti
Diamagnetic Susceptibility and Massieu function of some Diatomic molecules subject to a Harmonic Oscillating System
This work investigates the characteristics of thermodynamic properties, Massieu function and diamagnetic susceptibility of some diatomic molecules in a non-relativistic one-dimensional harmonic oscillating system. The proper quantization rule was employed to obtain the energy levels, from where we derived the partition function, vibrational mean energy (U), vibrational free energy (F), entropy (S), heat capacity (C) and the Massieu function 〖(F〗_m). We apply Hellmann-Feynman theorem to evaluate the expectation value of the square of position 〈x^2 〉 required for the calculation of the diamagnetic susceptibility. We found that the thermodynamic properties of some diatomic molecules depend not just on temperature but also on the vibrational frequencies (ω) and the number of states (n). The number of accessible vibrational states increases as the temperature increases and that the heaviest molecule has the highest accessible vibrational state. It was also discovered that diamagnetic susceptibility decreases linearly as atomic number (z), and number of states n increases. The molecules in the ground state experienced the strongest effect of diamagnetic susceptibility.

31. OUSMANE SAMARY Dine
Universite d\'Abomey-Calavi
New Aspect on the functional renormalization group for matrix models
Nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this paper we focus on matrix models, and address the question of the compatibility between the approximations used to solve the exact renormalization group equation and the modified Ward identities coming from the regulator. We show in particular that standard local potential approximation strongly violate the Ward identities, especially in the vicinity of the relevant interacting fixed point. Extending the theory space including derivative couplings, we recover a relevant interacting fixed point with a critical exponent not so far from the exact result, but with a nonzero value for derivative couplings, evoking a strong dependence with respect to the regulator. Finally, we consider a modified regulator, allowing to keep the flow not so far from the ultra-local region, and recover the results of the literature up to a slight improvement.

32. OYEWUMI Kayode John
University of Ilorin
Effects of minimal uncertainty length on information measures and (2+1)-dimensional Dirac oscillator under a magnetic monopole field and an AB potential
Study on the (2+1)-dimensional Dirac oscillator under a magnetic monopole and an Aharonov-Bohm field within a minimal length are carried out. The explicit form of energy eigenvalues and the wave functions are obtained. The following investigation: the dependence of the energy spectrum on the Aharonov-Bohm and the magnetic monopole strengths and the effects of the energy on the minimal length parameters and other parameters, wave functions, angular frequencies, and other relations are investigated. Scaling properties of composite information-theoretic measures, such as: Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio and Fisher-Shannon products are obtained for the position and momentum spaces for the hydrogen atom in the presence of a magnetic monopole and an AB potential. Physical significance of the investigation are discussed.

33. RIVASSEAU Vincent
Universite Paris-Sud
Random Geometry and Physics
The title of the talk is tentative and can be refined later.

34. YAU Hou
FDNL Research
Spin-1/2 Particle in a Quantum Field with Time as a Dynamical Variable
Despite nature\'s preference for symmetries, the treatment of time and space in quantum theory is not symmetrical. To restore the symmetry, we introduce an additional degree of freedom allowing matter to vibrate not only in the spatial directions but also in the temporal direction. We find that a system with matters vibrating in space and time obeys the Klein-Gordon equation and Schrödinger equation. This real scalar field has the same basic properties as a zero-spin bosonic field. Furthermore, the internal time of this system can be represented by a self-adjoint operator without contradicting Pauli’s theorem. Based on the properties developed, we further our study for the intrinsic spin of a particle in the system. We find that the intrinsic angular momentum obtained can describe the properties of a spin-1/2 particle, and obeys the transformation rules of group SU(2). To measure the temporal and spatial vibrations, neutrino can be an interesting candidate because of its extremely light weight. References [1] H. Y. Yau, “Self-adjoint time operator in a quantum field”, Int, J. Quant. Info. 1941016 (2020) [2] H. Y. Yau, “Temporal vibrations in a quantized field”, in Quantum Foundations, Probability and Information, 269 (Springer, Verlag, 2018) [3] H. Y. Yau, “Probabilistic nature of a field with time as a dynamical variable”, Lect. Notes Comp. Sci. 10106, 33 (2016) [4] H. Y. Yau, “Emerged quantum field of a deterministic system with vibrations in space and time”, AIP Conf. Proc. 1508, 514 (2012)

35. ZINSOU Bertin
University of the Witwatersrand
Dependence of eigenvalues of fourth order boundary value problems with transmission conditions
A general fourth-order regular ordinary differential equation with eigenvalue dependent boundary conditions and transmission conditions are considered. We prove that the eigenvalues depend continuously and smoothly on the coefficients of the differential equation and on the boundary and transmission matrices. We provide as well formulas for the derivatives with respect to each of these parameters.

Cotonou 2018

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