# Department of Mathematics

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Item A deterministic compartmental model for investigating the impact of escapees on the transmission dynamics of COVID-19(Healthcare Analytics, 2023) Mushanyu, J.; Chukwu, C.W.; Madubueze, C.E.; Chazuka, Z.; Ogbogbo, C.P.Show more The recent outbreak of the novel coronavirus (COVID-19) pandemic has devastated many parts of the globe. Non-pharmaceutical interventions are the widely available measures to combat and control the COVID-19 pandemic. There is great concern over the rampant unaccounted cases of individuals skipping the border during this critical period in time. We develop a deterministic compartmental model to investigate the impact of escapees (individuals who evade mandatory quarantine) on the transmission dynamics of COVID-19. A suitable Lyapunov function has shown that the disease-free equilibrium is globally asymptotically stable, provided 0 < 1. We performed a global sensitivity analysis using the Latin-hyper cube sampling method and partial rank correlation coefficients to determine the most influential model parameters on the short and long-term dynamics of the pandemic to minimize uncertainties associated with our variables and parameters. Results confirm a positive correlation between the number of escapees and the reported COVID-19 cases. It is shown that escapees are primarily responsible for the rapid increase in local transmissions. Also, the results from sensitivity analysis show that an increase in governmental role actions and a reduction in the illegal immigration rate will help to control and contain the disease spreadShow more Item On the distribution of eigenvalues of increasing trees(Discrete Mathematics, 2024) Dadedzi, K.; Wagner, S.Show more We prove that the multiplicity of a fixed eigenvalue α in a random recursive tree on n vertices satisfies a central limit theorem with mean and variance asymptotically equal to μαn and σ 2 αn respectively. It is also shown that μα and σ 2 α are positive for every totally real algebraic integer. The proofs are based on a general result on additive tree functionals due to Holmgren and Janson. In the case of the eigenvalue 0, the constants μ0 and σ 2 0 can be determined explicitly by means of generating functions. Analogous results are also obtained for Laplacian eigenvalues and binary increasing trees.Show more Item Modeling Interest Rate Dynamics for the Bank of Ghana Rates using the Hull-White Model(Applied Mathematics & Information Sciences An International Journal, 2023) Ogbogbo, C.P.Show more Interest rates play an important role in the financial environment, affecting business transactions directly or indirectly. Fluctuations in interest rates caused largely by demand and supply of credit, regulated by the apex banks, impacts business transactions in the Economy. Understanding the dynamics of interest rates is therefore very important to Financial institutions, individual and corporate investors. In this work, the dynamics of Bank of Ghana’s, daily interest rates, ( Jan 2020 - July 2021) is modeled using the Hull-White model. London interbank offer rates, for the same period are included in the analysis. By estimating the parameters of the model, and using a computation algorithm for the solution of the SDE of the model; It is found that the mean reverting model captured the BOG and LIBOR rates well, largely maintaining the trend of the data structure. It also pointed to the presence of jumps in the data setsShow more Item Markov Models on Share Price Movements in Nigeria Stock Market Capitalization(Applied Mathematics & Information Sciences An International Journal, 2023) Osu, B.O.; Emenyonu, S.C.; Ogbogbo, C.P.; Olunkwa, C.Show more The stock market’s trends can impact companies in different ways. The rise and fall of share price values affect a company?s market capitalization and therefore its market value, and are exposed to market risk. This study assumed share volatility as a stochastic process with Markov property. Thus proposed a first order, time homogenuous Markov chain model for trend prediction of two banks; that is Fidelity bank and Access bank closing share prices from 1-4-2016 to 23 -03-2022. The prediction was done by establishing three states that exist in stock price change which are share prices increase, decline (decrease) or steady. The transition matrix was generated. The powers of transition matrices and probability vectors were also generated for some years and equilibrium was attainedShow more Item Global Stein Theorem on Hardy Spaces(Analysis Mathematica, 2023) Bonami, A.; Grellier, S.; Sehba, B.F.Show more Let f be an integrable function which has integral 0 on ℝn. What is the largest condition on ❘ f ❘ that guarantees that f is in the Hardy space H1 (ℝn)? When f is compactly supported, it is well-known that the largest condition on ❘f❘ is the fact that ❘f❘ ∈ L log L(ℝn). We consider the same kind of problem here, but without any condition on the support. We do so for H1 (ℝn), as well as for the Hardy space Hlog (ℝn) which appears in the study of pointwise products of functions in H1 (ℝn) and in its dual BMO.Show more Item Path integral in position-deformed Heisenberg algebra with maximal length uncertainty(Annals of Physics, 2023) Lawson, L.M.; Osei, P.K.; Sodoga, K.; Soglohu, F.Show more In this work, we study the path integral in a position-deformed Heisenberg algebra with quadratic deformation which imple ments both minimal momentum and maximal length uncer tainties. We construct propagators of path integrals within this deformed algebra using the position space representation on the one hand and the Fourier transform and its inverse representa tions on the other. The result is remarkably similar to the one obtained by Pramanik (2022) from the Perivolaropoulos’s de formed algebra (Perivolaropoulos, 2017). Then, the propagators and the corresponding actions of a free particle and a simple harmonic oscillator are discussed as examples. We also show that the actions which describe the classical trajectories of both systems are bounded by the ordinary ones of classical mechanics due to the existence of this maximal length. Consequently, par ticles of these systems travel faster from one point to another with low kinetic and mechanical energies.Show more Item On the behaviour of the underrelaxed Hildreth’s row-action method for computing projections onto polyhedra(Springer, 2023) Katsekpor, T.Show more Abstract A strongly underrelaxed sequential version of the Hildreth’s iterative algorithm for norm minimization over linear inequalities is presented. Proofs are given showing that the algorithm converges from any starting point to its projection onto the linear constraint set in the feasible case and to the nearest least squares solution in the general case.Show more Item Common terms of k-Pell numbers and Padovan or Perrin numbers(Arabian Journal of Mathematics, 2022) Normenyo, B.V.; Rihane, S.E.; Togbé, A.Show more Abstract Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are 0,..., 0, 1 and each term afterwards is given by the linear recurrence P(k) n = 2P(k) n−1 + P(k) n−2 +···+ P(k) n−k . In this paper, we extend the previous work (Rihane and Togbé in Ann Math Inform 54:57–71, 2021) and investigate the Padovan and Perrin numbers in the k-Pell sequenceShow more Item Scrambling in Yang-Mills(Springer, 2021) Koch, R.M.; Gandote, E.; Mahu, A.L.Show more Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ p λ with λ the ’t Hooft coupling.Show more Item Martingale Transforms between Martingale Hardy-amalgam Space(Hindawi, 2021) Bansah, J.S.Show more We discuss martingale transforms between martingale Hardy-amalgam spaces Hs p,q, Qp,q and P p,q: Let 0 < p < q < ∞, p1 < p and q1 < q and let f = ðf n, n ∈ ℕÞ be a martingale in P p1,q1 ; then, we show that its martingale transforms are the martingales in P p,q for some p, q and similarly for Hs p,q and Qp,q:Show more Item On Constant Metric Dimension of Some Generalized Convex Polytopes(Hindawi, 2021) Zuo, X.; Ali, A.; Ali, G.; Siddiqui, M.K.; Rahim, M.T.; Asare-Tuah, A.Show more Metric dimension is the extraction of the affine dimension (obtained from Euclidean space Ed) to the arbitrary metric space. A family F =(Gn) of connected graphs with n ≥ 3 is a family of constant metric dimension if dim(G) = k (some constant) for all graphs in the family. Family F has bounded metric dimension if dim(Gn) ≤ M, for all graphs in F. Metric dimension is used to locate the position in the Global Positioning System (GPS), optimization, network theory, and image processing. It is also used for the location of hospitals and other places in big cities to trace these places. In this paper, we analyzed the features and metric dimension of generalized convex polytopes and showed that this family belongs to the family of bounded metric dimension.Show more Item Novel Degree-Based Topological Descriptors of Carbon Nanotubes(Hindawi, 2021) Shanmukha, M.C.; Usha, A.; Siddiqui, M.K.; Shilpa, K.C.; Asare-Tuah, A.Show more The most significant tool of mathematical chemistry is the numerical descriptor called topological index. Topological indices are extensively used in modelling of chemical compounds to analyse the studies on quantitative structure activity/property/toxicity relationships and combinatorial library virtual screening. In this work, an attempt is made in defining three novel descriptors, namely, neighborhood geometric-harmonic, harmonic-geometric, and neighborhood harmonic-geometric indices. Also, the aforementioned three indices along with the geometric-harmonic index are tested for physicochemical properties of octane isomers using linear regression models and computed for some carbon nanotubes.Show more Item On Topological Indices of Total Graph and Its Line Graph for Kragujevac Tree Networks(Hindawi, 2021) Kanwal, S.; Riasat, A.; Siddiqui, M.K.; Malik, S.; Sarwar, K.; Ammara, A.; Anton, A.Show more Item Sawyer-type characterizations and sharp weighted norm estimates for Bergman-type operators(Springer, 2021) Sehba, B.F.Show more We obtain Sawyer-type estimates for a family of Bergman-type operators. Combining these results with some off-diagonal extrapolation results, we derive sharp weighted bounds for these operators.Show more Item Semidual Kitaev lattice model and tensor network representation(Springer, 2021) Girelli, F.; Osei, P.K.; Osumanu, A.Show more Kitaev’s lattice models are usually defined as representations of the Drinfeld quantum double D(H) = H ./H op, as an example of a double cross product quantum group. We propose a new version based instead on M(H) = Hcop I/H as an example of Majid’s bicrossproduct quantum group, related by semidualisation or ‘quantum Born reciprocity’ to D(H). Given a finite-dimensional Hopf algebra H, we show that a quadrangulated oriented surface defines a representation of the bicrossproduct quantum group Hcop I/H. Even though the bicrossproduct has a more complicated and entangled coproduct, the construction of this new model is relatively natural as it relies on the use of the covariant Hopf algebra actions. Working locally, we obtain an exactly solvable Hamiltonian for the model and provide a definition of the ground state in terms of a tensor network representation.Show more Item Holography for tensor models(PHYSICAL REVIEW D, 2020-02-15) Mahu, A.L.; Tahiridimbisoa, N.H.; Gossman, D.; Koch, R.D-M.Show more In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrixlike subsectors that develop an extra holographic dimension. In particular, we develop the collective field theory for the matrixlike sector of an interacting tensor model. We check the correctness of the large N collective field by showing that it reproduces the perturbative expansion of large N expectation values. In contrast to this, we argue that melonic large N limits do not develop an extra dimension. This conclusion follows from the large N value for the melonic collective field, which has delta function support. The finite N physics of the model is also developed and nonperturbative effects in the 1 / N expansion are exhibited.Show more Item A generalization of the Carleson lemma and weighted norm inequalities for the maximal functions in the Orlicz setting(Journal of Mathematical Analysis and Applications, 2020-05-22) Sehba, B.F; Dje, J.M.T.; Feuto, J.Show more In this note we introduce the notion of Φ-Carleson sequence for Φa convex growth function and provide an equivalent characterization that is an extension of the off-diagonal Carleson embedding lemma. We apply this result to obtain Sawyer-type characterization and two-weight norm estimates for some maximal functions between different Orlicz spaces.Show more Item State of Mathematics in Africa and the Way Forward(Analysis and Partial Differential Equations: Perspectives from Developing Countries, 2019-01-28) Allotey, F.K.A.Show more The paper discusses some of the factors influencing students poor performance in mathematics in Africa and suggests ways to improve it. Examples of international centres and networks for capacity building in mathematical sciences are given.Show more Item Weighted Norm Inequalities for Fractional Bergman Operators(Constructive Approximation, 2019-06-25) Sehba, B.F.Show more We prove in this paper one weight norm inequalities for some positive Bergman-type operators.Show more Item Detecting Change in the Indonesian Seas(Frontiers in Marine Science, 2019-06-04) Ansong, J.K.; Sprintall, J.; Gordon, A.L.; Wijffels, S.E.; Feng, M.; Hu, S.; Koch-Larrouy, A.; Phillips, H.; Nugroho, D.; Napitu, A.; Pujiana, K.; Susanto, R.D.; Sloyan, B.; Peña-Molino, B.; Yuan, D.; Riama, N.F.; Siswanto, S.; Kuswardani1, A.; Arifin, Z.; Wahyudi, A.J.; Zhou, H.; Nagai, T.; Bourdalle-Badié, R.; Chanut, J.; Lyard, F.; Arbic, B.K.; Ramdhani, A.; Setiawan, A.Show more The Indonesian seas play a fundamental role in the coupled ocean and climate system with the Indonesian Throughflow (ITF) providing the only tropical pathway connecting the global oceans. Pacific warm pool waters passing through the Indonesian seas are cooled and freshened by strong air-sea fluxes and mixing from internal tides to form a unique water mass that can be tracked across the Indian Ocean basin and beyond. The Indonesian seas lie at the climatological center of the atmospheric deep convection associated with the ascending branch of the Walker Circulation. Regional SST variations cause changes in the surface winds that can shift the center of atmospheric deep convection, subsequently altering the precipitation and ocean circulation patterns within the entire Indo-Pacific region. Recent multi-decadal changes in the wind and buoyancy forcing over the tropical Indo-Pacific have directly affected the vertical profile, strength, and the heat and freshwater transports of the ITF. These changes influence the largescale sea level, SST, precipitation and wind patterns. Observing long-term changes in mass, heat and freshwater within the Indonesian seas is central to understanding the variability and predictability of the global coupled climate system. Although substantial progress has been made over the past decade in measuring and modeling the physical and biogeochemical variability within the Indonesian seas, large uncertainties remain. A comprehensive strategy is needed for measuring the temporal and spatial scales of variability that govern the various water mass transport streams of the ITF, its connectionwith the circulation and heat and freshwater inventories and associated air-sea fluxes of the regional and global oceans. This white paper puts forward the design of an observational array using multi-platforms combined with high-resolution models aimed at increasing our quantitative understanding of water mass transformation rates and advection within the Indonesian seas and their impacts on the air-sea climate system.Show more

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