Papers by Gabriel Obed Fosu
Eng. Appl. Sci. Lett., 2021
This paper discusses a gallery of useful results in connection with integrating factors that are ... more This paper discusses a gallery of useful results in connection with integrating factors that are often left as problems for discovery learning and are generally not taught in typical Ordinary Differential Equations courses. Most often than not the approach earlier writers employ is to give a possible form for an integrating factor that may results in an integrating curve without practical prove as far as the subject matter is concerned. In this write-up, an attempt is made by solving the resulting partial differential equation emanating from an underlining general differential equation of a non-exact form, by the use of the ratio theorem to establish various intricate possibilities of integrating factors that are seldom and often relegated to the background, even though they may be equally be applied as a function of a unitary variable or a linear combination of both the dependent and independent variables under certain conditions. Granted an integrating factor is found and such a function applied, the benefit is enormous especially the non-exact differential equation reduces into a known type which may be identified as exact, homogeneous, and or separable that yields a solution.
Open J. Math. Sci., 2021
The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-... more The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-geometric sequence, the Newton-Raphson recursive sequence, and the nested/composite recursive sequence. The three main hurdles for this prove processes are boundedness, monotonicity, and convergence. Oftentimes, these processes lie in the predominant use of prove by mathematical induction and also require some bit of creativity and inspiration drawn from the convergence monotone theorem. However, these techniques are not adopted here, rather, as a novelty, extensive use of basic manipulation of inequalities and useful equations are applied in illustrating convergence for these sequences. Moreover, we established a mathematical expression for the limit of the nested recurrence sequence in terms of its leading term which yields favorable results.
SN Partial Differ. Equ. Appl., 2021
Vehicular flow modeling has received much attention in the past decade due to the consequential e... more Vehicular flow modeling has received much attention in the past decade due to the consequential effect of the increasing number of vehicles. A notable effect is the congestion on urban and semi-urban roads. Traffic flow models are often the first point of reference in addressing these congestion problems. In that regard, a new viscous second-order macroscopic model is presented to explore some dynamics of multilane traffic. The new model accounts for viscosity and the velocity differentials across infinitely many countable lanes. It is realized that the wave properties of the proposed model are analogous to the driving setting on a Ghanaian highway. This is followed by a mathematical condition to achieving a stable traffic flow. Moreover, the viscous model is recast into its discrete form to address interdependency among unique multiple lanes. A simulation result of an eightlane infrastructure is presented to explain this conceptualization. Keywords Viscosity Á Multilane traffic Á Macroscopic model Á Speed-density profiles Mathematics Subject Classification 35L65 Á 65M06 Á 76L05 This article is part of the section ''Applications of PDEs'' edited by Hyeonbae Kang.
Applied Research Journal, 2020
The mathematics of disease transmission among a vector host could be linear or non-linear. Howeve... more The mathematics of disease transmission among a vector host could be linear or non-linear. However, the dynamics of some drug-resistant disease are well-explored using non-linear transmission models. Hither, the dynamics of a susceptible-infected-vaccinated-recovered model with power relationship incidence rate (I p S q) is formulated to analyze the dynamics of a typical two-dose vaccine disease. It is assumed an individual can be susceptible after receiving the first dose of the vaccine, hence a second dose is required to attain permanent immunity. The steady-states conditions of the disease-free equilibrium and the endemic equilibrium are critically presented. Numerical simulations are carried out to determine the impact of the exponential parameters on the infected population. It was realized that the disease dies-out when these parameters simultaneously approach zero. Moreover, the parameter q also forces the system to other equilibria irrespective of the value of p.
Mathematics in Applied Sciences and Engineering, 2022
The continual wearing of road surfaces results to crack and holes called potholes. These road sur... more The continual wearing of road surfaces results to crack and holes called potholes. These road surface irregularities often elongate travel time. In this paper, a second-order macroscopic traffic model is therefore proposed to account for these road surface irregularities that affect the smooth flow of vehicular traffic. Though potholes do vary in shape and size, for simplicity the paper assumes that all potholes have conic resemblances. The impact of different sized potholes on driving is experimented using fundamental diagrams. Besides, the width of these holes, driver reaction time amid these irregularities also determine the intensity of the flow rate and vehicular speed. Moreover, a local cluster analysis is performed to determine the effect of a small disturbance on flow. The results revealed that the magnitude of amplification on a road surface with larger cracks is not as severe as roads with smaller size holes, except at minimal and jam density where all amplifications quickly fade out.
Asian Journal of Applied Sciences
In this study we looked at the theorm Azela-Ascoli and its application to functional analysis, or... more In this study we looked at the theorm Azela-Ascoli and its application to functional analysis, ordinary dierential equations and complex analysis. This theorem simplies the checking of compactness for subsets of spaces of continuous functions in much the same way the Heine-Borel theorem does for subsets of Rn
International Journal of Physical and Social Sciences, 2014
British Journal of Mathematics Computer Science, Jan 20, 2015
British Journal of Mathematics Computer Science, Jan 20, 2015
Journal of Applied Mathematics and Computational Mechanics, 2020
In the past, the density-gradient term of second-order macroscopic models was replaced with a spe... more In the past, the density-gradient term of second-order macroscopic models was replaced with a speed-gradient term to rectify the rearward movement of traffic waves. Hither, a classical speed-gradient macroscopic model is extended to account for the lateral flow dynamics on a multi-lane road. The anisotropic model is modified to capture some inherent vehicular multi-lane traffic features; lateral viscosity and velocity differentials. These variables are quantized within the scope of a two-dimensional spatial domain as opposed to the existing one-dimensional model. A detailed exemplification of acceleration and deceleration waves, stop-and-go waves, and cluster effects are presented to explain the path of information flow. All these non-linear flow properties are evident throughout the simulation.
Journal of Mathematical Modelling, 2020
The relationship among vehicles on the road is modeled using fundamental traffic equations. In tr... more The relationship among vehicles on the road is modeled using fundamental traffic equations. In traffic modeling, a particular speed-density equation usually fits a peculiar dataset. The study seeks to parameterize some existing fundamental models so that a given equation could match different dataset. The new equations are surmisal offshoots from existing equations. The parameterized equations are used in the LWR model and solved using the Lax-Friedrichs differencing scheme. The simulation results illustrate different scenarios of acceleration and deceleration traffic wave profiles. The proposed models appropriately explain the varying transitions of different traffic regimes.
In this paper a Newton-type algorithm is used to generate non-singular symmetric matrices of ran... more In this paper a Newton-type algorithm is used to generate non-singular symmetric matrices of rank
one, using a singular symmetric matrix of the same rank as an initial matrix for the iteration. In particular,
numerical computations are performed with two different diagonal matrices which are in the neighbourhood
of the eigenvalues of the initial singular symmetric matrix to construct a three by three and a four by four
non-singular symmetric matrices to illustrate our result.
Journal of Mathematics and System Science, 2019
In this article, we discuss singular Hermitian matrices of rank greater or equal to four for an i... more In this article, we discuss singular Hermitian matrices of rank greater or equal to four for an inverse eigenvalue problem. Specifically, we look into how to generate n by n singular Hermitian matrices of ranks four and five from a prescribed spectrum. Numerical examples are presented in each case to illustrate these scenarios. It was established that given a prescribed spectral datum and it multiplies, then the solubility of the inverse eigenvalue problem for n by n singular Hermitian matrices of rank r exists.
International Journal of Mathematics & Computation, 2019
Sexual activity involving unmarried male and female students is categorized as an infectious dise... more Sexual activity involving unmarried male and female students is categorized as an infectious disease in this research. The paper presents a comprehensive constancy analysis of a proposed SIR sex model. The model has two steady states; an unrealistic sex-free equilibrium, and a pragmatic endemic equilibrium state. The global stability conditions for this model were obtained using Lyapunov functions along with the LaSalle’s invariant principle. Numerical perturbation of model parameters showed a continual existence of
this endemic in the host population.
Journal of Engineering Research and Reports, 2019
Multi-regime fundamental models use two or more equations to describe the association among the m... more Multi-regime fundamental models use two or more equations to describe the association among the main macroscopic traffic variables encountered in traffic analysis. The paper investigates specific properties of some multi-phase speed-density equations. It first compares the characteristics of each of these equations by solving the nonlinear continuity traffic equation. It was observed that predicting vehicular trajectories with these model equations could lead to misinformation. The kinematic wave and stable shockwave properties of these models were also ascertained. Based on the results, it was concluded that it would be more cumbersome to explain nonlinear traffic characteristics when these two and three regime models are adopted.
International Journal of Engineering & Scientific Research, 2014
The paper outlined two systems of differential equations: the Ramsey-Cass-Koopmans(RCK) growth mo... more The paper outlined two systems of differential equations: the Ramsey-Cass-Koopmans(RCK) growth model with exponential growth of labour(population) and Ramsey-Cass-Koopmans model with logistic growth rate of labour. The stability properties of these models are outlined in the neighbourhood of the steady state with a set of benchmark parameters. We compare the performance ability of this models in the case of developed and developing countries.
Journal of Global Research in Mathematical Archives, 2017
In transportation modelling, there is the need to track the positions of vehicles on a road segme... more In transportation modelling, there is the need to track the positions of vehicles on a road segment over a time period. As an exertion to estimate the characteristic profiles of these vehicles, the LWR model coupled with six different single-regime speed-density models are solved analytical to explain these features. These characteristic curves show the density profiles in the space-time plane. The Greenshields model, Underwood model, Pipes model, Drake model and MacNicholas model exhibited similar rarefaction wave. The Newell's speed-density model had an unparalleled density profile relative to the other models.
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Papers by Gabriel Obed Fosu
one, using a singular symmetric matrix of the same rank as an initial matrix for the iteration. In particular,
numerical computations are performed with two different diagonal matrices which are in the neighbourhood
of the eigenvalues of the initial singular symmetric matrix to construct a three by three and a four by four
non-singular symmetric matrices to illustrate our result.
this endemic in the host population.
one, using a singular symmetric matrix of the same rank as an initial matrix for the iteration. In particular,
numerical computations are performed with two different diagonal matrices which are in the neighbourhood
of the eigenvalues of the initial singular symmetric matrix to construct a three by three and a four by four
non-singular symmetric matrices to illustrate our result.
this endemic in the host population.