Everestus Eze | Michael Okpara University of Agriculture, Umudike (original) (raw)

Papers by Everestus Eze

Mathematical theory and modeling, 2016

In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing... more In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing’s type equation using fixed point theorem of Schauder and augmented by Schaefer’s Lemma.Our results include and improve some well-known results in literature

Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing t... more Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expect...

IOSR Journal of Mathematics, 2014

Our main purpose in this paper is to use the method of characteristics to solve traffic flow prob... more Our main purpose in this paper is to use the method of characteristics to solve traffic flow problems involving the conservation of cars. The method of characteristics is a technique of solving partial differential equations (PDEs) by imposing new coordinates, that is to say, change of coordinates. Note the traffic flow equation is classified as hyperbolic equation. We also discussed the relationship between flow rate, density and velocity.

Open Journal of Applied Sciences, 2019

In this paper, some stability results were reviewed. A suitable and complete Lyapunov function fo... more In this paper, some stability results were reviewed. A suitable and complete Lyapunov function for the hard spring model was constructed using the Cartwright method. This approach was compared with the existing results which confirmed a superior global stability result. Our contribution relies on its application to high damping door constructions. (2010 Mathematics Subject Classification: 34B15, 34C15, 34C25, 34K13.

Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing t... more Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expected number in the system is 0.9098. The expected waiting time in the queue is 1.276 and the expected total time lost waiting in one day is 3.2664 hours, the average cost per day for waiting is ₦65.328 and from the calculation of the comparing solutions, the average cost per day from waiting is ₦7.966 which means that there had been a saving in the expected cost of ₦65.328-₦7.966 = ₦57.362. This means that with three servers, the average cost from waiting is reduced. Hence we concluded that the aim and objectives of this paper was achieved.

New criteria for the existence of a maximum or antimaximum principle of a general second order op... more New criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions, as well as conditions for nonresonance, are provided and compared with the related literature.

R. H. Bruck's theorem [1] established the fact that any semigroup S can be embedded in a Simple S... more R. H. Bruck's theorem [1] established the fact that any semigroup S can be embedded in a Simple Semigroup which posses an identity element. In this paper, we discuss some of the properties which shares with any semigroup which posses an identity element. Thus we establish the following results i. Any regular (inverse) semigroup can be embedded in a Simple regular (Inverse) semigroup with an identity element ii. There exist simple inverse (and hence, regular) semigroups with an identity element which have an arbitrary cardinal number of D – classes. These results are new extensions arising from [1].

Results are available for boundedness and periodicity of solution for a second order non-linear o... more Results are available for boundedness and periodicity of solution for a second order non-linear ordinary differential equation. However the issue of stability of solutions in combination with boundedness and periodicity is rare in literature. In this paper, stability boundedness and periodicity of solutions have been shown to exist in a non-linear second order ordinary differential equation. This task has been achieved through the following: a. The use of Lyapunov functions with some peculiar properties to achieve stability and boundedness in the non-linear second order ordinary differential equation. b. The use of Leray-Shauder fixed point technique and an integrated equation as the mode for estimating the apriori bounds in achieving stability and boundedness of solutions.

In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing'... more In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing's type equation using fixed point theorem of Schauder and augmented by Schaefer's Lemma. Our results include and improve some well-known results in literature.

Stability is one of the properties of solutions of any differential systems. A dynamical system i... more Stability is one of the properties of solutions of any differential systems. A dynamical system in a state of equilibrium is said to be stable. In other words, a system has to be in a stable state before it can be asymptotically stable which means that stability does not necessarily imply asymptotic stability but asymptotic stability implies stability. For a system to be stable depends on the form and the space for which the system is formulated. Results are available for boundedness and periodicity of solutions of second order non-linear ordinary differential equation. However, the issue of stability, asymptotic stability, with boundedness and periodicity of solutions of Duffing's equation is rare in literature. In this paper, our objective is to investigate the stability, asymptotic stability, boundedness and periodicity of solutions of Duffings equation. We employed the Lyapunov theorems with some peculiarities and some exploits on the first order equivalent systems of a scalar differential equation to achieve asymptotic stability and hence stability of Duffings equation and again using Yoshizawas theorem we proved boundedness and periodicity of solutions of a Duffings equation. Furthermore, we use fixed point technique and integrated equation as the mode to confirm apriori-bounds in achieving periodicity and boundedness of the solution. The results obtained showed the consequences of the cyclic relationship between different properties of solutions because the asymptotic stability converges uniformly to a point and limit of the supremum of the absolute value of the difference between the distances existed and are unique and it is this uniqueness that implies the existence of stability. The space where this existed is the space which confirmed continuous closed and bounded nature of the solution and hence the existence of optimal solution and opened the window for application of abstract implicit function theorem in Banach'sSpace to guarantee uniqueness and asymptotic stability, ultimate boundedness and periodicity of solutions of Duffings equation. We concluded that the objectives for the paper were achieved based on our deductions.

Mathematical theory and modeling, 2016

In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing... more In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing’s type equation using fixed point theorem of Schauder and augmented by Schaefer’s Lemma.Our results include and improve some well-known results in literature

Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing t... more Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expect...

IOSR Journal of Mathematics, 2014

Our main purpose in this paper is to use the method of characteristics to solve traffic flow prob... more Our main purpose in this paper is to use the method of characteristics to solve traffic flow problems involving the conservation of cars. The method of characteristics is a technique of solving partial differential equations (PDEs) by imposing new coordinates, that is to say, change of coordinates. Note the traffic flow equation is classified as hyperbolic equation. We also discussed the relationship between flow rate, density and velocity.

Open Journal of Applied Sciences, 2019

In this paper, some stability results were reviewed. A suitable and complete Lyapunov function fo... more In this paper, some stability results were reviewed. A suitable and complete Lyapunov function for the hard spring model was constructed using the Cartwright method. This approach was compared with the existing results which confirmed a superior global stability result. Our contribution relies on its application to high damping door constructions. (2010 Mathematics Subject Classification: 34B15, 34C15, 34C25, 34K13.

Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing t... more Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expected number in the system is 0.9098. The expected waiting time in the queue is 1.276 and the expected total time lost waiting in one day is 3.2664 hours, the average cost per day for waiting is ₦65.328 and from the calculation of the comparing solutions, the average cost per day from waiting is ₦7.966 which means that there had been a saving in the expected cost of ₦65.328-₦7.966 = ₦57.362. This means that with three servers, the average cost from waiting is reduced. Hence we concluded that the aim and objectives of this paper was achieved.

New criteria for the existence of a maximum or antimaximum principle of a general second order op... more New criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions, as well as conditions for nonresonance, are provided and compared with the related literature.

R. H. Bruck's theorem [1] established the fact that any semigroup S can be embedded in a Simple S... more R. H. Bruck's theorem [1] established the fact that any semigroup S can be embedded in a Simple Semigroup which posses an identity element. In this paper, we discuss some of the properties which shares with any semigroup which posses an identity element. Thus we establish the following results i. Any regular (inverse) semigroup can be embedded in a Simple regular (Inverse) semigroup with an identity element ii. There exist simple inverse (and hence, regular) semigroups with an identity element which have an arbitrary cardinal number of D – classes. These results are new extensions arising from [1].

Results are available for boundedness and periodicity of solution for a second order non-linear o... more Results are available for boundedness and periodicity of solution for a second order non-linear ordinary differential equation. However the issue of stability of solutions in combination with boundedness and periodicity is rare in literature. In this paper, stability boundedness and periodicity of solutions have been shown to exist in a non-linear second order ordinary differential equation. This task has been achieved through the following: a. The use of Lyapunov functions with some peculiar properties to achieve stability and boundedness in the non-linear second order ordinary differential equation. b. The use of Leray-Shauder fixed point technique and an integrated equation as the mode for estimating the apriori bounds in achieving stability and boundedness of solutions.

In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing'... more In this paper, a sufficient criteria is given to determine the bounds of solutions for a Duffing's type equation using fixed point theorem of Schauder and augmented by Schaefer's Lemma. Our results include and improve some well-known results in literature.

Stability is one of the properties of solutions of any differential systems. A dynamical system i... more Stability is one of the properties of solutions of any differential systems. A dynamical system in a state of equilibrium is said to be stable. In other words, a system has to be in a stable state before it can be asymptotically stable which means that stability does not necessarily imply asymptotic stability but asymptotic stability implies stability. For a system to be stable depends on the form and the space for which the system is formulated. Results are available for boundedness and periodicity of solutions of second order non-linear ordinary differential equation. However, the issue of stability, asymptotic stability, with boundedness and periodicity of solutions of Duffing's equation is rare in literature. In this paper, our objective is to investigate the stability, asymptotic stability, boundedness and periodicity of solutions of Duffings equation. We employed the Lyapunov theorems with some peculiarities and some exploits on the first order equivalent systems of a scalar differential equation to achieve asymptotic stability and hence stability of Duffings equation and again using Yoshizawas theorem we proved boundedness and periodicity of solutions of a Duffings equation. Furthermore, we use fixed point technique and integrated equation as the mode to confirm apriori-bounds in achieving periodicity and boundedness of the solution. The results obtained showed the consequences of the cyclic relationship between different properties of solutions because the asymptotic stability converges uniformly to a point and limit of the supremum of the absolute value of the difference between the distances existed and are unique and it is this uniqueness that implies the existence of stability. The space where this existed is the space which confirmed continuous closed and bounded nature of the solution and hence the existence of optimal solution and opened the window for application of abstract implicit function theorem in Banach'sSpace to guarantee uniqueness and asymptotic stability, ultimate boundedness and periodicity of solutions of Duffings equation. We concluded that the objectives for the paper were achieved based on our deductions.