### African Journal ofMathematics and Computer Science Research

• Abbreviation: Afr. J. Math. Comput. Sci. Res.
• Language: English
• ISSN: 2006-9731
• DOI: 10.5897/AJMCSR
• Start Year: 2008
• Published Articles: 254

### AJMCSR Articles

A method for the solution of fractional differential equations using generalized Mittag-Leffler function

May 2014

This paper deals with the approximate and analytical solutions of non linear fractional differential equations namely, Lorenz System of Fractional Order and the obtained results are compared with the results of Homotopy Perturbation method and Variational Iteration method in the standard integer order form. The reason for using fractional order differential equations is that, fractional order differential equations are...

On integral invariants of ruled surface generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces in Lorentz-Minkowski 3-space

April 2014

In this paper, some characteristic properties of ruled surfaces which are generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces were studied in Lorentz-Minkowski 3-Space . Moreover, the relations between the Darboux frames, the Darboux derivate formulas, the apex angles, the pitchs, the geodesic curvatures, the normal curvatures, the geodesic torsions and the dralls of...

Optimal control model for the outbreak of cholera in Nigeria

April 2014

In this work two mathematical models that described the dynamics of cholera in Nigeria were presented. The first model examined the bacteria population using a logistic definition for its growth in the expected habitat and their interaction with the susceptible population. The second model is an optimal control model that includes two time- dependent control functions with one minimizing the contact between the...

A cubically convergent class of root finding iterative methods

February 2014

In this paper, we propose a new two-parameter class of iterative methods to solve a nonlinear equation. It is proved that any method in this class is cubically convergent if and only if the parameters sum up to one. Some of the existing third-order methods, by suitable selection of parameters, can be put in this class. Every iteration of the class requires an evaluation of the function, three of the first derivative,...

Application of exp (-ï¦(ï¸))- expansion method to find the exact solutions of Shorma-Tasso-Olver Equation

February 2014

In this work, we present traveling wave solutions for the Shorma-Tasso-Olver equation. The idea of exp (-f(x))- expansion method is used to obtain exact solutions of that equation. The traveling wave solutions are expressed by the exponential functions, the hyperbolic functions, the trigonometric functions solutions and the rational functions. It is shown that the method is awfully effective and can be used...

A stage-structured two species competition model under the effect of disease

February 2014

In this paper we study the dynamics of two competing species model, one of the competing species is stage structured and the disease spreads only in the other competing specie. In order to keep the model simple, we present it under the strong assumption that the disease cannot cross the species barrier. Dynamical behaviors such as positivity, roundedness, stability, bifurcation and persistence of the model, are studied...

Two-step two-point hybrid methods for general second order differential equations

November 2013

Two-step two-point hybrid numerical methods for direct solution of initial value problems of general second order differential equations are proposed in this study. Chebyshev polynomials without perturbation terms are used as basic function for the development of the methods in predictor-corrector mode. The collocation and interpolation equations are generated at both grid and off-grid points.  The resulting...

A fuzzy inference system for predicting depression risk levels

November 2013

This paper reports the findings from the experimental study of an intelligent system driven by Fuzzy Logic (FL) for depression risk diagnosis. Depression is a common psychological disorder that can cause serious health challenges if it remains undiagnosed, misdiagnosed or untreated. It represents a major public health problem identified by the world health organization (WHO) to have affected a vast majority of the...

Hybrid filters for medical image reconstruction

October 2013

The most significant feature of diagnostic medical images is to reduce Gaussian noise, and salt and pepper noise which is commonly found in medical images and make better image quality. In recent years, technological development has significantly improved analyzing medical imaging. This paper proposes different hybrid filtering techniques for the removal of Gaussian noise, and salt and pepper noise. The filters are...

L-stable implicit trapezoidal-like integrators for the solution of parabolic partial differential equations on manifolds

October 2013

A new Trapezoidal-type scheme is proposed for the direct numerical integration of time-dependent partial differential equations. The evolving system of ordinary differential equations after discretization is usually stiff, so it is desirable for the use of a numerical method in solving it to have good properties concerning stability. The method proposed in this article is L-stable and at least of algebraic order two. It...

Gain scheduled particle swarm optimization based internal model control for tank level system

August 2013

The proposed work attempts gain scheduled particle swarm optimization (PSO) based internal model control (IMC) for tank level process. IMC requires determining a single parameter l, the filter constant.  Optimal value of the filter constant is determined using PSO, an evolutionary technique. The tank process is nonlinear in nature. Model and inverse model are found for each linear region separately...

Age and space structured tumour invasion: A theoretical mathematical formulation

August 2013

In this article, the mathematical model used originally proposed by Bruce and co-workers was reviewed and extended. By assuming spherical symmetry of tumour, there were mathematical expressions in the form of partial differential equations along with some suitable conditions for density of proliferating tumor cells, quiescent tumor cells, surrounding tissue macromolecule (MM) and concentration of matrix...

A theoretical and experimental study of the Broyden-Fletcher-Goldfarb-Shano (BFGS) update

August 2013

This paper discusses theoretically the evolution of a conjugate direction algorithm for minimizing an arbitrary nonlinear, non quadratic function using Broyden-Fletcher-Goldfarb-Shano (BFGS) update in quasi-Newton Method. The updating rule is initialized by a Moore Penrose’s generalized inverse. Specifically, an approximation to the inverse Hessian is constructed and the updating rule for this...

A new version of the proof of

July 2013

The result gamma n times gamma 1-n is a useful result in the theory of gamma and beta function, it is used to solve a definite integral where the function in it has a multi-valued function, several authors have proved this result in a tedious way. In this paper, we obtain a new version of the proof of   and the Legendre duplicating formulas for positive integer n, by using a simple analytical...

Literature review on grid computing

July 2013

The concept of grid has emerged as a new approach to high performance distributed computing infrastructure. In general, Grids represent a new way of managing and organizing computer networks and mainly their deeper resource sharing. Grid computing has evolved into an important discipline within the computer industry by differentiating itself from distributed computing through an increased focus on resource...

N(A)-ternary semigroups

July 2013

In this paper, the terms, ‘A-potent’, ‘left A-divisor’, ‘right A-divisor’, ‘A-divisor’ elements, ‘N(A)-ternary semigroup’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary semigroup T then it is proved that (1)  (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent,...

Weakly symmetric and weakly ricciâ€“symmetric conditions on manifolds

June 2013

In this paper, we have researched the necessary and sufficient conditions for a manifold to be weakly symmetric and weakly Ricci–symmetric and examined the conditions over 1–forms involved in the definitions of weakly symmetric and weakly Ricci–symmetric conditions. We have evaluated some certain results of situations in which a weakly symmetric manifold is with parallel or...

Incidents of cancer in Sudan: Past trends and future forecasts

June 2013

Incidents of cancer in Sudan have been growing in numbers over the last five decades (1967-2010). Using data compiled regularly by radiations isotope of cancer in Khartoum (RICK) - which continued to be the only cancer treatment centre in Sudan for over the last half century- its trend is studied using Box-Jenkins methodology in time series analysis is the optimal method applied to the pattern. This method...

Peristaltic transport of micropolar fluid through porous medium in a symmetric channel with heat and mass transfer in the presence of generation and radiation

June 2013

The effect of heat generation and radiation on the peristaltic motion of micropolar fluid with heat and mass transfer through porous medium in a symmetric channel was investigated. The equations of motion for micropolar fluids were introduced as well as the equations of energy and concentration. The system of these equations written in two dimensions and then transformed using the transformations between a...

Accurate approximate analytical solutions to an anti-symmetric quadratic nonlinear oscillator

May 2013

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these algebraic...

Modified and a new spectral method for solving nonlinear ordinary differential equations

May 2013

In this paper, we present a modified and new version of spectral method which is based on minimization of obtained residual term in  norm, where  is a weight function with respect to Jacobi polynomials. Using this approach is efficient and effective rather than Tau and collocation methods. It reduces the nonlinear ordinary differential equations to the nonlinear programming problems which...

Starting the five steps Stomer-Cowell method by Adams-Bashforth method for the solution of the first order ordinary differential equations

May 2013

We developed a five-step Stomer-Cowell method using method of interpolation and collocation of power series approximate solution to obtain non linear systems of equation which is solved for the unknown parameters to give a continuous linear multi step method. The continuous linear multi-step is evaluated at selected grid points to give discrete linear multi-step method which serve as the corrector. The...

Cardinality and idempotency of partial one-one convex and contraction transformation semi group

May 2013

Let Xn be a set with finite number of elements following natural ordering of numbers. The formulae for the total number of elements in partial one – one convex and contraction transformation semigroup and its idempotents are obtained and discussed in this paper. The relationship between fix α and idempotency is obtained and stated; an element α is an idempotent if |Imα...

Heat absorption and chemical reaction effects on peristaltic motion of micropolar fluid through a porous medium in the presence of magnetic field

May 2013

In this paper, a study of the peristaltic motion of incompressible micropolar fluid through a porous medium in a two-dimensional channel under the effects of heat absorption and chemical reaction in the presence of magnetic field was studied. This phenomenon is modulated mathematically by a system of partial differential equations which govern the motion of the fluid. This system of equations is solved in...

On Pearson families of distributions and its applications

May 2013

In this study we are going to discuss an extended form of Pearson, including the reversed generalized Pearson curves distribution as its subfamily, and refer to it as the extended generalized same distribution. Because of many difficulties described in the literature in modeling the parameters, we propose here a new extended model. The model associated to this heuristic is implemented to validate the...

On fuzzy strongly C â€“ pre open sets and fuzzy strongly C â€“ pre closed sets in fuzzy topological spaces

May 2013

The concept of complement function is used to define a fuzzy closed subset of a fuzzy topological space. That is a fuzzy subset l is fuzzy closed if the standard complement 1-l = l¢ is fuzzy open. Here the standard complement is obtained by using the function C: [0, 1]® [0, 1] defined by C (x) = 1-x, for all x Î[0, 1]. Several fuzzy topologists used this type...

Information theoretic methods in parameter estimation

April 2013

In the present communication entropy optimization principles namely maximum entropy principle and minimum cross entropy principle are defined and a critical approach of parameter estimation methods using entropy optimization methods is described in brief. Maximum entropy principle and its applications in deriving other known methods in parameter estimation are discussed. The relation between maximum...

Specification parameters for linear estimators in probability proportional to size sampling scheme

April 2013

Estimation of population parameters using the generalized moment estimators under probability proportional to size sampling scheme requires that the specification parameter, k defining these moments differs from one population to the other due to varying statistical properties of the study and measure of size variables. In this study, the approximate value of the specification parameter that minimizes the...

A quasi Lindley distribution

April 2013

A two-parameter Quasi Lindley distribution (QLD), of which the Lindley distribution (LD) is a particular case, has been introduced. Its moments, failure rate function, mean residual life function and stochastic orderings have been discussed. It is found that the expressions for failure rate function, mean residual life function, and stochastic orderings of the QLD shows its flexibility over Lindley...

Profit maximization among dry season vegetable farmers

April 2013

Dry season vegetable production in Nigeria has become as important as income generating occupation that there are always shortages of suitable land for the numerous producers. Production is undertaken under irrigation and it is characterized by intense mixed cropping. Four major inputs are put into consideration apart from land allocation in vegetable production, they are: hired labor activities, fertilizer...

Statistical grouping of cassava mosaic disease-resistant varieties cultivated by the National Root Crops Research Institute, Umudike, Nigeria

March 2013

Similarity level of secondary data on proximate composition of fufu flour measured from 44 cassava mosaic diseases (CMD) resistant varieties was obtained in order to group the 44 cassava varieties. The distant coefficient generated between the 44 CMD resistant varieties ranged from 0.000 to 51.510. The distance measures with low coefficient are grouped together. The agglomerative hierarchical...

Solution of a class of singular two point boundary value problems by variational method

March 2013

In this study, He’s highly prolific variational iteration method (VIM) is applied effectively for showing the existence, uniqueness and solving a class of singular second order, two point boundary value problems. The process of finding solution involves generation of a sequence of appropriate and approximate iterative solution function equally likely to converge to an exact solution of the...

A model teaching for the cycloid curves by the use of dynamic software with multiple representations approach

March 2013

This study proposes the use of dynamic software that will enable students to explore a specific kind of parametric equation at the tertiary level. Firstly, it was aimed at visualizing the basic cycloid curve which is the trajectory of a point on the circle rolling along x-axis. Then, the mathematical meaning of the design process, which is mostly based on the syntax, was tried to be drawn out. It...

A study on hypo hamiltonian graphs

March 2013

A graph is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V(G) but does not return to the vertex in which it began. A graph G is said to be hypo hamiltonian if for each vV (G), the vertex sub graph G-v is Hamiltonian. This paper...

Two non-standard finite difference schemes for the Timoshenko beam

March 2013

In this paper, we derive two non-standard finite difference schemes for the Timoshenko beam problem. The schemes are uniform with respect to the thickness small parameter of the beam, thus, no locking phenomenon occurs. Numerical results are presented.   Key words: Timoshenko beam, non-standard difference scheme, locking phenomenon

Probabilistic analysis of two warm standby system with instructions at need

February 2013

This paper is concerned with two unit warm standby systems having one expert repairman and one assistant repairman. The assistant is called only if the expert repairman is busy. The assistant repairman who may repair the failed unit after getting instructions by his master; but sometimes the assistant repairman may repair it without having the need of instructions for doing repair with...

Bianchi Type I tilted perfect fluid cosmological model in general relativity

January 2013

In this paper, we have investigated a tilted Bianchi Type I cosmological model filled with dust of perfect fluid in general relativity because tilted dust models are quite homogeneous and expanding. To get a determinate solution, we have assumed a linear relation between shear and expansion, that is, = constant ( is shear tensor and is expansion of the model), which leads to A =...

Some new aspects on imputation in sampling

January 2013

The number of causes that affect the quality of survey and missing data is one of such that keeps sample incomplete. Many imputation methods are available in literature, and are used to replace missing observations like Mean method, Ratio method, Compromised method, Ahmed’s method, Factor-type (F-T) method etc. This paper suggests some new estimation aspects in imputation theory...

A stochastic knapsack problem with additive model of contagious distribution for the weight

December 2012

In this paper, our concern is on modelling a stochastic knapsack problem with the mixture of two known distributions (Gamma and Exponential) using additive form. The behavioural pattern of this mixed distribution is presented graphically and properly examined with different values of the parameters. It was shown that the new distribution is a proper probability density function (PDF) and its mean and variance...

The moment generating function of the distribution of

December 2012

This paper presents a proposed alternative method of expression of joint distribution of powers of two continuous random variables when both powers are necessarily not whole numbers. Hence, in finding the alternative moment generating function (AMGF) of the joint distribution of some functions of a given random variable, it is not necessary to find and use the joint distribution of these functions, it is...

Measuring strength of association in repeated samples

December 2012

This paper developed a measure of the strength of the association between populations based on ranks appropriate for the analysis of mixed effects model typed data with one observation per cell. We developed a test statistic for the proposed measure. From the result of the analysis, it was observed that  the proposed method is comparable to Kendal’s coefficient of concordance which assume the value...

Penalty function methods using matrix laboratory (MATLAB)

November 2012

The purpose of the study was to investigate how effectively the penalty function methods are able to solve constrained optimization problems. The approach in these methods is to transform the constrained optimization problem into an equivalent unconstrained problem and solved using one of the algorithms for unconstrained optimization problems. Algorithms and matrix laboratory (MATLAB) codes are...

Solving three-dimensional (3D) Laplace equations by successive over-relaxation method

November 2012

Motivated by the assertion that all physical systems exist in three space dimensions, and that representation in one or two space dimensions entails a large degree of approximations. The main objective of this paper is to extend the successive over-relaxation (SOR) method which is one of the widely used numerical methods in solving the Laplace equation, the most often encountered of the Elliptic partial...

Almost n-multiplicative maps

October 2012

Let  and  be two linear algebras. A linear map  is called an n-homomorphism if  for all . The continuity of n-homomorphisms between Banach algebras as well as the almost multiplicative linear operators has been recently studied. In this note, we have a verification on the behavior of almost n-multiplicative linear maps with .   Key...

Scheme for solving ordinary differential equations with derivative discontinuities: A new class of semi- implicit rational, Runge-Kutta

October 2012

In this paper, a class of semi- implicit Rational Runge –Kutta scheme is proposed for the integration of differential equations with derivative discontinuities. The method is motivated by varieties of application areas of this class of ordinary differential equations such as electrical transmission network, nuclear reactions, delay problems computer aided designs, economy affected by inflation as well as...

Comparison of simulated annealing and hill climbing in the course timetabling problem

September 2012

Course timetabling is a task that must be performed by all higher institutions. It is very difficult doing this manually and even classified as nondeterministic polynomial (NP) complete in five independent ways. Several methods (heuristics) are used to solve this problem including local search optimization methods like simulated annealing and hill climbing. This paper compares these methods used to solve the...

A deterministic model for HIV infection incorporating identification rate in a heterosexual population: Mathematical analysis

September 2012

In this research, we developed a model for investigating the spread of HIV infection, which can result in acquired immunodeficiency syndrome (AIDS), through vertical and horizontal transmissions and introduced the concept of identification program by considering identification rate in heterosexual population which was qualitatively and numerically analyzed. We obtained equilibrium points of the model at two...

Results of symmetric groups Sn (nâ‰¤7) acting on unordered triples and ordered quadruples

August 2012

In this paper, we examined the results of fixed point set of symmetric groups Sn (n≤7) acting on X (3)   and X [4]. In order to find the fixed point set| fix (g) | of these permutation groups, we used the method developed by Higman (1970) to compute the number of orbits, ranks and sub degrees of these actions. The results were used to find the number of orbits as proposed by...

Properties of the symmetric groups Sn (nâ‰¤7) acting on unordered triples

August 2012

In this paper, we investigated some properties associated with the action of symmetric group Sn (n≤7) acting on X(3). If Gx is the stabilizer of , the lengths of the orbits of Gx on X are called sub-degrees and the numbers of orbits are called ranks. Ranks and sub-degrees of symmetric groups Sn (n=1, 2, ----) acting on 2-elements subsets from the set X= (1, 2, ---, n)...

An overview of term rewriting systems

July 2012

It is well-known that termination of finite term of rewriting systems is generally undecidable. NoItwithstanding, a remarkable result is that, rewriting systems are Turing complete. A number of methods have been developed to establish termination for certain term of rewriting systems, particularly occurring in practical situations. In this paper, we present an overview of the existing methods used for...

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