Solving singular integral equations of the second kind using Chebyshev polynomials
October 2023
A numerical developed technique to solve Fredholm integral equation of the second kind with separable singular kernel is proposed. This technique relies on the truncated expansion functions of the kernels in the finite series of the weighted Chebyshev polynomials of first, second, third, and fourth kinds. Three numerical examples are presented for verification and validation of the developed technique. The results...
Euler-Maruyama method for solving first order uncertain stochastic differential equations
July 2023
Two forms of uncertainty are identified to be associated with dynamical systems, which are randomness and belief degree. The uncertain stochastic differential equation (USDE) is used to describe dynamical systems driven simultaneously by randomness and human uncertainty (belief degree). In this paper, the Euler-Maruyama method for solving USDEs is examined. The method is used to solve a stock pricing problem and the...
Degree of vertices and number of edges in a mixed graph
March 2023
In the study of a graph theory, degrees of vertices and number of edges are among the important theoretical terms that are helpful in showing discrete structures and their properties. This study attempts to present the relationship between number of edges and degrees of vertices in a mixed graph. Key words: Graph, directed graphs, undirected graphs, mixed graph, degree of vertex, number of edges.
Curriculum development and evaluation: New dimensions to enriching Mathematics Education in Nigeria
March 2023
This paper makes a case for curriculum development and evaluation. It emphasized the new dimensions to enrich mathematics education in Nigeria. The paper therefore examined the meaning of curriculum. It highlighted issues involved in planning the mathematics education curriculum such as purpose of the curriculum, current knowledge level of students and materials. Also, it examined the practical aspect of developing the...
Notes on the order of convergence, consistency and stability properties of newly derived schemes
January 2023
In this paper, two numerical integration methods for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), namely “Third Order One Step Scheme (TOOSS) and Second Order One Step Scheme (SOOSS)” have been considered. The order of convergence, consistency and the stability properties of the schemes have been investigated. From the analyses, it is observed that SOOSS and TOOSS have...
Moore-Penrose inverse of linear operators in Hilbert space
November 2022
In this paper, we investigate properties of with closed range satisfying the operator equations In particular, we investigate the invertibility of with closed range where the Moore-Penrose inverse of T turns out to be the usual inverse of T under some classes of operators. We also deduce the Moore-Penrose inverse of a perturbed linear operator with closed range where such...
Division by zero in real and complex number arithmetic and some of its implications
November 2022
In this paper, an attempt is made to include division by zero in ordinary arithmetic. Counting or measuring is done to get the value of multiples, powers, quotients, sums and differences of zeros. Zero divided by zero is taken to be equal to one. There are many infinities and many zeroes. The biggest of all infinities cannot be imagined and the smallest zero cannot be imagined also. An attempt is made to define a...
Calculation of a class of Gaussian integrals: Derivation of payoff at expiry for European option
March 2022
This work deals with the calculation of a class of Gaussian integral of the form where Completing the squares of the exponential and changing variables led to the solution where denotes the cumulative standard normal distribution function. An equation which corresponds to pay-off at expiry for European option was derived. Key words: Gaussian integral, Euler-Poisson integral, multivariable...
A novel 2-character randomized response technique model applicable to real life situations
December 2021
In this paper, we propose a model for estimating population proportion of a personality possessing two related sensitive attributes in survey sampling by extending Warner’s Randomized Response Technique (RRT). The proposed estimators are more efficient than Lee’s simple model estimators as the population proportion escalates. Our proposed model performs better than Lee’s crossed model estimators when...
Triple Shehu transform and its properties with applications
June 2021
In the current paper, the concept of one-dimensional Shehu Transform have been generalized into three-dimensional Shehu Transform namely, Triple Shehu Transform (TRHT). Further, some main properties, several theorems and properties related to the TRHT have been established. Triple Shehu transform was used in solving fractional partial differential equations, with the fractional derivative described in Caputo sense. The...
Convergences and numerical analysis of a contact problem with normal compliance and unilateral constraint
June 2021
This paper represents a continuation of a previous study on “Analysis of a Sliding Frictional Contact Problem with Unilateral Constraint”. This study considers a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraints, associated to a sliding version...
One kind of construction on sunflower with two petals*
January 2021
A sunflower (or ∆-system) with k petals and a core Y is a collection of sets S1,⋯, Sk such that Si∩Sj=Y for all i≠j; the sets S1\Y,⋯, Sk\ Y, are petals. In this paper, we first give a sufficient condition for the existence of a sunflower with 2 petals. Let F={A,B,C} be a family of subsets of a set { a1,⋯,am , b1,⋯,bn , c1,⋯,cn } with and A={a1,⋯,am}, B={ b1,⋯,bn } and C={ c1,⋯,cn } are...
A focus on the Riemann's hypothesis
November 2020
Riemann's hypothesis, formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin Academy of Mathematic. In that paper, he proposed that this function, called Riemann-zeta function takes values 0 on the complex plane when s=0.5+it. This hypothesis...
Integral Tau method for fourth-order ordinary differential equations with third degree over determination
August 2020
This paper is concerned with the solution of a class of fourth order initial value problems in ordinary differential equation by the integrated formulation of the Tau method. The initial focus is the class with a maximum of third degree overdetermination. The matrix equations were constructed based on the degree of overdetermination and for purpose of automation. The automated Tau system was tested on some selected...
The weighted Monsef distribution
August 2020
A two-parameter weighted Monsef distribution (WM) is proposed in this paper. WM is flexible and has the property that the hazard rate function can accommodate both increasing and bathtub shapes. Most of its mathematical properties, such as probability density function, hazard function, moments and mean residual life function, are derived. The maximum likelihood method is used to estimate the distribution parameters. A...
An automorphism in the LK_ITB5a H110F gene mutation
July 2020
Sanchez et al. (2005) have shown the structure of vector space genetic code over the Galois field GF(4) which relate to the physicochemical properties of the genetic code on proteins. From this vector space, an automorphism can be constructed to reflect the mutation process in the genetic code. This study investigates a type of transformation in the LK_ITB5a lipase gene mutation. The result of the study shows that there...
Funmatics: The future generation of African mathematical scientists - How their minds works
May 2020
Mathematics is the science that deals with the logic of shape, quantity and arrangement, and mathematical sciences have become important aspects of everyday life. It underpins many fields that provide benefits for humanities including but not limited to Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications (Hu, 2016)
Three-step optimized block backward differentiation formulae (TOBBDF) for solving stiff ordinary differential equations
April 2020
A three-step optimized block backward differentiation formulae for solving stiff ordinary differential equations of first-orderdifferential equations is presented. The method adopts polynomial of order 6 and three hybrid pointschosen appropriately to optimize the local truncation errors of the main formulas for the block. The method is zero-stable and consistent with sixth algebraic order. Some numerical examples were...
An internal heat source in temperature rate dependent thermoelastic medium subjected to the effect of rotation and gravity field
February 2020
The present work is devoted to study the effect of rotation and gravity field in a homogeneous, isotropic elastic semi- infinite, which is at initial temperature, and subjected to heat source and load moving with finite velocity. In view of calculating general problems, a numerical solution technique is to be used. For this purpose, the normal mode analysis method is used. The results for the displacement, stress...
A mathematical model for solving integer linear programming problems
February 2020
A suggested algorithm to solve fully rough integer linear programming (FRILP) problems is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are rough intervals (RIs). In real-life situations, the parameters of linear programming problem model may not be defined precisely,...
Volatility measure of Nigeria crude oil production as a tool to investigate production variability
January 2020
The interest to carry out volatility analysis of crude oil production in Nigeria in this paper is motivated by the shortfalls in quantities of crude oil produced in recent past, given the country’s high dependence on oil and its contribution to the nation’s economic development. In 2016 precisely, the country experienced drastic instability in prices of crude oil at international markets and dwindling...
Fixed lifetime inventory system with double order under useful lifetime based model
January 2020
The problem of outdating in the fixed lifetime inventory system has been the focus of researchers in the last decade. Results show that while outdating is being minimized, shortages have become a problem. To eliminate or reduce shortages in the fixed lifetime inventory system, we propose a model where, there are two orders, one period apart in arriving into the inventory system. The second order is designed to satisfy...
A short note on inequalities of interval-valued intuitionistic fuzzy matrices
November 2019
Inequality, also known as inequation, but unlike equation does not have rich history. After the introduction of equation, inequation captures its popularity in different fields namely algebra, geometry, trigonometry, probability, set theory, fuzzy set theory, logic, calculus etc. Whereas inequalities used in algebra are called algebraic inequalities, the ones used in geometry are called geometric inequalities etc....
Total revenue function for non-regular fixed lifetime inventory system
November 2019
The fixed lifetime inventory system assumes that outdated items are discarded from inventory. Such inventory system is here referred to as regular inventory system. The non-regular fixed lifetime inventory system assumes that outdated items are not discarded from inventory. The features of both the regular and non-regular inventory systems are compared in this work and the total revenue function for the non-regular...
An air quality composite index based on pollutant concentration factor analysis
October 2019
To overcome the problems of Air Quality Index in describing regional short-term air quality status and changing trend, based on the daily average concentrations of six air pollutants affecting regional air quality in Zhengzhou from 2015 to 2018, this paper analyzes their correlation characteristics and defines an air quality composite index instead of the original index by using factor analysis method, which not only...
Comparative study of the direct and inverse finite element methods for pricing American options
February 2019
This paper investigates the computational performance of direct and inverse finite element methods for pricing American options. The underlying concept of the direct approach is similar to that of conventional finite element method. But the inverse approach is a relatively new development that involves trading the roles of financial variables. Based on the same constitutive model and linear elements, a performance...
Proof of Beal’s conjecture
November 2018
In this research, a proof of Beal’s conjecture is presented. A possible Pythagorean algebraic relationship between the terms of the conjecture problem will be proposed and used to arrive at the proof results. In the process of seeking the proof the solution of the congruent number problem through a family of cubic curves will be discussed. Key words: Proof of Beal’s conjecture, proof of ABC conjecture,...
Comparison of open source data mining softwares on a data set
November 2018
Data mining is the process of extracting informative and useful rules or relations, that can be used to make predictions about the values of new instances, from existing data. A wide range of commercial and open source software programs are used for data mining. In this study, a comparison of several classification algorithms included in some open source softwares such as WEKA, Tanagra and Scikit-learn using SEER...
Derivation of a new block fifth order method for numerical solution of first order initial value problems
October 2018
A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of order explicit Runge-Kutta method. Key words: Predictor-corrector methods, ordinary differential equations,...
A study on exact solution of the telegraph equation by (G'/G)-expansion method
October 2018
In this article, an exact solution of the Telegraph equation is solved by -Expansion method and this is one of the most popular example both linear and non-linear partial differential equations. The -Expansion method is simple and powerful analyzed for getting some sets of exact solutions. To develop the theory and to visualize the graph, the mathematical software MAPLE was used. This method also gives us...
The half way series expansion
September 2018
A new formula for mathematics is derived which gives the upper half of the series expansion of the expression (ay+b)2n, where n, is a natural number. A proof of the new formula is given followed by a simple example to test its accuracy. This formula is helpful whenever n is large. Key words: Series Expansion, fluid models, Intermolecular Potential model
Maximizing profit in the poultry farming sector: An application of the robust linear programming technique
September 2018
Managing the limited resources of money, time and space poses a real problem in the livestock business in general and the poultry sector in particular. The stochastic linear programming with recourse will permit the formulation of a mathematical model that could easily be solved in order to attain the objective of maximizing profit but this will be hindered by the presence of some parameters like demand and supply which...
Multi parameter fuzzy soft set approach to decision making problem
August 2018
In this paper, a new approach for decision making problem is introduced by extending the definition of fuzzy soft set for multiple parameter sets and is called extended fuzzy soft set. Also, few operations such as “AND” and “ ” are defined on extended fuzzy soft sets and illustrated with examples. Further an algorithm for decision making using the concept of extended fuzzy soft set is presented....
Continuous frame in Hilbert space and its applications
August 2018
In this paper, we study continuous frames in Hilbert spaces using a family of linearly independent vectors called coherent state (CS) and applying it in any physical space. To accomplish this goal, the standard theory of frames in Hilbert spaces, using discrete bases, is generalized to one where the basis vectors may be labeled using discrete, continuous or a mixture of the two types of indices. A comprehensive...
Applications of Cauchy-Schwarz inequalities in the mapping structure of linear operator
June 2018
By applications of Cauchy-Schwarz inequalities, several sufficient conditions in terms of hypergeometric inequalities were found such that the linear operator preserves and transforms certain well known subclasses of univalent functions to another classes. Relevant connections of our work with the earlier work is pointed out. Key words: Analytic function, subordination, starlike function, convex...
Results on generalized fuzzy soft topological spaces
April 2018
In this manuscript, the concept of a generalized fuzzy soft point is introduced and some of its basic properties were studied. Also, the concepts of a generalized fuzzy soft base (subbase) and a generalized fuzzy soft subspace were introduced and some important theorems were established. Finally, the relationship between fuzzy soft set, intuitionistic fuzzy soft set, generalized fuzzy soft set and generalized...
Analytic solutions of time fractional diffusion equations by fractional reduced differential transform method (FRDTM)
March 2018
This paper examines a general recurrence relation by the use of fractional reduced differential transform and then a scheme (methodology) on how to find closed solutions of one dimensional time fractional diffusion equations with initial conditions in the form of infinite fractional power series and in terms of Mittag-Leffler function in one parameter as well as their exact solutions by the use of fractional reduced...
Distributional analysis with line transect methodology of the distance sampling techniques: Case of large mammals of the Mole National Park (MNP) of Ghana
January 2018
Distance sampling with line transect method has been applied by many researchers to monitor and observe varied animals and plants with the aim to estimating population density and/or abundance. The detection and detectabilities of plants and animals with line transect methodology appear to be described as seen in the application software DISTANCE by some four specific models or mathematical functions. This study has...
Adams completion and symmetric algebra
November 2017
Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, the symmetric algebra of a given algebra is shown to be the Adams completion of the algebra by considering a suitable set of morphisms in a suitable category. Key words: Category of fraction, calculus of left fraction, symmetric algebra, tensor algebra, Adams completion.
Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars
October 2017
The Galerkin method is used to numerically solve the exterior boundary value problem for the radiosity equation for the spherical quatrefoil. The radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces when their reflectivity and emissivity are given. On planet Mars the surface emissivity is closely related to its surface temperature. The radiosity of a surface is the rate...
A new approach to homotopy perturbation method for solving systems of Volterra integral equations of first kind
August 2017
In this article, He’s homotopy perturbation method was applied in a variant way to solve the system of Volterra integral equations of first kind. The results reveal that the proposed approach is very efficient for handling such system of integral equations. Some examples are given to show the ability of the proposed modification. Key words: Integral equations, Volterra integral equations of first...
Some propertıes of fuzzy contınuıty functıons
July 2017
In this study, some definitions and features related to fuzzy continuity, fuzzy membership functions and fuzzy continuous functions are examined. Using these definitions and properties, some theorems about fuzzy continuous functions have been proved. Key words: Fuzzy continuity, fuzzy function, fuzzy set.
More accurate approximate analytical solution of pendulum with rotating support
June 2017
Based on the energy balance method (EBM), a more accurate analytical solution of the pendulum equation with rotating support was presented. The results were compared with those obtained by the differential transformation method (DTM) and He’s improved energy balance method. It was shown that the results are more accurate than the said methods. Key words: Energy balance method, approximate solutions, nonlinear...
A multi-algorithm data mining classification approach for bank fraudulent transactions
June 2017
This paper proposes a multi-algorithm strategy for card fraud detection. Various techniques in data mining have been used to develop fraud detection models; it was however observed that existing works produced outputs with false positives that wrongly classified legitimate transactions as fraudulent in some instances; thereby raising false alarms, mismanaged resources and forfeit customers’ trust. This work was...
Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution
September 2016
In this paper, we prove the existence of at least one solution for Volterra- Hammerstein integral equation (V-HIE) of the second kind, under certain conditions, in the space , Ω is the domain of integration and T is the time. The kernel of Hammerstein integral term has a singularity, while the kernel of Volterra is continuous in time. Using a quadratic numerical method with respect to time, we have a system...
Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)
July 2016
Let n ≥ 1 be an integer. Define Ï•2(n) to be the number of positive integers x, 1 ≤ x ≤ n, for which both 6x−1 and 6x+1 are relatively prime to 6n. The primary goal of this study is to show that Ï•2 is a multiplicative function, that is, if gcd(m, n) = 1, then Ï•2(mn) = Ï•2(m)Ï•2(n). Key words: Euler phi-function, multiplicative function.
A fraud detection tool in E-auctions
January 2016
Due to rapid growth of the use of online auctions, fraudsters have taken advantage of these platforms to participate in their own auctions in order to raise prices (a practice called shilling). Innocent bidders have been forced to pay higher prices than they were willing to offer. This has resulted in the need to design and implement a shill detection algorithm. To eliminate this shilling problem, we designed a shilling...
Solvability of nonlinear Klein-Gordon equation by Laplace Decomposition Method
July 2015
In this study, Adomian Decomposition Method (ADM), Modified Decomposition Method (MD) and Laplace Decomposition Method (LDM) were used in solving nonlinear Klein-Gordon equation. It can be easily concluded that these three methods yielded exactly the same...
On two-stage fuzzy random programming for water resources management
June 2015
In this paper, a two-stage fuzzy random programming for a management problem in terms of water resources allocation having fuzzy random variable coefficients and decision vector of random variables is studied. The first results show the fact that a fuzzy pseudorandom optimal solution of a two-stage fuzzy random programming may be resolved into a two of pseudorandom optimal solutions of relative two-stage random...
Maximum flow–minimum cost algorithm of a distribution company in Ghana: Case of ‘NAAZO’ Bottling Company, Tamale Metropolis
April 2015
Every business entity’s primary objective is to maximize profit and satisfy its customers (end users). Since businesses are an integral part of our environment, their operations will be restricted by the environmental factors associated with it. The study seeks to model NAAZO Peki distribution in Tamale Metropolis (TM) as a network flow problem, and to determine the minimum cost of Peki soft drink distribution in...
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