Integral Tau method for fourth-order ordinary differential equations with third degree over determination
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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)
Let n ≥ 1 be an integer. Define ϕ2(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 ϕ2 is a multiplicative function, that is, if gcd(m, n) = 1, then ϕ2(mn) = ϕ2(m)ϕ2(n). Key words: Euler phi-function, multiplicative function.
A fraud detection tool in E-auctions
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
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
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
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...
On generalised fuzzy soft topological spaces
In this paper, union, and intersection of generalised fuzzy soft sets are introduced and some of their basic properties are studied. The objective of this paper is to introduce the generalised fuzzy soft topology over a soft universe with a fixed set of parameters. Generalised fuzzy soft points, generalised fuzzy soft closure, generalised fuzzy soft neighbourhood, generalised fuzzy soft interior, generalised fuzzy soft...
Applications of ig, dg, bg - Closed type sets in topological ordered spaces
In this paper we discuss possible applications of ig, dg and bg- closed type sets in topological ordered spaces. Key words: dg-closed, bg-closed, ig*-closed, dg*-closed, bg*-closed sets, Closed type sets, topological ordered spaces
A study of Green’s functions for three-dimensional problem in thermoelastic diffusion media
The purpose of the present paper is to study the three-dimensional general solution and Green’s functions in transversely isotropic thermoelastic diffuson media for static problem. With this objective, two displacement functions are introduced to simplify the basic equation and a general solution is then obtained by using the operator theory. Based on the obtained general solution, the three- dimensional...
Multivalent harmonic uniformly convex functions
In this paper, several properties of the multivalent harmonic uniformly convex classes and were investigated. Coefficient bounds, distortion theorem, extreme points, convolution condition, convex combinations and integral operator for these classes were obtained. Key words: Harmonic, multivalent functions, convex, convolution.
A study of some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods
In this paper, we introduce the solution of systems of nonlinear partial differential equations subject to the general initial conditions by using Adomian decomposition method (ADM) and Modified decomposition method (MDM). The proposed Adomian and Modified decomposition methods was applied to reformulated first and second order initial value problems, which leads the solution in terms of transformed variables, and the...
A highly efficient implicit Runge-Kutta method for first order ordinary differential equations
In this paper we develop a more efficient three-stage implicit Runge-Kutta method of order 6 for solving first order initial value problems of ordinary differential equations. Collocation method is used to derive Continuous schemes in which both the interpolation and collocation points are at perturbed Gaussian points. This gives a higher order scheme, which is more efficient and stable than the existing similar ones....
Comparative study of reliability parameter of a system under different types of distribution functions
In this paper a two unit standby system with single repair facility has been considered. When a working unit fails, it is immediately taken over by standby unit and repair on the failed unit is started immediately. Taking two types of distribution, namely, Weibull and Erlangian, various system effectiveness measures such as MTSF, Availability and Busy Periods are compared and results are interpreted numerically....
A method for the solution of fractional differential equations using generalized Mittag-Leffler function
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...
Optimal control model for the outbreak of cholera in Nigeria
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...
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
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...
A cubically convergent class of root finding iterative methods
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 (-())- expansion method to find the exact solutions of Shorma-Tasso-Olver Equation
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
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...
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