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Full-Text Articles in Physical Sciences and Mathematics

On Numerical Solution For Optimal Allocation Of Investment Funds In Portfolio Selection Problem, Yahaya Abubakar Dec 2012

On Numerical Solution For Optimal Allocation Of Investment Funds In Portfolio Selection Problem, Yahaya Abubakar

CBN Journal of Applied Statistics (JAS)

In this article, we present a procedure for obtaining an optimal solution to the Markowitz’s mean-variance portfolio selection problem based on the analytical solution developed in a previous research that lead to the emergence of an important model known as the Black Model. The procedure is well presented, illustrated and validated by a numerical example from real stocks dataset obtainable from a popular European stock market.


On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş Dec 2012

On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş

Applications and Applied Mathematics: An International Journal (AAM)

This paper is organized in the following ways: In the first part, we obtained the Klein Gordon Equation (KGE) in the Galilean space. In the second part, we applied Homotopy Perturbation Method (HPM) to this differential equation. In the third part, we gave two examples for the Klein Gordon equation. Finally, We compared the numerical results of this differential equation with their exact results. We also showed that approach used is easy and highly accurate.


A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad Dec 2012

A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad

Applications and Applied Mathematics: An International Journal (AAM)

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example.


On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar Dec 2012

On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar

Applications and Applied Mathematics: An International Journal (AAM)

Dichotomic maps are used to check the stability of ordinary differential equations and difference equations. In this paper, this method is extended to dynamic equations on time scales; the stability and asymptotic stability to the trivial solution of the first order system of dynamic equations are examined using dichotomic and strictly dichotomic maps. This method, in dynamic equations, also involves Lyapunov’s direct method.


Modification Of Truncated Expansion Method For Solving Some Important Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh Dec 2012

Modification Of Truncated Expansion Method For Solving Some Important Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we implemented modification of truncated expansion method for the exact solutions of the Konopelchenko-Dubrovsky equation the (n+1)-dimensional combined sinhcosh- Gordon equation and the Maccari system. Modification of truncated expansion method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method presents a wider applicability for handling nonlinear wave equations.


Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal Dec 2012

Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …


An Approximate Analytical Algorithm For Solving The Multispecies Lotka-Volterra Equations, Abdolsaeed Alavi, Asghar Ghorbani Dec 2012

An Approximate Analytical Algorithm For Solving The Multispecies Lotka-Volterra Equations, Abdolsaeed Alavi, Asghar Ghorbani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new efficient method called the parametric iteration method (PIM) is applied to accurately solve the multispecies Lotka–Volterra equations (MLVEs). Some cases of MLVEs are highlighted in order to show the simplicity and efficiency of the method. The results obtained in this work demonstrate that the present algorithm is a powerful analytic tool for the solution of MLVEs.


Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori Dec 2012

Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.


Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi Dec 2012

Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The …


On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk Dec 2012

On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk

Applications and Applied Mathematics: An International Journal (AAM)

The numerical solution of a mixed linear integro delay differential-difference equation with piecewise interval is presented using the Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving a mixed linear integro delay differential difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms a mixed linear integro delay differential-difference equations and the given conditions into a matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system …


Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy Dec 2012

Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, finite difference method (FDM) and Pade'-variational iteration method (Pade'- VIM) are successfully implemented for solving the nonlinear fractional Riccati differential equation. The fractional derivative is described in the Caputo sense. The existence and the uniqueness of the proposed problem are given. The resulting nonlinear system of algebraic equations from FDM is solved by using Newton iteration method; moreover the condition of convergence is verified. The convergence's domain of the solution is improved and enlarged by Pade'-VIM technique. The results obtained by using FDM is compared with Pade'-VIM. It should be noted that the Pade'-VIM is preferable because …


An Analysis Of The Career Length Of Professional Basketball Players, Kwame D. Fynn, Morgan Sonnenschein Aug 2012

An Analysis Of The Career Length Of Professional Basketball Players, Kwame D. Fynn, Morgan Sonnenschein

The Macalester Review

An interesting problem in professional basketball is predicting how long a player remains in the NBA League. Previous research on this problem has focused on factors such as race, performance in games, and size. We propose to analyze career duration in the NBA based on awards won, position played and biological variables such as height. Using Accelerated Failure Time models, Cox Proportional Hazards models and Kaplan-Meier analyses, we determine that both height and number of awards won lengthen career duration; however, only certain player positions significantly affect career length of a player.


Quantitative Reasoning And Sustainability, Corrine H. Taylor Jul 2012

Quantitative Reasoning And Sustainability, Corrine H. Taylor

Numeracy

Quantitative Reasoning and Sustainability have much in common. Both are complex, nuanced concepts with rather long definitions that have evolved over time. Both subjects are “everybody’s business” on college campuses, and must be approached in courses across the curriculum, not merely in one course on QR or in one course on Sustainability. The growing, wider presence of both QR and Sustainability on college campuses is due to their applicability in individuals’ personal, professional, and public lives. Moreover, QR and Sustainability support and enhance each other in and out of the classroom. Sustainability is an important, authentic, relevant context for lessons …


A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi Jun 2012

A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the determination of an unknown radiation term in the nonlinear boundary condition of a linear heat equation from an overspecified condition. First we study the existence and uniqueness of the solution via an auxiliary problem. Then a numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving the inverse heat conduction problem (IHCP) using temperature data containing significant noise is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. Some numerical experiments confirm the …


The First Integral Method To Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh, A. S. Paghaleh Jun 2012

The First Integral Method To Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh, A. S. Paghaleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we show the applicability of the first integral method for obtaining exact solutions of some nonlinear partial differential equations. By using this method, we found some exact solutions of the Landau-Ginburg-Higgs equation and generalized form of the nonlinear Schrödinger equation and approximate long water wave equations. The first integral method is a direct algebraic method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra.


Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv Jun 2012

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.


Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran Jun 2012

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.


An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi Jun 2012

An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi

Applications and Applied Mathematics: An International Journal (AAM)

The generalized differential transform method (GDTM) is a powerful tool for solving fractional equations. In this paper we solve the Mathieu fractional equation by this method. The approximate solutions obtained are compared with the exact solution. We also show that if both differential orders decrease, we can still have an approximate solution in the different interval of p.


A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem Jun 2012

A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.


Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah Jun 2012

Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah

Applications and Applied Mathematics: An International Journal (AAM)

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …


Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash Jun 2012

Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined …


Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori Jun 2012

Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended tanh method is used to construct exact solutions of the generalized Benjamin and (3 + 1)-dimensional gKP equation. This method is shown to be an efficient method for obtaining exact solutions of nonlinear partial differential equations. It can be applied to nonintegrable equations as well as to integrable ones.


Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji Jun 2012

Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper.


New Explicit Solutions For Homogeneous Kdv Equations Of Third Order By Trigonometric And Hyperbolic Function Methods, Marwan Alquran, Roba Al-Omary, Qutaibeh Katatbeh Jun 2012

New Explicit Solutions For Homogeneous Kdv Equations Of Third Order By Trigonometric And Hyperbolic Function Methods, Marwan Alquran, Roba Al-Omary, Qutaibeh Katatbeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study two-component evolutionary systems of the homogeneous KdV equation of the third order types (I) and (II). Trigonometric and hyperbolic function methods such as the sine-cosine method, the rational sine-cosine method, the rational sinh-cosh method, sech-csch method and rational tanh-coth method are used for analytical treatment of these systems. These methods, have the advantage of reducing the nonlinear problem to a system of algebraic equations that can be solved by computerized packages.


Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram Jun 2012

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …


A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal Jun 2012

A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal

Applications and Applied Mathematics: An International Journal (AAM)

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …


Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi Jun 2012

Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.


Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar Jun 2012

Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study a boundary stabilization of the torsional vibrations of a solar panel. The panel is held by a rigid hub at one end and is totally free at the other. The dynamics of the overall system leads to hybrid system of equations. It is set to a certain initial vibrations with a control torque as a stabilizer at the hub end only. Taking a non-linear damping as boundary stabilizer, a uniform exponential energy decay rate is obtained directly. Thus an explicit form of uniform stabilization of the system is achieved by means of the exponential energy …


Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma Jun 2012

Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …


Commutativity Results In Non Unital Real Topological Algebras, M. Oudadess, Y. Tsertos Jun 2012

Commutativity Results In Non Unital Real Topological Algebras, M. Oudadess, Y. Tsertos

Applications and Applied Mathematics: An International Journal (AAM)

We give conditions entailing commutativity in certain non unital real topological algebras. Several other results of complex algebras are also examined for real ones.