International Journal of Engineering Mathematics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions Tue, 01 Apr 2014 07:21:21 +0000 The th-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the th-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the th-order nonlinearity of a Boolean function is very complicated problem, especially when . This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form for all , , where , where , , and are integers such that and , and , where is a positive integer such that and . Brajesh Kumar Singh Copyright © 2014 Brajesh Kumar Singh. All rights reserved. Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions Mon, 24 Feb 2014 11:54:01 +0000 Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme. Ishfaq Ahmad Ganaie, Shelly Arora, and V. K. Kukreja Copyright © 2014 Ishfaq Ahmad Ganaie et al. All rights reserved. Several New Third-Order and Fourth-Order Iterative Methods for Solving Nonlinear Equations Sun, 23 Feb 2014 09:20:23 +0000 In order to find the zeros of nonlinear equations, in this paper, we propose a family of third-order and optimal fourth-order iterative methods. We have also obtained some particular cases of these methods. These methods are constructed through weight function concept. The multivariate case of these methods has also been discussed. The numerical results show that the proposed methods are more efficient than some existing third- and fourth-order methods. Anuradha Singh and J. P. Jaiswal Copyright © 2014 Anuradha Singh and J. P. Jaiswal. All rights reserved. Numerical Performance of Higher-Order Semicompact Scheme for Arbitrary Triangular Cavity Flow Tue, 04 Feb 2014 10:41:09 +0000 An efficient fourth-order semicompact finite difference scheme has been developed to solve steady incompressible Navier-Stokes (N-S) equations in stream function and vorticity formulation in a triangular cavity of arbitrary geometry. The governing equations are transformed into curvilinear coordinates by a simple linear transformation to handle the nonregular geometry of the problem. The main feature of the new higher-order semicompact scheme is that it can calculate a triangle flow with arbitrary shape for high Reynolds numbers. It is found that the solutions obtained with the present scheme are in good agreement with the analytical results or with the existing results depending on the availability. Xiaofeng Wang and Dongyang Shi Copyright © 2014 Xiaofeng Wang and Dongyang Shi. All rights reserved. Developing Buoyancy Driven Flow of a Nanofluid in a Vertical Channel Subject to Heat Flux Sun, 02 Feb 2014 08:43:22 +0000 The developing natural convective flow of a nanofluid in an infinite vertical channel with impermeable bounding walls has been investigated. It is assumed that the nanofluid is dominated by two specific slip mechanisms and that the channel walls are subject to constant heat flux and isothermal temperature, respectively. The governing nonlinear partial differential equations coupling different transport processes have been solved numerically. The variations of velocity, temperature, and nanoparticles concentration have been discussed in relation to a number of physical parameters. It is seen that the approach to the steady-state profiles of velocity and temperature in the present work is different from the ones reported in a previous study corresponding to isothermal wall conditions. Nirmal C. Sacheti, Pallath Chandran, Ashok K. Singh, and Beer S. Bhadauria Copyright © 2014 Nirmal C. Sacheti et al. All rights reserved. A Study of I-Function of Several Complex Variables Mon, 27 Jan 2014 12:29:36 +0000 The aim of this paper is to introduce a natural generalization of the well-known, interesting, and useful Fox H-function into generalized function of several variables, namely, the I-function of ‘‘’’ variables. For , we get the I-function introduced and studied by Arjun Rathie (1997) and, for , we get I-function of two variables introduced very recently by ShanthaKumari et al. (2012). Convergent conditions, elementary properties, and special cases have also been given. The results presented in this paper generalize the results of H-function of ‘‘’’ variables available in the literature. Prathima Jayarama, Vasudevan Nambisan Theke Madam, and Shantha Kumari Kurumujji Copyright © 2014 Prathima Jayarama et al. All rights reserved. Non-Darcy Mixed Convection in a Doubly Stratified Porous Medium with Soret-Dufour Effects Thu, 09 Jan 2014 08:23:33 +0000 This paper presents the nonsimilarity solutions for mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a doubly stratified fluid saturated porous medium in the presence of Soret and Dufour effects. The flow in the porous medium is described by employing the Darcy-Forchheimer based model. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms and then solved numerically. The influence of pertinent parameters on dimensionless velocity, temperature, concentration, heat, and mass transfer in terms of the local Nusselt and Sherwood numbers is discussed and presented graphically. D. Srinivasacharya and O. Surender Copyright © 2014 D. Srinivasacharya and O. Surender. All rights reserved. Effects of Mass Transfer, Radiation, Joule Heating, and Viscous Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection Sat, 14 Dec 2013 12:38:08 +0000 The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement. S. Mohammed Ibrahim Copyright © 2013 S. Mohammed Ibrahim. All rights reserved. Investigation of Through-Thickness Stresses in Composite Laminates Using Layerwise Theory Thu, 12 Dec 2013 15:36:23 +0000 In this study, an analytical method is developed to exactly obtain the interlaminar stresses near the free edges of laminated composite plates under the bending moment based on the reduced form of elasticity displacement field for a long laminate. The analytical and numerical studies were performed based on the Reddy’s layerwise theory for the boundary layer stresses within cross-ply, symmetric, angle-ply, and general composite laminates. Finally, a variety of numerical results are presented for the interlaminar normal and shear stresses along the interfaces and through thickness of laminates near the free edges. The results showed high stress gradient of interlaminar normal and shear stresses near the edges of laminates. Hamidreza Yazdani Sarvestani and Ali Naghashpour Copyright © 2013 Hamidreza Yazdani Sarvestani and Ali Naghashpour. All rights reserved. Sufficient Conditions of Asymptotic Stability of the Time-Varying Descriptor Systems Tue, 10 Dec 2013 18:35:07 +0000 We discuss the time-varying descriptor systems. Firstly, a sufficient condition of asymptotic stability and impulse-free is derived based on Riccati equation. Secondly, we design a state feedback controller to make the close-loop system asymptotically stable and impulse-free. Finally, a numerical example demonstrates the proposed results. Xiaoming Su and Yali Zhi Copyright © 2013 Xiaoming Su and Yali Zhi. All rights reserved. Asymptotic Solution for a Water Quality Model in a Uniform Stream Thu, 28 Nov 2013 10:32:34 +0000 We employ approximate analytical method, namely, Optimal Homotopy Asymptotic Method (OHAM), to investigate a one-dimensional steady advection-diffusion-reaction equation with variable inputs arises in the mathematical modeling of dispersion of pollutants in water is proposed. Numerical values are obtained via Runge-Kutta-Fehlberg fourth-fifth order method for comparison purpose. It was found that OHAM solution agrees well with the numerical solution. An example is included to demonstrate the efficiency, accuracy, and simplicity of the proposed method. Fazle Mabood and Nopparat Pochai Copyright © 2013 Fazle Mabood and Nopparat Pochai. All rights reserved. Effects of Magnetic Field and Thermal Radiation on Stagnation Flow and Heat Transfer of a Power-Law Fluid over a Shrinking Sheet Mon, 21 Oct 2013 13:51:34 +0000 An analysis is made on the steady two-dimensional boundary layer magnetohydrodynamic (MHD) stagnation-point flow and radiative heat transfer of an electrically conducting power-law fluid over a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. The similarity transformations are used to transform the boundary layer equations into a system of nonlinear ordinary differential equations which are then solved numerically using shooting technique. It is found that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on the magnetic parameter (M) and the power-law index parameter (n). The results pertaining to the present study indicate that as the strength of the magnetic parameter increases, the range of α where similarity solutions exist gradually increases. It is also observed that the temperature at a point decreases with increase in M for the first solution branch, whereas it increases with increase in M for the second solution branch. The reported results are in good agreement with the available published work in the literature. Samir Kumar Nandy Copyright © 2013 Samir Kumar Nandy. All rights reserved. Solution of Boundary Value Problems by Approaching Spline Techniques Mon, 30 Sep 2013 16:36:03 +0000 In the present work a nonpolynomial spline function is used to approximate the solution of the second order two point boundary value problems. The classes of numerical methods of second order, for a specific choice of parameters involved in nonpolynomial spline, have been developed. Numerical examples are presented to illustrate the applications of this method. The solutions of these examples are found at the nodal points with various step sizes and with various parameters (α, β). The absolute errors in each example are estimated, and the comparison of approximate values, exact values, and absolute errors of at the nodal points are shown graphically. Further, shown that nonpolynomial spline produces accurate results in comparison with the results obtained by the B-spline method and finite difference method. P. Kalyani and P. S. Rama Chandra Rao Copyright © 2013 P. Kalyani and P. S. Rama Chandra Rao. All rights reserved. Yoneda Philosophy in Engineering Tue, 24 Sep 2013 13:54:15 +0000 Mathematical models, such as sets of equations, are used in engineering to represent and analyze the behaviour of physical systems. The conventional notations in formulating engineering models do not clearly provide all the details required in order to fully understand the equations, and, thus, artifacts such as ontologies, which are the building blocks of knowledge representation models, are used to fulfil this gap. Since ontologies are the outcome of an intersubjective agreement among a group of individuals about the same fragment of the objective world, their development and use are questions in debate with regard to their competencies and limitations to univocally conceptualize a domain of interest. This is related to the following question: “What is the criterion for delimiting the specification of the main identifiable entities in order to consistently build the conceptual framework of the domain in question?” This query motivates us to view the Yoneda philosophy as a fundamental concern of understanding the conceptualization phase of each ontology engineering methodology. In this way, we exploit the link between the notion of formal concepts of formal concept analysis and a concluding remark resulting from the Yoneda embedding lemma of category theory in order to establish a formal process. Lambrini Seremeti and Ioannis Kougias Copyright © 2013 Lambrini Seremeti and Ioannis Kougias. All rights reserved. Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media Tue, 10 Sep 2013 09:30:31 +0000 Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation. R. S. Damor, Sushil Kumar, and A. K. Shukla Copyright © 2013 R. S. Damor et al. All rights reserved. Initiating a Mathematical Model for Prediction of 6-DOF Motion of Planing Crafts in Regular Waves Mon, 19 Aug 2013 08:23:09 +0000 Nowadays, most of the dynamic research on planing ships has been directed towards analyzing the ships motions in either 3-DOF (degrees of freedom) mode in the longitudinal vertical plane or in 3-DOF or 4-DOF mode in the lateral vertical plane. For this reason, the current authors have started a research program of describing the dynamic behavior of planing ships in a 6-DOF mathematical model. This program includes the developing of a 6-DOF computer simulation program in the time domain. This type of simulation can be used for predicting the response of these planing vessels to the environmental disturbances during high-speed sailing. In this paper, the development of the mathematical model will be presented. Furthermore, a discussion will be offered about the use of these static contributions in a time domain simulation for modeling the behavior of planing crafts in regular waves. Parviz Ghadimi, Abbas Dashtimanesh, and Yaser Faghfoor Maghrebi Copyright © 2013 Parviz Ghadimi et al. All rights reserved. Mathematical Modeling and Analysis of the Kinetics of Thermal Inactivation of Enzyme Mon, 12 Aug 2013 11:38:34 +0000 A theoretical model of Illeova et al. (2003) thermal inactivation of urease is discussed. Analytical expressions pertaining to the molar concentrations of the native and denatured enzyme are obtained in terms of second-order reaction rate constant. Simple and closed form of theoretical expression pertains to the temperature are also derived. In this paper, homotopy analysis method (HAM) is used to obtain approximate solutions for a nonlinear ordinary differential equation. The obtained approximate result in comparison with the numerical ones is found to be in satisfactory agreement. S. P. Ananthi, P. Manimozhi, T. Praveen, A. Eswari, and L. Rajendran Copyright © 2013 S. P. Ananthi et al. All rights reserved. Analytical Treatment and Convergence of the Adomian Decomposition Method for Instability Phenomena Arising during Oil Recovery Process Wed, 24 Jul 2013 08:24:39 +0000 An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model porous medium equation. Moreover, we prove that this decomposition scheme applied to a porous medium equation arising in instability phenomena in double phase flow through porous media is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration. Ramakanta Meher and Srikanta K. Meher Copyright © 2013 Ramakanta Meher and Srikanta K. Meher. All rights reserved. Influence of Hall Current and Thermal Radiation on MHD Convective Heat and Mass Transfer in a Rotating Porous Channel with Chemical Reaction Thu, 18 Jul 2013 11:44:23 +0000 A theoretical study is carried out to obtain an analytic solution of heat and mass transfer in a vertical porous channel with rotation and Hall current. A constant suction and injection is applied to the two insulating porous plates. A strong magnetic field is applied in the transverse direction. The entire system rotates with uniform angular velocity about the axis normal to the plates. The governing equations are solved by perturbation technique to obtain the analytical results for velocity, temperature, and concentration fields and shear stresses. The steady and unsteady resultant velocities along with the phase differences for various values of physical parameters are discussed in detail. The effects of rotation, buoyancy force, magnetic field, thermal radiation, and heat generation parameters on resultant velocity, temperature, and concentration fields are analyzed. Dulal Pal and Babulal Talukdar Copyright © 2013 Dulal Pal and Babulal Talukdar. All rights reserved. Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay Tue, 18 Jun 2013 09:24:24 +0000 This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results. Priyanka Kokil, V. Krishna Rao Kandanvli, and Haranath Kar Copyright © 2013 Priyanka Kokil et al. All rights reserved. Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse Mon, 17 Jun 2013 13:37:29 +0000 Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results. Zhenguo Luo, Jianhua Huang, Liping Luo, and Binxiang Dai Copyright © 2013 Zhenguo Luo et al. All rights reserved. Interval Arithmetic for Nonlinear Problem Solving Thu, 13 Jun 2013 18:59:22 +0000 Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to develop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using the computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than with previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this platform and applied to determine the solutions of selected nonlinear problems. Cases 1 and 2 demonstrate the effectiveness of the implementation applied to traditional polynomial problems. Case 3 demonstrates the robustness of the implementation in the case of multiple specific volume solutions. Case 4 exemplifies the robustness and effectiveness of the implementation in the determination of multiple critical points for a mixture of methane and hydrogen sulfide. The examples demonstrate the effectiveness of the method by finding all existing roots with mathematical certainty. Benito A. Stradi-Granados Copyright © 2013 Benito A. Stradi-Granados. All rights reserved. Falkner-Skan Flow of a Maxwell Fluid with Heat Transfer and Magnetic Field Sat, 08 Jun 2013 12:34:25 +0000 This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi…eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted. M. Qasim and S. Noreen Copyright © 2013 M. Qasim and S. Noreen. All rights reserved. The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid Sat, 25 May 2013 18:43:54 +0000 The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed. D. R. V. S. R. K. Sastry, A. S. N. Murti, and T. Poorna Kantha Copyright © 2013 D. R. V. S. R. K. Sastry et al. All rights reserved. Basicity of Systems of Sines with Linear Phase in Weighted Sobolev Spaces Sat, 18 May 2013 09:58:11 +0000 The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied. V. F. Salmanov and A. R. Safarova Copyright © 2013 V. F. Salmanov and A. R. Safarova. All rights reserved. New Application of -Expansion Method for Generalized (2+1)-Dimensional Nonlinear Evolution Equations Thu, 16 May 2013 13:15:59 +0000 We established -expansion method for (2+1)-dimensional nonlinear evolution equations. This method was used to construct travelling wave solutions of (2+1)-dimensional nonlinear evolution equations. (2+1)-Dimensional breaking soliton equation, (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation, and (2+1)-dimensional Bogoyavlenskii’s Breaking soliton equation are chosen to illustrate the effectiveness of the method. Mohammad Najafi, Maliheh Najafi, and Somayeh Arbabi Copyright © 2013 Mohammad Najafi et al. All rights reserved.