Journal of Applied Mathematics The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Generation Expansion Models including Technical Constraints and Demand Uncertainty Thu, 06 Apr 2017 00:00:00 +0000 This article presents a Generation Expansion Model of the power system taking into account the operational constraints and the uncertainty of long-term electricity demand projections. The model is based on a discretization of the load duration curve and explicitly considers that power plant ramping capabilities must meet demand variations. A model predictive control method is used to improve the long-term planning decisions while considering the uncertainty of demand projections. The model presented in this paper allows integrating technical constraints and uncertainty in the simulations, improving the accuracy of the results, while maintaining feasible computational time. Results are tested over three scenarios based on load data of an energy retailer in Colombia. P. Deossa, K. De Vos, G. Deconinck, and J. Espinosa Copyright © 2017 P. Deossa et al. All rights reserved. Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method Mon, 20 Mar 2017 00:00:00 +0000 The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency. Olumuyiwa A. Agbolade and Timothy A. Anake Copyright © 2017 Olumuyiwa A. Agbolade and Timothy A. Anake. All rights reserved. Sparse Optimization of Vibration Signal by ADMM Wed, 15 Feb 2017 00:00:00 +0000 In this paper, the alternating direction method of multipliers (ADMM) algorithm is applied to the compressed sensing theory to realize the sparse optimization of vibration signal. Solving the basis pursuit problem for minimizing the norm minimization under the equality constraints, the sparse matrix obtained by the ADMM algorithm can be reconstructed by inverse sparse orthogonal matrix inversion. This paper analyzes common sparse orthogonal basis on the reconstruction results, that is, discrete Fourier orthogonal basis, discrete cosine orthogonal basis, and discrete wavelet orthogonal basis. In particular, we will show that, from the point of view of central tendency, the discrete cosine orthogonal basis is more suitable, for instance, at the vibration signal data because its error is close to zero. Moreover, using the discrete wavelet transform in signal reconstruction there still are some outliers but the error is unstable. We also use the time complex degree and validity, for the analysis of the advantages and disadvantages of the ADMM algorithm applied to sparse signal optimization. The advantage of this method is that these abnormal values are limited in the control range. Song Wanqing Copyright © 2017 Song Wanqing. All rights reserved. First Integrals and Hamiltonians of Some Classes of ODEs of Maximal Symmetry Tue, 14 Feb 2017 06:33:31 +0000 Complete sets of linearly independent first integrals are found for the most general form of linear equations of maximal symmetry algebra of order ranging from two to eight. The corresponding Hamiltonian systems are constructed and it is shown that their general solutions can also be found by a simple superposition formula from the solutions of a scalar second-order source equation. J. C. Ndogmo Copyright © 2017 J. C. Ndogmo. All rights reserved. Bayesian Analysis for a Fractional Population Growth Model Mon, 23 Jan 2017 00:00:00 +0000 We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is carried out to show the performance of the estimators and the Bayes factor. Finally, we present a real data example to illustrate the effectiveness of the method proposed here and the pertinence of using a fractional model. Francisco J. Ariza-Hernandez, Jorge Sanchez-Ortiz, Martin P. Arciga-Alejandre, and Luis X. Vivas-Cruz Copyright © 2017 Francisco J. Ariza-Hernandez et al. All rights reserved. Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations Wed, 18 Jan 2017 09:11:45 +0000 A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at while its second and third derivatives are collocated at all points in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy. Mohammad Alkasassbeh and Zurni Omar Copyright © 2017 Mohammad Alkasassbeh and Zurni Omar. All rights reserved. Numerical Solution of Second-Order Fredholm Integrodifferential Equations with Boundary Conditions by Quadrature-Difference Method Wed, 11 Jan 2017 00:00:00 +0000 In this research, the quadrature-difference method with Gauss Elimination (GE) method is applied for solving the second-order of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and second-order finite-difference method are used to discretize the second-order of LFIDEs. This approximation equation will be used to generate a system of linear algebraic equations and will be solved by using Gauss Elimination. In addition, the formulation and the implementation of the quadrature-difference method are explained in detail. Finally, some numerical experiments were carried out to examine the accuracy of the proposed method. Chriscella Jalius and Zanariah Abdul Majid Copyright © 2017 Chriscella Jalius and Zanariah Abdul Majid. All rights reserved. Axioms for Consensus Functions on the -Cube Mon, 09 Jan 2017 10:01:11 +0000 A value of a sequence of elements of a finite metric space is an element for which is minimum. The –function with domain the set of all finite sequences on and defined by is a value of is called the –function on . The and functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the –functions on the -cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions. C. Garcia-Martinez, F. R. McMorris, O. Ortega, and R. C. Powers Copyright © 2017 C. Garcia-Martinez et al. All rights reserved. Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis Wed, 04 Jan 2017 09:05:32 +0000 The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in is guaranteed with when magnitude of is large. decreases with and . T. M. Ajayi, A. J. Omowaye, and I. L. Animasaun Copyright © 2017 T. M. Ajayi et al. All rights reserved. On the Usefulness of Cooperation in Person Games Tue, 13 Dec 2016 13:22:53 +0000 The person games in which each player maximizes his payoff function are considered. We have studied an interesting question for the cooperative game theory about the usefulness of uniting the players in a union. The aim of such cooperation is for each player to get a positive increase to his guaranteed payoff. We have obtained some effective sufficient conditions under which the joining of the players in union is useful for each player. The linear case, specially, is being considered. In the second part of the paper, we have studied the question about the usefulness of cooperation of the players in the presence of the th player, an ill-intentioned destructive player, whose whole aim is not to win but to harm each player individually, and also the union of these players, for example, global terrorism. It should be noted that the considered situation in the second part is related to A. V. Kryazhimskiy’s talk delivered in the summer of 2014. We obtain constructive conditions under which the union of the players is beneficial in this situation as well. Mikhail Sergeevich Nikolskii and Aboubacar Moussa Copyright © 2016 Mikhail Sergeevich Nikolskii and Aboubacar Moussa. All rights reserved. Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation Thu, 01 Dec 2016 11:29:47 +0000 Through an Alexandrov-Fenchel inequality, we establish the general Brunn-Minkowski inequality. Then we obtain the uniqueness of solutions to a nonlinear elliptic Hessian equation on . Siyuan Li Copyright © 2016 Siyuan Li. All rights reserved. Theoretical Analysis of the Noise Power Ratio of Nonlinear Power Amplifiers Thu, 01 Dec 2016 06:51:10 +0000 This paper presents a theoretical analysis and derives the amplifier output noise power spectral density result in a closed form when the input to the amplifier is a band limited Gaussian noise. From the computed power spectral density the NPR is evaluated by a simple subtraction. The method can be applied to any amplifier with known input-output characteristics. The method may be applied to analyze various other important characteristics of the nonlinear amplifier such as spectral regrowth that refers to the spreading of the signal bandwidth when a band limited signal is inputted to the nonlinear amplifier. The paper presents numerical results on the NPR as a function of the noise bandwidth, depth level of the notch, and the output power back-off obtained from the analysis presented in the paper. Rajendra Kumar Copyright © 2016 Rajendra Kumar. All rights reserved. A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling Thu, 24 Nov 2016 13:59:50 +0000 We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image with size of is scrambled by Arnold transformation to obtain a meaningless image . Then, the color host image with size of is divided into nonoverlapping pixel blocks. In each pixel block , we form a real matrix with the red, green, and blue components of and perform the SVD of . We then replace the three smallest singular values of by the red, green, and blue values of with scaling factor, to form a new watermarked host image . With the reserve procedure, we can extract the watermark from the watermarked host image. In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image. Ying Li, Musheng Wei, Fengxia Zhang, and Jianli Zhao Copyright © 2016 Ying Li et al. All rights reserved. On Graceful Spider Graphs with at Most Four Legs of Lengths Greater than One Wed, 23 Nov 2016 09:01:45 +0000 A graceful labeling of a tree with edges is a bijection such that equal to . A spider graph is a tree with at most one vertex of degree greater than . We show that all spider graphs with at most four legs of lengths greater than one admit graceful labeling. A. Panpa and T. Poomsa-ard Copyright © 2016 A. Panpa and T. Poomsa-ard. All rights reserved. A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices Wed, 09 Nov 2016 09:07:35 +0000 The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes. Hal Caswell and Silke F. van Daalen Copyright © 2016 Hal Caswell and Silke F. van Daalen. All rights reserved. The Order Classes of 2-Generator -Groups Tue, 08 Nov 2016 07:17:44 +0000 In order to classify a finite group using its elements orders, the order classes are defined. This partition determines the number of elements for each order. The aim of this paper is to find the order classes of 2-generator -groups of class 2. The results obtained here are supported by Groups, Algorithm and Programming (GAP). Mahmoud Bashir Alhasanat, Bilal Al-Hasanat, and Eman Al-Sarairah Copyright © 2016 Mahmoud Bashir Alhasanat et al. All rights reserved. Bounds on the Spectral Radius of a Nonnegative Matrix and Its Applications Sun, 06 Nov 2016 10:36:59 +0000 We obtain the sharp bounds for the spectral radius of a nonnegative matrix and then obtain some known results or new results by applying these bounds to a graph or a digraph and revise and improve two known results. Danping Huang and Lihua You Copyright © 2016 Danping Huang and Lihua You. All rights reserved. A Three-State Markov-Modulated Switching Model for Exchange Rates Mon, 31 Oct 2016 06:04:37 +0000 Several authors have examined the long swings hypothesis in exchange rates using a two-state Markov switching model. This study developed a model to investigate long swings hypothesis in currencies which may exhibit a -state pattern. The proposed model was then applied to euros, British pounds, Japanese yen, and Nigerian naira. Specification measures such as AIC, BIC, and HIC favoured a three-state pattern in Nigerian naira but a two-state one in the other three currencies. For the period January 2004 to May 2016, empirical results suggested the presence of asymmetric swings in naira and yen and long swings in euros and pounds. In addition, taking as the benchmark for smoothing probabilities, choice models provided a clear reading of the cycle in a manner that is consistent with the realities of the movements in corresponding exchange rate series. Idowu Oluwasayo Ayodeji Copyright © 2016 Idowu Oluwasayo Ayodeji. All rights reserved. An Analytically Tractable Model for Pricing Multiasset Options with Correlated Jump-Diffusion Equity Processes and a Two-Factor Stochastic Yield Curve Thu, 27 Oct 2016 07:16:46 +0000 This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options. Tristan Guillaume Copyright © 2016 Tristan Guillaume. All rights reserved. A New Algorithm for Positive Semidefinite Matrix Completion Tue, 25 Oct 2016 08:34:35 +0000 Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm regularized linear least squares model with positive semidefinite constraints. We apply the widely used alternating direction method of multipliers to solve the model and get a novel algorithm. The applicability and efficiency of the new algorithm are demonstrated in numerical experiments. Recovery results show that our algorithm is helpful. Fangfang Xu and Peng Pan Copyright © 2016 Fangfang Xu and Peng Pan. All rights reserved. ILS Heuristics for the Single-Machine Scheduling Problem with Sequence-Dependent Family Setup Times to Minimize Total Tardiness Thu, 20 Oct 2016 07:34:39 +0000 This paper addresses a single-machine scheduling problem with sequence-dependent family setup times. In this problem the jobs are classified into families according to their similarity characteristics. Setup times are required on each occasion when the machine switches from processing jobs in one family to jobs in another family. The performance measure to be minimized is the total tardiness with respect to the given due dates of the jobs. The problem is classified as -hard in the ordinary sense. Since the computational complexity associated with the mathematical formulation of the problem makes it difficult for optimization solvers to deal with large-sized instances in reasonable solution time, efficient heuristic algorithms are needed to obtain near-optimal solutions. In this work we propose three heuristics based on the Iterated Local Search (ILS) metaheuristic. The first heuristic is a basic ILS, the second uses a dynamic perturbation size, and the third uses a Path Relinking (PR) technique as an intensification strategy. We carry out comprehensive computational and statistical experiments in order to analyze the performance of the proposed heuristics. The computational experiments show that the ILS heuristics outperform a genetic algorithm proposed in the literature. The ILS heuristic with dynamic perturbation size and PR intensification has a superior performance compared to other heuristics. Vinícius Vilar Jacob and José Elias C. Arroyo Copyright © 2016 Vinícius Vilar Jacob and José Elias C. Arroyo. All rights reserved. Pricing Basket Options by Polynomial Approximations Wed, 05 Oct 2016 08:02:27 +0000 We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort. Pablo Olivares and Alexander Alvarez Copyright © 2016 Pablo Olivares and Alexander Alvarez. All rights reserved. A Formula for the Energy of Circulant Graphs with Two Generators Thu, 22 Sep 2016 08:34:43 +0000 We derive closed formulas for the energy of circulant graphs generated by and , where is an integer. We also find a formula for the energy of the complete graph without a Hamilton cycle. Justine Louis Copyright © 2016 Justine Louis. All rights reserved. Convergence Analysis on Unstructured Meshes of a DDFV Method for Flow Problems with Full Neumann Boundary Conditions Sun, 18 Sep 2016 14:00:47 +0000 A Discrete Duality Finite Volume (DDFV) method to solve on unstructured meshes the flow problems in anisotropic nonhomogeneous porous media with full Neumann boundary conditions is proposed in the present work. We start with the derivation of the discrete problem. A result of existence and uniqueness of a solution for that problem is given thanks to the properties of its associated matrix combined with adequate assumptions on data. Their theoretical properties, namely, stability and error estimates (in discrete energy norms and -norm), are investigated. Numerical test is provided. A. Kinfack Jeutsa, A. Njifenjou, and J. Nganhou Copyright © 2016 A. Kinfack Jeutsa et al. All rights reserved. Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel Sun, 04 Sep 2016 11:17:09 +0000 A numerical investigation is made to determine the occurrence of the multiple solutions of MHD Casson fluid in a porous channel. Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. Numerical technique known as shooting method is used to investigate the existence of the multiple solutions for the variations of different parameters. Effects of physical parameters on velocity profile, temperature, concentration, and skin friction are presented in pictorial and tabulation representation. Jawad Raza, Azizah Mohd Rohni, and Zurni Omar Copyright © 2016 Jawad Raza et al. All rights reserved. Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families Wed, 27 Jul 2016 08:35:57 +0000 Two-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex body is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on . These regions are bounded by arcs of involutes of and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self-contracting sets (with opposite orientation) are considered: necessary and/or sufficient conditions for them to be subsets of SDC are proved. Marco Longinetti, Paolo Manselli, and Adriana Venturi Copyright © 2016 Marco Longinetti et al. All rights reserved. Shape Preserving Interpolation Using Rational Cubic Spline Tue, 19 Jul 2016 14:26:22 +0000 This paper discusses the construction of new rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters , , and . The sufficient conditions for the positivity are derived on one parameter while the other two parameters and are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives , . Comparisons with existing schemes also have been done in detail. From all presented numerical results the new rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is is also investigated in detail. Samsul Ariffin Abdul Karim and Kong Voon Pang Copyright © 2016 Samsul Ariffin Abdul Karim and Kong Voon Pang. All rights reserved. Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions Sun, 10 Jul 2016 09:31:16 +0000 We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form. A. Sakabekov and Y. Auzhani Copyright © 2016 A. Sakabekov and Y. Auzhani. All rights reserved. Determination of the Creep Parameters of Linear Viscoelastic Materials Wed, 29 Jun 2016 14:57:54 +0000 Creep process of linear viscoelastic materials is described by the integral equation of Boltzmann-Volterra in which creep kernel is approximated by Rabotnov’s fractional exponential function. The creep equation contains four unknown parameters: , singularity parameter; , fading parameter; , rheological parameter; and , conditionally instantaneous strain. Two-stage determination method of creep parameters is offered. At the first stage, taking into account weak singularity properties of Abel’s function at the initial moment of loading, parameters and are determined. At the second stage, using already known parameters and , parameters and are determined. Analytical expressions for calculating these parameters are obtained. An accuracy evaluation of the offered method with using experimentally determined creep strains of material Nylon 6 and asphalt concrete showed its high accuracy. Alibay Iskakbayev, Bagdat Teltayev, and Sergei Alexandrov Copyright © 2016 Alibay Iskakbayev et al. All rights reserved. Retracted: Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation Tue, 28 Jun 2016 06:29:40 +0000 Journal of Applied Mathematics Copyright © 2016 Journal of Applied Mathematics. All rights reserved.