Journal of Applied Mathematics
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Sparse Optimization of Vibration Signal by ADMM
Wed, 15 Feb 2017 00:00:00 +0000
http://www.hindawi.com/journals/jam/2017/4612853/
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
http://www.hindawi.com/journals/jam/2017/7302081/
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 secondorder 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
http://www.hindawi.com/journals/jam/2017/9654506/
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. ArizaHernandez, Jorge SanchezOrtiz, Martin P. ArcigaAlejandre, and Luis X. VivasCruz
Copyright © 2017 Francisco J. ArizaHernandez et al. All rights reserved.

Implicit OneStep Block Hybrid ThirdDerivative Method for the Direct Solution of Initial Value Problems of SecondOrder Ordinary Differential Equations
Wed, 18 Jan 2017 09:11:45 +0000
http://www.hindawi.com/journals/jam/2017/8510948/
A new onestep block method with generalized three hybrid points for solving initial value problems of secondorder 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 secondorder 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 SecondOrder Fredholm Integrodifferential Equations with Boundary Conditions by QuadratureDifference Method
Wed, 11 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jam/2017/2645097/
In this research, the quadraturedifference method with Gauss Elimination (GE) method is applied for solving the secondorder of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and secondorder finitedifference method are used to discretize the secondorder 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 quadraturedifference 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
http://www.hindawi.com/journals/jam/2017/8025616/
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 wellstudied 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. GarciaMartinez, F. R. McMorris, O. Ortega, and R. C. Powers
Copyright © 2017 C. GarciaMartinez 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
http://www.hindawi.com/journals/jam/2017/1697135/
The problem of a nonNewtonian 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 temperaturedependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of twodimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the nonNewtonian 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 spacedependent heat source; plastic dynamic viscosity and thermal conductivity of the nonNewtonian 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 RungeKutta 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
http://www.hindawi.com/journals/jam/2016/9734615/
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 illintentioned 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
http://www.hindawi.com/journals/jam/2016/4649150/
Through an AlexandrovFenchel inequality, we establish the general BrunnMinkowski 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
http://www.hindawi.com/journals/jam/2016/8710860/
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 inputoutput 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 backoff 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
http://www.hindawi.com/journals/jam/2016/2497379/
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
http://www.hindawi.com/journals/jam/2016/5327026/
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. Poomsaard
Copyright © 2016 A. Panpa and T. Poomsaard. All rights reserved.

A Note on the vec Operator Applied to Unbalanced BlockStructured Matrices
Wed, 09 Nov 2016 09:07:35 +0000
http://www.hindawi.com/journals/jam/2016/4590817/
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 blockstructured 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 2Generator Groups
Tue, 08 Nov 2016 07:17:44 +0000
http://www.hindawi.com/journals/jam/2016/8435768/
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 2generator groups of class 2. The results obtained here are supported by Groups, Algorithm and Programming (GAP).
Mahmoud Bashir Alhasanat, Bilal AlHasanat, and Eman AlSarairah
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
http://www.hindawi.com/journals/jam/2016/3812736/
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 ThreeState MarkovModulated Switching Model for Exchange Rates
Mon, 31 Oct 2016 06:04:37 +0000
http://www.hindawi.com/journals/jam/2016/5061749/
Several authors have examined the long swings hypothesis in exchange rates using a twostate 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 threestate pattern in Nigerian naira but a twostate 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 JumpDiffusion Equity Processes and a TwoFactor Stochastic Yield Curve
Thu, 27 Oct 2016 07:16:46 +0000
http://www.hindawi.com/journals/jam/2016/8029750/
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, twofactor 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 twoasset 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
http://www.hindawi.com/journals/jam/2016/1659019/
Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and lowrank 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 SingleMachine Scheduling Problem with SequenceDependent Family Setup Times to Minimize Total Tardiness
Thu, 20 Oct 2016 07:34:39 +0000
http://www.hindawi.com/journals/jam/2016/9598041/
This paper addresses a singlemachine scheduling problem with sequencedependent 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 largesized instances in reasonable solution time, efficient heuristic algorithms are needed to obtain nearoptimal 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
http://www.hindawi.com/journals/jam/2016/9747394/
We propose a closedform approximation for the price of basket options under a multivariate BlackScholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponentialpower 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
http://www.hindawi.com/journals/jam/2016/1793978/
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
http://www.hindawi.com/journals/jam/2016/5891064/
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
http://www.hindawi.com/journals/jam/2016/7535793/
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
http://www.hindawi.com/journals/jam/2016/4873276/
Twodimensional 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. Selfcontracting 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
http://www.hindawi.com/journals/jam/2016/4875358/
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 SixMoment OneDimensional Nonlinear System Equations with the MaxwellAuzhan Boundary Conditions
Sun, 10 Jul 2016 09:31:16 +0000
http://www.hindawi.com/journals/jam/2016/5834620/
We prove existence and uniqueness of the solution of the problem with initial and MaxwellAuzhan boundary conditions for nonstationary nonlinear onedimensional Boltzmann’s sixmoment 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 onedimensional Boltzmann’s sixmoment 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
http://www.hindawi.com/journals/jam/2016/6568347/
Creep process of linear viscoelastic materials is described by the integral equation of BoltzmannVolterra 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. Twostage 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
http://www.hindawi.com/journals/jam/2016/3176846/
Journal of Applied Mathematics
Copyright © 2016 Journal of Applied Mathematics. All rights reserved.

Generated Surfaces via Inextensible Flows of Curves in
Tue, 07 Jun 2016 09:35:21 +0000
http://www.hindawi.com/journals/jam/2016/6178961/
We study the inextensible flows of curves in 3dimensional Euclidean space . The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves in . Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves in and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.
Rawya A. Hussien and Samah G. Mohamed
Copyright © 2016 Rawya A. Hussien and Samah G. Mohamed. All rights reserved.

Viscosity Solution of MeanVariance Portfolio Selection of a Jump Markov Process with NoShorting Constraints
Wed, 04 May 2016 11:27:34 +0000
http://www.hindawi.com/journals/jam/2016/4543298/
We consider the socalled meanvariance portfolio selection problem in continuous time under the constraint that the shortselling of stocks is prohibited where all the market coefficients are random processes. In this situation the HamiltonJacobiBellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation. In fact, the value function often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such cases can be interpreted as a viscosity solution. Here we show the unicity of the viscosity solution and we see that the optimal and the value functions are piecewise linear functions based on some Riccati differential equations. In particular we solve the open problem posed by Li and Zhou and Zhou and Yin.
Moussa Kounta
Copyright © 2016 Moussa Kounta. All rights reserved.