Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . 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. Generated Surfaces via Inextensible Flows of Curves in Tue, 07 Jun 2016 09:35:21 +0000 We study the inextensible flows of curves in 3-dimensional 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 Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints Wed, 04 May 2016 11:27:34 +0000 We consider the so-called mean-variance portfolio selection problem in continuous time under the constraint that the short-selling of stocks is prohibited where all the market coefficients are random processes. In this situation the Hamilton-Jacobi-Bellman (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. Split Common Fixed Point Problem for a Class of Total Asymptotic Pseudocontractions Thu, 28 Apr 2016 14:03:27 +0000 We study the split common fixed point problem (SCFP) for a class of total asymptotically pseudocontractive mappings. We obtain some important properties of our class of mappings including the demiclosedness property and the closedness and convexity of the fixed point set. We then propose an algorithm and prove weak and strong convergence theorems for the approximation of solutions of the SCFP for certain class of these mappings. E. E. Chima and M. O. Osilike Copyright © 2016 E. E. Chima and M. O. Osilike. All rights reserved. Self-Triggered Model Predictive Control for Linear Systems Based on Transmission of Control Input Sequences Wed, 27 Apr 2016 16:05:28 +0000 A networked control system (NCS) is a control system where components such as plants and controllers are connected through communication networks. Self-triggered control is well known as one of the control methods in NCSs and is a control method that for sampled-data control systems both the control input and the aperiodic sampling interval (i.e., the transmission interval) are computed simultaneously. In this paper, a self-triggered model predictive control (MPC) method for discrete-time linear systems with disturbances is proposed. In the conventional MPC method, the first one of the control input sequence obtained by solving the finite-time optimal control problem is sent and applied to the plant. In the proposed method, the first some elements of the control input sequence obtained are sent to the plant, and each element is sequentially applied to the plant. The number of elements is decided according to the effect of disturbances. In other words, transmission intervals can be controlled. Finally, the effectiveness of the proposed method is shown by numerical simulations. Koichi Kobayashi Copyright © 2016 Koichi Kobayashi. All rights reserved. The Variational Homotopy Perturbation Method for Solving Dimensional Burgers’ Equations Tue, 19 Apr 2016 13:55:34 +0000 The variational homotopy perturbation method VHPM is used for solving -dimensional Burgers’ system. Some examples are examined to validate that the method reduced the calculation size, treating the difficulty of nonlinear term and the accuracy. F. A. Hendi, B. S. Kashkari, and A. A. Alderremy Copyright © 2016 F. A. Hendi et al. All rights reserved. Pricing Strategies in the Remanufacturing Market for the Uncertain Market Size in the Second Period Thu, 31 Mar 2016 17:35:59 +0000 Our main endeavor is to investigate the effect of the uncertain market size in the second period on the pricing strategies in the remanufacturing market. Observing the previous research, we find that the market size in the second period is always supposed to be certain. However, there is substantial empirical and experimental evidence that the market size in reality deviates from this assumption. In fact, though the market size in the first period is definitized, it is difficult to confirm the change of the market scale in the second period, since this change is affected by all kinds of elements, such as the awareness of environmental protection, some consumers’ psychological factors, and the related governments’ policies. Hence, we pay attention to the case in which the change rate of the market scale in the second period is random variable. We suppose that this rate satisfies uniform distribution on . Underlying this assumption, we further provide an insight into the game-playing relationship between original equipment manufacturers (OEMs) and remanufacturers. Moreover, we delicately and subtly incorporate the game theory, stochastic analysis, adversarial risk analysis (ARA), and optimization methods into the pricing strategies in the remanufacturing market. Last but not least, considerable efforts and attempts have been made to subtly test the sensitivity of an optimal solution to the different parameters. Liurui Deng and Shenggang Yang Copyright © 2016 Liurui Deng and Shenggang Yang. All rights reserved. Noise Folding in Completely Perturbed Compressed Sensing Wed, 30 Mar 2016 11:12:55 +0000 This paper first presents a new generally perturbed compressed sensing (CS) model , which incorporated a general nonzero perturbation into sensing matrix and a noise into signal simultaneously based on the standard CS model and is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property () and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noise , signal noise , and perturbation involved. Limin Zhou, Xinxin Niu, and Jing Yuan Copyright © 2016 Limin Zhou et al. All rights reserved. Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes Wed, 30 Mar 2016 08:55:00 +0000 Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology. Ye-Mao Xia and Jian-Wei Gou Copyright © 2016 Ye-Mao Xia and Jian-Wei Gou. All rights reserved. Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source Thu, 10 Mar 2016 09:11:48 +0000 Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd’s type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or “two-butterfly,” and chaotic attractor has been examined. B. S. Bhadauria Copyright © 2016 B. S. Bhadauria. All rights reserved. Limit Cycles for the Class of -Dimensional Polynomial Differential Systems Mon, 07 Mar 2016 09:52:14 +0000 We perturb the differential system , , and for inside the class of all polynomial differential systems of degree in , and we prove that at most limit cycles can be obtained for the perturbed system using the first-order averaging theory. Zouhair Diab and Amar Makhlouf Copyright © 2016 Zouhair Diab and Amar Makhlouf. All rights reserved.