Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. On Types of Distance Fibonacci Numbers Generated by Number Decompositions Thu, 23 Oct 2014 06:47:27 +0000 We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the number we give a sequence of identities for them. Moreover, we give matrix generators for distance Fibonacci numbers and their direct formulas. Anetta Szynal-Liana, Andrzej Włoch, and Iwona Włoch Copyright © 2014 Anetta Szynal-Liana et al. All rights reserved. Robust Analysis and Parameters Identification of the Nonlinear Multistage Dynamical System in Batch Fermentation of Glycerol Tue, 21 Oct 2014 00:00:00 +0000 This paper discusses a complex biological problem which is the fermentation of glycerol by Klebsiella pneumoniae in batch culture. We set up an improved multistage model involving the concentration of intracellular substances. Furthermore, the existence, uniqueness, and continuity of solutions with respect to the parameters are discussed. On the condition that glycerol and 1,3-propanediol are assumed to pass the cell membrane by passive diffusion coupled with facilitated transport, we take the relative errors between experimental data and computational values of the extracellular substances concentrations and the biological robustness of the intracellular substances concentrations as the performance index. Then we establish a parameter identification model and construct the particle swarm optimization algorithm to solve it. Finally, the numerical result shows that the improved model could describe the glycerol fermentation in batch culture well. Xu Zhang, Xinying Wang, Enmin Feng, and Zhilong Xiu Copyright © 2014 Xu Zhang et al. All rights reserved. Chirp Signal Transform and Its Properties Mon, 20 Oct 2014 12:51:36 +0000 The chirp signal is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the chirp signals for an even or odd number and the continuous version. We study the fundamental properties of the transform and how it can be applied to recursion problems and differential equations. Furthermore, when is not prime and  , we define a transform skipped and develop the theory for it. Mio Horai, Hideo Kobayashi, and Takashi G. Nitta Copyright © 2014 Mio Horai et al. All rights reserved. Nonlinear Dynamical Analysis for the Cable Excited with Parametric and Forced Excitation Sun, 19 Oct 2014 10:29:16 +0000 Considering the deck vibration effect on the cable in cable-stayed bridge, using nonlinear structure dynamics theory, the nonlinear dynamical equation for the stayed cable excited with deck vibration is proposed. Research shows that the vertical vibration of the deck has a combined parametric and forced excitation effect on the cable when the angle of the cable is taken into consideration. Using multiscale method, the 1/2 principle parametric resonance is studied and the bifurcation equation is obtained. Despite the parameters analysis, the bifurcation characters of the dynamical system are studied. At last, by means of numerical method and software MATHMATIC, the effect rules of system parameters to the dynamical behavior of the system are studied, and some useful conclusions are obtained. C. Z. Qian, C. P. Chen, and G. W. Zhou Copyright © 2014 C. Z. Qian et al. All rights reserved. Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate Thu, 16 Oct 2014 08:45:24 +0000 Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques. Ji-Hun Yoon Copyright © 2014 Ji-Hun Yoon. All rights reserved. Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation Wed, 15 Oct 2014 00:00:00 +0000 We derive a new method of conditional Karhunen-Loève (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field. Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models. This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest. We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly. Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator. We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS). We also compare efficiency and stochastic convergence with that of stochastic collocation. Mina E. Ossiander, Malgorzata Peszynska, and Veronika S. Vasylkivska Copyright © 2014 Mina E. Ossiander et al. All rights reserved. Channels Coordination Game Model Based on Result Fairness Preference and Reciprocal Fairness Preference: A Behavior Game Forecasting and Analysis Method Mon, 13 Oct 2014 13:53:16 +0000 In a distribution channel, channel members are not always self-interested, but altruistic in some conditions. Based on this assumption, this paper adopts a behavior game method to analyze and forecast channel members’ decision behavior based on result fairness preference and reciprocal fairness preference by embedding a fair preference theory in channel research of coordination. The behavior game forecasts that a channel can achieve coordination if channel members consider behavior elements. Using the behavior game theory model we established, we can prove that if retailers only consider the result fairness preference and they are not jealous of manufacturers’ benefit, manufacturers will be more friendly to retailers. In such case, the total utility of the channel is higher compared with that of self-interest channel, and the utility of channel members is Pareto improved. If both manufactures and retailers consider reciprocal fairness preference, the manufacturers will give a lower wholesale price to the retailers. In return, the retailers will also reduce retail prices. Therefore, the total utility of the channels will not be less than the total utility of the channel coordination, as long as the reciprocity wholesale prices meet certain conditions. Chuan Ding, Kaihong Wang, and Xiaoying Huang Copyright © 2014 Chuan Ding et al. All rights reserved. Robust Stability Clearance of Flight Control Law Based on Global Sensitivity Analysis Mon, 13 Oct 2014 13:46:59 +0000 To validate the robust stability of the flight control system of hypersonic flight vehicle, which suffers from a large number of parametrical uncertainties, a new clearance framework based on structural singular value () theory and global uncertainty sensitivity analysis (SA) is proposed. In this framework, SA serves as the preprocess of uncertain model to be analysed to help engineers to determine which uncertainties affect the stability of the closed loop system more slightly. By ignoring these unimportant uncertainties, the calculation of can be simplified. Instead of analysing the effect of uncertainties on which involves solving optimal problems repeatedly, a simpler stability analysis function which represents the effect of uncertainties on closed loop poles is proposed. Based on this stability analysis function, Sobol’s method, the most widely used global SA method, is extended and applied to the new clearance framework due to its suitability for system with strong nonlinearity and input factors varying in large interval, as well as input factors subjecting to random distributions. In this method, the sensitive indices can be estimated via Monte Carlo simulation conveniently. An example is given to illustrate the efficiency of the proposed method. Liuli Ou, Lei Liu, Shuai Dong, and Yongji Wang Copyright © 2014 Liuli Ou et al. All rights reserved. Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions Sun, 12 Oct 2014 10:23:18 +0000 Partial fraction expansion (pfe) is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles. Youneng Ma, Jinhua Yu, and Yuanyuan Wang Copyright © 2014 Youneng Ma et al. All rights reserved. A New Iterative Procedure for Deconvolution of Seismic Ground Motion in Dam-Reservoir-Foundation Systems Thu, 18 Sep 2014 00:00:00 +0000 The concrete gravity dams are designed to perform satisfactorily during an earthquake since the consequence of failure is catastrophic to the downstream communities. The foundation in a dam is usually modeled by a substructuring approach for the purpose of seismic response analysis. However, the substructuring cannot be used for solving nonlinear dynamic problems that may be encountered in dam-reservoir-foundation systems. For that reason, the time domain approach is preferred for such systems. The deconvolved earthquake input model is preferred as it can remove the seismic scattering effects due to artificial boundaries of the semi-infinite foundation domain. Deconvolution is a mathematical process that allows the adjustment of the amplitude and frequency contents of a seismic ground motion applied at the base of the foundation in order to get the desired output at the dam-foundation interface. It is observed that the existing procedures of deconvolution are not effective for all types of earthquake records. A modified procedure has been proposed here for efficient deconvolution of all types of earthquake records including high-frequency and low-frequency ground motions. Gurinderbir S. Sooch and Ashutosh Bagchi Copyright © 2014 Gurinderbir S. Sooch and Ashutosh Bagchi. All rights reserved. Model Based Adaptive Piecewise Linear Controller for Complicated Control Systems Wed, 17 Sep 2014 10:07:51 +0000 A model based adaptive piecewise linear control scheme for industry processes with specifications on peak overshoots and rise times is proposed. It is a gain stabilized control technique. Large gain is used for large tracking error to get fast response. Small gain is used between large and small tracking error for good performance. Large gain is used again for small tracking error to cope with large disturbance. Parameters of the three-segment piecewise linear controller are found by an automatic regulating time series which is function of output characteristics of the plant and reference model. The time series will be converged to steady values after the time response of the considered system matching that of the reference model. The proposed control scheme is applied to four numerical examples which have been compensated by PID controllers. Parameters of PID controllers are found by optimization method. It gives an almost command independent response and gives significant improvements for response time and performance. Tain-Sou Tsay Copyright © 2014 Tain-Sou Tsay. All rights reserved. Fall-Detection Algorithm Using 3-Axis Acceleration: Combination with Simple Threshold and Hidden Markov Model Wed, 17 Sep 2014 05:06:55 +0000 Falls are a serious medical and social problem among the elderly. This has led to the development of automatic fall-detection systems. To detect falls, a fall-detection algorithm that combines a simple threshold method and hidden Markov model (HMM) using 3-axis acceleration is proposed. To apply the proposed fall-detection algorithm and detect falls, a wearable fall-detection device has been designed and produced. Several fall-feature parameters of 3-axis acceleration are introduced and applied to a simple threshold method. Possible falls are chosen through the simple threshold and are applied to two types of HMM to distinguish between a fall and an activity of daily living (ADL). The results using the simple threshold, HMM, and combination of the simple method and HMM were compared and analyzed. The combination of the simple threshold method and HMM reduced the complexity of the hardware and the proposed algorithm exhibited higher accuracy than that of the simple threshold method. Dongha Lim, Chulho Park, Nam Ho Kim, Sang-Hoon Kim, and Yun Seop Yu Copyright © 2014 Dongha Lim et al. All rights reserved. Garage Location Selection for Public Transportation System in Istanbul: An Integrated Fuzzy AHP and Fuzzy Axiomatic Design Based Approach Sun, 14 Sep 2014 09:33:30 +0000 We try to determine the best location for a bus garage, in which maintenance and repair activities are operated, for public transportation system in Istanbul. An integrated multicriteria decision making technique (MCDM) is used to obtain reliable results. Firstly, various criteria related to garage location selection are specified and weighted by fuzzy AHP (analytical hierarchy process). Then, these weights are used in fuzzy axiomatic design (AD) technique to determine the precedencies of the alternative garage locations. Özge Nalan Bilişik, Nurgül Demirtaş, Umut Rıfat Tuzkaya, and Hayri Baraçlı Copyright © 2014 Özge Nalan Bilişik et al. All rights reserved. A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders Sun, 14 Sep 2014 08:31:41 +0000 We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one. Young Ik Kim and Young Hee Geum Copyright © 2014 Young Ik Kim and Young Hee Geum. All rights reserved. Dynamics of a Predator-Prey System with Mixed Functional Responses Sun, 14 Sep 2014 08:08:55 +0000 A predator-prey system with two preys and one predator is considered. Especially, two different types of functional responses, Holling type and Beddington-DeAngelis type, are adopted. First, the boundedness of system is showed. Stabilities analysis of system is investigated via some properties about equilibrium points and stabilities of two subsystems without one of the preys of system. Also, persistence conditions of system are found out and some numerical examples are illustrated to substantiate our theoretical results. Hunki Baek and Dongseok Kim Copyright © 2014 Hunki Baek and Dongseok Kim. All rights reserved. Some Inevitable Remarks on “Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings” Thu, 11 Sep 2014 08:51:22 +0000 We advise that the proof of Theorem 12 given by Borcut et al. (2014) is not correct, and it cannot be corrected using the same technique. Furthermore, we present some similar results as an approximation to the opened question if that statement is valid. Hamed H. Alsulami, Antonio-Francisco Roldán-López-de-Hierro, Erdal Karapınar, and Stojan Radenović Copyright © 2014 Hamed H. Alsulami et al. All rights reserved. Solution of Moving Boundary Space-Time Fractional Burger’s Equation Thu, 11 Sep 2014 08:20:20 +0000 The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed. E. A.-B. Abdel-Salam, E. A. Yousif, Y. A. S. Arko, and E. A. E. Gumma Copyright © 2014 E. A.-B. Abdel-Salam et al. All rights reserved. Awakened Oscillations in Coupled Consumer-Resource Pairs Wed, 10 Sep 2014 08:19:38 +0000 The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses. Almaz Mustafin Copyright © 2014 Almaz Mustafin. All rights reserved. Pseudospectral Renormalization Method for Solitons in Quasicrystal Lattice with the Cubic-Quintic Nonlinearity Wed, 10 Sep 2014 07:03:37 +0000 We modified the spectral renormalization method as the pseudospectral renormalization method in order to find the localized solutions. The pseudospectral renormalization method can be applied to a large class of problems including different homogeneities. Using this computational method, we demonstrate the existence of two different solitons in optical media described by the self-focusing cubic and the self-defocusing quintic nonlinear Schrödinger equation with quasicrystal lattice. It is shown that there are two different lattice solitons corresponding to the first and the second renormalization factors for the self-focusing cubic and the self-defocusing quintic model. However, the self-focusing quintic nonlinearity without optical lattice does not support two different solitons. We showed that the lattice solitons corresponding to the first and the second renormalization factors have the same powers and amplitudes. We also demonstrate that quintic nonlinearity supports bistable solitons by adding the optical lattice such as a quasicrystal lattice. The linear and nonlinear stabilities of these solitons are investigated using direct simulation of the nonlinear Schrödinger equation with the cubic-quintic nonlinearity and its linearized equation. Nalan Antar Copyright © 2014 Nalan Antar. All rights reserved. Fair Optimization and Networks: Models, Algorithms, and Applications Wed, 10 Sep 2014 05:16:04 +0000 Wlodzimierz Ogryczak, Hanan Luss, Dritan Nace, and Michał Pióro Copyright © 2014 Wlodzimierz Ogryczak et al. All rights reserved. A Matrix PRNG with S-Box Output Filtering Mon, 08 Sep 2014 09:01:36 +0000 We describe a modification to a previously published pseudorandom number generator improving security while maintaining high performance. The proposed generator is based on the powers of a word-packed block upper triangular matrix and it is designed to be fast and easy to implement in software since it mainly involves bitwise operations between machine registers and, in our tests, it presents excellent security and statistical characteristics. The modifications include a new, key-derived s-box based nonlinear output filter and improved seeding and extraction mechanisms. This output filter can also be applied to other generators. Rafael Alvarez and Antonio Zamora Copyright © 2014 Rafael Alvarez and Antonio Zamora. All rights reserved. Mathematical Model of Movement of the Observation and Tracking Head of an Unmanned Aerial Vehicle Performing Ground Target Search and Tracking Mon, 08 Sep 2014 08:45:46 +0000 The paper presents the kinematics of mutual movement of an unmanned aerial vehicle (UAV) and a ground target. The controlled observation and tracking head (OTH) is a device responsible for observing the ground, searching for a ground target, and tracking it. The preprogrammed movement of the UAV on the circle with the simultaneous movement of the head axis on Archimedes’ spiral during searching for a ground target, both fixed (bunkers, rocket missiles launching positions, etc.) and movable (tanks, infantry fighting vehicles, etc.), is considered. Dynamics of OTH during the performance of the above mentioned activities is examined. Some research results are presented in a graphical form. Izabela Krzysztofik and Zbigniew Koruba Copyright © 2014 Izabela Krzysztofik and Zbigniew Koruba. All rights reserved. Robust AIC with High Breakdown Scale Estimate Mon, 08 Sep 2014 06:33:57 +0000 Akaike Information Criterion (AIC) based on least squares (LS) regression minimizes the sum of the squared residuals; LS is sensitive to outlier observations. Alternative criterion, which is less sensitive to outlying observation, has been proposed; examples are robust AIC (RAIC), robust Mallows Cp (RCp), and robust Bayesian information criterion (RBIC). In this paper, we propose a robust AIC by replacing the scale estimate with a high breakdown point estimate of scale. The robustness of the proposed methods is studied through its influence function. We show that, the proposed robust AIC is effective in selecting accurate models in the presence of outliers and high leverage points, through simulated and real data examples. Shokrya Saleh Copyright © 2014 Shokrya Saleh. All rights reserved. Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation Mon, 08 Sep 2014 00:00:00 +0000 We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented. Sergey Igorevich Kabanikhin, M. A. Shishlenin, D. B. Nurseitov, A. T. Nurseitova, and S. E. Kasenov Copyright © 2014 Sergey Igorevich Kabanikhin et al. All rights reserved. Advances in Matrices, Finite and Infinite, with Applications 2014 Sun, 07 Sep 2014 07:25:52 +0000 P. N. Shivakumar, Panayiotis J. Psarrakos, K. C. Sivakumar, Yang Zhang, and Carlos M. da Fonseca Copyright © 2014 P. N. Shivakumar et al. All rights reserved. Fuzzy Similar Priority Method for Mixed Attributes Wed, 03 Sep 2014 11:02:06 +0000 Fuzzy similar priority ratio method is to select the most suitable one to the specific object from feasible alternatives. However, this method considering only the index values of real number has its disadvantages of inaccuracy in result and complexity in calculation. So, this method was extended to handle mixed attributes including real number, interval number, triangular fuzzy number, and trapezoidal fuzzy number. The proposed method decides the optimal alternative by the minimum of integrated nearness degrees calculated by all index vectors and the fixed index vectors based on the theory of similarity. The improved method can not only address mixed attributes but also simplify the calculation and improve the accuracy of result. A case study illustrated this method. Jinshan Ma, Changsheng Ji, and Jing Sun Copyright © 2014 Jinshan Ma et al. All rights reserved. Grey Relational Analysis and Its Application Based on the Angle Perspective in Time Series Wed, 03 Sep 2014 09:08:47 +0000 The research scope of grey relational analysis has not been developed in recent years, and the exiting GRA models are all based on three perspectives, including distance perspective, slope perspective, and area perspective. Under this situation, a novel model called grey relational analysis based on angle perspective (GRAAP) was developed in this paper for the first time, and this model can expand the research scope of GRA. Like other GRA models, GRAAP not only has the properties of symmetry, uniqueness, comparability, and so forth but also can be used to make predictions, assessments, classifications, and so on. Finally, this novel model was proved to be rational and effective through a comparative study on the similar degree of four time series. Guodong Xu, Peng Guo, Xuemei Li, and Yingying Jia Copyright © 2014 Guodong Xu et al. All rights reserved. Fair Optimization and Networks: A Survey Wed, 03 Sep 2014 07:44:17 +0000 Optimization models related to designing and operating complex systems are mainly focused on some efficiency metrics such as response time, queue length, throughput, and cost. However, in systems which serve many entities there is also a need for respecting fairness: each system entity ought to be provided with an adequate share of the system’s services. Still, due to system operations-dependant constraints, fair treatment of the entities does not directly imply that each of them is assigned equal amount of the services. That leads to concepts of fair optimization expressed by the equitable models that represent inequality averse optimization rather than strict inequality minimization; a particular widely applied example of that concept is the so-called lexicographic maximin optimization (max-min fairness). The fair optimization methodology delivers a variety of techniques to generate fair and efficient solutions. This paper reviews fair optimization models and methods applied to systems that are based on some kind of network of connections and dependencies, especially, fair optimization methods for the location problems and for the resource allocation problems in communication networks. Wlodzimierz Ogryczak, Hanan Luss, Michał Pióro, Dritan Nace, and Artur Tomaszewski Copyright © 2014 Wlodzimierz Ogryczak et al. All rights reserved. The Congruence Class of the Solutions to a System of Matrix Equations Wed, 03 Sep 2014 07:17:38 +0000 We present the congruence class of the least-square and the minimum norm least-square solutions to the system of complex matrix equation by generalized singular value decomposition and canonical correlation decomposition. Yu-Ping Zhang and Chang-Zhou Dong Copyright © 2014 Yu-Ping Zhang and Chang-Zhou Dong. All rights reserved. Linear SVM-Based Android Malware Detection for Reliable IoT Services Wed, 03 Sep 2014 05:48:59 +0000 Current many Internet of Things (IoT) services are monitored and controlled through smartphone applications. By combining IoT with smartphones, many convenient IoT services have been provided to users. However, there are adverse underlying effects in such services including invasion of privacy and information leakage. In most cases, mobile devices have become cluttered with important personal user information as various services and contents are provided through them. Accordingly, attackers are expanding the scope of their attacks beyond the existing PC and Internet environment into mobile devices. In this paper, we apply a linear support vector machine (SVM) to detect Android malware and compare the malware detection performance of SVM with that of other machine learning classifiers. Through experimental validation, we show that the SVM outperforms other machine learning classifiers. Hyo-Sik Ham, Hwan-Hee Kim, Myung-Sup Kim, and Mi-Jung Choi Copyright © 2014 Hyo-Sik Ham et al. All rights reserved.