Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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. Laplacian Spectral Characterization of Some Unicyclic Graphs Wed, 03 Sep 2014 00:00:00 +0000 Let be the unicyclic graph with vertices obtained by attaching two paths of lengths and at two adjacent vertices of cycle . Let be the unicyclic graph with vertices obtained by attaching paths of lengths at the same vertex of cycle . In this paper, we prove that and are determined by their Laplacian spectra when is even. Lijun Yu, Hui Wang, and Jiang Zhou Copyright © 2014 Lijun Yu et al. All rights reserved. A New Pricing Scheme for Controlling Energy Storage Devices in Future Smart Grid Wed, 03 Sep 2014 00:00:00 +0000 Improvement of the overall efficiency of energy infrastructure is one of the main anticipated benefits of the deployment of smart grid technology. Advancement in energy storage technology and two-way communication in the electric network are indispensable components to achieve such a vision, while efficient pricing schemes and appropriate storage management are also essential. In this paper, we propose a universal pricing scheme which permits one to indirectly control the energy storage devices in the grid to achieve a more desirable aggregate demand profile that meets a particular target of the grid operator such as energy generation cost minimization and carbon emission reduction. Such a pricing scheme can potentially be applied to control the behavior of energy storage devices installed for integration of intermittent renewable energy sources that have permission to grid connection and will have broader applications as an increasing number of novel and low-cost energy storage technologies emerge. Jingwei Zhu, Michael Z. Q. Chen, and Baozhu Du Copyright © 2014 Jingwei Zhu et al. All rights reserved. Product Demand Forecasting and Dynamic Pricing considering Consumers’ Mental Accounting and Peak-End Reference Effects Tue, 02 Sep 2014 14:08:01 +0000 We introduce a demand forecasting model for a monopolistic company selling products to consumers with double-entry mental accounting, which means consumers experience pleasure when consuming goods or service and feel pains when paying for them. Moreover, as the monopolist changes prices, consumers form a reference price that adjusts an anchoring standard based on the lowest price that they perceived, namely, the peak-end anchoring. We obtain the steady state prices under three different payment schemes for two- and infinite-period. We also analyze the relationship between these steady prices and maximal profit and compare the steady state prices of different payment schemes by changing the double-entry mental accounting’s parameters through numerical examples. The proposed model is computationally tractable for demand forecasting of realistic size. Wenjie Bi and Mengqi Liu Copyright © 2014 Wenjie Bi and Mengqi Liu. All rights reserved. Active Power Filter DC Bus Voltage Piecewise Reaching Law Variable Structure Control Tue, 02 Sep 2014 12:15:26 +0000 The DC bus voltage stability control is one key technology to ensure that Active Power Filter (APF) operates stably. The external disturbances such as power grid and load fluctuation and the system parameters changing may affect the stability of APF DC bus voltage and the normal operation of APF. The mathematical model of DC bus voltage is established according to power balance principle and a DC bus voltage piecewise reaching law variable structure control algorithm is proposed to solve the above problem, and the design method is given. The simulation and experiment results proved that the proposed variable structure control algorithm can eliminate the chattering problem existing in traditional variable structure control effectively, is insensitive to system disturbance, and has good robustness and fast dynamic response speed and stable DC bus voltage with small fluctuation. The above advantages ensure the compensation effect of APF. Baolian Liu, Zujun Ding, Huanyu Zhao, and Defei Jin Copyright © 2014 Baolian Liu et al. All rights reserved. Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System Tue, 02 Sep 2014 11:27:15 +0000 A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results. Shengliang Guo, Zhijun Liu, and Huili Xiang Copyright © 2014 Shengliang Guo et al. All rights reserved. Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance Tue, 02 Sep 2014 11:07:11 +0000 This paper proposes a profile empirical likelihood for the partial parameters in ARMA models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method. Jinyu Li, Wei Liang, and Shuyuan He Copyright © 2014 Jinyu Li et al. All rights reserved. Improved Filter-SQP Algorithm with Active Set for Constrained Minimax Problems Tue, 02 Sep 2014 09:41:54 +0000 An improved filter-SQP algorithm with active set for constrained finite minimax problems is proposed. Firstly, an active constraint subset is obtained by a pivoting operation procedure. Then, a new quadratic programming (QP) subproblem is constructed based on the active constraint subset. The main search direction is obtained by solving this (QP) subproblem which is feasible at per iteration point and need not to consider the penalty function by using the filter technique. Under some suitable conditions, the global convergence of our algorithm is established. Finally, some numerical results are reported to show the effectiveness of the proposed algorithm. Zhijun Luo and Lirong Wang Copyright © 2014 Zhijun Luo and Lirong Wang. All rights reserved. Frank Aggregation Operators for Triangular Interval Type-2 Fuzzy Set and Its Application in Multiple Attribute Group Decision Making Tue, 02 Sep 2014 07:04:07 +0000 This paper investigates an approach to multiple attribute group decision-making (MAGDM) problems, in which the individual assessments are in the form of triangle interval type-2 fuzzy numbers (TIT2FNs). Firstly, some Frank operation laws of triangle interval type-2 fuzzy set (TIT2FS) are defined. Secondly, some Frank aggregation operators such as the triangle interval type-2 fuzzy Frank weighted averaging (TIT2FFWA) operator and the triangle interval type-2 fuzzy Frank weighted geometric (TIT2FFWG) operator are developed for aggregation TIT2FNs. Furthermore, some desirable properties of the two aggregation operators are analyzed in detail. Finally, an approach based on TIT2FFWA (or TIT2FFWG) operator to solve MAGDM is developed. An illustrative example about supplier selection is provided to illustrate the developed procedures. The results demonstrate the practicality and effectiveness of our new method. Jindong Qin and Xinwang Liu Copyright © 2014 Jindong Qin and Xinwang Liu. All rights reserved. On the Existence of Global Weak Solutions for a Weakly Dissipative Hyperelastic Rod Wave Equation Tue, 02 Sep 2014 00:00:00 +0000 Assuming that the initial value belongs to the space , we prove the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation in the space . The limit of the viscous approximation for the equation is used to establish the existence. Haibo Yan, Ls Yong, Yu Yang, and Yang Wang Copyright © 2014 Haibo Yan et al. All rights reserved. New Uncertainty Measure of Rough Fuzzy Sets and Entropy Weight Method for Fuzzy-Target Decision-Making Tables Mon, 01 Sep 2014 13:01:31 +0000 In the rough fuzzy set theory, the rough degree is used to characterize the uncertainty of a fuzzy set, and the rough entropy of a knowledge is used to depict the roughness of a rough classification. Both of them are effective, but they are not accurate enough. In this paper, we propose a new rough entropy of a rough fuzzy set combining the rough degree with the rough entropy of a knowledge. Theoretical studies and examples show that the new rough entropy of a rough fuzzy set is suitable. As an application, we introduce it into a fuzzy-target decision-making table and establish a new method for evaluating the entropy weight of attributes. Huani Qin and Darong Luo Copyright © 2014 Huani Qin and Darong Luo. All rights reserved. New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation Mon, 01 Sep 2014 09:58:19 +0000 The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics. Peng Guo, Xiang Wu, and Liangbi Wang Copyright © 2014 Peng Guo et al. All rights reserved. Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops Mon, 01 Sep 2014 08:50:37 +0000 Synthetic biology opens up the possibility of creating circuits that would not survive in the natural world and studying their behaviors in living cells, expanding our notion of biology. Based on this, we analyze on a synthetic biological system the effect of coupling between two instability-generating mechanisms. The systems considered are two topologically equivalent synthetic networks. In addition to simple periodic oscillations and stable steady state, the system can exhibit a variety of new modes of dynamic behavior: coexistence between two stable periodic regimes (birhythmicity) and coexistence of a stable periodic regime with a stable steady state (hard excitation). Birhythmicity and hard excitation have been proved to exist in biochemical networks. Through bifurcation analysis on these two synthetic cellular networks, we analyze the function of network structure for the collapse and revival of birhythmicity and hard excitation with the variation of parameters. The results have illustrated that the bifurcation space can be divided into four subspaces for which the dynamical behaviors of the system are generically distinct. Our analysis corroborates the results obtained by numerical simulation of the dynamics. Aimin Chen, Caixia Liu, and Junwei Wang Copyright © 2014 Aimin Chen et al. All rights reserved.