Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Multisorted Tree-Algebras for Hierarchical Resources Allocation Mon, 29 Jun 2015 08:46:11 +0000 This paper presents a generic abstract model for the study of disparities between goals and results in hierarchical multiresources allocation systems. In an organization, disparities in resource allocation may occur, when, after comparison of a resource allocation decision with an allocation reference goal or property, some agents have surplus resources to accomplish their tasks, while at the same time other agents have deficits of expected resources. In the real world, these situations are frequently encountered in organizations facing scarcity of resources and/or inefficient management. These disparities can be corrected using allocation decisions, by measuring and reducing gradually such disparities and their related costs, without totally canceling the existing resource distribution. While a lot of research has been carried out in the area of resource allocation, this specific class of problems has not yet been formally studied. The paper exposes the results of an exploratory research study of this class of problems. It identifies the commonalities of the family of hierarchical multiresource allocation systems and proposes the concept of multisorted tree-algebra for the modeling of these problems. The research presented here is not yet an in-depth descriptive research study of the mathematical theory of multisorted tree-algebra, but a formal study on modelling hierarchical multiresource allocation problems. Erick Patrick Zobo and Marcel Fouda Ndjodo Copyright © 2015 Erick Patrick Zobo and Marcel Fouda Ndjodo. All rights reserved. Shape Preserving Data Interpolation Using Rational Cubic Ball Functions Wed, 24 Jun 2015 06:19:36 +0000 A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness is . The outputs from a number of numerical experiments are presented. Ayser Nasir Hassan Tahat, Abd Rahni Mt Piah, and Zainor Ridzuan Yahya Copyright © 2015 Ayser Nasir Hassan Tahat et al. All rights reserved. Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames Mon, 22 Jun 2015 08:32:11 +0000 We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes. Martin Ehler Copyright © 2015 Martin Ehler. All rights reserved. Method of Integral Equations for the Problem of Electrical Tomography in a Medium with Ground Surface Relief Tue, 16 Jun 2015 07:14:24 +0000 The direct task of the subsurface exploration of a homogeneous medium with surface relief by the resistivity method is analyzed. To calculate the resistivity field for such a medium, the method of integral equations was successfully applied for the first time. The corresponding integral equation for the density of secondary current sources on the surface of the medium was established. The method of computational grid construction, adapted to the characteristics of the surface relief, was developed for the numerical solution of the integral equation. This method enables the calculation of the resistivity field of a point source on a surface that is not smooth and allows for steep ledges. Numerical examples of the calculation of resistivity fields and apparent resistivity are shown. The anomalies of apparent resistivity arising from the deviation of the surface shape from a flat medium were quantitatively established as model examples. Calculations of apparent resistivity for the direct current sounding method were carried out using modifications of the electrical tomography approach. Tolkyn Mirgalikyzy, Balgaisha Mukanova, and Igor Modin Copyright © 2015 Tolkyn Mirgalikyzy et al. All rights reserved. Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate Thu, 11 Jun 2015 09:22:02 +0000 The resonant tunneling device (RTD) has attracted much attention because of its unique negative differential resistance characteristic and its functional versatility and is more suitable for implementing the threshold logic gate. The universal logic gate has become an important unit circuit of digital circuit design because of its powerful logic function, while the threshold logic gate is a suitable unit to design the universal logic gate, but the function synthesis algorithm for the -variable logical function implemented by the RTD-based universal logic gate (UTLG) is relatively deficient. In this paper, three-variable threshold functions are divided into four categories; based on the Reed-Muller expansion, two categories of these are analyzed, and a new decomposition algorithm of the three-variable nonthreshold functions is proposed. The proposed algorithm is simple and the decomposition results can be obtained by looking up the decomposition table. Then, based on the Reed-Muller algebraic system, the arbitrary -variable function can be decomposed into three-variable functions, and a function synthesis algorithm for the -variable logical function implemented by UTLG and XOR2 is proposed, which is a simple programmable implementation. Maoqun Yao, Kai Yang, Congyuan Xu, and Jizhong Shen Copyright © 2015 Maoqun Yao et al. All rights reserved. A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton Thu, 11 Jun 2015 07:38:43 +0000 The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter with delay. Such delay is given by a fuzzy number due to the uncertainty of the effects of both pharmacological and intracellular delays. A cellular automaton is utilized to estimate the parameters of the system. The effects of antiretroviral therapy in the cellular automaton are modeled using a fuzzy rule-based system with two inputs: the medication potency and the treatment adhesion for three hypothetical individuals. For each of them, we determine the infection rate of CD4+ T lymphocytes, which is different from zero, as opposed to other studies reported in the literature. As the infection rate is considered a fuzzy parameter, we determine the fuzzy and the defuzzified solutions for the infected CD4+ T lymphocytes. We obtain the maximum values of infected cells for individuals that receive low, medium, and high potency medication and treatment adhesion. The results obtained are in accordance qualitatively with what would be expected in a real situation. R. Motta Jafelice, C. A. F. Silva, L. C. Barros, and R. C. Bassanezi Copyright © 2015 R. Motta Jafelice et al. All rights reserved. Optimization of the Aedes aegypti Control Strategies for Integrated Vector Management Mon, 08 Jun 2015 13:52:40 +0000 We formulate an infinite-time quadratic functional minimization problem of Aedes aegypti mosquito population. Three techniques of mosquito population management, chemical insecticide control, sterile insect technique control, and environmental carrying capacity reduction, are combined in order to obtain the most sustainable strategy to reduce mosquito population and consequently dengue disease. The solution of the optimization control problem is based on the ideas of the Dynamic Programming and Lyapunov Stability using State-Dependent Riccati Equation (SDRE) control method. Different scenarios are analyzed combining three mentioned population management efforts in order to assess the most sustainable policy to reduce the mosquito population. Marat Rafikov, Elvira Rafikova, and Hyun Mo Yang Copyright © 2015 Marat Rafikov et al. All rights reserved. On -Vertex-Antimagic Edge Labeling of Regular Graphs Mon, 08 Jun 2015 13:29:28 +0000 An -vertex-antimagic edge labeling (or an -VAE labeling, for short) of is a bijective mapping from the edge set of a graph to the set of integers with the property that the vertex-weights form an arithmetic sequence starting from and having common difference , where and are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called -antimagic if it admits an -VAE labeling. In this paper, we investigate the existence of -VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept -vertex-antimagic edge deficiency, as an extension of -VAE labeling, for measuring how close a graph is away from being an -antimagic graph. Furthermore, the -VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks. Martin Bača, Andrea Semaničová-Feňovčíková, Tao-Ming Wang, and Guang-Hui Zhang Copyright © 2015 Martin Bača et al. All rights reserved. A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems Mon, 08 Jun 2015 12:34:27 +0000 A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in predictor-corrector form are implemented in block form as simultaneous numerical integrators over nonoverlapping intervals. Numerical results obtained using the proposed block form reveal that the new methods are efficient and highly competitive with existing methods in the literature. F. F. Ngwane and S. N. Jator Copyright © 2015 F. F. Ngwane and S. N. Jator. All rights reserved. The Hadamard Product of a Nonsingular General H-Matrix and Its Inverse Transpose Is Diagonally Dominant Thu, 04 Jun 2015 07:23:28 +0000 We study the combined matrix of a nonsingular H-matrix. These matrices can belong to two different H-matrices classes: the most common, invertible class, and one particular class named mixed class. Different results regarding diagonal dominance of the inverse matrix and the combined matrix of a nonsingular H-matrix belonging to the referred classes are obtained. We conclude that the combined matrix of a nonsingular H-matrix is always diagonally dominant and then it is an H-matrix. In particular, the combined matrix in the invertible class remains in the same class. Rafael Bru, Maria T. Gassó, Isabel Giménez, and José A. Scott Copyright © 2015 Rafael Bru et al. All rights reserved. Corrigendum to “Solving Dynamic Traveling Salesman Problem Using Dynamic Gaussian Process Regression” Sun, 31 May 2015 14:25:18 +0000 Stephen M. Akandwanaho, Aderemi O. Adewumi, and Ayodele A. Adebiyi Copyright © 2015 Stephen M. Akandwanaho et al. All rights reserved. Perturbation and Truncation of Probability Generating Function Methods for Stiff Chemical Reactions Thu, 28 May 2015 11:40:28 +0000 One can reformulate chemical master equations of the stochastic reaction network into a partial differential equation (PDE) of a probability generating function (PGF). In this paper, we present two improvements in such PGF-PDE approach, based on perturbation and double-truncation, respectively. The stiff system that involves fast and slow reactions together often requires high computational cost. By applying the perturbation method to PGF-PDEs, we expand the equation in terms of a small reaction rate which is often responsible for such stiffness of the system. Also by doubly truncating, we dump relatively small terms and reduce the computational load significantly at each time step. The terms corresponding to rare events are sieved out through truncations of Taylor expansion. It is shown through numerical examples of enzyme kinetics, transition model, and Brusselator model that the suggested method is accurate and efficient for approximation of the state probabilities. Soyeong Jeong, Pilwon Kim, and Chang Hyeong Lee Copyright © 2015 Soyeong Jeong et al. All rights reserved. Synchronized Control for Five-Story Building under Earthquake Loads Thu, 07 May 2015 11:45:25 +0000 Synchronized control is implemented for a five-story building under earthquake loads and its capabilities are investigated for protection of building under earthquake. In this regard, we applied control algorithm in form of synchronized control for structural vibration reduction. Simulation results of modeling indicated that not only the provided control is able to reduce the responses of vibrations for the structure, but also it is even capable of supplying the objectives of synchronized control at the same time. Numerical results for uncontrolled, traditional control and synchronized control coupled with algorithm are presented. It is shown that for El Centro and Bam earthquakes the synchronized control is more efficient to reduce damage to the given structures. Javad Mesbahi and Alaeddin Malek Copyright © 2015 Javad Mesbahi and Alaeddin Malek. All rights reserved. Piecewise Model and Parameter Obtainment of Governor Actuator in Turbine Tue, 05 May 2015 06:06:50 +0000 The governor actuators in some heat-engine plants have nonlinear valves. This nonlinearity of valves may lead to the inaccuracy of the opening and closing time constants calculated based on the whole segment fully open and fully close experimental test curves of the valve. An improved mathematical model of the turbine governor actuator is proposed to reflect the nonlinearity of the valve, in which the main and auxiliary piecewise opening and closing time constants instead of the fixed oil motive opening and closing time constants are adopted to describe the characteristics of the actuator. The main opening and closing time constants are obtained from the linear segments of the whole fully open and close curves. The parameters of proportional integral derivative (PID) controller are identified based on the small disturbance experimental tests of the valve. Then the auxiliary opening and closing time constants and the piecewise opening and closing valve points are determined by the fully open/close experimental tests. Several testing functions are selected to compare genetic algorithm and particle swarm optimization algorithm (GA-PSO) with other basic intelligence algorithms. The effectiveness of the piecewise linear model and its parameters are validated by practical power plant case studies. Jie Zhao, Li Wang, Dichen Liu, and Jun Wang Copyright © 2015 Jie Zhao et al. All rights reserved. Stochastic Multicriteria Acceptability Analysis Based on Choquet Integral Sun, 03 May 2015 06:12:12 +0000 To reflect the interactions among criteria, Choquet integral is employed to stochastic multicriteria acceptability analysis. Models are first given to roughly identify the best and worst ranking orders of each alternative, based on which the weight information spaces are explored to support some alternative for ranking at some position and calculate the acceptability indices of alternatives. Models are then given to analyze the characters of information spaces, which can describe what kind of information supports alternatives for ranking at some position and can give an analysis about the effect of characters on the decision result. The proposed method considers not only the interactions between two criteria, but also the interactions among three, four, and more criteria. The proposed method can be considered as an extension of the existing ones. Meimei Xia Copyright © 2015 Meimei Xia. All rights reserved. Taming Chaos by Linear Regulation with Bound Estimation Tue, 28 Apr 2015 06:50:51 +0000 Chaos control has become an important area of research and consequently many approaches have been proposed to control chaos. This paper proposes a linear regulation method. Different from the existing approaches is that it can provide region of attraction while estimating the bounding behaviour of the norm of the states. The proposed method also possesses design flexibility and can be easily used to cater for special requirement such that control signal should be generated via single input, single state, static feedback and so forth. The applications to the Tigan system, the Genesio chaotic system, the novel chaotic system, and the Lorenz chaotic system justify the above claims. Jiqiang Wang and Weijian Chen Copyright © 2015 Jiqiang Wang and Weijian Chen. All rights reserved. A Time Scales Approach to Coinfection by Opportunistic Diseases Tue, 21 Apr 2015 12:22:35 +0000 Traditional biomedical approaches treat diseases in isolation, but the importance of synergistic disease interactions is now recognized. As a first step we present and analyze a simple coinfection model for two diseases simultaneously affecting a population. The host population is affected by the primary disease, a long-term infection whose dynamics is described by a SIS model with demography, which facilitates individuals acquiring a second disease, secondary (or opportunistic) disease. The secondary disease is instead a short-term infection affecting only the primary infected individuals. Its dynamics is also represented by a SIS model with no demography. To distinguish between short- and long-term infection the complete model is written as a two-time-scale system. The primary disease acts at the slow time scale while the secondary disease does at the fast one, allowing a dimension reduction of the system and making its analysis tractable. We show that an opportunistic disease outbreak might change drastically the outcome of the primary epidemic process, although it does among the outcomes allowed by the primary disease. We have found situations in which either acting on the opportunistic disease transmission or recovery rates or controlling the susceptible and infected population size allows eradicating/promoting disease endemicity. Marcos Marvá, Ezio Venturino, and Rafael Bravo de la Parra Copyright © 2015 Marcos Marvá et al. All rights reserved. On the Study of Oscillating Viscous Flows by Using the Adomian-Padé Approximation Thu, 16 Apr 2015 09:22:18 +0000 The Adomian-Padé technique is applied to examine two oscillating viscous flows, the Stokes’ second problem and the pressure-driven pulsating flow. Main purposes for studying oscillating flows are not only to verify the accuracy of the approximation solution, but also to provide a basis for analyzing more problems by the present method with the help of Fourier analysis. Results show that the Adomian-Padé approximation presents a very excellent behavior in comparison with the exact solution of Stokes’ second problem. For the pulsating flow, only the Adomian decomposition method is required to perform the calculation as the fluid domain is finite where the Padé approximant may not provide a better solution. Based on present results, more problems can be mathematically solved by using the Adomian-Padé technique, the Fourier analysis, and powerful computers. Chi-Min Liu Copyright © 2015 Chi-Min Liu. All rights reserved. MIMO Detection for High Order QAM by Canonical Dual Approach Sun, 05 Apr 2015 13:47:45 +0000 We develop a canonical dual approach for solving the MIMO problem. First, a special linear transformation is introduced to reformulate the original problem into a constrained quadratic programming problem. Then, we derive a canonical dual problem which is piecewise continuous problem with no duality gap. Under certain conditions, the canonical problem becomes a concave maximization dual problem over a convex feasible domain. By getting the stationary point of the canonical dual problem, we can find either an optimal or approximate solution of the original problem. A gradient decent algorithm is proposed to solve the MIMO problem and simulation results are provided to demonstrate the effectiveness of the method. Ye Tian and Jr-Fong Dang Copyright © 2015 Ye Tian and Jr-Fong Dang. All rights reserved. Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms Tue, 31 Mar 2015 12:29:12 +0000 We study lightlike hypersurfaces of an indefinite generalized Sasakian space form , with indefinite trans-Sasakian structure of type , subject to the condition that the structure vector field of is tangent to . First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type . Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form. Dae Ho Jin Copyright © 2015 Dae Ho Jin. All rights reserved. Computational Science in Smart Grids and Energy Systems Sun, 29 Mar 2015 07:57:43 +0000 Hongjie Jia, Ned Djilali, Xinghuo Yu, H. D. Chiang, and Gongnan Xie Copyright © 2015 Hongjie Jia et al. All rights reserved. Estimating Potential Evapotranspiration by Missing Temperature Data Reconstruction Thu, 26 Mar 2015 12:33:29 +0000 This work studies the statistical characteristics of potential evapotranspiration calculations and their relevance within the water balance used to determine water availability in hydrological basins. The purpose of this study was as follows: first, to apply a missing data reconstruction scheme in weather stations of the Rio Queretaro basin; second, to reduce the generated uncertainty of temperature data: mean, minimum, and maximum values in the evapotranspiration calculation which has a paramount importance in the manner of obtaining the water balance at any hydrological basin. The reconstruction of missing data was carried out in three steps: (1) application of a 4-parameter sinusoidal type regression to temperature data, (2) linear regression to residuals to obtain a regional behavior, and (3) estimation of missing temperature values for a certain year and during a certain season within the basin under study; estimated and observed temperature values were compared. Finally, using the obtained temperature values, the methods of Hamon, Papadakis, Blaney and Criddle, Thornthwaite, and Hargreaves were employed to calculate potential evapotranspiration that was compared to the real observed values in weather stations. With the results obtained from the application of this procedure, the surface water balance was corrected for the case study. Eladio Delgadillo-Ruiz, Eusebio Jr. Ventura-Ramos, Julián González Trinidad, Hugo Enrique Júnez-Ferreira, Carlos Francisco Bautista-Capetillo, and Olivia Delgadillo-Ruiz Copyright © 2015 Eladio Delgadillo-Ruiz et al. All rights reserved. Iterative Methods and Applications 2014 Thu, 26 Mar 2015 07:51:34 +0000 Giuseppe Marino, Filomena Cianciaruso, Claudio H. Morales, Luigi Muglia, and D. R. Sahu Copyright © 2015 Giuseppe Marino et al. All rights reserved. A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications Wed, 25 Mar 2015 12:19:58 +0000 Solving systems of nonlinear equations plays a major role in engineering problems. We present a new family of optimal fourth-order Jarratt-type methods for solving nonlinear equations and extend these methods to solve system of nonlinear equations. Convergence analysis is given for both cases to show that the order of the new methods is four. Cost of computations, numerical tests, and basins of attraction are presented which illustrate the new methods as better alternates to previous methods. We also give an application of the proposed methods to well-known Burger's equation. Moin-ud-Din Junjua, Saima Akram, Nusrat Yasmin, and Fiza Zafar Copyright © 2015 Moin-ud-Din Junjua et al. All rights reserved. Lie Group Analysis on Brownian Motion and Thermophoresis Effect on Free Convective Boundary-Layer Flow on a Vertical Cylinder Embedded in a Nanofluid-Saturated Porous Medium Wed, 25 Mar 2015 08:47:45 +0000 Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters. Mohammad Ferdows, Mohammed Abdul Ali Hamad, and Mohamed Ali Copyright © 2015 Mohammad Ferdows et al. All rights reserved. Modeling and Control of Complex Dynamic Systems 2014 Wed, 25 Mar 2015 08:42:43 +0000 Zhiwei Gao, De-Xing Kong, and Michael Z. Q. Chen Copyright © 2015 Zhiwei Gao et al. All rights reserved. Advanced Mathematics and Numerical Modeling of IoT Wed, 25 Mar 2015 08:15:04 +0000 Young-Sik Jeong, Mohammad S. Obaidat, Jianhua Ma, and Laurence T. Yang Copyright © 2015 Young-Sik Jeong et al. All rights reserved. Parallel Dynamical Systems over Graphs and Related Topics: A Survey Tue, 24 Mar 2015 13:05:58 +0000 In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph. The update of the states is determined by the relations of the entities and some local functions which together constitute (global) evolution operator of the dynamical system. If the states of the entities are updated in a synchronous manner, the system is called a parallel dynamical system. This paper is devoted to review the main results on the dynamical behavior of parallel dynamical systems over graphs which constitute a generic tool for modeling discrete processes. Juan A. Aledo, Silvia Martinez, and Jose C. Valverde Copyright © 2015 Juan A. Aledo et al. All rights reserved. Numerical Methods of Complex Valued Linear Algebraic System Tue, 24 Mar 2015 09:49:17 +0000 Shi-Liang Wu, Shu-Qian Shen, Masoud Hajarian, Jia Liu, and Lev A. Krukier Copyright © 2015 Shi-Liang Wu et al. All rights reserved. LSMR Iterative Method for General Coupled Matrix Equations Mon, 23 Mar 2015 13:55:49 +0000 By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations , , (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups , such as symmetric, generalized bisymmetric, and -symmetric matrix groups. By this iterative method, for any initial matrix group , a solution group can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method. F. Toutounian, D. Khojasteh Salkuyeh, and M. Mojarrab Copyright © 2015 F. Toutounian et al. All rights reserved.