Journal of Applied Mathematics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. A Method to Construct Generalized Fibonacci Sequences Sun, 14 Feb 2016 12:15:10 +0000 The main purpose of this paper is to study the convergence properties of Generalized Fibonacci Sequences and the series of partial sums associated with them. When the proper values of an real matrix are real and different, we give a necessary and sufficient condition for the convergence of the matrix sequence to a matrix . Adalberto García-Máynez and Adolfo Pimienta Acosta Copyright © 2016 Adalberto García-Máynez and Adolfo Pimienta Acosta. All rights reserved. Steady Flow of Couple-Stress Fluid in Constricted Tapered Artery: Effects of Transverse Magnetic Field, Moving Catheter, and Slip Velocity Wed, 03 Feb 2016 07:29:21 +0000 Steady flow of a couple-stress fluid in constricted tapered artery has been studied under the effects of transverse magnetic field, moving catheter, and slip velocity. With the help of Bessel’s functions, analytic expressions for axial velocity, flow rate, impedance, and wall shear stress have been obtained. It is of interest to note that these solutions can be used for different types of fluid flow in tubes and not only the case of blood. The effects of various geometric parameters, the parameters arising out of the fluid considered and the magnetic field, are discussed by considering the slip velocity, the catheter velocity, and tapering angle. The study of the above model is very important as it has direct applications in the treatment of cardiovascular diseases. Hamzah Bakhti and Lahcen Azrar Copyright © 2016 Hamzah Bakhti and Lahcen Azrar. All rights reserved. Chemical Entropy Generation and MHD Effects on the Unsteady Heat and Fluid Flow through a Porous Medium Wed, 20 Jan 2016 09:42:04 +0000 Chemical entropy generation and magnetohydrodynamic effects on the unsteady heat and fluid flow through a porous medium have been numerically investigated. The entropy generation due to the use of a magnetic field and porous medium effects on heat transfer, fluid friction, and mass transfer have been analyzed numerically. Using a similarity transformation, the governing equations of continuity, momentum, and energy and concentration equations, of nonlinear system, were reduced to a set of ordinary differential equations and solved numerically. The effects of unsteadiness parameter, magnetic field parameter, porosity parameter, heat generation/absorption parameter, Lewis number, chemical reaction parameter, and Brinkman number parameter on the velocity, the temperature, the concentration, and the entropy generation rates profiles were investigated and the results were presented graphically. Gamal M. Abdel-Rahman Rashed Copyright © 2016 Gamal M. Abdel-Rahman Rashed. All rights reserved. Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints Wed, 06 Jan 2016 11:21:02 +0000 Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example. A. Srinivasan and G. Geetharamani Copyright © 2016 A. Srinivasan and G. Geetharamani. All rights reserved. The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission Tue, 05 Jan 2016 13:40:59 +0000 An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction number is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four-dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results. Raid Kamel Naji and Reem Mudar Hussien Copyright © 2016 Raid Kamel Naji and Reem Mudar Hussien. All rights reserved. The Optimal Insurance Policy for the General Fixed Cost of Handling an Indemnity under Rank-Dependent Expected Utility Thu, 31 Dec 2015 05:51:42 +0000 Based on Bernard et al.’s research, we focus on the Pareto optimal insurance design with the insured’s Rank-Dependent Expected Utility (RDEU). Compared with their previous work, our novelties are the more general fixed cost function of the insurer and the discussion of adverse selection and moral hazard. In particular, Bernard et al. only consider the case in which the fixed cost function of handling an indemnity is the linear function. However, the fixed cost function is not just linear functions in real insurance market. So, we explore the more general fixed cost function including both the linear and nonlinear functions. On the other hand, we consider adverse selection and moral hazard which are involved by Bernard et al. Leading adverse selection and moral hazard into our research makes our results more practical and meaningful. Moreover, we provide an insight into the sensitivity of an optimal solution for the insured’s initial wealth and the parameters related to the fixed cost function of handling an indemnity. We further compare the two different utility functions of the insured in terms of influence of optimal policy analysis. Liurui Deng Copyright © 2015 Liurui Deng. All rights reserved. Extremal Trees with respect to Number of -Edge Colourings Mon, 14 Dec 2015 06:51:11 +0000 We determine the smallest and the largest number of -edge colourings in trees. We prove that the star is a unique tree that maximizes the number of all of the -edge colourings and that the path is a unique tree that minimizes it. Krzysztof Piejko Copyright © 2015 Krzysztof Piejko. All rights reserved. Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition Sun, 06 Dec 2015 11:25:46 +0000 Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process. Igor V. Malyk Copyright © 2015 Igor V. Malyk. All rights reserved. Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms Wed, 02 Dec 2015 14:19:52 +0000 The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases. M. Mustafa Bahşi and Mehmet Çevik Copyright © 2015 M. Mustafa Bahşi and Mehmet Çevik. All rights reserved. Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media Sun, 29 Nov 2015 09:09:47 +0000 Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well. Yu Bai, Ali Harajli, and Yunping Xi Copyright © 2015 Yu Bai et al. All rights reserved. Explicit Solutions for the Solomon-Wilson-Alexiades’s Mushy Zone Model with Convective or Heat Flux Boundary Conditions Mon, 23 Nov 2015 11:08:08 +0000 We complete the Solomon-Wilson-Alexiades’s mushy zone model (Solomon, 1982) for the one-phase Lamé-Clapeyron-Stefan problem by obtaining explicit solutions when a convective or heat flux boundary condition is imposed on the fixed face for a semi-infinite material. We also obtain the necessary and sufficient condition on data in order to get the explicit solutions for both cases which is new with respect to the original model. Moreover, when these conditions are satisfied, the two phase-change problems are equivalent to the same problem with a temperature boundary condition on the fixed face and therefore an inequality for the coefficient which characterized one of the two free interfaces of the model is also obtained. Domingo A. Tarzia Copyright © 2015 Domingo A. Tarzia. All rights reserved. Motion of Bishop Frenet Offsets of Ruled Surfaces in Thu, 19 Nov 2015 14:17:24 +0000 The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space . In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. H. N. Abd-Ellah Copyright © 2015 H. N. Abd-Ellah. All rights reserved. Algebrization of Nonautonomous Differential Equations Mon, 09 Nov 2015 09:53:18 +0000 Given a planar system of nonautonomous ordinary differential equations, , conditions are given for the existence of an associative commutative unital algebra with unit and a function on an open set such that and the maps and are Lorch differentiable with respect to for all , where and represent variables in . Under these conditions the solutions of the differential equation over define solutions of the planar system. María Aracelia Alcorta-García, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, and Elifalet López-González Copyright © 2015 María Aracelia Alcorta-García et al. All rights reserved. Total Graph Interpretation of the Numbers of the Fibonacci Type Mon, 19 Oct 2015 13:53:33 +0000 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give the lower bound and the upper bound for the number of all -edge colourings in trees. Urszula Bednarz, Iwona Włoch, and Małgorzata Wołowiec-Musiał Copyright © 2015 Urszula Bednarz et al. All rights reserved. Nature-Inspired Algorithms for Real-World Optimization Problems Wed, 07 Oct 2015 10:35:16 +0000 Wei Fang, Xiaodong Li, Mengjie Zhang, and Mengqi Hu Copyright © 2015 Wei Fang et al. All rights reserved. Numerical Study on Similarity of Plume’s Infrared Radiation from Reduced Scaling Solid Rocket Mon, 05 Oct 2015 12:52:26 +0000 Similarity of plume radiation between reduced scaling solid rocket models and full scale ones in ground conditions has been taken for investigation. Flow and radiation of plume from solid rockets with scaling ratio from 0.1 to 1 have been computed. The radiative transfer equation (RTE) is solved by the finite volume method (FVM) in infrared band 2~6 μm. The spectral characteristics of plume gases have been calculated with the weighted-sum-of-gray-gas (WSGG) model, and those of the Al2O3 particles have been solved by the Mie scattering model. Our research shows that, with the decreasing scaling ratio of the rocket engine, the radiation intensity of the plume decreases with 1.5~2.5 power of the scaling ratio. The infrared radiation of the plume gases shows a strong spectral dependency, while that of the Al2O3 particles shows grey property. Spectral radiation intensity of the high temperature core of the solid rocket plume increases greatly in the peak absorption spectrum of plume gases. Al2O3 particle is the major radiation composition in the rocket plume, whose scattering coefficient is much larger than its absorption coefficient. There is good similarity between spectral variations of plumes from different scaling solid rockets. The directional plume radiation rises with the increasing azimuth angle. Xiaoying Zhang and Rui Li Copyright © 2015 Xiaoying Zhang and Rui Li. All rights reserved. Metaheuristic Approaches for Hydropower System Scheduling Mon, 05 Oct 2015 07:04:19 +0000 This paper deals with the short-term scheduling problem of hydropower systems. The objective is to meet the daily energy demand in an economic and safe way. The individuality of the generating units and the nonlinearity of their efficiency curves are taken into account. The mathematical model is formulated as a dynamic, mixed integer, nonlinear, nonconvex, combinatorial, and multiobjective optimization problem. We propose two solution methods using metaheuristic approaches. They combine Genetic Algorithm with Strength Pareto Evolutionary Algorithm and Ant Colony Optimization. Both approaches are divided into two phases. In the first one, to maximize the plant’s net generation, the problem is solved for each hour of the day (static dispatch). In the second phase, to minimize the units’ switching on-off, the day is considered as a whole (dynamic dispatch). The proposed methodology is applied to two Brazilian hydroelectric plants, in cascade, that belong to the national interconnected system. The nondominated solutions from both approaches are presented. All of them meet demand respecting the physical, electrical, and hydraulic constraints. Ieda G. Hidalgo, Regiane S. de Barros, Jéssica P. T. Fernandes, João Paulo F. Estrócio, and Paulo B. Correia Copyright © 2015 Ieda G. Hidalgo et al. All rights reserved. Coincidence Detection Using Spiking Neurons with Application to Face Recognition Sun, 04 Oct 2015 08:52:02 +0000 We elucidate the practical implementation of Spiking Neural Network (SNN) as local ensembles of classifiers. Synaptic time constant is used as learning parameter in representing the variations learned from a set of training data at classifier level. This classifier uses coincidence detection (CD) strategy trained in supervised manner using a novel supervised learning method called Prediction which adjusts the precise timing of output spikes towards the desired spike timing through iterative adaptation of . This paper also discusses the approximation of spike timing in Spike Response Model (SRM) for the purpose of coincidence detection. This process significantly speeds up the whole process of learning and classification. Performance evaluations with face datasets such as AR, FERET, JAFFE, and CK+ datasets show that the proposed method delivers better face classification performance than the network trained with Supervised Synaptic-Time Dependent Plasticity (STDP). We also found that the proposed method delivers better classification accuracy than nearest neighbor, ensembles of NN, and Support Vector Machines. Evaluation on several types of spike codings also reveals that latency coding delivers the best result for face classification as well as for classification of other multivariate datasets. Fadhlan Kamaruzaman, Amir Akramin Shafie, and Yasir M. Mustafah Copyright © 2015 Fadhlan Kamaruzaman et al. All rights reserved. Numerical Investigation of Laminar Natural Convection in Inclined Square Enclosure with the Influence of Discrete Heat Source Thu, 01 Oct 2015 11:52:47 +0000 Natural convection heat transfer in a two-dimensional square enclosure at various angles of inclination is investigated numerically using a finite volume based computational procedure. The heat transfer is from a constant temperature heat source of finite length centred at one of the walls to the cold wall on the opposite side while the remaining walls are insulated. The effect of area ratio of the heat source from 0.2 to 1.0, Rayleigh number Ra from 103 to 107, and angle of inclination of the enclosure varying from 0° to 360° on the flow field and heat transfer characteristics are investigated. Streamline and isothermal line patterns are found to be similar at low Rayleigh numbers whereas at high Rayleigh numbers the differences are significant due to the influence of the parameters considered. Average Nusselt number decreases drastically as the position of the heat source is moved above the horizontal centre line of the enclosure. Correlation of the average Nusselt number which depends on the parameters of interest is obtained in the general form . The correlation coefficients are determined by multiple regression analysis for the entire range of Rayleigh numbers analysed and the values found by correlation equations are in good agreement with the numerical results. Chithra Devaraj, Eswaramurthi Muthuswamy, and Sundararaj Kandasamy Copyright © 2015 Chithra Devaraj et al. All rights reserved. Gravitational Search Algorithm and Selection Approach for Optimal Distribution Network Configuration Based on Daily Photovoltaic and Loading Variation Thu, 01 Oct 2015 11:43:14 +0000 Network reconfiguration is an effective approach to reduce the power losses in distribution system. Recent studies have shown that the reconfiguration problem considering load profiles can give a significant improvement on the distribution network performance. This work proposes a novel method to determine the optimal daily configuration based on variable photovoltaic (PV) generation output and the load profile data. A good combination and coordination between these two varying data may give the lowest power loss in the system. Gravitational Search Algorithm (GSA) is applied to determine the optimum tie switches positions for 33-Bus distribution system. GSA based proposed method is also compared with Evolutionary Programming (EP) to examine the effectiveness of GSA algorithm. Obtained results show that the proposed optimal daily configuration method is able to improve the distribution network performance in term of its power loss reduction, number of switching minimization and voltage profile improvement. Koong Gia Ing, H. Mokhlis, H. A. Illias, M. M. Aman, and J. J. Jamian Copyright © 2015 Koong Gia Ing et al. All rights reserved. Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient Thu, 01 Oct 2015 11:38:02 +0000 An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated. Te-Wen Tu and Sen-Yung Lee Copyright © 2015 Te-Wen Tu and Sen-Yung Lee. All rights reserved. Migrating Birds Optimization for the Seaside Problems at Maritime Container Terminals Thu, 01 Oct 2015 11:36:22 +0000 Sea freight transportation involves moving huge amounts of freights among maritime locations widely spaced by means of container vessels. The time required to serve container vessels is the most relevant indicator when assessing the competitiveness of a maritime container terminal. In this paper, two main logistic problems stemming from the transshipment of containers in the seaside of a maritime container terminal are addressed, namely, the Berth Allocation Problem aimed at allocating and scheduling incoming vessels into berthing positions along the quay and the Quay Crane Scheduling Problem, whose objective is to schedule the loading and unloading tasks associated with a container vessel. For solving them, two Migrating Birds Optimization (MBO) approaches are proposed. The MBO is a recently proposed nature-inspired algorithm based on the V-formation flight of migrating birds. In this algorithm, a set of solutions of the problem at hand, called birds, cooperate among themselves during the search process by sharing information within a V-line formation. The computational experiments performed over well-known problem instances reported in the literature show that the performance of our proposed MBO approaches is highly competitive and presents a better performance in terms of running time than the best approximate approach proposed in the literature. Eduardo Lalla-Ruiz, Christopher Expósito-Izquierdo, Jesica de Armas, Belén Melián-Batista, and J. Marcos Moreno-Vega Copyright © 2015 Eduardo Lalla-Ruiz et al. All rights reserved. An UWB LNA Design with PSO Using Support Vector Microstrip Line Model Thu, 01 Oct 2015 11:33:14 +0000 A rigorous and novel design procedure is constituted for an ultra-wideband (UWB) low noise amplifier (LNA) by exploiting the 3D electromagnetic simulator based support vector regression machine (SVRM) microstrip line model. First of all, in order to design input and output matching circuits (IMC-OMC), source and load termination impedance of matching circuit, which are necessary to obtain required input VSWR (), noise (), and gain (), are determined using performance characterisation of employed transistor, NE3512S02, between 3 and 8 GHz frequencies. After the determination of the termination impedance, to provide this impedance with IMC and OMC, dimensions of microstrip lines are obtained with simple, derivative-free, easily implemented algorithm Particle Swarm Optimization (PSO). In the optimization of matching circuits, highly accurate and fast SVRM model of microstrip line is used instead of analytical formulations. ADCH-80a is used to provide ultra-wideband RF choking in DC bias. During the design process, it is aimed that = 1.85, = , and = all over operating frequency band. Measurements taken from the realized LNA demonstrate the success of this approximation over the band. Salih Demirel, Filiz Gunes, and A. Kenan Keskin Copyright © 2015 Salih Demirel et al. All rights reserved. Coupled Analysis of the Film-Cooling and Infrared Characteristics of an Axisymmetric Vectored Nozzle Thu, 01 Oct 2015 08:33:36 +0000 This study adopts a narrow band model to investigate the cooling and radiation of a vectoring nozzle and to compute the gas spectral characteristic in infrared band. The radiative heat transfer between the hot gas and the wall is considered with an enclosure model. The calculation of film cooling is performed through a cooling effectiveness method. A coupled heat balance equation of heat flux and wall temperature is established on the multilayer structure of the nozzle, including the wall, heat shield, and outer shield, and a Newton-Raphson scheme is taken for solution. Temperature on the expansion part of an experimental nozzle in NASA TN D-1988 is investigated for verification. Another vectoring nozzle with a multirow of film cooling is also investigated. This study shows that the film in the heat shield remarkably cools the convergent part of the nozzle, thereby increasing the temperature on the expansion part of the nozzle. The deflection of the nozzle can change the distribution of the wall temperature and the radiation on the expansion part, which is lower on the deflection side than on the opposite side. The radiation from the nozzle outlet is high, particularly along the deflection direction in the rear hemisphere. Xiaoying Zhang and Rui Li Copyright © 2015 Xiaoying Zhang and Rui Li. All rights reserved. Effect of Mesh on Springback in 3D Finite Element Analysis of Flexible Microrolling Thu, 01 Oct 2015 07:28:32 +0000 In flexible microrolling, springback in thickness direction is a critical indicator to determine the forming quality. Accurate prediction of springback is one of the significant aspects in the finite element analysis of flexible microrolling. Meshing is a step of great importance in finite element analysis of manufacturing process as it directly determines the accuracy of the FEA results as well as the requested computational time. This paper presents a numerical study on revealing the mesh effects on the accuracy of springback estimation utilising ABAQUS/Standard for modelling and analyses. Two types of meshes with six mesh sizes for each mesh type are considered in this study and the optimal mesh type and mesh size have been found to obtain accurate value of springback while saving as much computational time as possible. Feijun Qu, Zhengyi Jiang, and Haina Lu Copyright © 2015 Feijun Qu et al. All rights reserved. Finite Element Simulation of the Compaction and Springback of Alumix 321 PM Alloy Wed, 30 Sep 2015 14:23:33 +0000 A finite element simulation of the compaction and springback of an aluminum-based powder metallurgy alloy (Alumix 321) was developed and validated using the LS-DYNA hydrocode. The present work aims to directly address the current scarcity of modeling works on this popular alloy system. The Alumix 321 constitutive material parameters are presented. The model can predict the results of single-action compaction as well as the amount of springback experienced by a compact upon ejection from the die. The model has been validated using a series of experiments including powder compaction, optical densitometry, and the creation of a compaction curve. Stanley G. Selig and Darrel A. Doman Copyright © 2015 Stanley G. Selig and Darrel A. Doman. All rights reserved. New Numerical Solution of von Karman Equation of Lengthwise Rolling Wed, 30 Sep 2015 10:29:28 +0000 The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening. Rudolf Pernis and Tibor Kvackaj Copyright © 2015 Rudolf Pernis and Tibor Kvackaj. All rights reserved. Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups Tue, 29 Sep 2015 10:49:11 +0000 Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior. Masatomo Iwasa Copyright © 2015 Masatomo Iwasa. All rights reserved. Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core Mon, 28 Sep 2015 07:16:58 +0000 This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (, ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method. Jun Guo, Guozheng Yan, and Mingjian Cai Copyright © 2015 Jun Guo et al. All rights reserved. Experimental Game Theory and Its Application in Sociology and Political Science Sun, 20 Sep 2015 13:26:53 +0000 Arthur Schram, Vincent Buskens, Klarita Gërxhani, and Jens Großer Copyright © 2015 Arthur Schram et al. All rights reserved.