Search results for: word problem

Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

Abstract:

In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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Authors: V. Goremikins, K. Rocens, D. Serdjuks

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Suspended cable structures are most preferable for large spans covering due to rational use of structural materials, but the problem of suspended cable structures is initial shape change under the action of non-symmetrical load. The problem can be solved by increasing of relation of dead weight and imposed load, but this methods cause increasing of materials consumption.Prestressed cable truss usage is another way how the problem of shape change under the action of non-symmetrical load can be fixed. The better results can be achieved if we replace top chord with cable truss with cross web. Rational structure of the cable truss for prestressed cable truss top chord was developed using optimization realized in FEM program ANSYS 12 environment. Single cable and cable truss model work was discovered.Analytical and model testing results indicate, that usage of cable truss with the cross web as a top chord of prestressed cable truss instead of single cable allows to reduce total displacements by 13-16% in the case of non-symmetrical load. In case of uniformly distributed load single cable is preferable.

Keywords: Cable trusses, Non-symmetrical load, Cable truss models, Vertical displacements

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Authors: S. Park, J. Hwang, K. Rou, E. Kim

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In this paper, we consider a new particle filter inspired by biological evolution. In the standard particle filter, a resampling scheme is used to decrease the degeneracy phenomenon and improve estimation performance. Unfortunately, however, it could cause the undesired the particle deprivation problem, as well. In order to overcome this problem of the particle filter, we propose a novel filtering method called the genetic filter. In the proposed filter, we embed the genetic algorithm into the particle filter and overcome the problems of the standard particle filter. The validity of the proposed method is demonstrated by computer simulation.

Keywords: Particle filter, genetic algorithm, evolutionary algorithm.

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Authors: José M. Merigó, Pilar López-Jurado, M.Carmen Gracia, Montserrat Casanovas

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We present a method for the selection of students in interdisciplinary studies based on the hybrid averaging operator. We assume that the available information given in the problem is uncertain so it is necessary to use interval numbers. Therefore, we suggest a new type of hybrid aggregation called uncertain induced generalized hybrid averaging (UIGHA) operator. It is an aggregation operator that considers the weighted average (WA) and the ordered weighted averaging (OWA) operator in the same formulation. Therefore, we are able to consider the degree of optimism of the decision maker and grades of importance in the same approach. By using interval numbers, we are able to represent the information considering the best and worst possible results so the decision maker gets a more complete view of the decision problem. We develop an illustrative example of the proposed scheme in the selection of students in interdisciplinary studies. We see that with the use of the UIGHA operator we get a more complete representation of the selection problem. Then, the decision maker is able to consider a wide range of alternatives depending on his interests. We also show other potential applications that could be used by using the UIGHA operator in educational problems about selection of different types of resources such as students, professors, etc.

Keywords: Decision making, Selection of students, Uncertainty, Aggregation operators.

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Authors: K. Adu Michael, K. Alese Boniface

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Developing a reliable and sustainable software products is today a big challenge among up–coming software developers in Nigeria. The inability to develop a comprehensive problem statement needed to execute proper requirements engineering process is missing. The need to describe the ‘what’ of a system in one document, written in a natural language is a major step in the overall process of Software Engineering. Requirements Engineering is a process use to discover, analyze and validate system requirements. This process is needed in reducing software errors at the early stage of the development of software. The importance of each of the steps in Requirements Engineering is clearly explained in the context of using detailed problem statement from client/customer to get an overview of an existing system along with expectations from the new system. This paper elicits inadequate Requirements Engineering principle as the major cause of poor software development in developing nations using a case study of final year computer science students of a tertiary-education institution in Nigeria.

Keywords: Client/Customer, Problem Statement, Requirements Engineering, Software Developers.

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Authors: Mohammad Reza Karami Nejad

Abstract:

A hybrid learning automata-genetic algorithm (HLGA) is proposed to solve QoS routing optimization problem of next generation networks. The algorithm complements the advantages of the learning Automato Algorithm(LA) and Genetic Algorithm(GA). It firstly uses the good global search capability of LA to generate initial population needed by GA, then it uses GA to improve the Quality of Service(QoS) and acquiring the optimization tree through new algorithms for crossover and mutation operators which are an NP-Complete problem. In the proposed algorithm, the connectivity matrix of edges is used for genotype representation. Some novel heuristics are also proposed for mutation, crossover, and creation of random individuals. We evaluate the performance and efficiency of the proposed HLGA-based algorithm in comparison with other existing heuristic and GA-based algorithms by the result of simulation. Simulation results demonstrate that this paper proposed algorithm not only has the fast calculating speed and high accuracy but also can improve the efficiency in Next Generation Networks QoS routing. The proposed algorithm has overcome all of the previous algorithms in the literature.

Keywords: Routing, Quality of Service, Multicaset, Learning Automata, Genetic, Next Generation Networks.

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Authors: Ilqar Ramazanli

Abstract:

The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

Keywords: Matrix completion, adaptive learning, heterogeneous cost, Matroid optimization.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation on basic problems about the zeros of analytic theta functions. A brief introduction to analytic representation of finite quantum systems is given. The zeros of this function and there evolution time are discussed. Two open problems are introduced. The first problem discusses the cases when the zeros follow the same path. As the basis change the quantum state |f transforms into different quantum state. The second problem is to define a map between two toruses where the domain and the range of this map are the analytic functions on toruses.

Keywords: open problems, constraint, change of basis.

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Authors: Cheng Seong Khor, Xiao Qi Yeoh

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This work concerns the topological optimization problem for determining the optimal petroleum refinery configuration. We are interested in further investigating and hopefully advancing the existing optimization approaches and strategies employing logic propositions to conceptual process synthesis problems. In particular, we seek to contribute to this increasingly exciting area of chemical process modeling by addressing the following potentially important issues: (a) how the formulation of design specifications in a mixed-logical-and-integer optimization model can be employed in a synthesis problem to enrich the problem representation by incorporating past design experience, engineering knowledge, and heuristics; and (b) how structural specifications on the interconnectivity relationships by space (states) and by function (tasks) in a superstructure should be properly formulated within a mixed-integer linear programming (MILP) model. The proposed modeling technique is illustrated on a case study involving the alternative processing routes of naphtha, in which significant improvement in the solution quality is obtained.

Keywords: Mixed-integer linear programming (MILP), petroleum refinery, process synthesis, superstructure.

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Authors: A. R. Seifi

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This work presents a new algorithm based on a combination of fuzzy (FUZ), Dynamic Programming (DP), and Genetic Algorithm (GA) approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The novel formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses fuzzy reasoning for sitting of capacitors in radial distribution feeders, DP for sizing and finally GA for finding the optimum shape of membership functions which are used in fuzzy reasoning stage. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem.

Keywords: Capacitor planning, Fuzzy logic method, Genetic Algorithm, Dynamic programming, Radial Distribution feeder

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Authors: Younis R. Elhaddad, Aiman S.Gannous

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The particular interests of this paper is to explore if the simple Genetic Algorithms (GA) starts with population of only two individuals and applying different crossover technique over these parents to produced 104 children, each one has different attributes inherited from their parents; is better than starting with population of 100 individuals; and using only one type crossover (order crossover OX). For this reason we implement GA with 52 different crossover techniques; each one produce two children; which means 104 different children will be produced and this may discover more search space, also we implement classic GA with order crossover and many experiments were done over 3 Travel Salesman Problem (TSP) to find out which method is better, and according to the results we can say that GA with Multi-crossovers is much better.

Keywords: Artificial intelligence, genetic algorithm, order crossover, travel salesman problem.

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.

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Authors: M. M. Kassem, A. S. Rashed

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The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.

Keywords: Time dependent, chemical convection, grouptransformation method, perturbation method.

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Authors: Kittisak Kerdprasop, Nittaya Kerdprasop

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The problem of frequent pattern discovery is defined as the process of searching for patterns such as sets of features or items that appear in data frequently. Finding such frequent patterns has become an important data mining task because it reveals associations, correlations, and many other interesting relationships hidden in a database. Most of the proposed frequent pattern mining algorithms have been implemented with imperative programming languages. Such paradigm is inefficient when set of patterns is large and the frequent pattern is long. We suggest a high-level declarative style of programming apply to the problem of frequent pattern discovery. We consider two languages: Haskell and Prolog. Our intuitive idea is that the problem of finding frequent patterns should be efficiently and concisely implemented via a declarative paradigm since pattern matching is a fundamental feature supported by most functional languages and Prolog. Our frequent pattern mining implementation using the Haskell and Prolog languages confirms our hypothesis about conciseness of the program. The comparative performance studies on line-of-code, speed and memory usage of declarative versus imperative programming have been reported in the paper.

Keywords: Frequent pattern mining, functional programming, pattern matching, logic programming.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

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In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves and circles.

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Authors: Shahryar Shaghaghi G., Paria Violette Shakiba , Gholamreza Irani

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Nowadays, the earth is countered with serious problem of air pollution. This problem has been started from the industrial revolution and has been faster in recent years, so that leads the earth to ecological and environmental disaster. One of its results is the global warming problem and its related increase in global temperature. The most important factors in air pollution especially in urban environments are Automobiles and residential buildings that are the biggest consumers of the fossil energies, so that if the residential buildings as a big part of the consumers of such energies reduce their consumption rate, the air pollution will be decreased. Since Metropolises are the main centers of air pollution in the world, assessment and analysis of efficient strategies in decreasing air pollution in such cities, can lead to the desirable and suitable results and can solve the problem at least in critical level. Tabriz city is one of the most important metropolises in North west of Iran that about two million people are living there. for its situation in cold dry climate, has a high rate of fossil energies consumption that make air pollution in its urban environment. These two factors, being both metropolis and in cold dry climate, make this article try to analyze the strategies of climatic design in old districts of the city and use them in new districts of the future. These strategies can be used in this city and other similar cities and pave the way to reduce energy consumption and related air pollution to save whole world.

Keywords: Air pollution, Urban Environment, Metropolis, Residential building, Fossil energies.

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Authors: Bachir Bentouati, Lakhdar Chaib, Saliha Chettih, Gai-Ge Wang

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The problem of economic dispatch (ED) is the basic problem of power framework, its main goal is to find the most favorable generation dispatch to generate each unit, reduce the whole power generation cost, and meet all system limitations. A heuristic algorithm, recently developed called Stud Krill Herd (SKH), has been employed in this paper to treat non-convex ED problems. The proposed KH has been modified using Stud selection and crossover (SSC) operator, to enhance the solution quality and avoid local optima. We are demonstrated SKH effects in two case study systems composed of 13-unit and 40-unit test systems to verify its performance and applicability in solving the ED problems. In the above systems, SKH can successfully obtain the best fuel generator and distribute the load requirements for the online generators. The results showed that the use of the proposed SKH method could reduce the total cost of generation and optimize the fulfillment of the load requirements.

Keywords: Stud Krill Herd, economic dispatch, crossover, stud selection, valve-point effect.

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Authors: S. Ramana Babu, V. Ramachandra Raju, K. Ramji

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This paper presents the effect of actuation schemes on the performance of parallel manipulators and also how the singularity loci have been changed in the reachable workspace of the manipulator with the choice of actuation scheme to drive the manipulator. The performance of the eight possible actuation schemes of 3RRR planar parallel manipulator is compared with each other. The optimal design problem is formulated to find the manipulator geometry that maximizes the singularity free conditioned workspace for all the eight actuation cases, the optimization problem is solved by using genetic algorithms.

Keywords: Actuation schemes, GCI, genetic algorithms.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: Nisha Singhal, Usha Chouhan

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At present, application of the extension of soft set theory in decision making problems in day to day life is progressing rapidly. The concepts of fuzzy soft set and its properties have been evolved as an area of interest for the researchers. The generalization of the concepts recently got importance and a rapid growth in the research in this area witnessed its vital-ness. In this paper, an application of the concept of generalized fuzzy soft set to make decision in a social problem is presented. Further, this paper also highlights some of the key issues of the related areas.

Keywords: Soft set, Fuzzy Soft set, Generalized Fuzzy Soft set, Membership and Non-Membership Score.

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Authors: Yeskendirov N.R., Karjaubaeva S.K., Ahmet A. K.

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A number of theoretical and methodological problems connected with substantiation of a new approach and searches of a new research paradigm and the analysis of features of formation and development of the Kazakh stage are considered in the article. The wide spectrum of questions connected with genesis of the Kazakh stage art has caused necessity of consideration of world outlook and social cultural aspects which have affected formation of the given phenomenon in the Kazakh culture. But how can we define the form of expression and aesthetics of the national theatre? Probably, the answer to this question we will find if we apply to deep world view sources, and, as a consequence, it is necessary to study deeply the plot dramaturgy, which is based on myths, rites and eposes, mastering of symbolic gestures and mimics, allegory of a word, etc.

Keywords: Tradition, theater, art, culture, nomadic Kazakhs.

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Authors: Y. Bai, M. Bodlak, V. Frolov, S. Huber, V. Jary, I. Konorov, D. Levit, J. Novy, D. Steffen, O. Subrt, M. Virius

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In general, state-of-the-art Data Acquisition Systems (DAQ) in high energy physics experiments must satisfy high requirements in terms of reliability, efficiency and data rate capability. This paper presents the development and deployment of a debugging tool named DAQ Debugger for the intelligent, FPGA-based Data Acquisition System (iFDAQ) of the COMPASS experiment at CERN. Utilizing a hardware event builder, the iFDAQ is designed to be able to readout data at the average maximum rate of 1.5 GB/s of the experiment. In complex softwares, such as the iFDAQ, having thousands of lines of code, the debugging process is absolutely essential to reveal all software issues. Unfortunately, conventional debugging of the iFDAQ is not possible during the real data taking. The DAQ Debugger is a tool for identifying a problem, isolating the source of the problem, and then either correcting the problem or determining a way to work around it. It provides the layer for an easy integration to any process and has no impact on the process performance. Based on handling of system signals, the DAQ Debugger represents an alternative to conventional debuggers provided by most integrated development environments. Whenever problem occurs, it generates reports containing all necessary information important for a deeper investigation and analysis. The DAQ Debugger was fully incorporated to all processes in the iFDAQ during the run 2016. It helped to reveal remaining software issues and improved significantly the stability of the system in comparison with the previous run. In the paper, we present the DAQ Debugger from several insights and discuss it in a detailed way.

Keywords: DAQ debugger, data acquisition system, FPGA, system signals, Qt framework.

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Authors: R. Gomathi, D. Sharmila

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The emergence of the Semantic Web technology increases day by day due to the rapid growth of multiple web pages. Many standard formats are available to store the semantic web data. The most popular format is the Resource Description Framework (RDF). Querying large RDF graphs becomes a tedious procedure with a vast increase in the amount of data. The problem of query optimization becomes an issue in querying large RDF graphs. Choosing the best query plan reduces the amount of query execution time. To address this problem, nature inspired algorithms can be used as an alternative to the traditional query optimization techniques. In this research, the optimal query plan is generated by the proposed SAPSO algorithm which is a hybrid of Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms. The proposed SAPSO algorithm has the ability to find the local optimistic result and it avoids the problem of local minimum. Experiments were performed on different datasets by changing the number of predicates and the amount of data. The proposed algorithm gives improved results compared to existing algorithms in terms of query execution time.

Keywords: Semantic web, RDF, Query optimization, Nature inspired algorithms, PSO, SA.

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Authors: Yanti Rosmunie Bujang, Husnayati Hussin

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This paper attempts to discuss the spam issue from the Malaysian e-mail users- perspective. The purpose is to discover how Malaysian users handle the spam e-mail problem. From the experiences we hope to discover the necessary effort needed to be undertaken to face this problem in the context of Malaysia. A survey was conducted to understand how Malaysian individual perceived spam and what they actually do with the spam e-mail they received in their daily life. The findings indicate that the level of awareness on spam issue in action is still low and need some extra effort by government and relevant agencies to increase their level of awareness.

Keywords: E-mail, Malaysia, spam, users' perspective.

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Authors: N. Bolong, J. Makinda, I. Saad

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Laboratory activities have produced benefits in student learning. With current drives of new technology resources and evolving era of education methods, renewal status of learning and teaching in laboratory methods are in progress, for both learners and the educators. To enhance learning outcomes in laboratory works particularly in engineering practices and testing, learning via handson by instruction may not sufficient. This paper describes and compares techniques and implementation of traditional (expository) with open-ended laboratory (problem-based) for two consecutive cohorts studying environmental laboratory course in civil engineering program. The transition of traditional to problem-based findings and effect were investigated in terms of course assessment student feedback survey, course outcome learning measurement and student performance grades. It was proved that students have demonstrated better performance in their grades and 12% increase in the course outcome (CO) in problem-based open-ended laboratory style than traditional method; although in perception, students has responded less favorable in their feedback.

Keywords: Engineering education, open-ended laboratory, environmental engineering lab.

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Authors: Gyumin Hwang, Jihong Lee

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This paper studied the CSS-based indoor localization system which is easy to implement, inexpensive to compose the systems, additionally CSS-based indoor localization system covers larger area than other system. However, this system has problem which is affected by reflected distance data. This problem in localization is caused by the multi-path effect. Error caused by multi-path is difficult to be corrected because the indoor environment cannot be described. In this paper, in order to solve the problem by multi-path, we have supplemented the localization system by using pattern matching method based on extended database. Thereby, this method improves precision of estimated. Also this method is verified by experiments in gymnasium. Database was constructed by 1m intervals, and 16 sample data were collected from random position inside the region of DB points. As a result, this paper shows higher accuracy than existing method through graph and table.

Keywords: Chirp Spread Spectrum (CSS), Indoor Localization, Pattern-Matching, Time of Arrival (ToA), Multi-Path, Mahalanobis Distance, Reception Rate, Simultaneous Localization and Mapping (SLAM), Laser Range Finder (LRF).

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Authors: Mohammad Shahid Jamil, Mohamed Chabi

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In this study, students’ learning has been investigated and satisfaction in one of the course offered at Qatar University Foundation Program. Innovative teaching has been implied methodology that emphasizes on enhancing students’ thinking skills, decision making, and problem solving skills. Some interesting results were found which could be used to further improvement of the teaching methodology. In Fall 2012 in Foundation Program Math department at Qatar University has started implementing new ways of teaching Math by introducing MyMathLab (MML) as an innovative interactive tool in addition of the use Blackboard to support standard teaching such as Discussion board in Virtual class to engage students outside of classroom and to enhance independent, active learning that promote students’ critical thinking skills, decision making, and problem solving skills through the learning process.

Keywords: Blackboard, MyMathLab, study plan, discussion board, critical thinking, active and independent learning, problem solving.

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Authors: Sunita Dhingra, Satinder Bal Gupta, Ranjit Biswas

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Multiprocessor task scheduling is a NP-hard problem and Genetic Algorithm (GA) has been revealed as an excellent technique for finding an optimal solution. In the past, several methods have been considered for the solution of this problem based on GAs. But, all these methods consider single criteria and in the present work, minimization of the bi-criteria multiprocessor task scheduling problem has been considered which includes weighted sum of makespan & total completion time. Efficiency and effectiveness of genetic algorithm can be achieved by optimization of its different parameters such as crossover, mutation, crossover probability, selection function etc. The effects of GA parameters on minimization of bi-criteria fitness function and subsequent setting of parameters have been accomplished by central composite design (CCD) approach of response surface methodology (RSM) of Design of Experiments. The experiments have been performed with different levels of GA parameters and analysis of variance has been performed for significant parameters for minimisation of makespan and total completion time simultaneously.

Keywords: Multiprocessor task scheduling, Design of experiments, Genetic Algorithm, Makespan, Total completion time.

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Authors: Sebastian Kusch, Markus Kaiser

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In this paper we analyze the application of a formal proof system to the discrete logarithm problem used in publickey cryptography. That means, we explore a computer verification of the ElGamal encryption scheme with the formal proof system Isabelle/HOL. More precisely, the functional correctness of this algorithm is formally verified with computer support. Besides, we present a formalization of the DSA signature scheme in the Isabelle/HOL system. We show that this scheme is correct what is a necessary condition for the usefulness of any cryptographic signature scheme.

Keywords: Formal proof system, higher-order logic, formal verification, cryptographic signature scheme.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

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Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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