Search results for: University course timetabling problem

Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: Aisha Othman, Crinela Pislaru, Ahmed Impes

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This paper provides an identification of the existing practical skills gap between school-based learning (SBL) and laboratory based learning (LBL) in the Computing Department within the Faculty of Science at Omar Al-Mukhtar University in Libya. A survey has been conducted and the first author has elicited the responses of two groups of stakeholders, namely the academic teachers and students.

The primary goal is to review the main strands of evidence available and argue that there is a gap between laboratory and school-based learning in terms of opportunities for experiment and application of skills. In addition, the nature of experimental work within the laboratory at Omar Al-Mukhtar University needs to be reconsidered. Another goal of our study was to identify the reasons for students’ poor performance in the laboratory and to determine how this poor performance can be eliminated by the modification of teaching methods. Bloom’s taxonomy of learning outcomes has been applied in order to classify questions and problems into categories, and the survey was formulated with reference to third year Computing Department students. Furthermore, to discover students’ opinions with respect to all the issues, an exercise was conducted. The survey provided questions related to what the students had learnt and how well they had learnt. We were also interested in feedback on how to improve the course and the final question provided an opportunity for such feedback.

Keywords: Bloom’s taxonomy, e-learning, Omar Al-Mukhtar University.

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Authors: C. Bruni, F. Delli Priscoli, G. Koch, I. Marchetti

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The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.

Keywords: Connection Admission Control, Optimal Control, Integer valued Linear Programming, Quality of Service Requirements, Robust Control.

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Authors: Luedech Girdwichai, Suwaree Yordchim, Phusit Phukamchanoad

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This research aimed to study about motivation for students of Suan Sunandha Rajabhat University to follow and happily live according to Sufficiency Economy Philosophy. Having collected 394 questionnaires, the result showed that most students had great motivation to follow this philosophy at a high level, especially in terms of righteousness in profession; besides, students’ determination and intention to apply this philosophy in everyday lives was impressive though the students’ families were not completely ready. Each of students, in fact, consulted their families for plans of any activities without tiredness and discouragement based on the saying, “Where there’s a will, there’s a way.” On the part of universities life, students interacted with society and created projects that supported income to the community including exercises, sports, recreational activities, and community services.

Keywords: Livelihood, Motivation, Sufficiency Economy Philosophy, Undergraduate Students of Suan Sunandha Rajabhat University.

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Authors: Said Baadel

Abstract:

The belief of a heavenly God is enshrined to all Abrahamic religions which form the three major religions of the world today. Muslims believe in Allah who is above the seven heavens. The youth in the United Arab Emirates (UAE) study Islamic courses as part of their high school curriculum and are required to take at least one Islamic course at the university level to gain credit hours towards their general education (GENED). This paper provides an insight of what the youth studying in the UAE think of where Allah is. Our analysis shows that a big number of Muslim youth were not sure, especially those from the Middle Eastern and Arab countries bringing to conclusion that this subject needs to be revisited again in the course work.

Keywords: Allah, Islam, Tawheed.

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Authors: H. Taghvafard, G. H. Erjaee

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A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Noboru Abe, Yoshinori Amai, Toshinori Nakatake, Sumio Masuda, Kazuaki Yamaguchi

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We consider the problem of placing labels of the points on a plane. For each point, its position, the size of its label and a priority are given. Moreover, several candidates of its label positions are prespecified, and each of such label positions is assigned a priority. The objective of our problem is to maximize the total sum of priorities of placed labels and their points. By refining a labeling algorithm that can use these priorities, we propose a new heuristic algorithm which is more suitable for treating the assigned priorities.

Keywords: Map labeling, greedy algorithm, heuristic algorithm, priority.

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Authors: Babatunde Kasim Oladele

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One of the major objectives of the Nigeria national policy on education is the provision of equal educational opportunities to all citizens at different levels of education. With regards to higher education, an aspect of the policy encourages distance learning to be organized and delivered by tertiary institutions in Nigeria. This study therefore, determines how much of the Government resources are committed, how the resources are utilized and what alternative sources of funding are available for this system of education. This study investigated the trends in recurrent costs between 2004/2005 and 2013/2014 at University of Ibadan Distance Learning Centre (DLC). A descriptive survey research design was employed for the study. Questionnaire was the research instrument used for the collection of data. The population of the study was 280 current distance learning education students, 70 academic staff and 50 administrative staff. Only 354 questionnaires were correctly filled and returned. Data collected were analyzed and coded using the frequencies, ratio, average and percentages were used to answer all the research questions. The study revealed that staff salaries and allowances of academic and non-academic staff represent the most important variable that influences the cost of education. About 55% of resources were allocated to this sector alone. The study also indicates that costs rise every year with increase in enrolment representing a situation of diseconomies of scale. This study recommends that Universities who operates distance learning program should strive to explore other internally generated revenue option to boost their revenue. University of Ibadan, being the premier university in Nigeria, should be given foreign aid and home support, both financially and materially, to enable the institute to run a formidable distance education program that would measure up in planning and implementation with those of developed nation.

Keywords: Open education, distance education, University of Ibadan, cost of education, Nigeria.

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Authors: Naeem Ahmed

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Social work is a professional activity based on the approach of “helping people to help themselves” (Stroup). Social work education and practice both are based on humanitarian philosophy in which social workers try to increase the happiness of the society and to reduce the problems of society. Labour welfare is a specialised field of social work which especially focuses on welfare of organised and unorganised labour. In India labour is facing numerous problems in both organised and unorganised sectors because of ignorance, illiteracy, high rate of unemployment etc. In most of the Indian social work institutions we have this specialization with different names like Human Resource Management or Industrial Relation and Personnel Management or Industrial Relations and Labour Welfare or Industrial Social Work etc. Field work practice is integrated part of social work education curriculum in all specialised field. In India we have different field work practice models being followed in different institutions. The main objective of this paper is to prepare a universal field work practicum model in the field of labour welfare. This paper is exploratory in nature, researcher used personal experience and secondary data (model of field work practice in different institutions like Aligarh Muslim University, Pondicherry University, Central University of Karnataka, University of Lucknow, MJP Rohilkhand University Bareilly etc.) Researcher found that there is an immediate need to upgrade the curriculum or field work practice in this particular field, as more than 40 percent of total population engaged in either unorganised or organised sector (NSSO 2011-12) and they are not aware about their rights. In this way a social worker can play an important role in existing labour welfare facilities by making them aware.

Keywords: Fieldwork, labour welfare, organised labour, social work practice, unorganised labour.

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Authors: Seongykyoon Jeong, Sungki Lee, Jaeyun Kim, Seunghun Oh, Kiho Kwak

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The purpose of this article is to identify the practical strategies of R&D (research and development) entities for developing converging technology in organizational context. Based on the multi-assignation technological domains of patents derived from entire government-supported R&D projects for 13 years, we find that technology convergence is likely to occur when a university solely develops technology or when university develops technology as one of the collaborators. These results reflect the important role of universities in developing converging technology

Keywords: Interdisciplinary, Research and development strategy, Technology convergence

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

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Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: Miloš Šeda

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In this paper, we deal with the Steiner tree problem (STP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. We propose a modification of the shortest paths approximation based on the fuzzy shortest paths (FSP) evaluations. Since a fuzzy min operation using the extension principle leads to nondominated solutions, we propose another approach to solving the FSP using Cheng's centroid point fuzzy ranking method.

Keywords: Steiner tree, single shortest path problem, fuzzyranking, binary heap, priority queue.

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Authors: Y. T. Tsai, Jin H. Huang

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The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: Inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method.

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Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

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In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

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Authors: Xun Ge

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Recently, X. Ge and J. Qian investigated some relations between higher mathematics scores and calculus scores (resp. linear algebra scores, probability statistics scores) for Chinese university students. Based on rough-set theory, they established an information system S = (U,CuD,V, f). In this information system, higher mathematics score was taken as a decision attribute and calculus score, linear algebra score, probability statistics score were taken as condition attributes. They investigated importance of each condition attribute with respective to decision attribute and strength of each condition attribute supporting decision attribute. In this paper, we give further investigations for this issue. Based on the above information system S = (U, CU D, V, f), we analyze the decision rules between condition and decision granules. For each x E U, we obtain support (resp. strength, certainty factor, coverage factor) of the decision rule C —>x D, where C —>x D is the decision rule induced by x in S = (U, CU D, V, f). Results of this paper gives new analysis of on higher mathematics scores for Chinese university students, which can further lead Chinese university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, support, strength, certainty factor, coverage factor.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Kgomotso Matobole, Pascal Mwenge, Tumisang Seodigeng

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The global urbanisation and worldwide economic growth have caused a high rate of food waste generation, resulting in environmental pollution. Food waste disposed on landfills decomposes to produce methane (CH₄), a greenhouse gas. Inadequate waste management practices contribute to food waste polluting the environment. Thus effective organic fraction of municipal solid waste (OFMSW) management and treatment are attracting widespread attention in many countries. This problem can be minimised by the employment of anaerobic digestion process, since food waste is rich in organic matter and highly biodegradable, resulting in energy generation and waste volume reduction. The current study investigated the Biomethane Potential (BMP) of the Vaal University of Technology canteen food waste using anaerobic digestion. Tests were performed on canteen food waste, as a substrate, with total solids (TS) of 22%, volatile solids (VS) of 21% and moisture content of 78%. The tests were performed in batch reactors, at a mesophilic temperature of 37 °C, with two different types of inoculum, primary and digested sludge. The resulting CH₄ yields for both food waste with digested sludge and primary sludge were equal, being 357 Nml/g VS. This indicated that food waste form this canteen is rich in organic and highly biodegradable. Hence it can be used as a substrate for the anaerobic digestion process. The food waste with digested sludge and primary sludge both fitted the first order kinetic model with k for primary sludge inoculated food waste being 0.278 day^-1 with R² of 0.98, whereas k for digested sludge inoculated food waste being 0.034 day^-1, with R² of 0.847.

Keywords: Anaerobic digestion, biogas, biomethane potential, food waste.

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Authors: D.Venkatesan, K.Kannan, S. Raja Balachandar

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In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operators forms a competitive algorithm to the existing ones. Computational results show that the proposed algorithm is capable of obtaining high quality solutions for problems of standard randomly generated knapsack instances. Comparative study of CMGA with simple GA in terms of results for unbounded knapsack instances of size up to 200 show the superiority of CMGA. Thus CMGA is an efficient tool of solving UKP and this algorithm is competitive with other Genetic Algorithms also.

Keywords: Genetic Algorithm, Unbounded Knapsack Problem, Combinatorial Optimization, Meta-Heuristic, Center of Mass

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Authors: Steve Fish, Chris Lambert

Abstract:

Cumbria is a geo-political county in Northwest England within which the Lake District National Park, a UNESCO World Heritage site is located. Whilst the area has a formidable reputation for natural beauty and historic assets, the innovation ecosystem is described as ‘patchy’ for a number of reasons. The county is one of the largest in England by area and is sparsely populated. This paper describes the needs, development and delivery of an SME business-support programme funded by the European Regional Development Fund, Lancaster University and the University of Cumbria. The Cumbria Innovations Platform (CUSP) Project has been designed to respond to the nuanced needs of SMEs in this locale, whilst promoting the adoption of research and innovation. CUSP utilizes a funnel method to support rural businesses with access to university innovation intervention. CUSP has been built on a three-tier model: Communicate, Collaborate and Create. The paper describes this project in detail and presents results in terms of output indicators achieved, a beneficiary telephone survey and wider economic forecasts. From a pragmatic point-of-view, the paper provides experiences and reflections of those people who are delivering and evaluating knowledge exchange. The authors discuss some of the benefits, challenges and implications for both policy makers and practitioners. Finally, the paper aims to serve as an invitation to others who may consider adopting a similar method of university-industry collaboration in their own region.

Keywords: Regional business support, rural business support, university-industry collaboration, collaborative R&D, SMEs, knowledge exchange.

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Authors: Chartree Sithananun, Teekayu Limchamroon, Tanawat Limwathanagura, Thanyarat Singhanart

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The objective of this paper is to present the development of the frame of Chulalongkorn University team in TSAE Auto Challenge Student Formula and Student Formula SAE Competition of Japan. Chulalongkorn University's SAE team, has established since year 2003, joined many competitions since year 2006 and became the leading team in Thailand. Through these 5 years, space frame was the most selected and developed year by year through six frame designs. In this paper, the discussions on the conceptual design of these frames are introduced, focusing on the mass and torsional stiffness improvement. The torsional stiffness test was performed on the real used frames and the results are compared. It can be seen that the 2010-2011 frame is firstly designed based on the analysis and experiment that considered the required mass and torsional stiffness. From the torsional stiffness results, it can be concluded that the frames were developed including the decreasing of mass and the increasing torsional stiffness by applying many techniques.

Keywords: SAE Student Formula, Space Frame, Torsional Stiffness

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Authors: Mohammed T. Shukri

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The failure of bridges due to excessive local scour during floods poses a challenging problem to hydraulic engineers. The failure of bridges piers is due to many reasons such as localized scour combined with general riverbed degradation. In this paper, we try to estimate the temporal variation of scour depth at nonuniform cylindrical bridge pier, by experimental work conducted in hydraulic laboratories of Gaziantep University Civil Engineering Department on a flume having dimensions of 8.3 m length, 0.8 m width and 0.9 m depth. The experiments will be carried on 20 cm depth of sediment layer having d₅₀=0.4 mm. Three bridge pier shapes having different scaled models will be constructed in a 1.5m of test section in the channel.

Keywords: Scour, local scour, bridge piers, scour depth.

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Authors: Fury Khristianty Fitriyah

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This study aims to identify the extent of the role of the Satuan Pengawas Intern (Internal Audit Unit) in detecting and preventing fraud in public universities in West Java under the Ministry of Research, Technology and Higher Education. The research method applied was a qualitative case study approach, while the unit of analysis for this study is the Internal Audit Unit at each public university. Results of this study indicate that the Internal Audit Unit is able to detect and prevent fraud within a public university environment by means of red flags to mark accounting anomalies. These stem from inaccurate budget planning that prompts inappropriate use of funds, exacerbated by late disbursements of funds, which potentially lead to fictitious transactions, and discrepancies in recording state-owned assets into a state property management system (SIMAK BMN), which, if not conducted properly, potentially causes loss to the state.

Keywords: Internal Audit Unit, efficiency, fraud, public university.

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Authors: Behrouz Afshar Nadjafi

Abstract:

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where production period length is constrained. In this paper, we address the problem of deciding the optimal production quantity and the number of minor setups within each cycle, in which, production period length is constrained but a minor setup is possible for pass the constraint. A mathematical model is developed and Iterated Local Search (ILS) is proposed to solve this problem. Finally, solution procedure illustrated with a numerical example and results are analyzed.

Keywords: EPQ, Inventory control, minor setup, ILS.

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Authors: Hamidullah Sokout, Samiullah Paracha, Abdul Rashid Ahmadi

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Passing the entrance exam to a university is a major step in one's life. University entrance exam commonly known as Kankor is the nationwide entrance exam in Afghanistan. This examination is prerequisite for all public and private higher education institutions at undergraduate level. It is usually taken by students who are graduated from high schools. In this paper, we reflect the major educational school graduates issues and propose ICT-based test preparation environment, known as ‘Online Kankor Exam Prep System’ to give students the tools to help them pass the university entrance exam on the first try. The system is based on Intelligent Tutoring System (ITS), which introduced an essential package of educational technology for learners that features: (I) exam-focused questions and content; (ii) self-assessment environment; and (iii) test preparation strategies in order to help students to acquire the necessary skills in their carrier and keep them up-to-date with instruction.

Keywords: Web-based test prep systems, Learner-centered design, E-Learning, Intelligent tutoring system.

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Authors: Mustafa Resa Becan

Abstract:

The performance of a type of fuzzy sliding mode control is researched by considering the nonlinear characteristic of a missile-target interception problem to obtain a robust interception process. The variable boundary layer by using fuzzy logic is proposed to reduce the chattering around the switching surface then is applied to the interception model which was derived. The performances of the sliding mode control with constant and fuzzy boundary layer are compared at the end of the study and the results are evaluated.

Keywords: Sliding mode control, fuzzy, boundary layer, interception problem.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

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Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: P. Shunmugapriya, S. Kanmani, P. Jude Fredieric, U. Vignesh, J. Reman Justin, K. Vivek

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Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem and it is quite difficult to find an optimal solution consisting of a set of routes for vehicles whose total cost is minimum. Evolutionary and swarm intelligent (SI) algorithms play a vital role in solving optimization problems. While the SI algorithms perform search, the diversity between the solutions they exploit is very important. This is because of the need to avoid early convergence and to get an appropriate balance between the exploration and exploitation. Therefore, it is important to check how far the solutions are diverse. In this paper, we measure the similarity between solutions, which ABC exploits while optimizing VRP. The similar solutions found are discarded at the end of the iteration and only unique solutions are passed on to the next iteration. The bees of discarded solutions become scouts and they start searching for new solutions. This process is continued and results show that the solution is optimized at lesser number of iterations but with the overhead of computing similarity in all the iterations. The problem instance from Solomon benchmarked dataset has been used for evaluating the presented methodology.

Keywords: ABC algorithm, vehicle routing problem, optimization, Jaccard’s similarity measure.

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Authors: Hsuan-Ku Liu, Ming Long Liu

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In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Pirada Techaratpong

Abstract:

This qualitative research has 2 objectives: to study marketing management of the cultural learning center in Suansunandha Rajabhat University and to suggest guidelines to improve its marketing management. This research is based on a case study of the Arts and Culture Office in Suansunandha Rajabhat University, Bangkok. This research found the Art and Culture Office has no formal marketing management. However, the marketing management is partly covered in the overall business plan, strategic plan, and action plan. The process can be divided into 5 stages. The marketing concept has long been introduced to its policy but not apparently put into action due to inflexible system. Some gaps are found in the process. The research suggests the Art and Culture Office implement the concept of marketing orientation, meeting the needs and wants of its target customers and adapt to the changing situation. Minor guidelines for improvement are provided.

Keywords: Marketing, management, museum, cultural learning center.

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

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This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: Distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm.

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