Search results for: school function assessment.

Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

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In the present paper, we investigate a differential subordination involving multiplier transformation related to a sector in the open unit disk E = {z : |z| < 1}. As special cases to our main result, certain sufficient conditions for strongly starlike and strongly convex functions are obtained.

Keywords: Analytic function, Multiplier transformation, Strongly starlike function, Strongly convex function.

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Authors: Zoja Raud, Valery Vodovozov

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The paper focuses on the distance laboratory organisation for training the electrical engineering staff and students in the fields of electrical drive and power electronics. To support online knowledge acquisition and professional enhancement, new challenges in remote education based on an active learning approach with self-assessment have been emerged by the authors. Following the literature review and explanation of the improved assessment methodology, the concept and technological basis of the labs arrangement are presented. To decrease the gap between the distance study of the up-to-date equipment and other educational activities in electrical engineering, the improvements in the following-up the learners’ progress and feedback composition are introduced. An authoring methodology that helps to personalise knowledge acquisition and enlarge Web-based possibilities is described. Educational management based on self-assessment is discussed.

Keywords: Advanced training, active learning, distance learning, electrical engineering, remote laboratory, self-assessment.

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Authors: Niaz Latif, Joy L. Colwell

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Following implementation of a master’s level graduate degree program in technology, a research-based assessment of the program was undertaken to determine how well the program met its goals and objectives, and the impact of the degree program on the objectives and the needs of its graduates. Upon review of the survey data, it was concluded that the program was meeting its goals and objectives, and that the directed project option should be encouraged.

Keywords: Master’s Degree, Graduate Program, Assessment.

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Authors: Samira Malekmohammadi Golsefid, Mehdi Ghazanfari, Somayeh Alizadeh

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The goal of this paper is to segment the countries based on the value of export from Iran during 14 years ending at 2005. To measure the dissimilarity among export baskets of different countries, we define Dissimilarity Export Basket (DEB) function and use this distance function in K-means algorithm. The DEB function is defined based on the concepts of the association rules and the value of export group-commodities. In this paper, clustering quality function and clusters intraclass inertia are defined to, respectively, calculate the optimum number of clusters and to compare the functionality of DEB versus Euclidean distance. We have also study the effects of importance weight in DEB function to improve clustering quality. Lastly when segmentation is completed, a designated RFM model is used to analyze the relative profitability of each cluster.

Keywords: Customers segmentation, Customer relationship management, Clustering, Data Mining

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Authors: Vilma Zydziunaite, Vaida Jurgile, Roman Balandiuk

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Good, great, and leading teachers are expected to be the role models for students, society, professional community. Their role model includes expertise, trustworthiness, originality, facilitating, cooperation and communication. Teachers demonstrate their professional passion through their professionalism and professional attitudes. Usually, we call them teacher(s) leaders by integrating three notions such as good, great, and leading in a one-teacher leader. Here are described essences of three concepts: ‘good teacher,’ ‘great teacher,’ ‘and teacher leader’ as they are inseparable in teaching practices, teacher’s professional life, and educational interactions with students, fellow teachers, school administration, students’ families and school communities.

Keywords: Great teacher, good teacher, leading teacher, school, student.

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Authors: Mohammed Qasim, Kyoung-Dae Kim

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In this paper, we present the design of the super-ellipsoidal potential function (SEPF), that can be used for autonomous collision avoidance of an unmanned aerial vehicle (UAV) in a 3-dimensional space. In the design of SEPF, we have the full control over the shape and size of the potential function. In particular, we can adjust the length, width, height, and the amount of flattening at the tips of the potential function so that the collision avoidance motion vector generated from the potential function can be adjusted accordingly. Based on the idea of the SEPF, we also propose an approach for the local autonomy of a UAV for its collision avoidance when the UAV is teleoperated by a human operator. In our proposed approach, a teleoperated UAV can not only avoid collision autonomously with other surrounding objects but also track the operator’s control input as closely as possible. As a result, an operator can always be in control of the UAV for his/her high-level guidance and navigation task without worrying too much about the UAVs collision avoidance while it is being teleoperated. The effectiveness of the proposed approach is demonstrated through a human-in-the-loop simulation of quadrotor UAV teleoperation using virtual robot experimentation platform (v-rep) and Matlab programs.

Keywords: Artificial potential function, autonomy, collision avoidance, teleoperation, quadrotor, UAV.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

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The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: M. Rodionov, Z. Dedovets

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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: Mathematics, motivation, secondary school, student, practical problem.

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Authors: Rachel C. F. Sun

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This study aimed to examine the similarities and differences between teachers’ and students’ causal explanations of classroom misbehavior. In-depth semi-structured interviews were conducted with twelve teachers and eighteen Grade 7-9 students. The qualitative data were analyzed, in which the attributed causes of classroom misbehavior were categorized into student, family, school and peer factors. Findings showed that both interviewed teachers and students shared similarity in attributing to student factors, such as ‘fun and pleasure seeking’ and ‘attention seeking’ as the leading causes of misbehavior. However, the students accounted to school factors, particularly ‘boring lessons’ as the next attributed causes, while the teachers accounted to family factors, such as ‘lack of parent demandingness’. By delineating the factors at student, family, school, and peer levels, these findings help drawing corresponding implications for preventing and mitigating misbehavior in school.

Keywords: Causal explanation, misbehavior, student, teacher.

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Authors: Meryem Elif Çelebi Yakartepe, Ayşe Betül Gökarslan

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Today, preservation of the historical constructions in "single construction" scale creates an inadequate preservation model in terms of the integrity of the historical environment in which they are located. However, in order to preserve these structures forming this integrity with a holistic approach, the structures either need to continue their unique functions or to be reshaped for function conforming to today's comfort conditions brought by the modern life.

In this work, the preservation of Ayazma Social Complex located in Ayazma Neighborhood of Üsküdar, one of the most important historical districts of İstanbul, with integrated preservation method has been discussed. In the conventional Turkish architecture, the social complex is a structure complex formed via constructing the public buildings required for the daily life of the people living in a settlement. Thus, the preservation of the social complexes within the scope of "integrated preservation" has gained importance. Ayazma Social Complex that forms the examination area of this work consists of a mosque in its center and structures around this mosque such as sultan mansion, time assignment center, primary school, stores, bath and water reservoirs. Mosque, sultan mansion and the water reservoirs survived to today as mostly preserved status. However, time assignment center, primary school and the stores didn't survive to today and new structures were built on their plots. The bath was mostly damaged and only the wall residues survive to today. Thus, it's urgent and crucial especially carry out the preservation restoration of the bath in accordance with integrated preservation principles. The preservation problems of the bath based on the social complex were determined as a working method and preservation suggestions were made to overcome these problems and to include the bath into daily life. Furthermore, it was suggested that the bath should be reshaped for a different function in order to be preserved with the social complex.

Keywords: Üsküdar, Ayazma Complex, Ayazma Bath, Conservation, Restoration.

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Authors: Hooman Hoodat, Hassan Rashidi

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Despite various methods that exist in software risk management, software projects have a high rate of failure. When complexity and size of the projects are increased, managing software development becomes more difficult. In these projects the need for more analysis and risk assessment is vital. In this paper, a classification for software risks is specified. Then relations between these risks using risk tree structure are presented. Analysis and assessment of these risks are done using probabilistic calculations. This analysis helps qualitative and quantitative assessment of risk of failure. Moreover it can help software risk management process. This classification and risk tree structure can apply to some software tools.

Keywords: Risk analysis, risk assessment, risk classification, risk tree.

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Authors: Sevgi Birsel Nemlioğlu, Hasan Atak

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Aggression is a behavior that cannot be approved by the society. Vandalism which is aggression towards objects is an action that tends to damage public or personal property. The behaviors that are described as vandalism can often be observed in the schools as well. According to Zwier and Vaughan (1) previous research about the reasons of and precautionary measures for vandalism in schools can be grouped in three tendency categories: conservative, liberal and radical. In this context, the main aim of this study is to discover which ideological tendency of the reasons of school vandalism is adopted by the teachers and what are their physical, environmental, school system and societal solutions for vandalism. A total of 200 teachers participated in this study, and the mean age was 34.20 years (SD = 6.54). The sample was made up of 109 females and 91 males. For the analysis of the data, SPSS 15.00, frequency, percentage, and t-test were used. The research showed that the teachers have tendencies in the order of conservative, liberal and radical for the reasons of vandalism. The research also showed that the teachers do not have any tendency for eliminating vandalism physically and general solutions on the level of society; on the other hand they mostly adopt a conservative tendency in terms of precautions against vandalism in the school system. Second most, they adopt the liberal tendency in terms of precautions against vandalism in the school system. . It is observed that the findings of this study are comparable to the existing literature on the subject. Future studies should be conducted with multiple variants and bigger sampling.

Keywords: Vandalism, School, Vandal, Turkey, Teacher, Tendency.

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Authors: Nameesh Miglani, Rajeev Saha, R. S. Parihar

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Estimation of the quality regarding higher education within a university is practically long drawn process besides being difficult to measure primarily due to lack of a standard scale. National Assessment and Accreditation Council (NAAC) evolved a methodology of assessment which involves self-appraisal by each university/college and an assessment of performance by an expert committee. The attributes involved in assessing a university may not be totally independent from each other thereby necessitating the consideration of interdependencies. The present study focuses on evaluation of assessment criteria using graph theoretic approach and fuzzy treatment of data collected from the students. The technique will provide a suitable platform to university management team to cross check assessment of education quality by considering interdependencies of the attributes using graph theory.

Keywords: Graph theory, NAAC accreditation criteria, Indian University accreditation process.

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Authors: Citlali Aguilera Lira, David Lynch Steinicke, Andrea León Garcia

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One of the challenges that higher education faces is to find how to approach the sustainability in an inclusive way to the student within all the different academic areas, how to move the sustainable development from the abstract field to the operational field. This research comes from the ecoliteracy and the pedagogical praxis as tools for rebuilding the teaching processes inside of universities. The purpose is to determine and describe which are the factors involved in the process of learning particularly in the Greenhouse-School Siembra UV. In the Greenhouse-School Siembra UV, of the University of Veracruz, are cultivated vegetables, medicinal plants and small cornfields under the usage of eco-technologies such as hydroponics, Wickingbed and Hugelkultur, which main purpose is the saving of space, labor and natural resources, as well as function as agricultural production alternatives in the urban and periurban zones. The sample was formed with students from different academic areas and who are actively involved in the greenhouse, as well as institutes from the University of Veracruz and governmental and nongovernmental departments. This project comes from a pedagogic praxis approach, from filling the needs that the different professional profiles of the university students have. All this with the purpose of generate a pragmatic dialogue with the sustainability. It also comes from the necessity to understand the factors that intervene in the students’ praxis. In this manner is how the students are the fundamental unit in the sphere of sustainability. As a result, it is observed that those University of Veracruz students who are involved in the Greenhouse-school, Siembra UV, have enriched in different levels the sense of urban and periurban agriculture because of the diverse academic approaches they have and the interaction between them. It is concluded that the ecotechnologies act as fundamental tools for ecoliteracy in society, where it is strengthen the nutritional and food security from a sustainable development approach.

Keywords: Farming eco-technologies, food security, multidisciplinary, pedagogical praxis.

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Authors: Hsuan-Chu Li

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We demonstrate a way to count the number of Young tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding Schur function. This result gives an answer to the question that was put out by Jenny Buontempo and Brian Hopkins.

Keywords: Young tableau, Schur function.

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Authors: P. M. Arun Kumar, S. Chandramathi

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The proliferation of multimedia technology and services in today’s world provide ample research scope in the frontiers of visual signal processing. Wide spread usage of video based applications in heterogeneous environment needs viable methods of Video Quality Assessment (VQA). The evaluation of video quality not only depends on high QoS requirements but also emphasis the need of novel term ‘QoE’ (Quality of Experience) that perceive video quality as user centric. This paper discusses two vital video quality assessment methods namely, subjective and objective assessment methods. The evolution of various video quality metrics, their classification models and applications are reviewed in this work. The Mean Opinion Score (MOS) based subjective measurements and algorithm based objective metrics are discussed and their challenges are outlined. Further, this paper explores the recent progress of VQA in emerging technologies such as mobile video and 3D video.

Keywords: 3D-Video, no reference metric, quality of experience, video quality assessment, video quality metrics.

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Authors: Hadi Taghvafard

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We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

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

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Authors: Lilac Al Safadi, Rana Abu Nafesa, Regina Garcia

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Motivated by Microsoft Co. Academic Program initiative, the department of Information Technology in King Saud University has adopted Microsoft products in three courses. The initiative aimed at enhancing the abilities of the university graduates and equipping them with skills that would help them in the job market. A number of methods of collecting assessment data were used to evaluate the course adoption initiative. Assessment data indicated that the goal of the course adoption is being achieved and that the students were much better prepared to design applications and administrate networks.

Keywords: course adoption, assessment, programming, technologies

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Authors: H. Salonen, E. Castagnoli, C. Vornanen-Winqvist, R. Mikkola, C. Duchaine, L. Morawska, J. Kurnitski

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A wide range of health effects among occupants are associated with the exposure to bioaerosols from fungal sources. Although the accurate role of these aerosols in causing the symptoms and diseases is poorly understood, the important effect of bioaerosol exposure on human health is well recognized. Thus, there is a need to determine all of the contributing factors related to the concentration of fungi in indoor air. In this study, we reviewed and summarized the different factors affecting the concentrations of viable fungi in school buildings. The literature research was conducted using Pubmed and Google Scholar. In addition, we searched the lists of references of selected articles. According to the literature, the main factors influencing the concentration of viable fungi in the school buildings are moisture damage in building structures, the season (temperature and humidity conditions), the type and rate of ventilation, the number and activities of occupants and diurnal variations. This study offers valuable information that can be used in the interpretation of the fungal analysis and to decrease microbial exposure by reducing known sources and/or contributing factors. However, more studies of different local factors contributing to the human microbial exposure in school buildings—as well as other type of buildings and different indoor environments—are needed.

Keywords: Fungi, concentration, indoor, school, contributing factor.

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Authors: Marko A. Rodriguez

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There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Moataz M. Naguib, Hatem Khater, A. Baith Mohamed

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MARS is a shared-key (symmetric) block cipher algorithm supporting 128-bit block size and a variable key size of between 128 and 448 bits. MARS has a several rounds of cryptographic core that is designed to take advantage of the powerful results for improving security/performance tradeoff over existing ciphers. In this work, a new function added to improve the ciphering process it is called, Meta-Morphic function. This function use XOR, Rotating, Inverting and No-Operation logical operations before and after encryption process. The aim of these operations is to improve MARS cipher process and makes a high confusion criterion for the Ciphertext.

Keywords: AES, MARS, Metamorphic, Cryptography, Block Cipher.

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Authors: Miguel A. Campano, Jesica Fernández-Agüera, Samuel Domínguez-Amarillo, Juan J. Sendra

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An analysis of the air tightness level is performed on a representative sample of school classrooms in Southern Spain, which allows knowing the infiltration level of these classrooms, mainly through its envelope, which can affect both energy demand and occupant's thermal comfort. By using a pressurization/depressurization equipment (Blower-Door test), a characterization of 45 multipurpose classrooms have been performed in nine non-university educational institutions of the main climate zones of Southern Spain. In spite of having two doors and a high ratio between glass surface and outer surface, it is possible to see in these classrooms that there is an adequate level of airtightness, since all the n50 values obtained are lower than 9.0 ACH, with an average value around 7.0 ACH.

Keywords: Air infiltration, energy efficiency, school buildings, thermal comfort, indoor air quality, ventilation.

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Authors: Oh Hyeon Jeon, WooYoung Jung

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In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

Keywords: Weir structure, seepage, flood disaster fragility, probabilistic risk assessment, Monte-Carlo Simulation, permeability coefficient.

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Authors: Bozena Dohnalkova, Jakub Hodul, Rostislav Drochytka, Jana Kosikova

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This paper deals with a proposal of a new methodology for durability assessment of solidification product for its safe further use. The new methodology is based on a review of the current state of assessment of treated waste in Czech Republic and abroad. The aim of the paper is to propose an optimal evaluation methodology for verifying properties of solidification product to ensure its safe further use in building industry.

Keywords: Solidification/stabilization, durability, waste.

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Authors: Pedro Padilha Gonçalves, Doris C. C. K. Kowaltowski, Benjamin Cleveland

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Trends in education affect schooling, needing incorporation into design concepts to support desired learning processes with appropriate and stimulating environments. A design process for school architecture demands research, debates, reflections, and efficient decision-making methods. This paper presents research on evidence-based design, related to middle schools, based on a systematic literature review and the elaboration of a set of architectural design patterns, through a graphic translation of new concepts for classroom configurations, to support programming debates and the synthesis phase of design. The investigation resulted in nine patterns that configure the concepts of boundaries, flexibility, levels of openness, mindsets, neighborhoods, movement and interaction, territories, opportunities for learning, and sightlines for classrooms. The research is part of a continuous investigation of design methods, on contemporary school architecture to produce an architectural pattern matrix based on scientific information translated into an insightful graphic design language.

Keywords: School architecture, design process, design patterns, evidence-based design.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

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Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: K. Shimola, M. Krishnaveni

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This paper examines vulnerability assessment of water resources in a semi-arid basin using the 4-step approach. The vulnerability assessment framework is developed to study the water resources vulnerability which includes the creation of GIS-based vulnerability maps. These maps represent the spatial variability of the vulnerability index. This paper introduces the 4-step approach to assess vulnerability that incorporates a new set of indicators. The approach is demonstrated using a framework composed of a precipitation data for (1975–2010) period, temperature data for (1965–2010) period, hydrological model outputs and the water resources GIS data base. The vulnerability assessment is a function of three components such as exposure, sensitivity and adaptive capacity. The current water resources vulnerability is assessed using GIS based spatio-temporal information. Rainfall Coefficient of Variation, monsoon onset and end date, rainy days, seasonality indices, temperature are selected for the criterion ‘exposure’. Water yield, ground water recharge, evapotranspiration (ET) are selected for the criterion ‘sensitivity’. Type of irrigation and storage structures are selected for the criterion ‘Adaptive capacity’. These indicators were mapped and integrated in GIS environment using overlay analysis. The five sub-basins, namely Arjunanadhi, Kousiganadhi, Sindapalli-Uppodai and Vallampatti Odai, fall under medium vulnerability profile, which indicates that the basin is under moderate stress of water resources. The paper also explores prioritization of sub-basinwise adaptation strategies to climate change based on the vulnerability indices.

Keywords: Adaptive capacity, exposure, overlay analysis, sensitivity, vulnerability.

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Authors: R. Uthayakumar, G. Arockia Prabakar

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In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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Authors: Hamid Abdi, Abolfazl Salami, Abolfazl Ahmadi

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Programmable logic controllers are the main controllers in the today's industries; they are used for several applications in industrial control systems and there are lots of examples exist from the PLC applications in industries especially in big companies and plants such as refineries, power plants, petrochemical companies, steel companies, and food and production companies. In the PLCs there are some functions in the function library in software that can be used in PLC programs as basic program elements. The aim of this project are introducing and implementing a new function block of a neural network to the function library of PLC. This block can be applied for some control applications or nonlinear functions calculations after it has been trained for these applications. The implemented neural network is a Perceptron neural network with three layers, three input nodes and one output node. The block can be used in manual or automatic mode. In this paper the structure of the implemented function block, the parameters and the training method of the network are presented by considering the especial method of PLC programming and its complexities. Finally the application of the new block is compared with a classic simulated block and the results are presented.

Keywords: Programmable Logic Controller, PLC Programming, Neural Networks, Perception Network, Intelligent Control.

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Authors: Sizhong Zhou, Hongxia Liu

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Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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