Search results for: Topological Importance
1323 Laplace Transformation on Ordered Linear Space of Generalized Functions
Authors: K. V. Geetha, N. R. Mangalambal
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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12391322 Some New Bounds for a Real Power of the Normalized Laplacian Eigenvalues
Authors: Ayşe Dilek Maden
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For a given a simple connected graph, we present some new bounds via a new approach for a special topological index given by the sum of the real number power of the non-zero normalized Laplacian eigenvalues. To use this approach presents an advantage not only to derive old and new bounds on this topic but also gives an idea how some previous results in similar area can be developed.
Keywords: Degree Kirchhoff index, normalized Laplacian eigenvalue, spanning tree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22031321 Strongly Screenableness and its Tychonoff Products
Authors: Jianjun Wang, Peiyong Zhu
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In this paper, we prove that if X is regular strongly screenable DC-like (C-scattered), then X ×Y is strongly screenable for every strongly screenable space Y . We also show that the product i∈ω Yi is strongly screenable if every Yi is a regular strongly screenable DC-like space. Finally, we present that the strongly screenableness are poorly behaved with its Tychonoff products.
Keywords: Topological game, strongly screenable, scattered, Cscattered.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13381320 Component Criticality Importance Measures in Thermal Power Plants Design
Authors: Smajo Bisanovic, Mensur Hajro, Mersiha Samardzic
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This paper presents quantitative component criticality importance indices applicable for identifying and ranking critical components in the phase of thermal power plants design. Identifying critical components for power plant reliability provides one important input to decision-making and guidance throughout the development project. The study of components criticality importance indices to several characteristic structural schemes of conventional thermal power plant is presented and discussed.
Keywords: Component criticality importance measures, discrete event, reliability, thermal power plant.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25291319 Recursive Similarity Hashing of Fractal Geometry
Authors: Timothee G. Leleu
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A new technique of topological multi-scale analysis is introduced. By performing a clustering recursively to build a hierarchy, and analyzing the co-scale and intra-scale similarities, an Iterated Function System can be extracted from any data set. The study of fractals shows that this method is efficient to extract self-similarities, and can find elegant solutions the inverse problem of building fractals. The theoretical aspects and practical implementations are discussed, together with examples of analyses of simple fractals.Keywords: hierarchical clustering, multi-scale analysis, Similarity hashing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18641318 Solitons and Universes with Acceleration Driven by Bulk Particles
Authors: A. C. Amaro de Faria Jr, A. M. Canone
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Considering a scenario where our universe is taken as a 3d domain wall embedded in a 5d dimensional Minkowski space-time, we explore the existence of a richer class of solitonic solutions and their consequences for accelerating universes driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role at the beginning of the expansion process. We present some of these solutions in cosmological scenarios that can be applied to models that describe the inflationary period of the Universe.Keywords: Solitons, topological defects, Branes, kinks, accelerating universes in Brane scenarios.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7971317 New Approach for Constructing a Secure Biometric Database
Authors: A. Kebbeb, M. Mostefai, F. Benmerzoug, Y. Chahir
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The multimodal biometric identification is the combination of several biometric systems; the challenge of this combination is to reduce some limitations of systems based on a single modality while significantly improving performance. In this paper, we propose a new approach to the construction and the protection of a multimodal biometric database dedicated to an identification system. We use a topological watermarking to hide the relation between face image and the registered descriptors extracted from other modalities of the same person for more secure user identification.
Keywords: Biometric databases, Multimodal biometrics, security authentication, Digital watermarking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20931316 The Importance of Intellectual Property for Universities of Technology in South Africa: Challenges Faced and Proposed Way Forward
Authors: Martha E. Ikome, John M. Ikome
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Intellectual property should be a day-to-day business decision due to its value, but increasingly, a number of institution are still not aware of the importance. Intellectual Property (IP) and its value are often not adequately appreciated. In the increasingly knowledge-driven economy, IP is a key consideration in day-to-day business decisions because new ideas and products appear almost daily in the market, which results in continuous innovation and research. Therefore, this paper will focus on the importance of IP for universities of technology and also further demonstrates how IP can become an economic tool and the challenges faced by these universities in implementing an IP system.Keywords: Intellectual property, institutions, challenges, protection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17071315 Algebras over an Integral Domain and Immediate Neighbors
Authors: Shai Sarussi
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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented.Keywords: Algebras over integral domains, Alexandroff topology, immediate neighbors, integral domains.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5951314 Labyrinth Fractal on a Convex Quadrilateral
Authors: Harsha Gopalakrishnan, Srijanani Anurag Prasad
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Quadrilateral Labyrinth Fractals are a type of fractals presented in this paper. They belong to a unique class of fractals on any plane quadrilateral. The previously researched labyrinth fractals on the unit square and triangle inspire this form of fractal. This work describes how to construct a quadrilateral labyrinth fractal and looks at the circumstances in which it can be understood as the attractor of an iterated function system. Furthermore, some of its topological properties and the Hausdorff and box-counting dimensions of the quadrilateral labyrinth fractals are studied.
Keywords: Fractals, labyrinth fractals, dendrites, iterated function system, non-self similar, non-self affine, connected, path connected.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 841313 The "Project" Approach in Urban: A Response to Uncertainty
Authors: Nedjima Mouhoubi, Souad Sassi Boudemagh
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In this paper, we will try to demonstrate the importance of the project approach in the urban to deal with uncertainty, the importance of the involvement of all stakeholders in the urban project process and that the absence of an actor can lead to project failure but also the importance of the urban project management. These points are handled through the following questions: Does the urban adhere to the theory of complexity? Does the project approach bring hope and solution to make urban planning "sustainable"? How converging visions of actors for the same project? Is the management of urban project the solution to support the urban project approach?Keywords: Strategic planning, project, urban project stakeholders, management.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12881312 Reliability Optimization for 3G Cellular Access Networks
Authors: Ekkaluk Eksook, Chutima Prommak
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This paper address the network reliability optimization problem in the optical access network design for the 3G cellular systems. We presents a novel 0-1 integer programming model for designing optical access network topologies comprised of multi-rings with common-edge in order to guarantee always-on services. The results show that the proposed model yields access network topologies with the optimal reliablity and satisfies both network cost limitations and traffic demand requirements.Keywords: Network Reliability, Topological Network Design, 3G Cellular Networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15421311 Visual Analytics of Higher Order Information for Trajectory Datasets
Authors: Ye Wang, Ickjai Lee
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Due to the widespread of mobile sensing, there is a strong need to handle trails of moving objects, and trajectories. This paper proposes three visual analytics approaches for higher order information of trajectory datasets based on the higher order Voronoi diagram data structure. Proposed approaches reveal geometrical, topological, and directional information. Experimental resultsdemonstrate the applicability and usefulness of proposed three approaches.
Keywords: Visual Analytics, Higher Order Information, Trajectory Datasets, Spatio-temporal data.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16411310 Periodic Solutions for a Two-prey One-predator System on Time Scales
Authors: Changjin Xu
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In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13711309 The Importance of Sustainable Urban Development and Its Impacts on Turkey’s Urban Environmental Laws
Authors: Azadeh Rezafar, Sevkiye Sence Turk
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Rapid population growth in urban areas and extinction danger of natural resources in order to meet the food needs of these population, has revealed the need for sustainability. It did not last long that city planners realized the importance of an equal access to natural resources with protecting and managing them in cities, in accordance with the concept of sustainable development. Like in other countries The Turkish Government is aware of the importance of the sustainable development in their cities. The government issued new laws for protection of environmental assets and so that the preservation of natural ecology. The main objective of this article is to emphasis the importance of the sustainable development in the context of the developing world by giving special information about the method of the Turkish Government for protecting nature with approval of difference laws in this area.
Keywords: Population Growth, Sustainable Development, Turkey, Turkish Urban Environmental Laws.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33111308 Positive Periodic Solutions in a Discrete Competitive System with the Effect of Toxic Substances
Authors: Changjin Xu, Qianhong Zhang
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In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.
Keywords: Competitive system, periodic solution, discrete time delay, topological degree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14591307 Students' Perceptions of the Value of the Elements of an Online Learning Environment: An Investigation of Discipline Differences
Authors: Stuart Palmer, Dale Holt
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This paper presents a large scale, quantitative investigation of the impact of discipline differences on the student experience of using an online learning environment (OLE). Based on a representative sample of 2526 respondents, a number of significant differences in the mean rating by broad discipline area of the importance of, and satisfaction with, a range of elements of an OLE were found. Broadly speaking, the Arts and Science and Technology discipline areas reported the lowest importance and satisfaction ratings for the OLE, while the Health and Behavioural Sciences area was the most satisfied with the OLE. A number of specific, systematic discipline differences are reported and discussed. Compared to the observed significant differences in mean importance ratings, there were fewer significant differences in mean satisfaction ratings, and those that were observed were less systematic than for importance ratings.
Keywords: Discipline difference, learning management system, online learning environment, student evaluation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13751306 Oman’s Position in U.S. Tourists’ Mind: The Use of Importance-Performance Analysis on Destination Attributes
Authors: Mohammed Gamil Montasser, Angelo Battaglia
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Tourism is making its presence felt across the Sultanate of Oman. The story is one of the most recognized phenomena as a sustainable solid growth and is considered a remarkable outcome for any destination. The competitive situation and challenges within the tourism industry worldwide entail a better understanding of the destination position and its image to achieve Oman’s aspiration to retain its international reputation as one of the most desirable destinations in the Middle East. To access general perceptions of Oman’s attributes, their importance and their influences among U.S. tourists, an online survey was conducted with 522 American travelers who have traveled internationally, including non-visitors, virtual-visitors and visitors to Oman. This research involved a total of 36 attributes in the survey. Participants were asked to rate their agreement on how each attribute represented Oman and how important each attribute was for selecting destinations on 5- point Likert Scale. They also indicated if each attribute has a positive, neutral or negative influence on their destination selection. Descriptive statistics and importance performance analysis (IPA) were conducted. IPA illustrated U.S. tourists’ perceptions of Oman’s destination attributes and their importance in destination selection on a matrix with four quadrants, divided by actual mean value in each grid for importance (M=3.51) and performance (M=3.57). Oman tourism organizations and destination managers may use these research findings for future marketing and management efforts toward the U.S. travel market.
Keywords: Analysis of importance and performance, destination attributes, Oman’s position, U.S. tourists.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15251305 On Fuzzy Weakly-Closed Sets
Authors: J. Mahanta, P.K. Das
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A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
Keywords: Fuzzy weakly-closed set, fuzzy weakly-closed space, fuzzy weakly-compactness, MSC: 54A40, 54D30.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17851304 Perception of the Frequency and Importance of Peer Social Support by Students with Special Educational Needs in Inclusive Education
Authors: Lucia Hrebeňárová, Jarmila Žolnová, Veronika Palková
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Inclusive education of students with special educational needs has been on the increase in the Slovak Republic, facing many challenges. Preparedness of teachers for inclusive education is one of the most frequent issues; teachers lack skills when it comes to the use of effective instruction depending on the individual needs of students, improvement of classroom management and social skills, and support of inclusion within the classroom. Social support is crucial for the school success of students within inclusive settings. The aim of the paper is to analyse perception of the frequency and importance of peer social support by students with special educational needs in inclusive education. The data collection tool used was the Child and Adolescent Social Support Scale (CASSS). The research sample consisted of 953 fourth grade students – 141 students with special educational needs educated in an inclusive setting and 812 students of the standard population. No significant differences were found between the students with special educational needs and the students without special educational needs in an inclusive setting when it comes to the perception of frequency and importance of social support of schoolmates and friends. However, the perception of frequency and importance of a friend’s social support was higher than the perception of frequency and importance of a classmate’s social support in both groups of students.Keywords: Inclusive education, peer social support, peer, student with special educational needs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13111303 Analyzing the Importance of Technical Writing in Professional Industry of Pakistan
Authors: Sadaf Khalid, Jahanzaib Sarwar, Rabia Tauseef
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No matter how much perfect we become in our practical skills regarding the implementation of learned ideas, the need of technical writing capability cannot be neglected being a professional. Technical writing is a way of communicating the ideas in written which otherwise need to be presented orally. Technical writing skills have always been the need of the time, as they are required for internal as well as external official communication in both formal and informal manner. Moreover, they are the best way to capture the attention of your customers by presenting information in effective manner. This paper aims to analyze the importance of technical writing skills in professional industries of Pakistan by conducting a survey. Survey results presented in this paper clearly depicts the importance of formal and informal written communication media used in different professional industries in Pakistan. Analysis and discussion of the extent to which the alternative ways of communication besides technical writing have got importance in Pakistan is also an important aspect of this survey.
Keywords: Technical writing, Survey, Oral communication, Globalization, Communication trends, Formal Communication Media, Informal Communication, Audience
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 69851302 Terminal Wiener Index for Graph Structures
Authors: J. Baskar Babujee, J. Senbagamalar,
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The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i Keywords:
Graph,
Degree,
Distance,
Pendent vertex,
Wiener index,
Tree.
1301 The Importance of Compulsory Pre-School Education from the Parents’ Perspective in the Czech Republic
Authors: Beata Horníckova, Sona Lorencova
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The study deals with the presentation of the results of quantitatively oriented research. The research was conducted as part of a questionnaire survey with the aim to find out what are the attitudes of parents to compulsory preschool education in the Czech Republic. This research presents results from the area of importance of compulsory pre-school education from the parents’ perspective. The research method was a questionnaire, which was distributed to respondents through an online platform. The research involved 107 parents, who answered a total of 36 questions that found out their attitudes to last year’s compulsory preschool attendance. The results show that compulsory pre-school attendance has increased the importance of pre-school education. However, the results also show that the compulsory last year of preschool education is not more important according to parents than in previous years. Most participants consider compulsory pre-school attendance to be important and are happy that their child attends it. The results reveal the fact that the introduction of compulsory pre-school attendance has contributed to the importance of parents’ perceptions of pre-primary education.
Keywords: compulsory pre-school education, education of preschool children, kindergarten, parents
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5891300 Power Transformer Risk-Based Maintenance by Optimization of Transformer Condition and Transformer Importance
Authors: Kitti Leangkrua
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This paper presents a risk-based maintenance strategy of a power transformer in order to optimize operating and maintenance costs. The methodology involves the study and preparation of a database for the collection the technical data and test data of a power transformer. An evaluation of the overall condition of each transformer is performed by a program developed as a result of the measured results; in addition, the calculation of the main equipment separation to the overall condition of the transformer (% HI) and the criteria for evaluating the importance (% ImI) of each location where the transformer is installed. The condition assessment is performed by analysis test data such as electrical test, insulating oil test and visual inspection. The condition of the power transformer will be classified from very poor to very good condition. The importance is evaluated from load criticality, importance of load and failure consequence. The risk matrix is developed for evaluating the risk of each power transformer. The high risk power transformer will be focused firstly. The computerized program is developed for practical use, and the maintenance strategy of a power transformer can be effectively managed.Keywords: Asset management, risk-based maintenance, power transformer, health index.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13641299 Logistic and Its Importance in Turkish Food Sector and an Analysis of the Logistics Sector in Turkey
Authors: Şule Turhan, Özlem Turan
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Permanence in the international markets for many global companies is about being known as having effective logistics which targets customer satisfaction management and lower costs. Under competitive conditions, the necessity of providing the products to customers quickly and on time for the companies which constantly aim to improve their profitability increased the strategic importance of the logistics concept. Food logistic is one of the most difficult areas in logistics. In the process from manufacturer to final consumer, quality and hygiene standards must be provided constantly. In food logistics, reliable and extensive service network has great importance and on time delivery is the target. Developing logistics industry provide the supply of foods in the country and the development of export markets more quickly and has an important role in providing added value to the country's economy. Turkey that creates a bridge between the east and the west is an attractive market for logistics companies. In this study, by examining both the place and the importance of logistics in Turkish food sector, recommendations will be made for the food industry.Keywords: Logistics, Turkish food industry, competition, food industry.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13381298 A Quantitative Study of the Evolution of Open Source Software Communities
Authors: M. R. Martinez-Torres, S. L. Toral, M. Olmedilla
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Typically, virtual communities exhibit the well-known phenomenon of participation inequality, which means that only a small percentage of users is responsible of the majority of contributions. However, the sustainability of the community requires that the group of active users must be continuously nurtured with new users that gain expertise through a participation process. This paper analyzes the time evolution of Open Source Software (OSS) communities, considering users that join/abandon the community over time and several topological properties of the network when modeled as a social network. More specifically, the paper analyzes the role of those users rejoining the community and their influence in the global characteristics of the network.
Keywords: Open source communities, social network analysis, time series, virtual communities.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20041297 Intelligent Design of Reconfigurable Machines
Authors: Majid Tolouei-Rad
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This paper presents methodologies for developing an intelligent CAD system assisting in analysis and design of reconfigurable special machines. It describes a procedure for determining feasibility of utilizing these machines for a given part and presents a model for developing an intelligent CAD system. The system analyzes geometrical and topological information of the given part to determine possibility of the part being produced by reconfigurable special machines from a technical point of view. Also feasibility of the process from a economical point of view is analyzed. Then the system determines proper positioning of the part considering details of machining features and operations needed. This involves determination of operation types, cutting tools and the number of working stations needed. Upon completion of this stage the overall layout of the machine and machining equipment required are determined.Keywords: CAD, Knowledge based system, Reconfigurable
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14231296 The e-DELPHI Method to Test the Importance Competence and Skills: Case of the Lifelong Learning Spanish Trainers
Authors: Xhevrie Mamaqi, Jesus Miguel, Pilar Olave
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The lifelong learning is a crucial element in the modernization of European education and training systems. The most important actors in the development process of the lifelong learning are the trainers, whose professional characteristics need new competences and skills in the current labour market. The main objective of this paper is to establish an importance ranking of the new competences, capabilities and skills that the lifelong learning Spanish trainers must possess nowadays. A wide study of secondary sources has allowed the design of a questionnaire that organizes the trainer-s skills and competences. The e-Delphi method is used for realizing a creative, individual and anonymous evaluation by experts on the importance ranking that presents the criteria, sub-criteria and indicators of the e-Delphi questionnaire. Twenty Spanish experts in the lifelong learning have participated in two rounds of the e- DELPHI method. In the first round, the analysis of the experts- evaluation has allowed to establish the ranking of the most importance criteria, sub-criteria and indicators and to eliminate the least valued. The minimum level necessary to reach the consensus among experts has been achieved in the second round.Keywords: competences and skills, lifelong learningtrainers, Spain, e-DELHI method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16841295 The Frequency Graph for the Traveling Salesman Problem
Authors: Y. Wang
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Traveling salesman problem (TSP) is hard to resolve when the number of cities and routes become large. The frequency graph is constructed to tackle the problem. A frequency graph maintains the topological relationships of the original weighted graph. The numbers on the edges are the frequencies of the edges emulated from the local optimal Hamiltonian paths. The simplest kind of local optimal Hamiltonian paths are computed based on the four vertices and three lines inequality. The search algorithm is given to find the optimal Hamiltonian circuit based on the frequency graph. The experiments show that the method can find the optimal Hamiltonian circuit within several trials.Keywords: Traveling salesman problem, frequency graph, local optimal Hamiltonian path, four vertices and three lines inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17781294 Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales
Authors: Changjin Xu, Qianhong Zhang
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In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.
Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1403