Search results for: entity relation graph

Authors: Valeria M. Pequeno, Joao Carlos G. M. Pires

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Data Warehouses (DWs) are repositories which contain the unified history of an enterprise for decision support. The data must be Extracted from information sources, Transformed and integrated to be Loaded (ETL) into the DW, using ETL tools. These tools focus on data movement, where the models are only used as a means to this aim. Under a conceptual viewpoint, the authors want to innovate the ETL process in two ways: 1) to make clear compatibility between models in a declarative fashion, using correspondence assertions and 2) to identify the instances of different sources that represent the same entity in the real-world. This paper presents the overview of the proposed framework to model the ETL process, which is based on the use of a reference model and perspective schemata. This approach provides the designer with a better understanding of the semantic associated with the ETL process.

Keywords: conceptual data model, correspondence assertions, data warehouse, data integration, ETL process, object relational database.

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Authors: A. Abdikian

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A quantum breathing mode has been theatrically studied in quantum dusty plasma. By using linear quantum hydrodynamic model, not only the quantum dispersion relation of rotation mode but also void structure has been derived in the presence of an external magnetic field. Although the phase velocity of the magnetized quantum breathing mode is greater than that of unmagnetized quantum breathing mode, attenuation of the magnetized quantum breathing mode along radial distance seems to be slower than that of unmagnetized quantum breathing mode. Clearly, drawing the quantum breathing mode in the presence and absence of a magnetic field, we found that the magnetic field alters the distribution of dust particles and changes the radial and azimuthal velocities around the axis. Because the magnetic field rotates the dust particles and collects them, it could compensate the void structure.

Keywords: The linear quantum hydrodynamic model, the magnetized quantum breathing mode, the quantum dispersion relation of rotation mode, void structure.

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Authors: Tomáš Bublík, Miroslav Virius

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This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and subgraph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, Scripthon, source code recognition

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Authors: M. F. Yilmaz, B. Ö. Çağlayan

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Fragility curve is an effective common used tool to determine the earthquake performance of structural and nonstructural components. Also, it is used to determine the nonlinear behavior of bridges. There are many historical bridges in the Turkish railway network; the earthquake performances of these bridges are needed to be investigated. To derive fragility curve Intensity measures (IMs) and Engineering demand parameters (EDP) are needed to be determined. And the relation between IMs and EDP are needed to be derived. In this study, a typical simply supported steel girder riveted railway bridge is studied. Fragility curves of this bridge are derived by two parameters lognormal distribution. Time history analyses are done for selected 60 real earthquake data to determine the relation between IMs and EDP. Moreover, efficiency, practicality, and sufficiency of three different IMs are discussed. PGA, Sa(0.2s) and Sa(1s), the most common used IMs parameters for fragility curve in the literature, are taken into consideration in terms of efficiency, practicality and sufficiency.

Keywords: Railway bridges, earthquake performance, fragility analyses, selection of intensity measures.

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Authors: A. S. Tolba, A.H. El-Baz, A.A. El-Harby

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The task of face recognition has been actively researched in recent years. This paper provides an up-to-date review of major human face recognition research. We first present an overview of face recognition and its applications. Then, a literature review of the most recent face recognition techniques is presented. Description and limitations of face databases which are used to test the performance of these face recognition algorithms are given. A brief summary of the face recognition vendor test (FRVT) 2002, a large scale evaluation of automatic face recognition technology, and its conclusions are also given. Finally, we give a summary of the research results.

Keywords: Combined classifiers, face recognition, graph matching, neural networks.

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Authors: V. Hepsiba Mabel, K. Alagarsamy, Justus S.

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Chord formation in western music notations is an intelligent art form which is learnt over the years by a musician to acquire it. Still it is a question of creativity that brings the perfect chord sequence that matches music score. This work focuses on the process of forming chords using a custom-designed knowledgebase (KB) of Music Expert System. An optimal Chord-Set for a given music score is arrived by using the chord-pool in the KB and the finding the chord match using Jusic Distance (JD). Conceptual Graph based knowledge representation model is followed for knowledge storage and retrieval in the knowledgebase.

Keywords: Knowledge, Music, Representation, Knowledgebase, Chord-Set.

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Authors: Vijay Pal Singh, Yogesh Chandra Kotiyal

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Structures are a combination of various load carrying members which transfer the loads to the foundation from the superstructure safely. At the design stage, the loading of the structure is defined and appropriate material choices are made based upon their properties, mainly related to strength. The strength of materials kept on reducing with time because of many factors like environmental exposure and deformation caused by unpredictable external loads. Hence, to predict the strength of materials used in structures, various techniques are used. Among these techniques, Non-destructive techniques (NDT) are the one that can be used to predict the strength without damaging the structure. In the present study, the compressive strength of concrete has been predicted using Artificial Neural Network (ANN). The predicted strength was compared with the experimentally obtained actual compressive strength of concrete and equations were developed for different models. A good co-relation has been obtained between the predicted strength by these models and experimental values. Further, the co-relation has been developed using two NDT techniques for prediction of strength by regression analysis. It was found that the percentage error has been reduced between the predicted strength by using combined techniques in place of single techniques.

Keywords: Rebound, ultra-sonic pulse, penetration, ANN, NDT, regression.

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Authors: Chris Ewe, Naoum Jamous, Holger Schrödl

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Like most entrepreneurs, data center operators pursue goals such as profit-maximization, improvement of the company’s reputation or basically to exist on the market. Part of those aims is to guarantee a given quality of service. Quality characteristics are specified in a contract called the service level agreement. Central part of this agreement is non-functional properties of an IT service. The system availability is one of the most important properties as it will be shown in this paper. To comply with availability requirements, data center operators can use virtualization technologies. A clear model to assess the effect of virtualization functions on the parts of a data center in relation to the system availability is still missing. This paper aims to introduce a basic model that shows these connections, and consider if the identified effects are positive or negative. Thus, this work also points out possible disadvantages of the technology. In consequence, the paper shows opportunities as well as risks of data center virtualization in relation to system availability.

Keywords: Availability, cloud computing IT service, quality of service, service level agreement, virtualization.

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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: Peter Clutterbuck, Terry Rowlands, Owen Seamons

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In this paper we describe one critical research program within a complex, ongoing multi-year project (2010 to 2014 inclusive) with the overall goal to improve the learning outcomes for first year undergraduate commerce/business students within an Information Systems (IS) subject with very large enrolment. The single research program described in this paper is the analysis of student attitudes and decision making in relation to the availability of formative assessment feedback via Web-based real time conferencing and document exchange software (Adobe Connect). The formative assessment feedback between teaching staff and students is in respect of an authentic problem-based, team-completed assignment. The analysis of student attitudes and decision making is investigated via both qualitative (firstly) and quantitative (secondly) application of the Theory of Planned Behavior (TPB) with a two statistically-significant and separate trial samples of the enrolled students. The initial qualitative TPB investigation revealed that perceived self-efficacy, improved time-management, and lecturer-student relationship building were the major factors in shaping an overall favorable student attitude to online feedback, whilst some students expressed valid concerns with perceived control limitations identified within the online feedback protocols. The subsequent quantitative TPB investigation then confirmed that attitude towards usage, subjective norms surrounding usage, and perceived behavioral control of usage were all significant in shaping student intention to use the online feedback protocol, with these three variables explaining 63 percent of the variance in the behavioral intention to use the online feedback protocol. The identification in this research of perceived behavioral control as a significant determinant in student usage of a specific technology component within a virtual learning environment (VLE) suggests that VLEs could now be viewed not as a single, atomic entity, but as a spectrum of technology offerings ranging from the mature and simple (e.g., email, Web downloads) to the cutting-edge and challenging (e.g., Web conferencing and real-time document exchange). That is, that all VLEs should not be considered the same. The results of this research suggest that tertiary students have the technological sophistication to assess a VLE in this more selective manner.

Keywords: Formative assessment feedback, virtual learning environment, theory of planned behavior, perceived behavioral control.

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Authors: Ali Ghiaseddin , Akram Nemati

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In a pilot plant scale of a fluidized bed reactor, a reduction reaction of sodium sulfate by natural gas has been investigated. Natural gas is applied in this study as a reductant. Feed density, feed mass flow rate, natural gas and air flow rate (independent parameters)and temperature of bed and CO concentration in inlet and outlet of reactor (dependent parameters) were monitored and recorded at steady state. The residence time was adjusted close to value of traditional reaction [1]. An artificial neural network (ANN) was established to study dependency of yield and carbon gradient on operating parameters. Resultant 97% accuracy of applied ANN is a good prove that natural gas can be used as a reducing agent. Predicted ANN model for relation between other sources carbon gradient (accuracy 74%) indicates there is not a meaningful relation between other sources carbon variation and reduction process which means carbon in granule does not have significant effect on the reaction yield.

Keywords: reduction by natural gas, fluidized bed, sulfate, sulfide, artificial neural network

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Authors: Rahmatollah Amirjani

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By the emergence of the debate over the failure of Regionalism in the late 1970s, Critical Regional­ism was introduced as a different way to respond to the state of architecture in the post-war era. Critical Regionalism is most often understood as a discourse that not only mediates the language of modern architecture with the local cultures but also revives the relation between architecture and spectator as indexed by capitalism. Since the inception of Critical Regionalism, a large number of architectural practices have emerged around the globe; however, the work of the well-known Portuguese architect, Álvaro Siza, is considered as a unique case amongst works associated with the discourse of Critical Regionalism. This paper intends to respond to a number of questions, including; what are the origins of Critical Regionalism? How does Siza’s design strategy correspond to the thematic of Critical Regionalism? How does Siza recover the relation between object and subject in most of his projects? Using Siza’s housing project for the Malagueira district in Évora, Portugal, this article will attempt to answer these questions, and highlight Alvaro Siza’s design procedure which goes beyond the existing discourse of Critical Regionalism and contributes to our understanding of this practice.

Keywords: Alvaro Siza, critical regionalism, Malagueira Housing, placelessness.

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes

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This article deals with the conceptual modeling under uncertainty. First, the division of information systems with their definition will be described, focusing on those where the construction of a conceptual model is suitable for the design of future information system database. Furthermore, the disadvantages of the traditional approach in creating a conceptual model and database design will be analyzed. A comprehensive methodology for the creation of a conceptual model based on analysis of client requirements and the selection of a suitable domain model is proposed here. This article presents the expert system used for the construction of a conceptual model and is a suitable tool for database designers to create a conceptual model.

Keywords: Conceptual model, conceptual modeling, database, methodology, uncertainty, information system, entity, attribute, relationship, conceptual domain model, fuzzy.

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Authors: Kwa-Sur Tam

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This paper reviews various approaches that have been used for the modeling and simulation of large-scale engineering systems and determines their appropriateness in the development of a RICS modeling and simulation tool. Bond graphs, linear graphs, block diagrams, differential and difference equations, modeling languages, cellular automata and agents are reviewed. This tool should be based on linear graph representation and supports symbolic programming, functional programming, the development of noncausal models and the incorporation of decentralized approaches.

Keywords: Interdisciplinary, dynamic, functional programming, object-oriented.

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Authors: C.Natarajan, S.K.Ayyaswamy

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Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: Kai-Siou Wu, Justie Su-Tzu Juan

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In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = ⟨u_0, u_1, u_2, ..., u_{n−1}, u_0⟩ and C_2 = ⟨v_0, v_1, v_2, ..., v_{n−1}, v_0⟩ in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.

Keywords: Hamiltonian, independent, cycle, Cartesian product, mutually independent Hamiltonicity

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Authors: Cătălin Nicolae Albu, Nadia Albu, Maria Mădălina Gîrbină

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There is limited evidence from various countries about the possible impact of various criteria to be used to determine the scope of the IFRS for SMEs issued in 2009 and, research is needed in this area. We provide evidence from Romania, an emerging economy member of the European Union. The aim of this paper is to analyze in a local setting if size is a relevant factor for deciding between local and global standards for SMEs. Our results indicate that size is a moderate indicator of the existence of possible users interested in financial statements and that there is a difference between the scopes of the standard determined on various criteria.. Also, we suggest that the international exposure is quite reduced in the case of SMEs, but is sufficient to suggest that at least some SMEs would benefit from international comparability of financial statements

Keywords: SMEs, IFRS for SMEs, accounting regulation, entity's size.

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Authors: D. A. Binas, M. Konidari, C. Bourgioti, L. Angela Moulopoulou, T. L. Economopoulos, G. K. Matsopoulos

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High grade ovarian epithelial cancer (OEC) is the most fatal gynecological cancer and poor prognosis of this entity is closely related to considerable intratumoral genetic heterogeneity. By examining imaging data, it is possible to assess the heterogeneity of tumorous tissue. This study presents a methodology for aligning, segmenting and finally visualizing information from various magnetic resonance imaging series, in order to construct 3D models of heterogeneity maps from the same tumor in OEC patients. The proposed system may be used as an adjunct digital tool by health professionals for personalized medicine, as it allows for an easy visual assessment of the heterogeneity of the examined tumor.

Keywords: K-means segmentation, ovarian epithelial cancer, quantitative characteristics, registration, tumor visualization.

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Authors: M. M. M. Jaradat, M. K. Al-Qeyyam

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The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

Keywords: Cycle space, minimum cycle basis, wreath product.

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Authors: Ornst J., Voracek J., Allouache A., Allouache D.

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Lack of resources for road infrastructure financing is a problem that currently affects not only eastern European economies but also many other countries especially in relation to the impact of global financial crisis. In this context, we are talking about the socalled short-investment problem as a result of long-term lack of investment resources. Based on an analysis of road infrastructure financing in the Czech Republic this article points out at weaknesses of current system and proposes a long-term planning methodology supported by system approach. Within this methodology and using created system dynamic model the article predicts the development of short-investment problem in the Country and in reaction on the downward trend of certain sources the article presents various scenarios resulting from the change of the structure of financial sources. In the discussion the article focuses more closely on the possibility of introduction of tax on vehicles instead of taxes with declining revenue streams and estimates its approximate price in relation to reaching various solutions of short-investment in time.

Keywords: Road financing, road infrastructure development, system dynamics

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Authors: Orawan Boriban, Phatthanan Chaiyabut

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The purpose of this research is to study motivation factors and also to study factors relation to job performance to compare motivation factors under the personal factor classification such as gender, age, income, educational level, marital status, and working duration; and to study the relationship between Motivation Factors and Job Performance with job satisfactions. The sample groups utilized in this research were 400 Suan Sunandha Rajabhat University employees. This research is a quantitative research using questionnaires as research instrument. The statistics applied for data analysis including percentage, mean, and standard deviation. In addition, the difference analysis was conducted by t value computing, one-way analysis of variance and Pearson’s correlation coefficient computing. The findings of the study results were as follows the findings showed that the aspects of job promotion and salary were at the moderate levels. Additionally, the findings also showed that the motivations that affected the revenue branch chiefs’ job performance were job security, job accomplishment, policy and management, job promotion, and interpersonal relation.

Keywords: Motivation Factors, Job Performance, Suan Sunandha Rajabhat University Employee.

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Authors: B. Selma

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The aim of this study is to test the feasibility of SIPINA method to predict the harmfulness parameters controlling the seismic response. The approach developed takes into consideration both the focal depth and the peak ground acceleration. The parameter to determine is displacement. The data used for the learning of this method and analysis nonlinear seismic are described and applied to a class of models damaged to some typical structures of the existing urban infrastructure of Jassy, Romania. The results obtained indicate an influence of the focal depth and the peak ground acceleration on the displacement.

Keywords: SIPINA method, seism, focal depth, peak ground acceleration, displacement.

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Authors: Youssou Faye, Ibrahima Niang, Thomas Noel

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Access control is a critical security service in Wire- less Sensor Networks (WSNs). To prevent malicious nodes from joining the sensor network, access control is required. On one hand, WSN must be able to authorize and grant users the right to access to the network. On the other hand, WSN must organize data collected by sensors in such a way that an unauthorized entity (the adversary) cannot make arbitrary queries. This restricts the network access only to eligible users and sensor nodes, while queries from outsiders will not be answered or forwarded by nodes. In this paper we presentee different access control schemes so as to ?nd out their objectives, provision, communication complexity, limits, etc. Using the node density parameter, we also provide a comparison of these proposed access control algorithms based on the network topology which can be flat or hierarchical.

Keywords: Access Control, Authentication, Key Management, Wireless Sensor Networks.

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Authors: Ashok V. Borhade, Sanjay G. Wakchaure

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Pure phase gallosilicate nitrite sodalite has been synthesized in a single step by low temperature (373 oK) hydrothermal technique. The product obtained was characterized using a combination of techniques including X-ray powder diffraction, IR, Raman spectroscopy, SEM, MAS NMR spectroscopy as well as thermogravimetry. Sodalite with an ideal composition was obtained after synthesis at 3730K and seven days duration using alkaline medium. The structural features of the Na8[GaSiO4]6(NO2)2 sodalite were investigated by IR, MAS NMR spectroscopy of 29Si and 23Na nuclei and by Reitveld refinement of X-ray powder diffraction data. The crystal structure of this sodalite has been refined in the space group P 4 3n; with a cell parameter 8.98386Å, V= 726.9 Å, (Rwp= 0.077 and Rp=0.0537) and Si-O-Ga angle is found to be 132.920 . MAS NMR study confirms complete ordering of Si and Ga in the gallosilicate framework. The surface area of single entity with stoichiometry Na8[GaSiO4]6(NO2)2 was found to be 8.083 x10-15 cm2/g.

Keywords: Gallosilicate, hydrothermal, nitrite, Reitveldrefinement.

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Authors: Hanan A. M. Abd Alla, Lilac A. E. Al-Safadi

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In this paper, a novel multi join algorithm to join multiple relations will be introduced. The novel algorithm is based on a hashed-based join algorithm of two relations to produce a double index. This is done by scanning the two relations once. But instead of moving the records into buckets, a double index will be built. This will eliminate the collision that can happen from a complete hash algorithm. The double index will be divided into join buckets of similar categories from the two relations. The algorithm then joins buckets with similar keys to produce joined buckets. This will lead at the end to a complete join index of the two relations. without actually joining the actual relations. The time complexity required to build the join index of two categories is Om log m where m is the size of each category. Totaling time complexity to O n log m for all buckets. The join index will be used to materialize the joined relation if required. Otherwise, it will be used along with other join indices of other relations to build a lattice to be used in multi-join operations with minimal I/O requirements. The lattice of the join indices can be fitted into the main memory to reduce time complexity of the multi join algorithm.

Keywords: Multi join, Relation, Lattice, Join indices.

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Authors: Abbas Moshref Razavi, Rodina Ahmad

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To motivate users to adopt and use information systems effectively, the nature of motivation should be carefully investigated. People are usually motivated within ongoing processes which include a chain of states such as perception, stimulation, motivation, actions and reactions and finally, satisfaction. This study assumes that the relevant motivation processes should be executed in a proper and continuous manner to be able to persistently motivate and re-motivate people in organizational settings and towards information systems. On this basis, the study attempts to propose possible relationships between this process-nature view of motivation in terms of the common chain of states and the nearly unique properties of information systems as is perceived by users in the sense of a knowledgeable and authoritative entity. In the conclusion section, some guidelines for practitioners are suggested to ease their tasks for motivating people to adopt and use information systems.

Keywords: Information Systems, Satisfaction, Motivation

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Authors: C. Iihoshi, G.A. MacRae, G.W. Rodgers, J.G. Chase

Abstract:

Slab sliding system (SSS) with Coulomb friction  interface between slab and supporting frame is a passive structural  vibration control technology. The system can significantly reduce the  slab acceleration and accompanied lateral force of the frame. At the  same time it is expected to cause the slab displacement magnification  by sliding movement. To obtain the general comprehensive seismic  response of a single story structure, inelastic response spectra were  computed for a large ensemble of ground motions and a practical range  of structural periods and friction coefficient values. It was shown that  long period structures have no trade-off relation between force  reduction and displacement magnification with respect to elastic  response, unlike short period structures. For structures with the  majority of mass in the slab, the displacement magnification value can  be predicted according to simple inelastic displacement relation for  inelastically responding SDOF structures because the system behaves  elastically to a SDOF structure.

 

Keywords: Earthquake, Isolation, Slab, Sliding.

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Authors: Daya Weerasinghe

Abstract:

Parental expectations often differ to that of their children and the influence and involvement of parents, at home, may affect the student performance in the classroom. This paper presents results from a survey of Asian and European background secondary school mathematics students (N=128) in Melbourne, Australia. Student responses to survey questions were analysed using confirmatory factor analysis, followed by t-tests and ANOVA. The aim of the analysis was to identify similarities and differences in parental expectations in relation to ethnicity, gender, and the year level of the students. The notable findings from the analysis showed no significant difference (at 0.05 level) in parental expectations and student performance, in relation to ethnicity or gender. Conversely, there was a significant difference in both parental expectations and student performance between year 7 and year 12 students. Further, whilst there was a significant difference in parental expectations between year 7 and year 11 students, the students’ performances were not significantly different. The results suggest further research may be needed to understand the parental expectations and student performance between the lower and upper secondary school mathematics students.

Keywords: Ethnic background, gender, parental expectations, student performance, year level.

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Authors: Gouri Prakash

Abstract:

One of the common problems encountered in software engineering is addressing and responding to the changing nature of requirements. While several approaches have been devised to address this issue, ranging from instilling resistance to changing requirements in order to mitigate impact to project schedules, to developing an agile mindset towards requirements, the approach discussed in this paper is one of conceptualizing the delta in requirement and modeling it, in order to plan a response to it. To provide some context here, change is first formally identified and categorized as either formal change or informal change. While agile methodology facilitates informal change, the approach discussed in this paper seeks to develop the idea of facilitating formal change. To collect, document meta-requirements that represent the phenomena of change would be a pro-active measure towards building a realistic cognition of the requirements entity that can further be harnessed in the software engineering process.

Keywords: Change Management, Agile methodology, Metarequirements

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Authors: Abraham V. M., I. Sahul Hamid

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A decomposition of a graph G is a collection ψ of graphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by ¤Çia(G). Similarly the cyclic decomposition number ¤Çc(G) is defined. In this paper we begin an investigation of these parameters.

Keywords: Cycle decomposition, Induced acyclic path decomposition, Induced acyclic path decomposition number.

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