Search results for: SPARQL Query Transformation

Authors: Sanaa Chafik, ImaneDaoudi, Mounim A. El Yacoubi, Hamid El Ouardi

Abstract:

Locality Sensitive Hashing (LSH) is one of the most promising techniques for solving nearest neighbour search problem in high dimensional space. Euclidean LSH is the most popular variation of LSH that has been successfully applied in many multimedia applications. However, the Euclidean LSH presents limitations that affect structure and query performances. The main limitation of the Euclidean LSH is the large memory consumption. In order to achieve a good accuracy, a large number of hash tables is required. In this paper, we propose a new hashing algorithm to overcome the storage space problem and improve query time, while keeping a good accuracy as similar to that achieved by the original Euclidean LSH. The Experimental results on a real large-scale dataset show that the proposed approach achieves good performances and consumes less memory than the Euclidean LSH.

Keywords: Approximate Nearest Neighbor Search, Content based image retrieval (CBIR), Curse of dimensionality, Locality sensitive hashing, Multidimensional indexing, Scalability.

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Authors: Krishnamoorthi R., Sheba Kezia Malarchelvi P. D.

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In this paper, an image adaptive, invisible digital watermarking algorithm with Orthogonal Polynomials based Transformation (OPT) is proposed, for copyright protection of digital images. The proposed algorithm utilizes a visual model to determine the watermarking strength necessary to invisibly embed the watermark in the mid frequency AC coefficients of the cover image, chosen with a secret key. The visual model is designed to generate a Just Noticeable Distortion mask (JND) by analyzing the low level image characteristics such as textures, edges and luminance of the cover image in the orthogonal polynomials based transformation domain. Since the secret key is required for both embedding and extraction of watermark, it is not possible for an unauthorized user to extract the embedded watermark. The proposed scheme is robust to common image processing distortions like filtering, JPEG compression and additive noise. Experimental results show that the quality of OPT domain watermarked images is better than its DCT counterpart.

Keywords: Orthogonal Polynomials based Transformation, Digital Watermarking, Copyright Protection, Visual model.

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Authors: Youssef Khmou, Said Safi

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In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  Indeed, the unitary transformation of Partial Propagator (UPP) for narrowband sources is proposed and applied on Uniform Linear Array (ULA).

Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP). The results demonstrates that when some of the sources are fully correlated and closer than the Rayleigh angular limit resolution of the broadside array, the UPP method outperforms the FBPP in both of spatial resolution and complexity.

Keywords: DOA, Uniform Linear Array, Narrowband, Propagator, Real valued transformation, Subspace, Unitary Operator.

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

Abstract:

the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction

Keywords: function, Differential subordination, Multiplier transformation.

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Authors: Asmawi A., Affendey L. S., Udzir N. I., Mahmod R.

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The topic of enhancing security in XML databases is important as it includes protecting sensitive data and providing a secure environment to users. In order to improve security and provide dynamic access control for XML databases, we presented XLog file to calculate user trust values by recording users’ bad transaction, errors and query severities. Severity-aware trust-based access control for XML databases manages the access policy depending on users' trust values and prevents unauthorized processes, malicious transactions and insider threats. Privileges are automatically modified and adjusted over time depending on user behaviour and query severity. Logging in database is an important process and is used for recovery and security purposes. In this paper, the Xlog file is presented as a dynamic and temporary log file for XML databases to enhance the level of security.

Keywords: XML database, trust-based access control, severity-aware, trust values, log file.

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Authors: Syed Musharaf Ali, Muhammad Younus Javed, Naveed Sarfraz Khattak, Athar Mohsin, UmarFarooq

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This paper introduces the effective speckle reduction of synthetic aperture radar (SAR) images using inner product spaces in undecimated wavelet domain. There are two major areas in projection onto span algorithm where improvement can be made. First is the use of undecimated wavelet transformation instead of discrete wavelet transformation. And second area is the use of smoothing filter namely directional smoothing filter which is an additional step. Proposed method does not need any noise estimation and thresholding technique. More over proposed method gives good results on both single polarimetric and fully polarimetric SAR images.

Keywords: Directional Smoothing, Inner product, Length ofvector, Undecimated wavelet transformation.

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Authors: F. Amin, S. Feizi

Abstract:

This paper describes the complex nature of organizational culture and its role in telecom organizations. To set the stage for culture change, the literature is reviewed for perspective on the role and function of culture in organizations. Organizational the­orists as well as business consultants report that a strong organizational culture is essential for success because the shared assumptions, values and culture of an organization influence the behavior of its individual members.

Keywords: Component, Telecommunication, Management, Cultural, Transformation.

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Authors: Girija Chetty, Renuka Biswas

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In this paper, we propose novel algorithmic models based on information fusion and feature transformation in crossmodal subspace for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quantization features, their transformation in cross-modal subspace, and their multimodal fusion, for emulated copy-move tamper scenario shows a significant improvement in tamper detection accuracy as compared to single mode features without transformation in cross-modal subspace.

Keywords: image tamper detection, digital forensics, correlation features image fusion

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Authors: Meltem Serhatli, Ferda N. Alpaslan

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Processing the data by computers and performing reasoning tasks is an important aim in Computer Science. Semantic Web is one step towards it. The use of ontologies to enhance the information by semantically is the current trend. Huge amount of domain specific, unstructured on-line data needs to be expressed in machine understandable and semantically searchable format. Currently users are often forced to search manually in the results returned by the keyword-based search services. They also want to use their native languages to express what they search. In this paper, an ontology-based automated question answering system on software test documents domain is presented. The system allows users to enter a question about the domain by means of natural language and returns exact answer of the questions. Conversion of the natural language question into the ontology based query is the challenging part of the system. To be able to achieve this, a new algorithm regarding free text to ontology based search engine query conversion is proposed. The algorithm is based on investigation of suitable question type and parsing the words of the question sentence.

Keywords: Description Logics, ontology, question answering, reasoning.

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Authors: Ahmed M. Elhabashy, A. Baes Mohamed, Abou El Nasr Mohamad

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Distributed Computing Systems are usually considered the most suitable model for practical solutions of many parallel algorithms. In this paper an enhanced distributed system is presented to improve the time complexity of Binary Indexed Trees (BIT). The proposed system uses multi-uniform processors with identical architectures and a specially designed distributed memory system. The analysis of this system has shown that it has reduced the time complexity of the read query to O(Log(Log(N))), and the update query to constant complexity, while the naive solution has a time complexity of O(Log(N)) for both queries. The system was implemented and simulated using VHDL and Verilog Hardware Description Languages, with xilinx ISE 10.1, as the development environment and ModelSim 6.1c, similarly as the simulation tool. The simulation has shown that the overhead resulting by the wiring and communication between the system fragments could be fairly neglected, which makes it applicable to practically reach the maximum speed up offered by the proposed model.

Keywords: Binary Index Tree (BIT), Least Significant Bit (LSB), Parallel Adder (PA), Very High Speed Integrated Circuits HardwareDescription Language (VHDL), Distributed Parallel Computing System(DPCS).

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Authors: Jakub Havlicek, Jiri Cajthaml

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The article describes the effect of the replacement of the used reference coordinate system in the georeferencing of an old map of Europe. The map was georeferenced into three types of projection – the equal-area conic (original cartographic projection), cylindrical Plate Carrée and cylindrical Mercator map projection. The map was georeferenced by means of the affine and the second-order polynomial transformation. The resulting georeferenced raster datasets from the Plate Carrée and Mercator projection were projected into the equal-area conic projection by means of projection equations. The output is the comparison of drawn graphics, the magnitude of standard deviations for individual projections and types of transformation.

Keywords: Georeferencing, reference coordinate system, transformation, standard deviation.

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Authors: Sadife Güngör, Sevilay Konya, Zeynep Karaçor

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Inflation and foreign trade are the most important economic indicator of a country. In this study, Turkey's economy with the policies adopted after 2000, given how performs an economic transformation. This transformation of the economy is discussed with inflation and foreign trade. In this context, attention is drawn to 2001 Strong Economy and Transition Program and 2006 Inflation Targeting Regime. The evaluation was performed of after the year 2000 inflation and foreign trade figures in Turkey economy. When we looked the progress, after 2000 in Turkey economy, we can say a new process was built up.

Keywords: Inflation, foreign trade, 2001 strong economy program, 2006 ınflation targeting regime.

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Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

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This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Michael Zimba, Darlison Nyirenda

Abstract:

A novel copy-move image forgery, CMIF, detection method is proposed. The proposed method presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, the proposed algorithm firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilized to extract robust features. The extracted features are invariant to additive noise, JPEG compression, and affine transformation. Finally, same affine transformation selection, SATS, a duplication verification method, is applied to detect duplicated regions. SATS is a better option than the common shift vector method because SATS is insensitive to affine transformation. Consequently, the proposed CMIF algorithm is not only fast but also more robust to attacks compared to the existing related CMIF algorithms. The experimental results show high detection rates, as high as 100% in some cases.

Keywords: Affine transformation, Radix sort, SATS, Virtual electrostatic field.

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Authors: T. Sakamoto, N. Hori

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A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: Nazira Kakulia

Abstract:

The analysis of transformation of institutional changes outlines two important characteristics. These are: the speed of the changes and their sequence. Successful transformation must be carried out in three different stages; On the first stage, macroeconomic stabilization must be achieved with the help of fiscal and monetary tools. Two-tier banking system should be established and the active functions of central bank should be replaced by the passive ones (reserve requirements and refinancing rate), together with the involvement growth of private sector. Fiscal policy by itself here means the creation of tax system which must replace previously existing direct state revenues; the share of subsidies in the state expenses must be reduced also. The second stage begins after reaching the macroeconomic stabilization at a time of change of formal institutes which must stimulate the private business. Corporate legislation creates a competitive environment at the market and the privatization of state companies takes place. Bankruptcy and contract law is created. he third stage is the most extended one, which means the formation of all state structures that is necessary for the further proper functioning of a market economy. These three stages about the cycle period of political and social transformation and the hierarchy of changes can also be grouped by the different methodology: on the first and the most short-term stage the transfer of power takes place. On the second stage institutions corresponding to new goal are created. The last phase of transformation is extended in time and it includes the infrastructural, socio-cultural and socio-structural changes. The main goal of this research is to explore and identify the features of such kind of models.

Keywords: Competitive, environment, fiscal policy, macro-economic stabilization.

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Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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Authors: F. Roger, A. Traidia, B. Reynier

Abstract:

Arc welding creates a weld pool to realize continuity between pieces of assembly. The thermal history of the weld is dependent on heat transfer and fluid flow in the weld pool. The metallurgical transformation during welding and cooling are modeled in the literature only at solid state neglecting the fluid flow. In the present paper we associate a heat transfer – fluid flow and metallurgical model for the 16MnD5 steel. The metallurgical transformation model is based on Leblond model for the diffusion kinetics and on the Koistinen-Marburger equation for Marteniste transformation. The predicted thermal history and metallurgical transformations are compared to a simulation without fluid phase. This comparison shows the great importance of the fluid flow modeling.

Keywords: Arc welding, Weld pool, Fluid flow, Metallurgical transformations.

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Authors: L. Sterken, S. Sebben, L. Löfdahl

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In this paper an alternative visualisation approach of the wake behind different vehicle body shapes with simplified and fully-detailed underbody has been proposed and analysed. This allows for a more clear distinction among the different wake regions. This visualisation is based on a transformation of the cartesian coordinates of a chosen wake plane to polar coordinates, using as filter velocities lower than the freestream. This transformation produces a polar wake plot that enables the division and quantification of the wake in a number of sections. In this paper, local drag has been used to visualise the drag contribution of the flow by the different sections. Visually, a balanced wake can be observed by the concentric behaviour of the polar plots. Alternatively, integration of the local drag of each degree section as a ratio of the total local drag yields a quantifiable approach of the wake uniformity, where different sections contribute equally to the local drag, with the exception of the wheels.

Keywords: Coordinate transformation, ground vehicle, local drag, wake.

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

Abstract:

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: Ryosuke Ito, Goro Obinata, Chikara Nagai, Youngwoo Kim

Abstract:

This paper proposes a new parameter identification method based on Linear Fractional Transformation (LFT). It is assumed that the target linear system includes unknown parameters. The parameter deviations are separated from a nominal system via LFT, and identified by organizing I/O signals around the separated deviations of the real system. The purpose of this paper is to apply LFT to simultaneously identify the parameter deviations in systems with fewer outputs than unknown parameters. As a fundamental example, this method is implemented to one degree of freedom vibratory system. Via LFT, all physical parameters were simultaneously identified in this system. Then, numerical simulations were conducted for this system to verify the results. This study shows that all the physical parameters of a system with fewer outputs than unknown parameters can be effectively identified simultaneously using LFT.

Keywords: Identification, Linear Fractional Transformation, Right inverse system

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Authors: E. Zippelius

Abstract:

Urban design aims to provide a stage for public life that, when once brought to life, is right away subject to subtle but continuous transformation. This paper explores such transformations and searches for ways how public life can be reinforced in the case of a housing settlement for the displaced in Nicosia, Cyprus. First, a sound basis of theoretical knowledge is established through literature review, notably the theory of the Production of Space by Henri Lefebvre, exploring its potential and defining key criteria for the following empirical analysis. The analysis is pinpointing the differences between spatial practice, representation of space and spaces of representation as well as their interaction, alliance, or even conflict. In doing so uncertainties, chances and challenges are unraveled that will be consequently linked to practice and action and lead to the formulation of a design strategy. A strategy, though, that does not long for achieving an absolute, finite certainty but understands the three dimensions of space formulated by Lefebvre as equal and space as continuously produced, hence, unfinished.

Keywords: Production of space, public space, urban life, urban transformation.

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Authors: Sana Hamdi, Emna Bouazizi, Sami Faiz

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In recent years, real-time spatial applications, like location-aware services and traffic monitoring, have become more and more important. Such applications result dynamic environments where data as well as queries are continuously moving. As a result, there is a tremendous amount of real-time spatial data generated every day. The growth of the data volume seems to outspeed the advance of our computing infrastructure. For instance, in real-time spatial Big Data, users expect to receive the results of each query within a short time period without holding in account the load of the system. But with a huge amount of real-time spatial data generated, the system performance degrades rapidly especially in overload situations. To solve this problem, we propose the use of data partitioning as an optimization technique. Traditional horizontal and vertical partitioning can increase the performance of the system and simplify data management. But they remain insufficient for real-time spatial Big data; they can’t deal with real-time and stream queries efficiently. Thus, in this paper, we propose a novel data partitioning approach for real-time spatial Big data named VPA-RTSBD (Vertical Partitioning Approach for Real-Time Spatial Big data). This contribution is an implementation of the Matching algorithm for traditional vertical partitioning. We find, firstly, the optimal attribute sequence by the use of Matching algorithm. Then, we propose a new cost model used for database partitioning, for keeping the data amount of each partition more balanced limit and for providing a parallel execution guarantees for the most frequent queries. VPA-RTSBD aims to obtain a real-time partitioning scheme and deals with stream data. It improves the performance of query execution by maximizing the degree of parallel execution. This affects QoS (Quality Of Service) improvement in real-time spatial Big Data especially with a huge volume of stream data. The performance of our contribution is evaluated via simulation experiments. The results show that the proposed algorithm is both efficient and scalable, and that it outperforms comparable algorithms.

Keywords: Real-Time Spatial Big Data, Quality Of Service, Vertical partitioning, Horizontal partitioning, Matching algorithm, Hamming distance, Stream query.

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Authors: D. A. K. S. Gunaratna, N. D. Kodikara, H. L. Premaratne

Abstract:

Automatic currency note recognition invariably depends on the currency note characteristics of a particular country and the extraction of features directly affects the recognition ability. Sri Lanka has not been involved in any kind of research or implementation of this kind. The proposed system “SLCRec" comes up with a solution focusing on minimizing false rejection of notes. Sri Lankan currency notes undergo severe changes in image quality in usage. Hence a special linear transformation function is adapted to wipe out noise patterns from backgrounds without affecting the notes- characteristic images and re-appear images of interest. The transformation maps the original gray scale range into a smaller range of 0 to 125. Applying Edge detection after the transformation provided better robustness for noise and fair representation of edges for new and old damaged notes. A three layer back propagation neural network is presented with the number of edges detected in row order of the notes and classification is accepted in four classes of interest which are 100, 500, 1000 and 2000 rupee notes. The experiments showed good classification results and proved that the proposed methodology has the capability of separating classes properly in varying image conditions.

Keywords: Artificial intelligence, linear transformation and pattern recognition.

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Authors: Bekim Avdiaj

Abstract:

Everyday life is and will be influenced depending on the developments that society undergoes throughout the history. Particularly, countries undergoing transition from one system to another sustain the greatest impact in trying to embrace the modern system. Kosovo society had the fortune to experience a change, which began in late 1999 to continue up to date. One of the 'developments' of the time with the evolution in Kosovo society was the transition from the traditional education system into the modern one. This transformation began immediately after the war, to continue even today. It was started by internationals, which governed and administered Kosovo society, including education. There was a great 'evolution', because almost the entire system was 'changed'. Among other things, for the first time it was enabled the opening of private schools from the lowest level up to the colleges and universities. This paper will address: how much was ready the society to embrace such a 'cultural' change in education, respectively, how much were prepared teachers for such changes; as it was actually thought to be a modern education system, how much was it according to international standards; what are the results and current situation in Kosovo education.

Keywords: Education, evolution, reform, transformation.

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Authors: Prompt Udomdech, Eleni Papadonikolaki, Andrew Davies

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Building Information Modelling (BIM) is the major technological trend among built environment organisations. Digitalising businesses and operations, BIM brings forth a digital transformation in any built environment industry. The adoption of BIM presents challenges for organisations, especially Small- and Medium-sized Enterprises (SMEs). The main problem for built environment SMEs is the lack of project actors with adequate BIM competences. The research highlights learning in projects as the key and explores into the learning of BIM in projects of designers and engineers within Thai design and engineering SMEs. The study uncovers three impeding attributes which are: a) lack of English proficiency; b) unfamiliarity with digital technologies; and c) absence of public standards. This research expands on the literature of BIM competences and adoption.

Keywords: BIM competences and adoption, digital transformation, learning in projects, SMEs, and developing built environment industry.

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Authors: Jia Xu

Abstract:

There is a lot of bottom space in the teaching area of Zijingang Campus of Zhejiang University, which benefits to the ventilation, heat dissipation, circulation, partition of quiet and noisy areas and diversification of spaces. Hangzhou is hot in summer but cold in winter, so teachers and students spend much less time in the bottom space of buildings in winter than in summer. Recently, depending on the teachers and students’ proposals, the school transformed the bottom space in the teaching area to provide space for relaxing, chatting and staying in winter. Surveying and analyzing the existing ways to transform, the paper researches deeply on the transformation projects of bottom space in the teaching buildings. It is believed that this paper can be a salutary lesson to make the bottom space in the teaching areas of universities richer and bring more diverse activities for teachers and students.

Keywords: Bottom space, teaching area, transformation, Zijingang Campus of Zhejiang University.

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Authors: Hikmat A. M. Abd-El-Jaber, Tengku M. T. Sembok

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The information on the Web increases tremendously. A number of search engines have been developed for searching Web information and retrieving relevant documents that satisfy the inquirers needs. Search engines provide inquirers irrelevant documents among search results, since the search is text-based rather than semantic-based. Information retrieval research area has presented a number of approaches and methodologies such as profiling, feedback, query modification, human-computer interaction, etc for improving search results. Moreover, information retrieval has employed artificial intelligence techniques and strategies such as machine learning heuristics, tuning mechanisms, user and system vocabularies, logical theory, etc for capturing user's preferences and using them for guiding the search based on the semantic analysis rather than syntactic analysis. Although a valuable improvement has been recorded on search results, the survey has shown that still search engines users are not really satisfied with their search results. Using ontologies for semantic-based searching is likely the key solution. Adopting profiling approach and using ontology base characteristics, this work proposes a strategy for finding the exact meaning of the query terms in order to retrieve relevant information according to user needs. The evaluation of conducted experiments has shown the effectiveness of the suggested methodology and conclusion is presented.

Keywords: information retrieval, user profiles, semantic Web, ontology, search engine.

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Authors: A. Selmi

Abstract:

Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: Differential transformation method, functionally graded material, mode shape, natural frequency.

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