Search results for: power transformation

Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Tiexin Wang, Sebastien Truptil, Frederick Benaben

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Model transformation, as a pivotal aspect of Modeldriven engineering, attracts more and more attentions both from researchers and practitioners. Many domains (enterprise engineering, software engineering, knowledge engineering, etc.) use model transformation principles and practices to serve to their domain specific problems; furthermore, model transformation could also be used to fulfill the gap between different domains: by sharing and exchanging knowledge. Since model transformation has been widely used, there comes new requirement on it: effectively and efficiently define the transformation process and reduce manual effort that involved in. This paper presents an automatic model transformation methodology based on semantic and syntactic comparisons, and focuses particularly on granularity issue that existed in transformation process. Comparing to the traditional model transformation methodologies, this methodology serves to a general purpose: crossdomain methodology. Semantic and syntactic checking measurements are combined into a refined transformation process, which solves the granularity issue. Moreover, semantic and syntactic comparisons are supported by software tool; manual effort is replaced in this way.

Keywords: Automatic model transformation, granularity issue, model-driven engineering, semantic and syntactic comparisons.

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Authors: Nan-Chyuan Tsai, Sheng-Liang Hsu

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An innovative tri-axes micro-power receiver is proposed. The tri-axes micro-power receiver consists of two sets 3-D micro-solenoids and one set planar micro-coils in which iron core is embedded. The three sets of micro-coils are designed to be orthogonal to each other. Therefore, no matter which direction the flux is present along, the magnetic energy can be harvested and transformed into electric power. Not only dead space of receiving power is mostly reduced, but also transformation efficiency of electromagnetic energy to electric power can be efficiently raised. By employing commercial software, Ansoft Maxwell, the preliminary simulation results verify that the proposed micro-power receiver can efficiently pick up the energy transmitted by magnetic power source. As to the fabrication process, the isotropic etching technique is employed to micro-machine the inverse-trapezoid fillister so that the copper wire can be successfully electroplated. The adhesion between micro-coils and fillister is much enhanced.

Keywords: Wireless Power Transmission, Magnetic Flux, Tri-axes Micro-power Receiver

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Authors: Sinnakkrishnan Perumal, Nitish Pandey

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Business transformation initiatives are required by any organization to jump from its normal mode of operation to the one that is suitable for the change in the environment such as competitive pressures, regulatory requirements, changes in labor market, etc., or internal such as changes in strategy/vision, changes in the capability, change in the management, etc. Recent advances in information technology in automating the business processes have the potential to transform an organization to provide it with a sustained competitive advantage. Process constitutes the skeleton of a business. Thus, for a business to exist and compete well, it is essential for the skeleton to be robust and agile. This paper details “transformation" from a business perspective, methodologies to bring about an effective transformation, process-based transformation, and the role of services computing in this. Further, it details the benefits that could be achieved through services computing.

Keywords: Business Transformation, Services Oriented Architecture, Business Processes, Process-based Transformation.

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Authors: M.Nafar, A.H.Gheisari, A.Alesaadi

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Since large power transformers are the most expensive and strategically important components of any power generator and transmission system, their reliability is crucially important for the energy system operation. Also, Circuit breakers are very important elements in the power transmission line so monitoring the events gives a knowledgebase to determine time to the next maintenance. This paper deals with the introduction of the comparative method of the state estimation of transformers and Circuit breakers using continuous monitoring of voltage, current. This paper gives details a new method based on wavelet to apparatus insulation monitoring. In this paper to insulation monitoring of transformer, a new method based on wavelet transformation and neutral point analysis is proposed. Using the EMTP tools, fault in transformer winding and the detailed transformer winding model were simulated. The current of neutral point of winding was analyzed by wavelet transformation. It is shown that the neutral current of the transformer winding has useful information about fault in insulation of the transformer.

Keywords: Wavelet, Power Transformer, EMTP, CircuitBreaker, Monitoring

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Authors: C. G. Jinimole, A. Harsha

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One of the key problems facing in the analysis of Computed Tomography (CT) images is the poor contrast of the images. Image enhancement can be used to improve the visual clarity and quality of the images or to provide a better transformation representation for further processing. Contrast enhancement of images is one of the acceptable methods used for image enhancement in various applications in the medical field. This will be helpful to visualize and extract details of brain infarctions, tumors, and cancers from the CT image. This paper presents a comparison study of five contrast enhancement techniques suitable for the contrast enhancement of CT images. The types of techniques include Power Law Transformation, Logarithmic Transformation, Histogram Equalization, Contrast Stretching, and Laplacian Transformation. All these techniques are compared with each other to find out which enhancement provides better contrast of CT image. For the comparison of the techniques, the parameters Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE) are used. Logarithmic Transformation provided the clearer and best quality image compared to all other techniques studied and has got the highest value of PSNR. Comparison concludes with better approach for its future research especially for mapping abnormalities from CT images resulting from Brain Injuries.

Keywords: Computed tomography, enhancement techniques, increasing contrast, PSNR and MSE.

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Authors: Ayman El-Garem, Riham Adel

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Digital transformation is about identifying the necessary changes of the entire business model, rethinking how to transform the traditional operations into digital ones that can create better value to its customers. Efforts are common across industries, but they often fail due to a lack of understanding of the factors required to focus on and change to be able to embark in digital transformation successfully. Further research is required to bridge the knowledge gap between academia and industry to support companies starting their digital transformation journey. To date there is no consensus on digital transformation key success factors. Therefore, the aim of this paper is to identify the success factors in digital transformation journey, throughout conducting a systematic literature review of 134 peer-reviewed articles to get better insights regarding the research progress in this field.  After completing the systematic literature review it will be followed by Delphi study to get experts consensus on the most significant factors affecting digital transformation implementation. The findings indicate that organizations undergoing digital transformation should focus mainly on (1) well managed digital transformation activities; (2) digital business strategy; (3) supportive culture; (4) top management support; (5) organizational change capabilities.

Keywords: Digital transformation, key success factors, literature review, Delphi study.

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Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: Frequency transformation, Bilinear z-transformation, Pre-warping frequency, Digital filters, Analog filters, Pascal’s triangle.

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Authors: Dong-Yan Huang, Ee Ping Ong, Susanto Rahardja, Minghui Dong, Haizhou Li

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The transformation of vocal characteristics aims at modifying voice such that the intelligibility of aphonic voice is increased or the voice characteristics of a speaker (source speaker) to be perceived as if another speaker (target speaker) had uttered it. In this paper, the current state-of-the-art voice characteristics transformation methodology is reviewed. Special emphasis is placed on voice transformation methodology and issues for improving the transformed speech quality in intelligibility and naturalness are discussed. In particular, it is suggested to use the modulation theory of speech as a base for research on high quality voice transformation. This approach allows one to separate linguistic, expressive, organic and perspective information of speech, based on an analysis of how they are fused when speech is produced. Therefore, this theory provides the fundamentals not only for manipulating non-linguistic, extra-/paralinguistic and intra-linguistic variables for voice transformation, but also for paving the way for easily transposing the existing voice transformation methods to emotion-related voice quality transformation and speaking style transformation. From the perspectives of human speech production and perception, the popular voice transformation techniques are described and classified them based on the underlying principles either from the speech production or perception mechanisms or from both. In addition, the advantages and limitations of voice transformation techniques and the experimental manipulation of vocal cues are discussed through examples from past and present research. Finally, a conclusion and road map are pointed out for more natural voice transformation algorithms in the future.

Keywords: Voice transformation, Voice Quality, Emotion, Individuality, Speaking Style, Speech Production, Speech Perception.

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Authors: Driss Kettani

Abstract:

In this paper, we shed light on the “Digital Divide 2.0,” which we see as COVID-19’s version of the digital divide. We believe that “fighting” against digital divide 2.0 necessitates for a country to be seriously advanced in the global digital transformation that is, naturally, a complex, delicate, costly and long-term process. We build an argument supporting our assumption and, from there, we present the foundations of a computational framework to guide and streamline digital transformation at all levels.

Keywords: Digital divide 2.0, digital transformation, ICTs for development, computational outcomes assessment.

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Authors: Hamze Torabian, Mohammad Mehrabioun Mohammadi

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Like many other industries, the payment industry has been affected by digital transformation. The importance of digital transformation in the payment industry is very crucial. Because the payment industry is considered a leading industry in digital and emerging technologies, and the digitalization of other industries such as retail, health, and telecommunication, it also depends on the growth rate of digitalized payment systems. One of the technological innovations in service management is Field Service Management (FSM). Despite the widespread use of FSM in various industries such as petrochemical, health, maintenance, etc., this technology can also be recruited in the payment industry, transforming the payment industry into a more agile and efficient one. Accordingly, the present study pays close attention to the application of FSM in the payment industry. Given the importance of merchants' bargaining power in the payment industry, this study aims to use FSM in the digital transformation initiative with a targeted focus on providing real-time services to merchants. The research method consists of three parts. Firstly, conducting the review of past research, applications of FSM in the payment industry are considered. In the next step, merchants' benefits such as emotional, functional, economic, and social benefits in using FSM are identified using in-depth interviews and content analysis methods. The related business model in helping the payment industry transforming into a more agile and efficient industry is considered in the following step. The results revealed the 10 main pillars required to realize the digital transformation of payment systems using FSM.

Keywords: Digital transformation, field service management, merchant support systems, payment industry.

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Authors: Dalia Suša Vugec, Ana-Marija Stjepić, Darija Ivandić Vidović

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Digital transformation is one of the latest trends on the global market. In order to maintain the competitive advantage and sustainability, increasing number of organizations are conducting digital transformation processes. Those organizations are changing their business processes and creating new business models with the help of digital technologies. In that sense, one should also observe the role of business process management (BPM) and its maturity in driving digital transformation. Therefore, the goal of this paper is to investigate the role of BPM in digital transformation process within one organization. Since experiences from practice show that organizations from financial sector could be observed as leaders in digital transformation, an insurance company has been selected to participate in the study. That company has been selected due to the high level of its BPM maturity and the fact that it has previously been through a digital transformation process. In order to fulfill the goals of the paper, several interviews, as well as questionnaires, have been conducted within the selected company. The results are presented in a form of a case study. Results indicate that digital transformation process within the observed company has been successful, with special focus on the development of digital strategy, BPM and change management. The role of BPM in the digital transformation of the observed company is further discussed in the paper.

Keywords: Business process management, case study, Croatia, digital transformation, insurance company.

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Authors: Jamal A. Gledan, Othman A. Azzeidani

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During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three – parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: Geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques.

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Authors: Anod H. Alhazmi, Hanaa A. Yamani

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The lack of digital transformation professionals could prevent Saudi Arabia’s universities from providing digital services. The task of understanding what digital skills are needed within an organization, measuring the existing skills, and developing or attracting talents is a complex task. This paper provides a comprehensive analysis of the digital transformation skills needed in the organizations who seek digital transformation and identifies the skills and competencies framework DigSC built on Skills Framework for the Informational Age (SFIA) framework that is adopted by the Ministry of Communications and Information Technology (MCIT) in Saudi Arabia. The framework adopted identifies the main digital transformation skills clusters, categories and levels of responsibilities for each job description to fill the gap between this requirement and the digital skills supplied by the Umm Alqura University (UQU).

Keywords: Competencies, digital transformation, framework, skills, Umm Alqura University.

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Authors: Dennis A. Apuan

Abstract:

Categorical data based on description of the agricultural landscape imposed some mathematical and analytical limitations. This problem however can be overcome by data transformation through coding scheme and the use of non-parametric multivariate approach. The present study describes data transformation from qualitative to numerical descriptors. In a collection of 103 random soil samples over a 60 hectare field, categorical data were obtained from the following variables: levels of nitrogen, phosphorus, potassium, pH, hue, chroma, value and data on topography, vegetation type, and the presence of rocks. Categorical data were coded, and Spearman-s rho correlation was then calculated using PAST software ver. 1.78 in which Principal Component Analysis was based. Results revealed successful data transformation, generating 1030 quantitative descriptors. Visualization based on the new set of descriptors showed clear differences among sites, and amount of variation was successfully measured. Possible applications of data transformation are discussed.

Keywords: data transformation, numerical descriptors, principalcomponent analysis

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Authors: Mohammed Abdalla Osman Mukhtar, Azween Abdullah, Alan Giffin Downe

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Model mapping and transformation are important processes in high level system abstractions, and form the cornerstone of model-driven architecture (MDA) techniques. Considerable research in this field has devoted attention to static system abstraction, despite the fact that most systems are dynamic with high frequency changes in behavior. In this paper we provide an overview of work that has been done with regard to behavior model mapping and transformation, based on: (1) the completeness of the platform independent model (PIM); (2) semantics of behavioral models; (3) languages supporting behavior model transformation processes; and (4) an evaluation of model composition to effect the best approach to describing large systems with high complexity.

Keywords: MDA; PIM, PSM, QVT, Model Transformation

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Authors: Kwok Tak Kit

Abstract:

This research focuses mainly on the transformation of circular economy and specifically on the building and construction industry in Hong Kong. This research is going to investigate the current status of development and transformation of linear economy of Hong Kong into circular economy. The research is based on literature review and different published reports to outline the possibilities for further development and transformation of circular economy in Hong Kong. Different key factors affecting the transformation particularly in building and construction industry are discussed.

Keywords: Circular economy, LEED net zero, carbon emission, waste reduction, waste management.

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Authors: Y. Rhazali, Y. Hadi, A. Mouloudi

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This paper proposes a method to automatic transformation of CIM level to PIM level respecting the MDA approach. Our proposal is based on creating a good CIM level through well-defined rules allowing as achieving rich models that contain relevant information to facilitate the task of the transformation to the PIM level. We define, thereafter, an appropriate PIM level through various UML diagram. Next, we propose set rules to move from CIM to PIM. Our method follows the MDA approach by considering the business dimension in the CIM level through the use BPMN, standard modeling business of OMG, and the use of UML in PIM advocated by MDA in this level.

Keywords: Model transformation, MDA, CIM, PIM.

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Authors: Sarah E. Stief, Anne Theresa Eidhoff, Markus Voeth

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Despite all progress firms are facing the increasing need to adapt and assimilate digital technologies to transform their business activities in order to pursue business development. By using new digital technologies, firms can implement major business improvements in order to stay competitive and foster new growth potentials. The corresponding phenomenon of digital transformation has received some attention in previous literature in respect to industries such as media and publishing. Nevertheless, there is a lack of understanding of the concept and its organization within firms. With the help of twenty-three in-depth field interviews with German experts responsible for their company’s digital transformation, we examined what digital transformation encompasses, how it is organized and which opportunities and challenges arise within firms. Our results indicate that digital transformation is an inevitable task for all firms, as it bears the potential to comprehensively optimize and reshape established business activities and can thus be seen as a strategy of business development.

Keywords: Business development, digitalization, digital strategies, digital transformation.

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Authors: D. E. Gourgoulis, C. G. Yakinthos, M. G. Vassiliadou

Abstract:

The scope of this paper is to describe a real electrical installation of renewable energy using photovoltaic cells. The displayed power grid connected network was established in 2007 at area of Northern Greece. The photovoltaic park is composed of 6120 photovoltaic cells able to deliver a total power of 1.101.600 Wp. For the transformation of DC voltage to AC voltage have been used 25 stand alone three phases inverters and for the connection at the medium voltage network of Greek Power Authority have been installed two oil immersed transformer of 630 kVA each one. Due to the wide space area of installation a specific external lightning protection system has been designed. Additionally, due to the sensitive electronics of the control and protection systems of park, surge protection, equipotent bonding and shielding were also of major importance.

Keywords: Inverter, Photovoltaic cells, Transformer.

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Authors: László Lengyel, Tihamér Levendovszky, Gergely Mezei, Hassan Charaf

Abstract:

Graph rewriting-based visual model processing is a widely used technique for model transformation. Visual model transformations often need to follow an algorithm that requires a strict control over the execution sequence of the transformation steps. Therefore, in Visual Model Processors (VMPs) the execution order of the transformation steps is crucial. This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This paper introduces VCFL, discusses its termination properties and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual ModelTransformation, OCL, Termination Properties, UML.

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Authors: Lawrence Gumbe

Abstract:

This paper concludes that, for economic development, and to ensure survival, Kenya and similar countries must industrialize their economy and mechanize their agriculture using modern large scale methods.

Keywords: Agriculture, mechanazation, transformation, industrialization.

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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: Vesna Bosilj Vukšić, Lucija Ivančić, Dalia Suša Vugec

Abstract:

While struggling to succeed in today’s complex market environment and provide better customer experience and services, enterprises encompass digital transformation as a means for reaching competitiveness and foster value creation. A digital transformation process consists of information technology implementation projects, as well as organizational factors such as top management support, digital transformation strategy, and organizational changes. However, to the best of our knowledge, there is little evidence about digital transformation endeavors in organizations and how they perceive it – is it only about digital technologies adoption or a true organizational shift is needed? In order to address this issue and as the first step in our research project, a literature review is conducted. The analysis included case study papers from Scopus and Web of Science databases. The following attributes are considered for classification and analysis of papers: time component; country of case origin; case industry and; digital transformation concept comprehension, i.e. focus. Research showed that organizations – public, as well as private ones, are aware of change necessity and employ digital transformation projects. Also, the changes concerning digital transformation affect both manufacturing and service-based industries. Furthermore, we discovered that organizations understand that besides technologies implementation, organizational changes must also be adopted. However, with only 29 relevant papers identified, research positioned digital transformation as an unexplored and emerging phenomenon in information systems research. The scarcity of evidence-based papers calls for further examination of this topic on cases from practice.

Keywords: Digital strategy, digital technologies, digital transformation, literature review.

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Authors: K. Chinda, P. Luangpaiboon

Abstract:

This paper presents the comparative study of coded data methods for finding the benefit of concealing the natural data which is the mercantile secret. Influential parameters of the number of replicates (rep), treatment effects (τ) and standard deviation (σ) against the efficiency of each transformation method are investigated. The experimental data are generated via computer simulations under the specified condition of the process with the completely randomized design (CRD). Three ways of data transformation consist of Box-Cox, arcsine and logit methods. The difference values of F statistic between coded data and natural data (Fc-Fn) and hypothesis testing results were determined. The experimental results indicate that the Box-Cox results are significantly different from natural data in cases of smaller levels of replicates and seem to be improper when the parameter of minus lambda has been assigned. On the other hand, arcsine and logit transformations are more robust and obviously, provide more precise numerical results. In addition, the alternate ways to select the lambda in the power transformation are also offered to achieve much more appropriate outcomes.

Keywords: Experimental Designs, Box-Cox, Arcsine, Logit Transformations.

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Authors: Y. Bek-Ali, K. Gabdullin

Abstract:

This paper explores transformation of higher education system in Kazakhstan since 1991. The research unravels successful experience in the field and challenges. It covers issues of institutional change, faculty, research, university, funding, standards and leadership. The paper offers recommendations in improving state of art in higher educational institutions of Kazakhstan based on international approaches and local realities.

Keywords: higher educational institution, Kazakhstan, transformation

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Authors: Tan Wee Choon, Abdul Saad Salleh, Saifulnizan Jamian, Mohd. Imran Ghazali

Abstract:

Phase transformation temperature is one of the most important parameters for the shape memory alloys (SMAs). The most popular method to determine these phase transformation temperatures is the Differential Scanning Calorimeter (DSC), but due to the limitation of the DSC testing itself, it made it difficult for the finished product which is not in the powder form. A novel method which uses the Universal Testing Machine has been conducted to determine the phase transformation temperatures. The Flexinol wire was applied with force and maintained throughout the experiment and at the same time it was heated up slowly until a temperature of approximately 1000C with direct current. The direct current was then slowly decreased to cool down the temperature of the Flexinol wire. All the phase transformation temperatures for Flexinol wire were obtained. The austenite start at 52.540C and austenite finish at 60.900C, while martensite start at 44.780C and martensite finish at 32.840C.

Keywords: Phase transformation temperature, Robotic, Shapememory alloy, Universal Testing Machine.

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Authors: A. Thabet, M. Boutayeb, M. N. Abdelkrim

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This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.

Keywords: Power system, Dynamic decoupled model, Extended Kalman Filter, Convergence analysis, Time computing.

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Authors: Liew Siaw Yee, Tahir Ahmad

Abstract:

In this paper, the Fuzzy Autocatalytic Set (FACS) is composed into Omega Algebra by embedding the membership value of fuzzy edge connectivity using the property of transitive affinity. Then, the Omega Algebra of FACS is a transformation semigroup which is a special class of semigroup is shown.

Keywords: Fuzzy autocatalytic set, omega algebra, semigroup, transformation semigroup.

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