Search results for: Gauss-Kronrod method of integration

Authors: Adama Sow, Abdoulaye Guiss´e, Oumar Niang

Abstract:

To assist medical diagnosis, we propose a federation of several existing and open medical ontologies and terminologies. The goal is to merge the strengths of all these resources to provide clinicians the access to a variety of shared knowledges that can facilitate identification and association of human diseases and all of their available characteristic signs such as symptoms and clinical signs. This work results to an integration model loaded from target known ontologies of the bioportal platform such as DOID, MESH, and SNOMED for diseases selection, SYMP, and CSSO for all existing signs.

Keywords: Medical decision, medical ontologies, ontologies integration, linked data, knowledge ingeneering, e-health system.

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Authors: Fudziah Ismail

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In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally implicit Runge-Kutta method. The results suggests the superiority of the new method.

Keywords: Runge-Kutta Nystrom, Special second orderproblems.

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Authors: U.K. Saha, L.K. Arora

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The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: Base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model.

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Authors: Roman Ružarovský, Radovan Holubek, Daynier Rolando Delgado Sobrino

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Currently is characterized production engineering together with the integration of industrial automation and robotics such very quick view of to manufacture the products. The production range is continuously changing, expanding and producers have to be flexible in this regard. It means that need to offer production possibilities, which can respond to the quick change. Engineering product development is focused on supporting CAD software, such systems are mainly used for product design. That manufacturers are competitive, it should be kept procured machines made available capable of responding to output flexibility. In response to that problem is the development of flexible manufacturing systems, consisting of various automated systems. The integration of flexible manufacturing systems and subunits together with product design and of engineering is a possible solution for this issue. Integration is possible through the implementation of CIM systems. Such a solution and finding a hyphen between CAD and procurement system ICIM 3000 from Festo Co. is engaged in the research project and this contribution. This can be designed the products in CAD systems and watch the manufacturing process from order to shipping by the development of methods and processes of integration, This can be modeled in CAD systems products and watch the manufacturing process from order to shipping to develop methods and processes of integration, which will improve support for product design parameters by monitoring of the production process, by creating of programs for production using the CAD and therefore accelerates the a total of process from design to implementation.

Keywords: CAD- Computer Aided Design, CAM- Computer Aided Manufacturing, CIM- Computer integrated manufacturing, iCIM 3000, integration, direct production from CAD.

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Authors: L. Aparecida Bastos, J. Leige Lopes, J. Crepaldi, R. Monteiro da Silva

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The objective of this study is to analyze the evolution of some social and economic indicators of Mercosur´s economies from 1980 to 2012, based on the statistics of the Latin American Integration Association (LAIA). The objective is to observe if after the accession of these economies to Mercosur (the first accessions occurred in 1994) these indicators showed better performance, in order to demonstrate if economic integration contributed to improved trade, macroeconomic performance, and level of social and economic development of member countries. To this end, the methodologies used will be a literature review and descriptive statistics. The theoretical framework that guides the work are the theories of Integration: Classical Liberal, Marxist and structural-proactive. The results reveal that most social and economic indicators showed better performance in those economies that joined Mercosur after 1994. This work is the result of an investigation already completed.

Keywords: Economic integration, mercosur, social indicators, economic indicators.

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Authors: Chintanu K. Sarmah, Sandhya Samarasinghe, Don Kulasiri, Daniel Catchpoole

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Gene expression profiling is rapidly evolving into a powerful technique for investigating tumor malignancies. The researchers are overwhelmed with the microarray-based platforms and methods that confer them the freedom to conduct large-scale gene expression profiling measurements. Simultaneously, investigations into cross-platform integration methods have started gaining momentum due to their underlying potential to help comprehend a myriad of broad biological issues in tumor diagnosis, prognosis, and therapy. However, comparing results from different platforms remains to be a challenging task as various inherent technical differences exist between the microarray platforms. In this paper, we explain a simple ratio-transformation method, which can provide some common ground for cDNA and Affymetrix platform towards cross-platform integration. The method is based on the characteristic data attributes of Affymetrix- and cDNA- platform. In the work, we considered seven childhood leukemia patients and their gene expression levels in either platform. With a dataset of 822 differentially expressed genes from both these platforms, we carried out a specific ratio-treatment to Affymetrix data, which subsequently showed an improvement in the relationship with the cDNA data.

Keywords: Gene expression profiling, microarray, cDNA, Affymetrix, childhood leukaemia.

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Authors: Maurício Covolan Rosito, Ricardo Melo Bastos

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Software projects are very dynamic and require recurring adjustments of their project plans. These settings can be understood as reconfigurations in the schedule, in the resources allocation and other design elements. Yet, during the planning and execution of a software project, the integration of specific activities in the projects with the activities that take part in the organization-s common activity flow should be considered. This article presents the results from a systematic review of aspects related to software projects- dynamic reconfiguration emphasizing the integration of project management with the organizational flows. A series of studies was analyzed from the year 2000 to the present. The results of this work show that there is a diversity of techniques and strategies for dynamic reconfiguration of software projects-. However, few approaches consider the integration of software project activities with the activities that take part in the organization-s common workflow.

Keywords: Dynamic Reconfiguration, Organizational workflows, Project Management, Systematic Review

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Authors: Mohsen Shirani, Micaela Demichela

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During the last decades, a number of food crises such as Bovine Spongiform Encephalopathy (BSE), Mad-Cow disease, Dioxin in chicken food, Food-and-Mouth Disease (FMD), have certainly inflected the reliability of the food industry. Consequently, the trend in applying different scientific methods of risk assessment in food safety has obtained more attentions in the academic and practice. However, lack of practical approach considering entire food supply chain is tangible in the academic literature. In this regard, this paper aims to apply risk assessment tool (FMEA) with integration of Human Factor along the entire supply chain of food production and test the method in a case study of Diary production, and analyze its results.

Keywords: Food Risk Assessment, FMEA, Human Factor.

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Authors: Christian Meinecke, Bernd Scholz-Reiter

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The integrated problem of production and distribution scheduling is relevant in many industrial applications. Thus, many heuristics to solve this integrated problem have been developed in the last decade. Most of these heuristics use a sequential working principal or a single decomposition and integration approach to separate and solve subproblems. A heuristic using a multi step decomposition and integration approach is presented in this paper and evaluated in a case study. The result show significant improved results compared with sequential scheduling heuristics.

Keywords: Production and outbound distribution, integrated planning, heuristic, decomposition and integration.

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Authors: Mohammad Hadi Bordbar, Timo Hyppänen

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The radiative exchange method is introduced as a numerical method for the simulation of radiative heat transfer in an absorbing, emitting and isotropically scattering media. In this method, the integro-differential radiative balance equation is solved by using a new introduced concept for the exchange factor. Even though the radiative source term is calculated in a mesh structure that is coarser than the structure used in computational fluid dynamics, calculating the exchange factor between different coarse elements by using differential integration elements makes the result of the method close to that of integro-differential radiative equation. A set of equations for calculating exchange factors in two and threedimensional Cartesian coordinate system is presented, and the method is used in the simulation of radiative heat transfer in twodimensional rectangular case and a three-dimensional simple cube. The result of using this method in simulating different cases is verified by comparing them with those of using other numerical radiative models.

Keywords: Exchange factor, Numerical simulation, Thermal radiation.

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Authors: Lan Wu

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China’s declared transformation towards a ‘new electricity system dominated by renewable energy’ requires a cleaner electricity consumption mix with high shares of renewable energy sourced-electricity (RES-E). Unfortunately, integration of RES-E into Chinese electricity markets remains a problem pending more robust legal support, evidenced by the curtailment of wind and solar power due to integration constraints. The upcoming Energy Law of the PRC (Energy Law) is expected to provide such long-awaiting support and coordinate the existing diverse sector-specific laws to deal with the weak implementation that dampening the delivery of their desired regulatory effects. However, in the shadow of the COVID-19 crisis, it remains uncertain how this new Energy Law brings synergies to RES-E integration, mindful of the significant impacts of the pandemic. Through the theoretical lens of the interplay between China’s electricity market reform and legislative development, this paper investigates whether there is a paradigm shift in Energy Law regarding renewable energy integration compared with the existing sector-specific energy laws. It examines the 2020 Draft for Comments on the Energy Law and analyses its relationship with sector-specific energy laws focusing on RES-E integration. The comparison is drawn upon five critical aspects of the RES-E integration issue, including the status of renewables, marketisation, incentive schemes, consumption mechanisms, access to power grids and dispatching. The analysis shows that it is reasonable to expect a more open and well-organised electricity market, enabling the absorption of high shares of RES-E. The present paper concludes that a period of prosperous development of RES-E in the post-COVID-19 era can be anticipated with the legal support by the upcoming Energy Law. It contributes to understanding the signals China is sending regarding the transition towards a cleaner energy future.

Keywords: energy law, energy transition, electricity market reform, renewable energy integration

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Authors: L. R. Ferreira, R. Biscaro, C. C. Danziger, C. M. Galhardi, L. C. Biscaro, R. C. Biscaro, I. S. Vasconcelos, L. C. R. Ferreira, R. Reis, L. H. Oliveira

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Introduction: There is a worldwide trend for the employer to be aware of investing in health promotion that goes beyond occupational hygiene approaches with the implementation of a comprehensive program with integration between occupational health and safety, and social/psychosocial responsibility in the workplace. Work accommodation is a necessity in most companies as it allows the worker to return to its function respecting its physical limitations. This study had the objective to verify if the integration of health and safety in the companies, with the inclusion of the concept of TWH promoted by an occupational health service has impacted in the management of absenteeism of workers in work accommodation. Method: A retrospective and paired cohort study was used, in which the impact of the implementation of the Program for the Health/Safety Integration and Total Worker Health Concept (PHSITWHC) was evaluated using the indices of absenteeism, health attestations, days and hours of sick leave of workers that underwent job accommodation/rehabilitation. This was a cohort study and the data were collected from January to September of 2017, prior to the initiation of the integration program, and compared with the data obtained from January to September of 2018, after the implementation of the program. For the statistical analysis, the student's t-test was used, with statistically significant differences being made at p < 0.05. Results: The results showed a 35% reduction in the number of absenteeism rate in 2018 compared to the same period in 2017. There was also a significant reduction in the total numbers of days of attestations/absences (mean of 2,8) as well as days of attestations, absence and sick leaves (mean of 5,2) in 2018 data after the implementation of PHSITWHC compared to 2017 data, means of 4,3 and 25,1, respectively, prior to the program. Conclusion: It can be concluded that the inclusion of the PHSITWHC was associated with a reduction in the rate of absenteeism of workers that underwent job accommodation. It was observed that, once health and safety were approached and integrated with the inclusion of the TWH concept, it was possible to reduce absenteeism, and improve worker’s quality of life and wellness, and work accommodation management.

Keywords: Absenteeism, health/safety integration, work accommodation management, total worker health.

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Authors: Joel Arrais, João E. Pereira, João Fernandes, José Luís Oliveira

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The scientific achievements coming from molecular biology depend greatly on the capability of computational applications to analyze the laboratorial results. A comprehensive analysis of an experiment requires typically the simultaneous study of the obtained dataset with data that is available in several distinct public databases. Nevertheless, developing a centralized access to these distributed databases rises up a set of challenges such as: what is the best integration strategy, how to solve nomenclature clashes, how to solve database overlapping data and how to deal with huge datasets. In this paper we present GeNS, a system that uses a simple and yet innovative approach to address several biological data integration issues. Compared with existing systems, the main advantages of GeNS are related to its maintenance simplicity and to its coverage and scalability, in terms of number of supported databases and data types. To support our claims we present the current use of GeNS in two concrete applications. GeNS currently contains more than 140 million of biological relations and it can be publicly downloaded or remotely access through SOAP web services.

Keywords: Data integration, biological databases

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Authors: Caspar von Seckendorff, Eldar Sultanow

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Many studies have shown that parallelization decreases efficiency [1], [2]. There are many reasons for these decrements. This paper investigates those which appear in the context of parallel data integration. Integration processes generally cannot be allocated to packages of identical size (i. e. tasks of identical complexity). The reason for this is unknown heterogeneous input data which result in variable task lengths. Process delay is defined by the slowest processing node. It leads to a detrimental effect on the total processing time. With a real world example, this study will show that while process delay does initially increase with the introduction of more nodes it ultimately decreases again after a certain point. The example will make use of the cloud computing platform Hadoop and be run inside Amazon-s EC2 compute cloud. A stochastic model will be set up which can explain this effect.

Keywords: Process delay, speedup, efficiency, parallel computing, data integration, E-Commerce, Amazon Elastic Compute Cloud (EC2), Hadoop, Nutch.

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Authors: Erick López-Ornelas

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As the world changes more rapidly, the demand for update information for resource management, environment monitoring, planning are increasing exponentially. Integration of Remote Sensing with GIS technology will significantly promote the ability for addressing these concerns. This paper presents an alternative way of update GIS applications using image processing and high resolution images. We show a method of high-resolution image segmentation using graphs and morphological operations, where a preprocessing step (watershed operation) is required. A morphological process is then applied using the opening and closing operations. After this segmentation we can extract significant cartographic elements such as urban areas, streets or green areas. The result of this segmentation and this extraction is then used to update GIS applications. Some examples are shown using aerial photography.

Keywords: GIS, Remote Sensing, image segmentation, feature extraction.

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Authors: Haitham S. Hamza, Mohamed Maher, Shourok Alaa, Aya Khattab, Hadeal Ismail, Kamilia Hosny

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Radio Frequency Identification (RFID) has become a key technology in the emerging concept of Internet of Things (IoT). Naturally, business applications would require the deployment of various RFID systems developed by different vendors that use different data formats and structures. This heterogeneity poses a challenge in developing real-life IoT systems with RFID, as integration is becoming very complex and challenging. Semantic integration is a key approach to deal with this challenge. To do so, ontology for RFID systems need to be developed in order to annotated semantically RFID systems, and hence, facilitate their integration. Accordingly, in this paper, we propose ontology for RFID systems. The proposed ontology can be used to semantically enrich RFID systems, and hence, improve their usage and reasoning.

Keywords: IoT, RFID, Semantic, sparql, Ontology.

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Authors: Wassila Kiamouche, Malek Benslama

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In order to derive important parameters concerning mobile subscriber MS with ongoing calls in Low Earth Orbit Mobile Satellite Systems LEO MSSs, a positioning system had to be integrated into MSS in order to localize mobile subscribers MSs and track them during the connection. Such integration is regarded as a complex implementation. We propose in this paper a novel method based on advantages of mobility model of Low Earth Orbit Mobile Satellite System LEO MSS called Evaluation Parameters Method EPM which allows for such systems the evaluation of different information concerning a MS with a call in progress even if its location is unknown.

Keywords: Cellular layout, LEO mobile satellite system, mobilitymodel, positioning system.

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Authors: Wen-Pai Wang, Mei-Ching Tang

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The service sector continues to grow and the percentage of GDP accounted for by service industries keeps increasing. The growth and importance of service to an economy is not just a phenomenon of advanced economies, service is now a majority of the world gross domestic products. However, the performance evaluation process of new service development problems generally involves uncertain and imprecise data. This paper presents a 2-tuple fuzzy linguistic computing approach to dealing with heterogeneous information and information loss problems while the processes of subjective evaluation integration. The proposed method based on group decision-making scenario to assist business managers in measuring performance of new service development manipulates the heterogeneity integration processes and avoids the information loss effectively.

Keywords: Heterogeneity, Multigranular linguistic computing, New service development, Performance evaluation.

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Authors: Phanu Waraporn

Abstract:

This paper discusses the designing of knowledge integration of clinical information extracted from distributed medical ontologies in order to ameliorate a machine learning-based multilabel coding assignment system. The proposed approach is implemented using a decision tree technique of the machine learning on the university hospital data for patients with Coronary Heart Disease (CHD). The preliminary results obtained show a satisfactory finding that the use of medical ontologies improves the overall system performance.

Keywords: Medical Ontology, Knowledge Integration, Machine Learning, Medical Coding, Text Assignment.

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Authors: T. Brettschneider, C. Dorrer, H. Suy, T. Braun, E. Jung, R. Hoofman, M. Bründel, R. Zengerle, F. Lärmer

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We present an integration approach of a CMOS biosensor into a polymer based microfluidic environment suitable for mass production. It consists of a wafer-level-package for the silicon die and laser bonding process promoted by an intermediate hot melt foil to attach the sensor package to the microfluidic chip, without the need for dispensing of glues or underfiller. A very good condition of the sensing area was obtained after introducing a protection layer during packaging. A microfluidic flow cell was fabricated and shown to withstand pressures up to Δp = 780 kPa without leakage. The employed biosensors were electrically characterized in a dry environment.

Keywords: CMOS biosensor, laser bonding, silicon polymer integration, wafer level packaging.

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Authors: Guangjie Liu

Abstract:

The main purpose of this paper is to research on the methodologies of BYD to implement the opportune innovation. BYD is a Chinese company which has the IT component manufacture, the rechargeable battery and the automobile businesses. The paper deals with the innovation methodology as the same as the IPR management BYD implements in order to obtain the rapid growth of technology development with the reasonable cost of money and time.

Keywords: Opportune innovation, vertical integration, unpatenting integration, patenting.

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Authors: Halil Ibrahim Demir, Tarık Cakar, Ibrahim Cil, Muharrem Dugenci, Caner Erden

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Conventionally, process planning, scheduling, and due-date assignment functions are performed separately and sequentially. The interdependence of these functions requires integration. Although integrated process planning and scheduling, and scheduling with due date assignment problems are popular research topics, only a few works address the integration of these three functions. This work focuses on the integration of process planning, WMS scheduling, and WPPW due date assignment. Another novelty of this work is the use of a weighted due date assignment. In the literature, due dates are generally assigned without considering the importance of customers. However, in this study, more important customers get closer due dates. Typically, only tardiness is punished, but the JIT philosophy punishes both earliness and tardiness. In this study, all weighted earliness, tardiness, and due date related costs are penalized. As no customer desires distant due dates, such distant due dates should be penalized. In this study, various levels of integration of these three functions are tested and genetic search and random search are compared both with each other and with ordinary solutions. Higher integration levels are superior, while search is always useful. Genetic searches outperformed random searches.

Keywords: Process planning, weighted scheduling, weighted due-date assignment, genetic algorithm, random search.

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Authors: Ahmet Baytak, Cenk Akbıyık

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The purpose of this paper is to present teacher candidates- beliefs about technology integration in their field of study, which is classroom teaching in this case. The study was conducted among the first year students in college of education in Turkey. This study is based on both quantitative and qualitative data. For the quantitative data- Likert scale was used and for the qualitative data pattern matching was employed. The primary findings showed that students defined educational technology as technologies that improve learning with their visual, easily accessible, and productive features. They also believe these technologies could affect their future students- learning positively.

Keywords: Educational technology, classroom teacher candidates, technology integration, teacher education.

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Authors: Stefano Degrassi, Marco Raciti Castelli, Ernesto Benini

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Since the European renewable energy directives set the target for 22.1% of electricity generation to be supplied by 2010 [1], there has been increased interest in using green technologies also within the urban enviroment. The most commonly considered installations are solar thermal and solar photovoltaics. Nevertheless, as observed by Bahaj et al. [2], small scale turbines can reduce the built enviroment related CO2 emissions. Thus, in the last few years, an increasing number of manufacturers have developed small wind turbines specifically designed for the built enviroment. The present work focuses on the integration into architectural systems of such installations and presents a survey of successful case studies.

Keywords: Wind turbines, architectural integration, wind resources, urban areas, built enviroment, renewable technologies.

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Authors: Wen-Pai Wang

Abstract:

The growing influence of service industries has prompted greater attention being paid to service operations management. However, service managers often have difficulty articulating the veritable effects of their service innovation. Especially, the performance evaluation process of service innovation problems generally involves uncertain and imprecise data. This paper presents a 2-tuple fuzzy linguistic computing approach to dealing with heterogeneous information and information loss problems while the processes of subjective evaluation integration. The proposed method based on group decision-making scenario to assist business managers in measuring performance of service innovation manipulates the heterogeneity integration processes and avoids the information loss effectively.

Keywords: Group decision-making, Heterogeneity, Linguisticcomputing, Multi-criteria, Service innovation

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Authors: Yan-Fang Niu

Abstract:

In view of current IT integration development of SOA, this paper examines AIS design based on SOA, including information sources collection, accounting business process integration and real-time financial reports. The main objective of this exploratory paper is to facilitate AIS research combing the Web Service, which is often ignored in accounting and computer research. It provides a conceptual framework that clarifies the interdependency between SOA and AIS, and also presents the major SOA functions in different areas of AIS

Keywords: AIS, SOA, Web Service

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Authors: Ibrahim A. Alkali

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There is no reservation on the outstanding contribution of patient families in restoration of hospitalised patients, hence their consideration as essential component of hospital ward regimen. The psychological and emotional support a patient requires has been found to be solely provided by the patient’s family. However, consideration of their presence as one of the major functional requirements of an inpatient setting design have always been a source of disquiet, especially in developing countries where policies, norms and protocols of healthcare administration have no consideration for the patients’ family. This have been a major challenge to the hospital ward facilities, a concern for the hospital administration and patient management. The study therefore is aimed at obtaining a consensus opinion on the best approach for family integration in the design of an inpatient setting.  A one day visioning charrette involving Architects, Nurses, Medical Doctors, Healthcare assistants and representatives from the Patient families was conducted with the aim of arriving at a consensus opinion on practical design approach for sustainable family integration. Patient’s family are found to be decisive character of hospital ward regimen that cannot be undermined. However, several challenges that impede family integration were identified and subsequently a recommendation for an ideal approach. This will serve as a guide to both architects and hospital management in implementing much desired Patient and Family Centred Care.

Keywords: Caregiving, Inpatient setting, Integration, Patient Families.

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Authors: Halil Ibrahim Demir, Caner Erden, Mumtaz Ipek, Ozer Uygun

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Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of these three important functions are not adequately addressed. Here, the integration of these three important functions is studied by using genetic, random-genetic hybrid, simulated annealing, random-simulated annealing hybrid and random search techniques. As well, the importance of the integration of these three functions and the power of meta-heuristics and of hybrid heuristics are studied.

Keywords: Process planning, weighted scheduling, weighted due-date assignment, genetic search, simulated annealing, hybrid meta-heuristics.

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Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

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Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

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