Search results for: Direct oxidization

Authors: Chalakorn Chitsaart, Suchada Rianmora, Noppawat Vongpiyasatit

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In order to reduce the transportation time and cost for direct interface between customer and manufacturer, the image processing technique has been introduced in this research where designing part and defining manufacturing process can be performed quickly. A3D virtual model is directly generated from a series of multi-view images of an object, and it can be modified, analyzed, and improved the structure, or function for the further implementations, such as computer-aided manufacturing (CAM). To estimate and quote the production cost, the user-friendly platform has been developed in this research where the appropriate manufacturing parameters and process detections have been identified and planned by CAM simulation.

Keywords: Image processing technique, Feature detections, Surface registrations, Capturing multi-view images, Production costs, and Manufacturing processes.

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Authors: Ashok Kumar Goel, Suresh Chandra Saxena, Surekha Bhanot

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In this work, a Modified Functional Link Artificial Neural Network (M-FLANN) is proposed which is simpler than a Multilayer Perceptron (MLP) and improves upon the universal approximation capability of Functional Link Artificial Neural Network (FLANN). MLP and its variants: Direct Linear Feedthrough Artificial Neural Network (DLFANN), FLANN and M-FLANN have been implemented to model a simulated Water Bath System and a Continually Stirred Tank Heater (CSTH). Their convergence speed and generalization ability have been compared. The networks have been tested for their interpolation and extrapolation capability using noise-free and noisy data. The results show that M-FLANN which is computationally cheap, performs better and has greater generalization ability than other networks considered in the work.

Keywords: DLFANN, FLANN, M-FLANN, MLP

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Authors: H. Ahmed, A. Persson, L. Sundqvist, B. Biorkman

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Numerous amounts of metallurgical dusts and sludge containing iron as well as some other valuable elements such as Zn, Pb and C are annually produced in the steelmaking industry. These alternative iron ore resources (fines) with unsatisfying physical and metallurgical properties are difficult to recycle. However, agglomerating these fines to be further used as a feed stock for existing iron and steelmaking processes is practiced successfully at several plants but for limited extent.

In the present study, briquettes of integrated steelmaking industry waste materials (namely, BF-dust and sludge, BOF-dust and sludge) were used as feed stock to produce direct reduced iron (DRI). Physical and metallurgical properties of produced briquettes were investigated by means of TGA/DTA/QMS in combination with XRD. Swelling, softening and melting behavior were also studied using heating microscope.

Keywords: Iron and Steel Wastes, Recycling, Self-Reducing Briquettes, Thermogravimetry.

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Authors: L. Horňák

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The aim of the paper is to analyze a longstanding problem in Slovakia – the effective education of Roma students coming from socially disadvantaged backgrounds. Although it is a relatively small country, there are over 630 communities in the Slovak Republic. The efficiency of the projects was verified by interviews with participants; questionnaires; and direct observations. Evaluation reports which summarized and evaluated the outcomes of the projects only confirmed their success. Slovakia realizes that appropriate social inclusion of marginalized citizens coming from the Roma ethnic group can only be achieved through education based on equality of all students and acceptance of diversity.

Keywords: Inclusive education, marginalized communities, Roma student, equality in education, socially disadvantaged backgrounds, social inclusion.

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Authors: Jiří Barta

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The paper deals with simulation programs of spread of harmful substances. Air pollution has a direct impact on the quality of human life and environmental protection is currently a very hot topic. Therefore, the paper focuses on the simulation of release of harmful substances. The first part of article deals with perspectives and possibilities of implementation outputs of simulations programs into the system which is education and of practical training of the management staff during emergency events in the frame of critical infrastructure. The last part shows the practical testing and evaluation of simulation programs. Of the tested simulations software been selected Symos97. The tool offers advanced features for setting leakage. Gradually allows the user to model the terrain, location, and method of escape of harmful substances.

Keywords: Computer Simulation, Symos97, spread, simulation software, harmful substances.

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Authors: Majed Omar Al-Dwairi

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This paper evaluate the multilevel modulation for different techniques such as amplitude shift keying (M-ASK), MASK, differential phase shift keying (M-ASK-Bipolar), Quaternary Amplitude Shift Keying (QASK) and Quaternary Polarization-ASK (QPol-ASK) at a total bit rate of 107 Gbps. The aim is to find a costeffective very high speed transport solution. Numerical investigation was performed using Monte Carlo simulations. The obtained results indicate that some modulation formats can be operated at 100Gbps in optical communication systems with low implementation effort and high spectral efficiency.

Keywords: Optical communication, multilevel amplitude shift keying (M-ASK), Differential phase shift keying (DPSK), Quaternary Amplitude Shift Keying (QASK), Quaternary Polarization-ASK (QPol-ASK).

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Authors: Farag Azzedin, Ali Rizvi

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In any trust model, the two information sources that a peer relies on to predict trustworthiness of another peer are direct experience as well as reputation. These two vital components evolve over time. Trust evolution is an important issue, where the objective is to observe a sequence of past values of a trust parameter and determine the future estimates. Unfortunately, trust evolution algorithms received little attention and the proposed algorithms in the literature do not comply with the conditions and the nature of trust. This paper contributes to this important problem in the following ways: (a) presents an algorithm that manages and models trust evolution in a P2P environment, (b) devises new mechanisms for effectively maintaining trust values based on the conditions that influence trust evolution , and (c) introduces a new methodology for incorporating trust-nurture incentives into the trust evolution algorithm. Simulation experiments are carried out to evaluate our trust evolution algorithm.

Keywords: P2P, Trust, Reputation, Incentives.

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Authors: Faten A. Khorshid

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Breast cancer is the most common malignancy in the world among women. Many therapies have been designed to treat this disease. Mamectomy, chemotherapy and radiotherapy are still the main therapies of breast cancer. However, the results were unsatisfactory and still far from the ideal treatment. PM 701is a natural product, has anticancer activity. The bioactive fraction PMF and subfraction PMFK had been isolated from PM701. PM 701 and its fractions were proved to have a cytotoxic properties against different cancer cell lines. This article is directed for the further examination of lyophilized PM701 and its active fractions on the growth of breast cancer cells (MCF-7). PM 701, PMF or PMFK were adding to the cultural medium, where MCF-7 is incubated. PM 701, PMF or PMFK were able to inhibit significantly the proliferation of MCF-7 cells, Moreover these new agents were proved to induce apoptosis of the breast cancer cells; through its direct effect on the nuclei.

Keywords: Anticancer agent, breast carcinoma, MCF-7 cell line, PM 701

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Authors: S. H. Mirhossaini, H. Godini, A. Jafari

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Biological Ammonia removal (nitrification), the oxidation of ammonia to nitrate catalyzed by bacteria, is a key part of global nitrogen cycling. In the first step of nitrification, chemolithoautotrophic ammonia oxidizer transform ammonia to nitrite, this subsequently oxidized to nitrate by nitrite oxidizing bacteria. This process can be affected by several factors. In this study the effect of influent COD on biological ammonia removal in a bench-scale biological reactor was investigated. Experiments were carried out using synthetic wastewater. The initial ammonium concentration was 25mgNH4 +-N L-1. The effect of COD between 247.55±1.8 and 601.08±3.24mgL-1 on biological ammonia removal was investigated by varying the COD loading supplied to reactor. From the results obtained in this study it could be concluded in the range of 247.55±1.8 to 351.35±2.05mgL-1, there is a direct relationship between amount of COD and ammonia removal. However more than 351.35±2.05 up to 601.08±3.24mgL-1 were found an indirect relationship between them.

Keywords: Ammonia biological removal, Nitrification, InfluentCOD.

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Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: Kuo Hung Huang, Chong-Ji Ke

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The purpose of this study is to explore the impacts of computer games on the mathematics instruction. First, the research designed and implemented the web-based games according to the content of existing textbook. And the researcher collected and analyzed the information related to the mathematics instruction integrating the computer games. In this study, the researcher focused on the learning motivation of mathematics, mathematics achievement, and pupil-teacher interactions in classroom. The results showed that students under instruction integrating computer games significantly improved in motivation and achievement. The teacher tended to use less direct teaching and provide more time for student-s active learning.

Keywords: computer games, mathematics instruction, pupil-teacher interaction, technology-enhanced learning

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Authors: Muritala Babatunde Hassan

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In the contemporary global political economy, foreign direct investment (FDI) is gaining currency on daily basis. Notably, the end of the Cold War has brought about the dominance of neoliberal ideology with its mantra of private-sector-led economy. As such, nation-states now see FDI attraction as an important element in their approach to national development. Governments and policy makers are preoccupying themselves with unraveling the best strategies to not only attract more FDI but also to attain the desired socio-economic development status. In Nigeria, the perceived development potentials of FDI have brought about aggressive hunt for foreign investors, most especially since transition to civilian rule in May 1999. Series of liberal and market oriented strategies are being adopted not only to attract foreign investors but largely to stimulate private sector participation in the economy. It is on this premise that this study interrogates the politics of FDI attraction for domestic development in Nigeria between 1999 and 2014, with the ultimate aim of examining the nexus between regime type and the ability of a state to attract and benefit from FDI. Building its analysis within the framework of institutional utilitarianism, the study posits that the essential FDI strategies for achieving the greatest happiness for the greatest number of Nigerians are political not economic. Both content analysis and descriptive survey methodology were employed in carrying out the study. Content analysis involves desk review of literatures that culminated in the development of the study’s conceptual and theoretical framework of analysis. The study finds no significant relationship between transition to democracy and FDI inflows in Nigeria, as most of the attracted investments during the period of the study were market and resource seeking as was the case during the military regime, thereby contributing minimally to the socio-economic development of the country. It is also found that the country placed much emphasis on liberalization and incentives for FDI attraction at the neglect of improving the domestic investment environment. Consequently, poor state of infrastructure, weak institutional capability and insecurity were identified as the major factors seriously hindering the success of Nigeria in exploiting FDI for domestic development. Given the reality of the currency of FDI as a vector of economic globalization and that Nigeria is trailing the line of private-sector-led approach to development, it is recommended that emphasis should be placed on those measures aimed at improving the infrastructural facilities, building solid institutional framework, enhancing skill and technological transfer and coordinating FDI promotion activities by different agencies and at different levels of government.

Keywords: Foreign capital, politics, socio-economic development, FDI attraction strategies, Redemocratization.

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Authors: Nareeluk Suwannobol, Lakkhana Suwachan

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The purpose of this study was to study the practical delivery room experience of nursing students. The respondents were 6 junior nursing students of Suranaree University of Technology who had a direct experience from practicing in a delivery room between January 9 and March 30, 2012 as part of Nursing Care of the Family and Midwifery 3. The data was collected by using in-depth interview, observation, and reflective report. The results of the study found that the practical delivery room experience of nursing students consisted of three issues: 1) stress and coping with stress during practical exercise, 2) changes in daily routine, and 3) source during practical exercise. The results of this study would lead to the understanding of the meaning of the practical exercise of nursing students.

Keywords: Delivery Room, Practical Experience, Nursing Students.

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Authors: Thomas Kalliath, Parveen Kalliath, Christopher C. A. Chan, Geetha Thachil

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Although considerable amount of research has attested to the link between work-to-family conflict (WFC) and family-to-work conflict (FWC) and psychological strain and wellbeing, there is a paucity of research investigating the phenomenon in the context of social workers. Moreover, very little is known about the impact of WFC and FWC in developing countries. The present study investigated the mediating effect of psychological strain on the relationship between WFC and FWC with wellbeing of social workers in India. Our findings show that WFC and FWC are influential antecedents of wellbeing; their influence is both direct on psychological strain, and indirect on wellbeing transmitted through psychological strain. Implications of the findings are discussed.

Keywords: Family-to-work conflict, psychological strain, wellbeing, work-to-family conflict.

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Authors: Young-Seok Choi

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Cerebellar ataxia is a steadily progressive neurodegenerative disease associated with loss of motor control, leaving patients unable to walk, talk, or perform activities of daily living. Direct motor instruction in cerebella ataxia patients has limited effectiveness, presumably because an inappropriate closed-loop cerebellar response to the inevitable observed error confounds motor learning mechanisms. Could the use of EEG based BCI provide advanced biofeedback to improve motor imagery and provide a “backdoor” to improving motor performance in ataxia patients? In order to determine the feasibility of using EEG-based BCI control in this population, we compare the ability to modulate mu-band power (8-12 Hz) by performing a cued motor imagery task in an ataxia patient and healthy control.

Keywords: Cerebellar ataxia, Electroencephalogram, brain-computer interface, motor imagery.

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Authors: Anqi Wang, Linye Zhang

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With the proliferation and development of mobile devices, various mobile apps have appeared to satisfy people’s needs. Metro, with the feature of convenient, punctuality and economic, is one of the most popular modes of transportation in cities. Yet, there are still some inconveniences brought by various factors, impacting tourists’ riding experience. The aim of this study is to help tourists to shorten the time of purchasing tickets, to provide them clear metro information and direct navigation, detailed schedule as well as a way to collect metro cards as souvenir. The study collects data through three phases, including observation, survey and test. Data collected from 106 tourists totally in Wuhan metro stations are discussed in the study. The result reflects tourists’ demand when they take the metro. It also indicates the feasibility of using mobile technology to improve passenger’s experience.

Keywords: Mobile App, metro, public transportation, ticket, mobile payment, indoors positioning, tourists.

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Authors: Peter Takáč, Dana Šimová, Terézia Szabová, Tomáš Bakalár

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The direct sewage sludge application is a relative cheap method for their liquidation. In the past heavy metal contents increase in soils treated with sewage sludge was observed. In 2003 there was acceptance on act n.188/2003 about sewage sludge application on soils. The basic philosophy of act is a safety of the environmental proof of sludge application on soils. The samples of soils from wastewater treatment plant (WTP) Poprad (35) and WTP Michalovce (33 samples) were analyzed which were chosen for sludge application on soils. According to the results only 14 areas for Poprad and 25 areas for Michalovce are suitable for sludge application according to act No. 188/2003. The application dose of sludge was calculated 50 t.ha-1 or 75 t. ha-1 once in 5 years to ensure that heavy metal contents in treated soils will be kept.

Keywords: Environmental safety, heavy metals in soils, sewagesludge application.

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Authors: J. H. Choi, S. J. Kim, M. S. Jung, S. J. Kim, S. J. Joo, S. C. Kim

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There are a many of needs for the development of SiC-based hydrogen sensor for harsh environment applications. We fabricated and investigated Pd/Ta2O5/SiC-based hydrogen sensors with MOS capacitor structure for high temperature process monitoring and leak detection applications in such automotive, chemical and petroleum industries as well as direct monitoring of combustion processes. In this work, we used silicon carbide (SiC) as a substrate to replace silicon which operating temperatures are limited to below 200°C. Tantalum oxide was investigated as dielectric layer which has high permeability for hydrogen gas and high dielectric permittivity, compared with silicon dioxide or silicon nitride. Then, electrical response properties, such as I-V curve and dependence of capacitance on hydrogen concentrations were analyzed in the temperature ranges of room temperature to 500°C for performance evaluation of the sensor.

Keywords: High temperature, hydrogen sensor, SiC, Ta2O5 dielectric layer.

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Authors: S. Sendhil Kumar, S. N. Vijayan

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Utilization of solar energy can be found in various domestic and industrial applications. The performance of any solar collector is largely affected by various parameters such as glazing, absorber plate, top covers, and heating pipes. Technology improvements have brought us another method for conversion of solar energy to direct electricity using solar photovoltaic system. Utilization and extraction of solar energy is the biggest problem in these conversion methods. This paper aims to overcome these problems and take the advantages of available energy from solar by maximizing the utilization through solar tracking system using a refrigerant as a working medium. The use of this tracking system can help increase the efficiency of conversion devices by maximum utilization of solar energy. The dual axis tracking system gives maximum energy output compared to single axis tracking system.

Keywords: Refrigerant, solar collector, solar energy, solar panel, solar tracking.

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Authors: M. Behbahani-Nejad, Y. Shekari

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A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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Authors: Tetyana Baydyk, Ernst Kussul, Sandra Bonilla Meza

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There are many articles that attempt to establish the role of different facial fragments in face recognition. Various approaches are used to estimate this role. Frequently, authors calculate the entropy corresponding to the fragment. This approach can only give approximate estimation. In this paper, we propose to use a more direct measure of the importance of different fragments for face recognition. We propose to select a recognition method and a face database and experimentally investigate the recognition rate using different fragments of faces. We present two such experiments in the paper. We selected the PCNC neural classifier as a method for face recognition and parts of the LFW (Labeled Faces in the Wild) face database as training and testing sets. The recognition rate of the best experiment is comparable with the recognition rate obtained using the whole face.

Keywords: Face recognition, Labeled Faces in the Wild (LFW) database, Random Local Descriptor (RLD), random features.

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Authors: Ghulam Ahmad

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In this paper comparison of Reflector Antenna analyzing techniques based on wave and ray nature of optics is presented for an offset reflector antenna using GRASP (General Reflector antenna Analysis Software Package) software. The results obtained using PO (Physical Optics), PTD (Physical theory of Diffraction), and GTD (Geometrical Theory of Diffraction) are compared. The validity of PO and GTD techniques in regions around the antenna, caustic behavior of GTD in main beam, and deviation of GTD in case of near-in sidelobes of radiation pattern are discussed. The comparison for far-out sidelobes predicted by PO, PO + PTD and GTD is described. The effect of Direct Radiations from feed which results in feed selection for the system is addressed.

Keywords: Geometrical optics & geometrical theory of diffraction, offset reflector antenna, physical optics & physical theory of diffraction, PO & GO comaprison.

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Authors: Wenjuan Du

Abstract:

The phase compensation method was proposed based on the concept of the damping torque analysis (DTA). It is a method for the design of a PSS (power system stabilizer) to suppress local-mode power oscillations in a single-machine infinite-bus power system. This paper presents the application of the phase compensation method for the design of a PSS in a multi-machine power system. The application is achieved by examining the direct damping contribution of the stabilizer to the power oscillations. By using linearized equal area criterion, a theoretical proof to the application for the PSS design is presented. Hence PSS design in the paper is an example of stable tending control by localized method.

Keywords: Phase compensation method, power system small-signal stability, power system stabilizer.

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Authors: H. Kelkoul, Y. Zaz

Abstract:

Nowadays, the vigorous popularity of video processing techniques has resulted in an explosive growth of multimedia data illegal use. So, watermarking security has received much more attention. The purpose of this paper is to explore some watermarking techniques in order to observe their specificities and select the finest methods to apply in digital cinema domain against movie piracy by creating an invisible watermark that includes the date, time and the place where the hacking was done. We have studied three principal watermarking techniques in the frequency domain: Spread spectrum, Wavelet transform domain and finally the digital cinema watermarking transform domain. In this paper, a detailed technique is presented where embedding is performed using direct sequence spread spectrum technique in DWT transform domain. Experiment results shows that the algorithm provides high robustness and good imperceptibility.

Keywords: Digital cinema, watermarking, wavelet, spread spectrum, JPEG2000.

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Authors: M. Ouagued, A. Khellaf

Abstract:

The objectif of the present work is to determinate the potential of the solar parabolic trough collector (PTC) for use in the design of a solar thermal power plant in Algeria. The study is based on a mathematical modeling of the PTC. Heat balance has been established respectively on the heat transfer fluid (HTF), the absorber tube and the glass envelop using the principle of energy conservation at each surface of the HCE cross-sectionn. The modified Euler method is used to solve the obtained differential equations. At first the results for typical days of two seasons the thermal behavior of the HTF, the absorber and the envelope are obtained. Then to determine the thermal performances of the heat transfer fluid, different oils are considered and their temperature and heat gain evolutions compared.

Keywords: Direct solar irradiance, solar radiation in Algeria, solar parabolic trough collector, heat balance, thermal oil performance

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Authors: M. Ovinis, D. Kerr, K. Bouazza-Marouf, M. Vloeberghs

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The use of machine vision to inspect the outcome of surgical tasks is investigated, with the aim of incorporating this approach in robotic surgery systems. Machine vision is a non-contact form of inspection i.e. no part of the vision system is in direct contact with the patient, and is therefore well suited for surgery where sterility is an important consideration,. As a proof-of-concept, three primary surgical tasks for a common neurosurgical procedure were inspected using machine vision. Experiments were performed on cadaveric pig heads to simulate the two possible outcomes i.e. satisfactory or unsatisfactory, for tasks involved in making a burr hole, namely incision, retraction, and drilling. We identify low level image features to distinguish the two outcomes, as well as report on results that validate our proposed approach. The potential of using machine vision in a surgical environment, and the challenges that must be addressed, are identified and discussed.

Keywords: Visual inspection, machine vision, robotic surgery.

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Authors: Raghav Lakhotia, Sameer Ganu, Anshul Goel, Abhishek Kumar

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In the age and times where women’s empowerment is a significant topic of discussion, we aim to analyze the potential gender diversity influence on box office revenues. The following research is carried out by collecting data from 400 Hollywood movies between the years 2014-2017 and performing regression analysis to find a correlation between the presence of female characters in movies and their return on investment (ROI). The paper finds that there is a positive relationship between the performance of the movies (its ROI) and the gender diversity i.e. the more the number of female characters, the higher the revenue generated. Another factor such as Number of Votes also has a direct impact on the revenue of the movie. The research not only takes into consideration the mere presence of women on screen but also the exchange of at least one dialogue among themselves, which is presented by the Bechdel Score of the movie.

Keywords: Bechdel, diversity, Hollywood, return on investment.

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Authors: P. Hajek, J. Stejskal

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The aim of this paper is to analyze the ability to identify and acquire knowledge from external sources at the regional level in the Czech Republic. The results show that the most important sources of knowledge for innovative activities are sources within the businesses themselves, followed by customers and suppliers. Furthermore, the analysis of relationships between the objective of the innovative activity and the ability to identify and acquire knowledge implies that knowledge obtained from (1) customers aims at replacing outdated products and increasing product quality; (2) suppliers aims at increasing capacity and flexibility of production; and (3) competing businesses aims at growing market share and increasing the flexibility of production and services. Regions should therefore direct their support especially into development and strengthening of networks within the value chain.

Keywords: Knowledge, acquisition, innovative business, Czech republic, region.

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Authors: Abdallah F. Abd El-Mohsen, Ahmed A. Abdelsamee, Nouby M. Ghazaly

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Engine exhaust noise is considered one of the largest sources of vehicle exterior noise. Further reduction of noise from the vehicle exhaust system will be required, as the vehicle exterior noise regulations become stricter. Therefore, the present study has been carried out to illustrate the role of engine operating parameters and exhaust system construction factors on exhaust noise emitted. The measurements carried out using different exhaust systems, which are mainly used in today’s vehicle. The effect of engine speed on the spectra level of exhaust noise is recorded at engine speeds of 900 rpm, 1800 rpm, 2700, rpm 3600 rpm and 4500 rpm. The results indicate that the increase of engine speed causes a significant increase in the spectrum level of exhaust noise. The increase in the number of the outlet of the expansion chamber also reduces the overall level of exhaust noise.

Keywords: Exhaust system, engine speed, expansion chamber.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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