Search results for: Mathematical Analysis courses.

Authors: Ali E. Abbas

Abstract:

This paper highlights some of the normative issues that might result by setting independent thresholds in risk analyses and particularly with safety regions. A second objective is to explain how such regions can be specified appropriately in a meaningful way. We start with a review of the importance of setting deterministic trade-offs among target requirements. We then show how to determine safety regions for risk analysis appropriately using utility functions.

Keywords: Decision analysis, thresholds, risk, reliability.

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Authors: S. Zeković, M. Vujošević, T. Maričić

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The paper provides a comprehensive analysis of the sustainable development in the Belgrade Metropolitan Region - BMA (level NUTS 2) preliminary evaluating the three chosen components: 1) economic growth and developmental changes; 2) competitiveness; and 3) territorial concentration and industrial specialization. First, we identified the main results of development changes and economic growth by applying Shift-share analysis on the metropolitan level. Second, the empirical evaluation of competitiveness in the BMA is based on the analysis of absolute and relative values of eight indicators by Spider method. Paper shows that the consideration of the national share, industrial mix and metropolitan/regional share in total Shift share of the BMA, as well as economic/functional specialization of the BMA indicate very strong process of deindustrialization. Allocative component of the BMA economic growth has positive value, reflecting the above-average sector productivity compared to the national average. Third, the important positive role of metropolitan/regional component in decomposition of the BMA economic growth is highlighted as one of the key results. Finally, comparative analysis of the industrial territorial concentration in the BMA in relation to Serbia is based on location quotient (LQ) or Balassa index as a valid measure. The results indicate absolute and relative differences in decrease of industry territorial concentration as well as inefficiency of utilizing territorial capital in the BMA. Results are important for the increase of regional competitiveness and territorial distribution in this area as well as for improvement of sustainable metropolitan and sector policies, planning and governance on this level.

Keywords: Belgrade Metropolitan Area (BMA), Comprehensive analysis/evaluation, economic growth and competitiveness, sustainable development.

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Authors: M. Kalichová, S. Hřebíčková, R. Labounková, P. Hedbávný, G. Bago

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The article deals with a biomechanics analysis of the classic bicross start with a backward movement of the bike. This is a case study analyzing this type of start in two bicross riders representing the Czech Republic. Based on the 3D kinematic analysis and with a special emphasis on the ankle movement we have divided the start into five phases – phase n. 1 – reaction time, phase n. 2 – preparation movements time, phase n. 3 – first pedal stroke time, phase n. 4 – dead point pedal passage time, phase n. 5 – second pedal stroke time. Further we have demonstrated the significance of kinematic characteristics in various stages of the bicross start including their values and the extent of change. These primarily include the vector of the instantaneous velocity of the head, wrists, elbows, shoulders, hip and knee joints. The significant angle characteristics have been noted in elbow, shoulder, hip and knee joints. The results of this work indicate the types of movement prevailing in the respective phases and as such are expected to serve as a basis for further analyses of this movement structure performed, however, on a large research sample.

Keywords: Bicross, start, kinematic analysis.

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Authors: Vipan Kumar Sohpal, Rajesh K Sharma

Abstract:

Diminishing of conventional fuels and hysterical vehicles emission leads to deterioration of the environment, which emphasize the research to work on biofuels. Biofuels from different sources attract the attention of research due to low emission and biodegradability. Emission of carbon monoxide, carbon dioxide and H-C reduced drastically using Biofuels (B-20) combustion. Contrary to the conventional fuel, engine emission results indicated that nitrous oxide emission is higher in Biofuels. So this paper examines and compares the nitrogen oxide emission of Jatropha Curcus (JCO) B-20% blends with the vegetable oil. In addition to that computational analysis of crude non edible oil performed to assess the impact of composition on emission quality. In conclusion, JCO have the potential feedstock for the biodiesel production after the genetic modification in the plant.

Keywords: Jatropha Curcus, computational analysis, emissions, biofuels.

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Authors: M. Pasbani Khiavi, A. R. M. Gharabaghi, K. Abedi

Abstract:

The mechanical behavior of porous media is governed by the interaction between its solid skeleton and the fluid existing inside its pores. The interaction occurs through the interface of gains and fluid. The traditional analysis methods of porous media, based on the effective stress and Darcy's law, are unable to account for these interactions. For an accurate analysis, the porous media is represented in a fluid-filled porous solid on the basis of the Biot theory of wave propagation in poroelastic media. In Biot formulation, the equations of motion of the soil mixture are coupled with the global mass balance equations to describe the realistic behavior of porous media. Because of irregular geometry, the domain is generally treated as an assemblage of fmite elements. In this investigation, the numerical formulation for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. A finite element model is developed and implemented into a computer code called DYNAPM for dynamic analysis of porous media. The weighted residual method with 8-node elements is used for developing of a finite element model and the analysis is carried out in the time domain considering the dynamic excitation and gravity loading. Newmark time integration scheme is developed to solve the time-discretized equations which are an unconditionally stable implicit method Finally, some numerical examples are presented to show the accuracy and capability of developed model for a wide variety of behaviors of porous media.

Keywords: Dynamic analysis, Interaction, Porous media, time domain

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Authors: E. Çetin, A. Kurşun, Ş. Aksoy, M. Tunay Çetin

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The closed form study deals with elastic stress analysis of annular bi-material discs with variable thickness subjected to the mechanical and thermomechanical loads. Those discs have many applications in the aerospace industry, such as gas turbines and gears. Those discs normally work under thermal and mechanical loads. Their life cycle can increase when stress components are minimized. Each material property is assumed to be isotropic. The results show that material combinations and thickness of profiles play an important role in determining the responses of bi-material discs and an optimal design of those structures. Stress distribution is investigated and results are shown as graphs.

Keywords: Bi-material discs, elastic stress analysis, mechanical loads, rotating discs.

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Authors: Kourosh Parand, Jamal Amani Rad

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In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: Milan Rippel, Petr Teply

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This paper focuses on operational risk measurement techniques and on economic capital estimation methods. A data sample of operational losses provided by an anonymous Central European bank is analyzed using several approaches. Loss Distribution Approach and scenario analysis method are considered. Custom plausible loss events defined in a particular scenario are merged with the original data sample and their impact on capital estimates and on the financial institution is evaluated. Two main questions are assessed – What is the most appropriate statistical method to measure and model operational loss data distribution? and What is the impact of hypothetical plausible events on the financial institution? The g&h distribution was evaluated to be the most suitable one for operational risk modeling. The method based on the combination of historical loss events modeling and scenario analysis provides reasonable capital estimates and allows for the measurement of the impact of extreme events on banking operations.

Keywords: operational risk, scenario analysis, economic capital, loss distribution approach, extreme value theory, stress testing

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Authors: F. Hejazi, J. Noorzaei, M. S. Jaafar, A. A. Abang Abdullah

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This paper describes the development of a numerical finite element algorithm used for the analysis of reinforced concrete structure equipped with shakes energy absorbing device subjected to earthquake excitation. For this purpose a finite element program code for analysis of reinforced concrete frame buildings is developed. The performance of developed program code is evaluated by analyzing of a reinforced concrete frame buildings model. The results are show that using damper device as seismic energy dissipation system effectively can reduce the structural response of framed structure during earthquake occurrence.

Keywords: Viscous Damper, finite element, program coding

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Authors: S. Parasuraman, Ler Shiaw Pei

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In this paper, the bio-mechanical analysis of human joints is carried out and the study is extended to the robot manipulator. This study will first focus on the kinematics of human arm which include the movement of each joint in shoulder, wrist, elbow and finger complexes. Those analyses are then extended to the design of a human robot manipulator. A simulator is built for Direct Kinematics and Inverse Kinematics of human arm. In the simulation of Direct Kinematics, the human joint angles can be inserted, while the position and orientation of each finger tips (end-effector) are shown. Inverse Kinematics does the reverse of the Direct Kinematics. Based on previous materials obtained from kinematics analysis, the human manipulator joints can be designed to follow prescribed position trajectories.

Keywords: Kinematics, Human Joints, Robotics, Robot Dynamics, Manipulators.

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Authors: A. Bumbová, J. Kellner, J. Navrátil, D. Pluskal, M. Kozubková, E. Kozubek

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The paper deals with the possibilities of modelling vapour propagation of explosive substances in the FLUENT software. With regard to very low tensions of explosive substance vapours the experiment has been verified as exemplified by mononitrotoluene. Either constant or time variable meteorological conditions have been used for calculation. Further, it has been verified that the eluent source may be time-dependent and may reflect a real situation or the liberation rate may be constant. The execution of the experiment as well as evaluation were clear and it could also be used for modelling vapour and aerosol propagation of selected explosive substances in the atmospheric boundary layer.

Keywords: atmospheric boundary layer, explosive substances, FLUENT software, modelling of propagation

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Authors: Radin Siti Aishah Radin A Rahman, Norasmah Othman, Zaidatol Akmaliah Lope Pihie, Hariyaty Ab. Wahid

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The recent instability in economy was found to be influencing the situation in Malaysia whether directly or indirectly. Taking that into consideration, the government needs to find the best approach to balance its citizen’s socio-economic strata level urgently. Through education platform is among the efforts planned and acted upon for the purpose of balancing the effects of the influence, through the exposure of social entrepreneurial activity towards youth especially those in higher institution level. Armed with knowledge and skills that they gained, with the support by entrepreneurial culture and environment while in campus; indirectly, the students will lean more on making social entrepreneurship as a career option when they graduate. Following the issues of marketability and workability of current graduates that are becoming dire, research involving how far the willingness of student to create social innovation that contribute to the society without focusing solely on personal gain is relevant enough to be conducted. With that, this research is conducted with the purpose of identifying the level of entrepreneurial intention and social entrepreneurship among higher institution students in Malaysia. Stratified random sampling involves 355 undergraduate students from five public universities had been made as research respondents and data were collected through surveys. The data was then analyzed descriptively using min score and standard deviation. The study found that the entrepreneurial intention of higher education students are on moderate level, however it is the contrary for social entrepreneurship activities, where it was shown on a high level. This means that while the students only have moderate level of willingness to be a social entrepreneur, they are very committed to created social innovation through the social entrepreneurship activities conducted. The implication from this study can be contributed towards the higher institution authorities in prediction the tendency of student in becoming social entrepreneurs. Thus, the opportunities and facilities for realizing the courses related to social entrepreneurship must be created expansively so that the vision of creating as many social entrepreneurs as possible can be achieved.

Keywords: Entrepreneurial intention, higher education institutions (HEIs), social entrepreneurship, social entrepreneurial activity, gender.

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Authors: P. Hedbávný, M. Kalichová

Abstract:

The contribution deals with problem of take-off phase of back somersault with twisting with various numbers of twists along longitudinal body axis. The aim was to evaluate the changes in angles during transition phase from back handspring to back somersault using 3D kinematic analysis of the somersaults. We used Simi Motion System for the 3D kinematic analysis of the observed gymnastic element performed by Czech Republic female representative and 2008 Summer Olympic Games participant. The results showed that the higher the number of twists, the smaller the touchdown angle in which the gymnasts lands on the pad in the beginning of take-off phase. In back somersault with one twist (180°) the average angle is 54°, in 1080° back somersault the average angle is 45.9°. These results may help to improve technical training of sports gymnasts.

Keywords: back somersault with twisting, biomechanicalanalysis, take-off

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Authors: Jairo Aparecido Martins, Estaner Claro Romão

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This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: Aluminum, industrial clutch, static and dynamic loading, numerical simulation.

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Authors: V. Precupas, A. Ivan, M. Ivan

Abstract:

The dome with ribs and rings, which covers the ROMEXPO pavilion from Bucharest, was designed after the collapse of the single layer reticulated dome. In this paper, it was made the checking of the structure, under the dynamic loads with three recorded accelerograms calibrated according to Romanian seismic design code P100-1/2006. Under the action the dynamic loadings, it was made a time-history analysis to determine the zones where the plastic hinges appear, at what accelerations and their position on the structure. The studied dome is formed by 32 spatial semi arches and three rings: one circular ring located at the top of the dome and another two rings, design as trusses, the first near the supports and the second as an intermediate rings above the skylights. Above the skylights up to the top, the dome is tight together with purlins and bracings.

Keywords: dome, dynamic analysis, plastic hinges, time-history

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Authors: Chun-Ta Chen, Te-Tan Liao, Hoang-Vuong Pham

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In this paper motion analysis on a winding stair-climbing is investigated using our proposed rotational arm type of robotic wheelchair. For now, the robotic wheelchair is operated in an open mode to climb winding stairs by a dynamic turning, therefore, the dynamics model is required to ensure a passenger-s safety. Equations of motion based on the skid-steering analysis are developed for the trajectory planning and motion analysis on climbing winding stairs. Since the robotic wheelchair must climb a winding staircase stably, the winding trajectory becomes a constraint equation to be followed, and the Baumgarte-s method is used to solve for the constrained dynamics equations. Experimental results validate the behavior of the prototype as it climbs a winding stair.

Keywords: Climb, robotic wheelchair, skid-steering, windingstair .

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

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In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: Y. Q. Chen, P. K. Wong, Z. C. Xie, H. W. Wu, K. U. Chan, J., L. Huang

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It is believed that continuously variable transmission (CVT) will dominate the automotive transmissions in the future. The most popular design is Van Doorne-s CVT with single metal pushing V-belt. However, it is only applicable to low power passenger cars because its major limitation is low torque capacity. Therefore, this research studies a novel dual-belt CVT system to overcome the limitation of traditional single-belt CVT, such that it can be applicable to the heavy-duty vehicles. This paper presents the mathematical model of the design and its experimental verification. Experimental and simulated results show that the model developed is valid and the proposed dual-belt CVT can really overcome the traditional limitation of single-belt Van Doorne-s CVT.

Keywords: Analytical model, CVT, Dual belts, Torque capacity.

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Authors: Luciano Garelli, Marco Schauer, Jorge D’Elia, Mario A. Storti, Sabine C. Langer

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This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM a software developed at Centro de Investigaci´on de M´etodos Computacionales –CIMEC. The structural part of the coupled process is computed by the research code elementary Parallel Solver – (ELPASO) of the Technische Universit¨at Braunschweig, Institut f¨ur Konstruktionstechnik (IK).

Keywords: Computational Fluid Dynamics (CFD), Fluid Structure Interaction (FSI), Finite Element Method (FEM).

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Authors: Darwin Gouwanda, S. M. N. Arosha Senanayake, M. M. Danushka Ranjana Marasinghe, Mervin Chandrapal, Jeya Mithra Kumar, Tung Mun Hon, Yulius

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This paper presents a real time force sensing instrument that is designed for human gait analysis purposes. This instrument mainly consists of three main elements: the force sensing mat, signal conditioning and switching circuit and data acquisition device. In order to control and to process the incoming signals from the force sensing mat, Force-Logger and Force-Reloader program are developed using Labview 8.0. This paper describes the architecture of the force sensing mat, signal conditioning and switching circuit and the real time streaming of the incoming data from the force sensing mat.

Keywords: Force platform, Force sensing resistor, human gait analysis

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Authors: Ilija Plecas, Uranija Kozmidis-Luburic, Radojica Pesic

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The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: bentonite, cement , radioactive waste, composite, disposal, diffusion

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Authors: Min Li, Tao Li

Abstract:

This paper constructs a four factors theoretical model of Chinese small and medium enterprises based on the “cartoon characters- reputation - enterprise marketing and management capabilities – protection of the cartoon image - institutional environment" by literature research, case studies and investigation. The empirical study show that the greatest impact on current merchandising rights income is the institutional environment friendliness, followed by marketing and management capabilities, input of character image protection and Cartoon characters- reputation through the real-time grey relational analysis, and the greatest impact on post-merchandising rights profit is Cartoon characters reputation, followed by the institutional environment friendliness, then marketing and management ability and input of character image protection through the time-delay grey relational analysis.

Keywords: Cartoon characters, merchandising rights, influencefactors, grey relational analysis

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Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

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In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: Information theory, prediction model, prosthetic alignment, transtibial prosthesis.

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Authors: John Cleary, Conor Slater, Dermot Diamond

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A portable sensor for the analysis of phosphate in aqueous samples has been developed. The sensor incorporates microfluidic technology, colorimetric detection, and wireless communications into a compact and rugged portable device. The detection method used is the molybdenum yellow method, in which a phosphate-containing sample is mixed with a reagent containing ammonium metavanadate and ammonium molybdate in an acidic medium. A yellow-coloured compound is generated and the absorption of this compound is measured using a light emitting diode (LED) light source and a photodiode detector. The absorption is directly proportional to the phosphate concentration in the original sample. In this paper we describe the application of this phosphate sensor to the analysis of wastewater at a municipal wastewater treatment plant in Co. Kildare, Ireland.

Keywords: Microfluidic, phosphate, sensor, wastewater.

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Authors: T. H. Fung

Abstract:

Coloured Petri net (CPN) has been widely adopted in various areas in Computer Science, including protocol specification, performance evaluation, distributed systems and coordination in multi-agent systems. It provides a graphical representation of a system and has a strong mathematical foundation for proving various properties. This paper proposes a novel representation of a coloured Petri net using an extension of logic programming called abductive logic programming (ALP), which is purely based on classical logic. Under such a representation, an implementation of a CPN could be directly obtained, in which every inference step could be treated as a kind of equivalence preserved transformation. We would describe how to implement a CPN under such a representation using common meta-programming techniques in Prolog. We call our framework CPN-LP and illustrate its applications in modeling an intelligent agent.

Keywords: Abduction, coloured petri net, intelligent agent, logic programming.

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Authors: Alessandro Bevilacqua, Alessandro Gherardi, Filippo Piccinini

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The mosaicing technique has been employed in more and more application fields, from entertainment to scientific ones. In the latter case, often the final evaluation is still left to human beings, that assess visually the quality of the mosaic. Many times, a lack of objective measurements in microscopic mosaicing may prevent the mosaic from being used as a starting image for further analysis. In this work we analyze three different metrics and indexes, in the domain of signal analysis, image analysis and visual quality, to measure the quality of different aspects of the mosaicing procedure, such as registration errors and visual quality. As the case study we consider the mosaicing algorithm we developed. The experiments have been carried out by considering mosaics with very different features: histological samples, that are made of detailed and contrasted images, and live stem cells, that show a very low contrast and low detail levels.

Keywords: Mosaicing, quality assessment, microscopy, stem cells.

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Authors: Ebtehag Tolba

Abstract:

The study presents a proposed program for nursery school children in Egypt. The program consists of a collection of artistic activities and aims to develop the language, mathematical, and artistic skills of preschool children. Furthermore, the researcher has presented a questionnaire to experts about the link between the target group and the content. Finally, the proposed program was applied to group of 30 children. In addition, the researcher has prepared another questionnaire for measuring the effect of the program. This questionnaire was used as a pre-test and post-test, and at the end of the study, a significant difference was determined in favour of the post-test results.

Keywords: Developing, concepts, nursery, children, artistic activities.

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Authors: Tomi Roinila, Aki Taskinen, Matti Vilkko

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Switched-mode converters play now a significant role in modern society. Their operation are often crucial in various electrical applications affecting the every day life. Therefore, the quality of the converters needs to be reliably verified. Recent studies have shown that the converters can be fully characterized by a set of frequency responses which can be efficiently used to validate the proper operation of the converters. Consequently, several methods have been proposed to measure the frequency responses fast and accurately. Most often correlation-based techniques have been applied. The presented measurement methods are highly sensitive to external errors and system nonlinearities. This fact has been often forgotten and the necessary uncertainty analysis of the measured responses has been neglected. This paper presents a simple approach to analyze the noise and nonlinearities in the frequency-response measurements of switched-mode converters. Coherence analysis is applied to form a confidence interval characterizing the noise and nonlinearities involved in the measurements. The presented method is verified by practical measurements from a high-frequency switchedmode converter.

Keywords: Switched-mode converters, Frequency analysis, CoherenceAnalysis.

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Authors: I. Razmi, N. Choupani

Abstract:

The incidence of mechanical fracture of an automobile piston rings prompted development of fracture analysis method on this case. The three rings (two compression rings and one oil ring) were smashed into several parts during the power-test (after manufacturing the engine) causing piston and liner to be damaged. The radial and oblique cracking happened on the failed piston rings. The aim of the fracture mechanics simulations presented in this paper was the calculation of particular effective fracture mechanics parameters, such as J-integrals and stress intensity factors. Crack propagation angles were calculated as well. Two-dimensional fracture analysis of the first compression ring has been developed in this paper using ABAQUS CAE6.5-1 software. Moreover, SEM fractography was developed on fracture surfaces and is discussed in this paper. Results of numerical calculations constitute the basis for further research on real object.

Keywords: Compression piston ring, Crack, Fracture mechanics, SEM fractography.

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Authors: Joon-Hyung Kim, Him-Chan Lee, Jin-Hyuk Kim, Yong-Kab Lee, Young-Seok Choi

Abstract:

The crude oil in an oil well exists in various phases such as gas, seawater, and sand, as well as oil. Therefore, a phase separator is needed at the front of a single-phase pump for pressurization and transfer. On the other hand, the application of a multiphase pump can provide such advantages as simplification of the equipment structure and cost savings, because there is no need for a phase separation process. Therefore, the crude oil transfer method using a multiphase pump is being applied to recently developed oil wells. Due to this increase in demand, technical demands for the development of multiphase pumps are sharply increasing, but the progress of research into related technologies is insufficient, due to the nature of multiphase pumps that require high levels of skills. This study was conducted to verify the reliability of pump performance evaluation using numerical analysis, which is the basis of the development of a multiphase pump. For this study, a model was designed by selecting the specifications of this study. The performance of the designed model was evaluated through numerical analysis and experiment. The results of the performance evaluation were compared to verify the reliability of the result using numerical analysis.

Keywords: Multiphase pump, Numerical analysis, Experiment, Performance evaluation, Reliability verification.

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