Search results for: Theoretical study

Authors: Abhay Utpat, R. B. Ingle, M. R. Nandgaonkar

Abstract:

The vibrations produced by a single point defect on various parts of the bearing under constant radial load are predicted by using a theoretical model. The model includes variation in the response due to the effect of bearing dimensions, rotating frequency distribution of load. The excitation forces are generated when the defects on the races strike to rolling elements. In case of the outer ring defect, the pulses generated are with periodicity of outer ring defect frequency where as for inner ring defect, the pulses are with periodicity of inner ring defect frequency. The effort has been carried out in preparing the physical model of the system. Different defect frequencies are obtained and are used to find out the amplitudes of the vibration due to excitation of the bearing parts. Increase in the radial load or severity of the defect produces a significant change in bearing signature characteristics.

Keywords: Condition monitoring, defect frequency, rolling element, vibration response.

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Authors: S. A. Gawish, F. A. Khalifa, R. M. Mostafa

Abstract:

This paper presents Simulation and experimental study aimed at investigating the effectiveness of an adaptive artificial neural network stabilizer on enhancing the damping torque of a synchronous generator. For this purpose, a power system comprising a synchronous generator feeding a large power system through a short tie line is considered. The proposed adaptive neuro-control system consists of two multi-layered feed forward neural networks, which work as a plant model identifier and a controller. It generates supplementary control signals to be utilized by conventional controllers. The details of the interfacing circuits, sensors and transducers, which have been designed and built for use in tests, are presented. The synchronous generator is tested to investigate the effect of tuning a Power System Stabilizer (PSS) on its dynamic stability. The obtained simulation and experimental results verify the basic theoretical concepts.

Keywords: Adaptive artificial neural network, power system stabilizer, synchronous generator.

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Authors: Guangbin Wang, Deyu Sun, Fuping Tan

Abstract:

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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Authors: L. McAllister, A. Dudau

Abstract:

This paper explores gender related barriers to interagency collaboration in statutory children safeguard partnerships against a theoretical framework that considers individuals, professions and organisations interacting as part of a complex adaptive system. We argue that gender-framed obstacles to effective communication between culturally discrepant agencies can ultimately impact on the effectiveness of policy delivery,. We focused our research on three partnership structures in Sefton Metropolitan Borough in order to observe how interactions occur, whether the agencies involved perceive their occupational environment as being gender affected and whether they believe this can hinder effective collaboration with other biased organisations. Our principal empirical findings indicate that there is a general awareness amongst professionals of the role that gender plays in each of the agencies reviewed, that gender may well constitute a barrier to effective communication, but there is a sense in which there is little scope for change in the short term. We aim to signal here, however, the need to change against the risk of service failure.

Keywords: Children's safeguard, gender, gendered professions, inter-agency collaboration, partnerships.

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Authors: Alessandro Cincotti, Shigetaka Komori, Hiroyuki Iida

Abstract:

In synchronized games players make their moves simultaneously rather than alternately. Synchronized Triomineering and Synchronized Tridomineering are respectively the synchronized versions of Triomineering and Tridomineering, two variants of a classic two-player combinatorial game called Domineering. Experimental results for small m × n boards (with m + n ≤ 12 for Synchronized Triomineering and m + n ≤ 10 for Synchronized Tridomineering) and some theoretical results for general k×n boards (with k = 3, 4, 5 for Synchronized Triomineering and k = 3 for Synchronized Tridomineering) are presented. Future research is indicated.

Keywords: Combinatorial games, Synchronized games, Triomineering, Tridomineering.

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Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.

Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.

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Authors: Khaled S. Ragab

Abstract:

This paper deals with behavior and capacity of punching shear force for flat slabs produced from steel fiber reinforced self compacting concrete (SFRSCC) by application nonlinear finite element method. Nonlinear finite element analysis on nine slab specimens was achieved by using ANSYS software. A general description of the finite element method, theoretical modeling of concrete and reinforcement are presented. The nonlinear finite element analysis program ANSYS is utilized owing to its capabilities to predict either the response of reinforced concrete slabs in the post elastic range or the ultimate strength of a flat slabs produced from steel fiber reinforced self compacting concrete (SFRSCC). In order to verify the analytical model used in this research using test results of the experimental data, the finite element analysis were performed then a parametric study of the effect ratio of flexural reinforcement, ratio of the upper reinforcement, and volume fraction of steel fibers were investigated. A comparison between the experimental results and those predicted by the existing models are presented. Results and conclusions may be useful for designers, have been raised, and represented.

Keywords: Nonlinear FEM, Punching shear behavior, Flat slabs and Steel fiber reinforced self compacting concrete (SFRSCC).

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Authors: Diego Renan G. Tudela, Veruska C. Dutra, Mary Lucia Gomes Silveira de Senna, Afonso R. Aquino

Abstract:

Tourism in the present is the largest industry in the world, being an important global activity that has grown a lot in recent times. In this context, the activity of cultural tourism is growing, being seen as an important source of knowledge and information enjoyed by visitors. This article aims to discuss the cultural tourism, archaeological records and indigenous communities and the importance of preserving these invaluable sources of information, focusing on the records of the first peoples inhabiting the South American and North American lands. The study was based on discussions, theoretical studies, bibliographical research. Archaeological records are an important source of knowledge and information. Indigenous ethnic tourism represents a rescue of the authenticity of indigenous traditional cultures and their relation to the natural habitat. Cultural and indigenous tourism activity requires long-term planning to make it a sustainable activity.

Keywords: Tourism, culture, preservation, discussions.

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Authors: Ora Geiger

Abstract:

This paper discusses the question whether a person diagnosed with dyslexia will necessarily have difficulty in reading musical notes. The author specifies the characteristics of alphabet reading in comparison to musical notation reading, and concludes that there should be no contra-indication for teaching standard music reading to children with dyslexia if an appropriate process is offered. This conclusion is based on a long term case study and relies on two main characteristics of music reading: (1) musical notation system is a systematic, logical, relative set of symbols written on a staff; and (2) music reading learning connected with playing a musical instrument is a multi-sensory activity that combines sight, hearing, touch, and movement. The paper describes music reading teaching procedures, using soprano recorders, and provides unique teaching methods that have been found to be effective for students who were diagnosed with dyslexia. It provides theoretical explanations in addition to guidelines for music education practices.

Keywords: Alphabet reading, music reading, multisensory teaching method, dyslexia, recorder playing.

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Authors: Ujjal K Ghosh, Ling Teen

Abstract:

Pervaporation has the potential to be an alternative to the other traditional separation processes such as distillation, adsorption, reverse osmosis and extraction. This study investigates the separation of phenol from water using a polyurethane membrane by pervaporation by applying the modified Maxwell-Stephen model. The modified Maxwell-Stefan model takes into account the non-ideal multi-component solubility effect, nonideal diffusivity of all permeating components, concentration dependent density of the membrane and diffusion coupling to predict various fluxes. Four cases has been developed to investigate the process parameters effects on the flux and weight fraction of phenol in the permeate values namely feed concentration, membrane thickness, operating temperature and operating downstream pressure. The model could describe semi-quantitatively the performance of the pervaporation membrane for the given system as a very good agreement between the observed and theoretical fluxes was observed.

Keywords: Pervaporation, Phenol, Polyurethane, Modified Maxwell-Stefan equation, Solution Diffusion

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Authors: Mariam Vardiashvili

Abstract:

The economic value of the asset impairment process is quite large. Impairment reflects the reduction of future economic benefits or service potentials itemized in the asset. The assets owned by public sector entities bring economic benefits or are used for delivery of the free-of-charge services. Consequently, they are classified as cash-generating and non-cash-generating assets. IPSAS 21 - Impairment of non-cash-generating assets, and IPSAS 26 - Impairment of cash-generating assets, have been designed considering this specificity.  When measuring impairment of assets, it is important to select the relevant methods. For measurement of the impaired Non-Cash-Generating Assets, IPSAS 21 recommends three methods: Depreciated Replacement Cost Approach, Restoration Cost Approach, and  Service Units Approach. Impairment of Value in Use of Cash-Generating Assets (according to IPSAS 26) is measured by discounted value of the money sources to be received in future. Value in use of the cash-generating asserts (as per IPSAS 26) is measured by the discounted value of the money sources to be received in the future. The article provides classification of the assets in the public sector  as non-cash-generating assets and cash-generating assets and, deals also with the factors which should be considered when evaluating  impairment of assets. An essence of impairment of the non-financial assets and the methods of measurement thereof evaluation are formulated according to IPSAS 21 and IPSAS 26. The main emphasis is put on different methods of measurement of the value in use of the impaired Cash-Generating Assets and Non-Cash-Generation Assets and the methods of their selection. The traditional and the expected cash flow approaches for calculation of the discounted value are reviewed. The article also discusses the issues of recognition of impairment loss and its reflection in the financial reporting. The article concludes that despite a functional purpose of the impaired asset, whichever method is used for measuring the asset, presentation of realistic information regarding the value of the assets should be ensured in the financial reporting. In the theoretical development of the issue, the methods of scientific abstraction, analysis and synthesis were used. The research was carried out with a systemic approach. The research process uses international standards of accounting, theoretical researches and publications of Georgian and foreign scientists.

Keywords: Non-cash-generating assets, cash-generating assets, recoverable value, recoverable service amount, value in use.

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Authors: Vinod Kumar, Surjit Angra

Abstract:

The objective of this theoretical study is to develop simple design formulas for the prediction of minimum film thickness and maximum mean film temperature rise in lightly loaded high-speed rolling/sliding lubricated elliptical contacts incorporating starvation effect. Herein, the reported numerical analysis focuses on thermoelastohydrodynamically lubricated rolling/sliding elliptical contacts, considering the Newtonian rheology of lubricant for wide range of operating parameters, namely load characterized by Hertzian pressure (PH = 0.01 GPa to 0.10 GPa), rolling speed (>10 m/s), slip parameter (S varies up to 1.0), and ellipticity ratio (k = 1 to 5). Starvation is simulated by systematically reducing the inlet supply. This analysis reveals that influences of load, rolling speed, and level of starvation are significant on the minimum film thickness. However, the maximum mean film temperature rise is strongly influenced by slip in addition to load, rolling speed, and level of starvation. In the presence of starvation, reduction in minimum film thickness and increase in maximum mean film temperature are observed. Based on the results of this study, empirical relations are developed for the prediction of dimensionless minimum film thickness and dimensionless maximum mean film temperature rise at the contacts in terms of various operating parameters.

Keywords: Starvation, lubrication, elliptical contact, traction, minimum film thickness.

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Authors: Pavlo Selyshchev

Abstract:

The theoretical approach is developed to describe the change of drops in the atmosphere of own steam and buffer gas under irradiation. It is shown that the irradiation influences on size of stable droplet and on the conditions under which the droplet exists. Under irradiation the change of drop becomes more complex: the not monotone and periodical change of size of drop becomes possible. All possible solutions are represented by means of phase portrait. It is found all qualitatively different phase portraits as function of critical parameters: rate generation of clusters and substance density.

Keywords: Irradiation, steam, plasma, cluster formation, liquid droplets, evolution.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.

Keywords: Hopfield Neural Networks, Exponential stability.

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Authors: Rubaiyat Jahan, Nasreen Sultana Mitu

Abstract:

This paper examines the theoretical construct of transformative practices, and reports some evidence of transformative practices from a couple of Bangladeshi English teachers. The idea of transformative practices calls for teachers’ capabilities to invest their intellectual labor in teaching with an assumption that along with the academic advancement of the learners, it aims for the personal transformation for both the learners as well for themselves. Following an ethnographic research approach, data for this study were collected through in-depth interviews, informal talks and classroom observations for a period of one year. In relevance to the English classroom of the Bangladeshi context, from this study, references of transformative practices have been underlined from the participant teachers’ views on English language teaching as well as from their actual practices. According to data of this research, some evidence of transformative practices in the form of critical language awareness and personal theories of practices emerge from the participants’ articulation of the beliefs on teaching; and from the participant teachers’ classroom practices evidence of self-directed acts of teaching, self-directed acts of professional development, and liberatory autonomy have been highlighted as the reflections of transformative practices. The implication of this paper refers to the significance of practicing teachers’ articulation of beliefs and views on teaching along with their orientation to critical pedagogical relations.

Keywords: Critical language awareness, personal theories of practices, teacher autonomy, transformative practices.

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Authors: Kuen-Ming Shu, Jyun-Wei Chen

Abstract:

Encapsulated O-rings are specifically designed to address the problem of sealing the most hostile chemicals and extreme temperature applications. Ultrasonic vibration hot embossing and ultrasonic welding techniques provide a fast and reliable method to fabricate encapsulated O-ring. This paper performs the design and analysis method of the acoustic horns with double extrusion to process tube double side flange simultaneously. The paper deals with study through Finite Element Method (FEM) of ultrasonic stepped horn used to process a capsulated O-ring, the theoretical dimensions of horns, and their natural frequencies and amplitudes are obtained through the simulations of COMOSOL software. Furthermore, real horns were fabricated, tested and verified to proof the practical utility of these horns. 

Keywords: Encapsulated O-rings, ultrasonic vibration hot embossing, flange making, acoustic horn, finite element analysis.

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Authors: Tiantian Gu, Dezhi Li, Mian Zhang, Ying Jiang

Abstract:

Considering the characteristics of residents’ participation in the governance of old community renewal (OCR), a theoretical model of the determinant of residents’ intention to participate in the governance of OCR has been built based on the theory of planned behavior. Seven old communities in Nanjing have been chosen as cases to conduct empirical analysis. The result indicates that participation attitude, subjective norm and perceived behavioral control have significant positive effects on residents’ intention to participate in the governance of the OCR. Recognition of the community, cognition of the OCR and perceived behavioral control have indirect positive effects on residents’ intention to participate in the OCR. In addition, the education level and the length of residence have positive effects on their participation intention, while the gender, age, and monthly income have little effect on it. The research result provides suggestions for the improvement of residents’ participation in the OCR.

Keywords: Old community renewal, residents’ participation in governance, intention, theory of planned behavior.

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Authors: Jan Newmarch

Abstract:

With the increasing spread of computers and the internet among culturally, linguistically and geographically diverse communities, issues of internationalization and localization and becoming increasingly important. For some of the issues such as different scales for length and temperature, there is a well-developed measurement theory. For others such as date formats no such theory will be possible. This paper fills a gap by developing a measurement theory for a class of scales previously overlooked, based on discrete and interval-valued scales such as spanner and shoe sizes. The paper gives a theoretical foundation for a class of data representation problems.

Keywords: Data representation, internationalisation, localisation, measurement theory.

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Authors: M. S. Gaafar, S. Y. Marzouk

Abstract:

Sodium borosilicate glasses doped with different content of NdF3 mol % have been prepared by rapid quenching method. Ultrasonic velocities (both longitudinal and shear) measurements have been carried out at room temperature and at ultrasonic frequency of 4 MHz. Elastic moduli, Debye temperature, softening temperature and Poisson's ratio have been obtained as a function of NdF3 modifier content. Results showed that the elastic moduli, Debye temperature, softening temperature and Poisson's ratio have very slight change with the change of NdF3 mol % content. Based on FTIR spectroscopy and theoretical (Bond compression) model, quantitative analysis has been carried out in order to obtain more information about the structure of these glasses. The study indicated that the structure of these glasses is mainly composed of SiO4 units with four bridging oxygens (Q4), and with three bridging and one nonbridging oxygens (Q3).

Keywords: Borosilicate glasses, ultrasonic velocity, elastic moduli, FTIR spectroscopy, bond compression model.

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Authors: Jaehun Joo, Mie-jung Kim, Ismatilla Normatov, Lyunhwa Kim

Abstract:

The purpose of this paper is to analyze determinants of information security affecting adoption of the Web-based integrated information systems (IIS). We introduced Web-based information systems which are designed to formulate strategic plans for Peruvian government. Theoretical model is proposed to test impact of organizational factors (deterrent efforts and severity; preventive efforts) and individual factors (information security threat; security awareness) on intentions to proactively use the Web-based IIS .Our empirical study results highlight that deterrent efforts and deterrent severity have no significant influence on the proactive use intentions of IIS, whereas, preventive efforts play an important role in proactive use intentions of IIS. Thus, we suggest that organizations need to do preventive efforts by introducing various information security solutions, and try to improve information security awareness while reducing the perceived information security threats.

Keywords: Information security, Deterrent efforts, deterrentseverity, preventive efforts, information security awareness, information security threats, integrated information systems

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Authors: C. Ardil

Abstract:

A new mathematical model for calculating the temperature field of the profile part of the cooled blades of gas turbines is developed. The theoretical substantiation of the method is based on the application of the method of potential theory (the method of boundary integral equations). The effectiveness of the implementation of the developed mathematical model is confirmed on the basis of a computational experiment.

Keywords: Modeling of temperature fields, gas turbine blades, integral methods, cooled blades, gas turbines.

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Authors: H. Asiaban, E. Farshidi

Abstract:

This paper presents a new true RMS-to-DC converter circuit based on a square-root-domain squarer/divider. The circuit is designed by employing up-down translinear loop and using of MOSFET transistors that operate in strong inversion saturation region. The converter offer advantages of two-quadrant input current, low circuit complexity, low supply voltage (1.2V) and immunity from the body effect. The circuit has been simulated by HSPICE. The simulation results are seen to conform to the theoretical analysis and shows benefits of the proposed circuit.

Keywords: Current-mode, squarer/divider, low-pass filter, converter, translinear loop, RMS-to-DC.

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Authors: Inês Ramalhete, Hugo Farias, Rui da Silva Pinto

Abstract:

Adequate housing has been a widely discussed theme in academic circles related to low-cost housing, whereas its physical features are easy to deal with, overcrowding (related to social, cultural and economic aspects) is still ambiguous, particularly regarding the set of indicators that can accurately reflect and measure it. This paper develops research on low-cost housing models for developing countries and what is the best method to embed overcrowding as an important parameter for adaptability. A critical review of international overcrowding indicators and their application in two developing countries, Cape Verde and Angola, is presented. The several rationales and the constraints for an accurate assessment of overcrowding are considered, namely baseline data (statistics), which can induce misjudgments, as well as social and cultural factors (such as personal choices of residents). This paper proposes a way to tackle overcrowding through housing adaptability, considering factors such as physical flexibility, functional ambiguity, and incremental expansion schemes. Moreover, a case-study is presented to establish a framework for the theoretical application of the proposed approach.

Keywords: Adaptive housing, low-cost housing, overcrowding.

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Authors: Chun-Der Chen, Yi-Wen Fan, Cheng-Kiang Farn

Abstract:

In today-s competitive global business environment, the concept of supply chain management (SCM) continues to become increasingly market-oriented, shifting the primary driver of the value chain from supply to demand. Recent recommendations encourage researchers to focus investigations on the supply chain process integration (SCPI) capabilities that integrate a focal firm with its network of suppliers and business customers to create value for it. However, theoretical and empirical researches pertaining to the antecedents and consequences of a focal firm-s SCPI capabilities have been limited and piecemeal. The purpose of this study is to investigate the critical determinants and consequences of a focal firm-s SCPI capabilities. We test our proposed research framework using a sample of 139 sales managers of manufacturing industries in Taiwan, our research findings show that (1) both perceived business customer-s power and focal firm-s market-oriented culture positively influences a focal firm-s SCPI capabilities, and (2) SCPI capabilities positively influence a focal firm-s SCM performance, both operational and strategic benefits. Implications for practitioners and researchers and suggestions for future research are also addressed in this study.

Keywords: Supply chain process integration capabilities, Perceived business customer's power, Market-oriented culture, Supply chain management performance.

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Authors: M. Hakak Khadem, S. Hossainpour, M. Shams

Abstract:

A numerical simulation of micro Poiseuille flow has performed for rarefied and compressible flow at slip flow regimes. The wall roughness is simulated in two cases with triangular microelements and random micro peaks distributed on wall surfaces to study the effects of roughness shape and distribution on flow field. Two values of Mach and Knudsen numbers have used to investigate the effects of rarefaction as well as compressibility. The numerical results have also checked with available theoretical and experimental relations and good agreements has achieved. High influence of roughness shape can be seen for both compressible and incompressible rarefied flows. In addition it is found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. It is also found that compressibility has more significant effects on Poiseuille number when relative roughness increases.

Keywords: Relative roughness, slip flow, Poiseuille number, roughness distribution.

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Authors: Ana Paula Melchiors Stahlschmidt, Cristina Py de Pinto Gomes Mairesse

Abstract:

This paper presents observations on the early supervised internships in Psychology, currently called basic internships in Brazil, and its importance in professional training. The work is an experience report and focuses on the Professional training, illustrated by the reality of a Brazilian institution, used as a case study. It was developed from the authors' experience as academic supervisors of this kind of practice throughout this undergraduate course, combined with aspects investigated in the post-doctoral research of one of them. Theoretical references on the subject and related national legislation are analyzed, as well as reports of students who experienced at least one semester of this type of practice, articulated to the observations of the authors. The results demonstrate the importance of the early supervised internships as a way of creating opportunities for the students of a first contact with the professional reality and the practice of psychologists in different fields of insertion, preparing them for further experiments that require more involvement in activities of training and practices in Psychology.

Keywords: Training of psychologists, Internships in Psychology, Supervised internships, Combination of theory and practice.

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Authors: Andreas Ahrens, Jelena Zascerinska

Abstract:

Emotions are crucial in online classes in adult education. Despite that, a little attention was devoted to the emotional experience of being an online teacher in the field of andragogy, and the online teacher’s emotional perspectives in ever changing environments have to be analysed. The paper aims at the analysis of teachers’ emotional experience in online classes in adult education in selected European countries. The research tends to propose implications for training of teachers who work in online classes in adult education. The survey was conducted in April 2022. In the selected European countries 78 respondents took part in the study. Among them, 30 respondents represented Germany, 28 respondents Greece, and 20 respondents were from Italy. The theoretical findings allow defining teacher emotional experience. The analysis of the elements of the respondents’ emotional experience allows concluding that teachers’ attitude to online classes has to be developed. The key content for teacher training is presented. Directions of further work are proposed.

Keywords: Adult education, online classes, teacher emotional experience, European countries.

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Authors: Shannon Steinmetz, Ellen Gethner

Abstract:

In this paper a theoretical foundation is developed to segment, analyze and associate patterns within audio. We explore this on imagery via sonified audio applied to our segmentation framework. The approach involves a geodesic estimator within the statistical manifold, parameterized by musical centricity. We demonstrate viability by processing a database of random imagery to produce statistically significant clusters of similar imagery content.

Keywords: Sonification, musical information geometry, image content extraction, automated quantification, audio segmentation, pattern recognition.

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Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Keywords: Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

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Authors: El Kaak, Rachid, El Bikri, Khalid, Benamar, Rhali

Abstract:

This paper describes a study of geometrically nonlinear free vibration of thin circular functionally graded (CFGP) plates resting on Winkler elastic foundations. The material properties of the functionally graded composites examined here are assumed to be graded smoothly and continuously through the direction of the plate thickness according to a power law and are estimated using the rule of mixture. The theoretical model is based on the classical Plate theory and the Von-Kármán geometrical nonlinearity assumptions. An homogenization procedure (HP) is developed to reduce the problem considered here to that of isotropic homogeneous circular plates resting on Winkler foundation. Hamilton-s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear fundamental frequency has also been analysed.

Keywords: Functionally graded materials, nonlinear vibrations, Winkler foundation.

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