Search results for: numerical integration

Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Renzhong Peng, Weiping Wu

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Based on the framework of Hofstede’s cultural dimension, this study conducted a comparative study on the similarities and differences between national cultures and corporate cultural values, analyzed and interpreted the reasons why Chinese overseas Mergers and Acquisitions (M&A) cultural integration results in the success or failure. The findings of this study indicate that in the process of M&A, the corporate cultural values from Chinese and western corporations are proved to be quite different as a result of their diversities of national cultures, and the strategies for the integration of cultural corporate values are of vital importance and can determine the effects of the M&A, which can be referential to managers who intend to have the idea of M&A and those who have cultural integration in the process of M&A.

Keywords: comparative study, cultural integration, corporate cultural values, Mergers and Acquisitions

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Authors: Amira Amamou, Mnaouar Chouchane

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This paper investigates the bifurcation and nonlinear behavior of two degrees of freedom model of a symmetrical balanced rigid rotor supported by two identical journal bearings. The fluid film hydrodynamic reactions are modeled by applying both the short and the long bearing approximation and using half Sommerfeld solution. A numerical integration of equations of the journal centre motion is presented to predict the presence and the size of stable or unstable limit cycles in the neighborhood of the stability critical speed. For their stability margins, a continuation method based on the predictor-corrector mechanism is used. The numerical results of responses show that stability and bifurcation behaviors of periodic motions depend strongly on bearing parameters and its dynamic characteristics.

Keywords: hydrodynamic journal bearing, nonlinear stability, continuation method, bifurcations

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: Abdalla Manur, Daniel Offin, Alessandro Arsie

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In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001. Chen’s solution was minimizing for one quarter of the period [0; T], where numerical integration had been used in his proof. This paper focuses on extending the minimization property to intervals of time [0; 2T] and [0; 4T].

Keywords: action, Hamiltoian, N-body, symmetry

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Authors: Peng Li, Er-xiang Song

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Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion.

Keywords: asynchronous input, longitudinal seismic response, tunnel structure, numerical simulation, traveling wave effect

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Authors: Surayyo Shaamirova, Anwar Hasan Abdullah Othman

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This study investigates the co-integration association between the top 10 cryptocurrencies, namely Bitcoin, Ethereum, Ripple, Bitcoin Cash, EOS, Cardano, Litecoin, Stellar, IOTA, and NEO. The study applies Johansen Juselius co-integration test to examine the long-run co-integration and utilize the Engle and Granger casualty test to examine the short-run relationship. The findings of the study show that there is a strong co-integration relationship among the cryptocurrencies; however, in the short run, there is no causal relationship among the crypto currencies. These results, therefore, suggest that there are portfolio diversification opportunities in the cryptocurrencies industry when it comes to long run investment decisions, on the other hand, the cryptocurrencies industry shows the characteristics of efficiency in the short-run. This is an indication of a non-speculation investment in the cryptocurrencies industry in the short term investment.

Keywords: cryptocurrencies, Johansen-Juselius co-integration test, Engle and Granger casualty test, portfolio diversification

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Authors: Ozge Karayalçin

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This study tries to find out the reasons for the integration problems of third generation Dutch-Turkish youngsters by particularly focusing on the socio-cultural and socio-economic situations of these people in the Netherlands. The results obtained from the field research are summed up under four sections. These four sections are education and language, labour market, cultural factors, religion, and nationality. The underlying reasons of the integration problems are reflected from two different perspectives. The first one is the effects of social and economic enforcements implemented on the Turkish immigrant society. The second one is the traditional Turkish values that are quite different from Dutch values. The problems experienced by third generation Turkish origin Dutch youngsters are not one-sided. To conclude, solution-oriented advisements are asserted.

Keywords: acculturation levels, Dutch-Turkish youngsters, integration, transnational migrants, identity conflicts

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

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In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability

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Authors: Iyad Alazzam, Kenneth Magel, Izzat Alsmadi

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The different activities and approaches in software testing try to find the most possible number of errors or failures with the least amount of possible effort. Mutation is a testing approach that is used to discover possible errors in tested applications. This is accomplished through changing one aspect of the software from its original and writes test cases to detect such change or mutation. In this paper, we present a mutation approach for testing software components integration aspects. Several mutation operations related to components integration are described and evaluated. A test case study of several open source code projects is collected. Proposed mutation operators are applied and evaluated. Results showed some insights and information that can help testing activities in detecting errors and improving coverage.

Keywords: software testing, integration testing, mutation, coverage, software design

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

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Authors: Bahar Ayhan

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The present paper is concerned with the numerical modeling of the inelastic behavior of the anisotropically damaged ductile materials, which are based on a generalized macroscopic theory within the framework of continuum damage mechanics. Kinematic decomposition of the strain rates into elastic, plastic and damage parts is basis for accomplishing the structure of continuum theory. The evolution of the damage strain rate tensor is detailed with the consideration of anisotropic effects. Helmholtz free energy functions are constructed separately for the elastic and inelastic behaviors in order to be able to address the plastic and damage process. Additionally, the constitutive structure, which is based on the standard dissipative material approach, is elaborated with stress tensor, a yield criterion for plasticity and a fracture criterion for damage besides the potential functions of each inelastic phenomenon. The finite element method is used to approximate the linearized variational problem. Stress and strain outcomes are solved by using the numerical integration algorithm based on operator split methodology with a plastic and damage (multiplicator) variable separately. Numerical simulations are proposed in order to demonstrate the efficiency of the formulation by comparing the examples in the literature.

Keywords: anisotropic damage, finite element method, plasticity, coupling

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Authors: Odoh Dickson Akpegi

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The paper is about the need for an indigenous language in order to meaningfully harness both our human and material resources for the nation’s integration. It then examines the notty issue of the national language question and advocates a piece meal approach in solving the problem. This approach allows for the development and use of local languages in minority areas, especially in Benue State, as a way of preparing them for consideration as possible replacement for English language as Nigeria’s national or official language. Finally, an arrangement to follow to prepare the languages for such competition at the national level is presented.

Keywords: indigenous language, English language, official language, National integration

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Authors: Mohammad Khamoushi, Reza Mirmahdi

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The aim of this research was the effect of sensory integration in reduction of stereotype behaviors in autistic children. The statistical population included 55 children with the age range 2/8 – 14 in Esfahan Ordibehesht autistic center. Purposive sampling was used for selecting the sample group and 20 children with random assignment were designated in two group; experimental and control . Research project was quasi-experimental two-group with pretest and posttest. Data collection tools included repetitive behavior scale-revised with six sub-scales: stereotype behavior, self-injurious behavior, compulsive behavior, ritualistic behavior, sameness behavior, restricted behavior. Analysis of covariance was used for analyzing hypotheses. Result show that sensory integration procedure was effective in reduction of stereotype behavior, compulsive behavior and self-injurious behavior in autistic children. According to the findings, it is suggested that effect sensory integration procedure in stereotype behavior of autism children should be studied and used for treatment of other disabilities of this children.

Keywords: autism, sensory integration procedure, stereotype behavior, compulsive behavior

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Angela Odero, Chrysoula Karathanasi, Michèle Baumann

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Integration of foreign communities has been a forefront issue in Luxembourg for some time now. The country’s continued progress depends largely on the successful integration of immigrants. The aim of our study was to analyze factors which intervene in the course of integration of Non-EU citizens through the discourse of Non-EU citizens residing in Luxembourg, who have signed the Welcome and Integration Contract (CAI). The two-year contract offers integration services to assist foreigners in getting settled in the country. Semi-structured focus group discussions with 50 volunteers were held in English, French, Spanish, Serbo-Croatian or Chinese. Participants were asked to talk about their integration experiences. Recorded then transcribed, the transcriptions were analyzed with the help of NVivo 10, a qualitative analysis software. A systematic and reiterative analysis of decomposing and reconstituting was realized through (1) the identification of predetermined categories (difficulties, challenges and integration needs) (2) initial coding – the grouping together of similar ideas (3) axial coding – the regrouping of items from the initial coding in new ways in order to create sub-categories and identify other core dimensions. Our results show that intervening factors include language acquisition, professional career and socio-cultural activities or events. Each of these factors constitutes different components whose weight shifts from person to person and from situation to situation. Connecting these three emergent factors are two elements essential to the success of the immigrant’s integration – the role of time and deliberate effort from the immigrants, the community, and the formal institutions charged with helping immigrants integrate. We propose a theoretical model where the factors described may be classified in terms of how they predispose, facilitate, and / or reinforce the process towards a successful integration. Measures currently in place propose one size fits all programs yet integrative measures which target the family unit and those customized to target groups based on their needs would work best.

Keywords: integration, integration services, non-eu citizens, qualitative analysis, third country nationals

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Authors: Aymen Laadhari

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During the last decade, an increasing number of contributions have been made in the fields of scientific computing and numerical methodologies applied to the study of the hemodynamics in the heart. In contrast, the numerical aspects concerning the interaction of pulsatile blood flow with highly deformable thin leaflets have been much less explored. This coupled problem remains extremely challenging and numerical difficulties include e.g. the resolution of full Fluid-Structure Interaction problem with large deformations of extremely thin leaflets, substantial mesh deformations, high transvalvular pressure discontinuities, contact between leaflets. Although the Lagrangian description of the structural motion and strain measures is naturally used, many numerical complexities can arise when studying large deformations of thin structures. Eulerian approaches represent a promising alternative to readily model large deformations and handle contact issues. We present a fully Eulerian finite element methodology tailored for the simulation of pulsatile blood flow in the aorta and sinus of Valsalva interacting with highly deformable thin leaflets. Our method enables to use a fluid solver on a fixed mesh, whilst being able to easily model the mechanical properties of the valve. We introduce a semi-implicit time integration scheme based on a consistent NewtonRaphson linearization. A variant of the classical Newton method is introduced and guarantees a third-order convergence. High-fidelity computational geometries are built and simulations are performed under physiological conditions. We address in detail the main features of the proposed method, and we report several experiments with the aim of illustrating its accuracy and efficiency.

Keywords: eulerian, level set, newton, valve

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Authors: Ayodeji Sowale, Athanasios Kolios, Beatriz Fidalgo, Tosin Somorin, Aikaterini Anastasopoulou, Alison Parker, Leon Williams, Ewan McAdam, Sean Tyrrel

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Recently, energy recovery systems are thriving and raising attention in the power generation sector, due to the request for cleaner forms of energy that are friendly and safe for the environment. This has created an avenue for cogeneration, where Combined Heat and Power (CHP) technologies have been recognised for their feasibility, and use in homes and small-scale businesses. The efficiency of combustors and the advantages of the free piston Stirling engines over other conventional engines in terms of output power and efficiency, have been observed and considered. This study presents the numerical analysis of a micro-combustor with a free piston Stirling engine in an integrated model of a Nano Membrane Toilet (NMT) unit. The NMT unit will use the micro-combustor to produce waste heat of high energy content from the combustion of human waste and the heat generated will power the free piston Stirling engine which will be connected to a linear alternator for electricity production. The thermodynamic influence of the combustor on the free piston Stirling engine was observed, based on the heat transfer from the flue gas to working gas of the free piston Stirling engine. The results showed that with an input of 25 MJ/kg of faecal matter, and flue gas temperature of 773 K from the micro-combustor, the free piston Stirling engine generates a daily output power of 428 W, at thermal efficiency of 10.7% with engine speed of 1800 rpm. An experimental investigation into the integration of the micro-combustor and free piston Stirling engine with the NMT unit is currently underway.

Keywords: free piston stirling engine, micro-combustor, nano membrane toilet, thermodynamics

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Authors: Yu Liang, Wei Wei

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Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed.

Keywords: approximate arithmetic, mental number line, numerical magnitude, preschooler

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Authors: Jo-Ann Müller

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The integration-responsiveness (IR) framework presents four distinct internationalization strategies which differ depending on the extent of pressure the company faces for local responsiveness and global integration. This study applies the framework to standards by examining differences in the relative importance of three types of standards depending on the role the subsidiary plays within the corporate group. Hypotheses are tested empirically in a two-stage procedure. First, the subsidiaries are grouped performing cluster analysis. In the second step, the relationship between cluster affiliation and subsidiary strategy is tested using multinomial Probit estimation. While the level of local responsiveness of a firm relates to the relative importance of national and international formal standards, the degree of vertical integration is associated with the application of internal company.

Keywords: FDI, firm-level data, standards, subsidiary strategy

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Authors: Dewi Indah Irianti

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Introduction: Street children include one of the populations at risk of HIV infection. Their vulnerability to these situations is increased by their lack of understanding of the changes associated with adolescence, the lack of knowledge and skills which could help them to make healthy choices. Social integration increased AIDS knowledge among migrant workers in Thailand. Although social integration has been incorporated into health research in other areas, it has received less attention in AIDS prevention research. This factor has not been integrated into models for HIV prevention. Objectives: The goal of this review is to summarize available knowledge about factors related to HIV/AIDS knowledge and to examine whether social integration was reviewed among street children. Methodology: This study performed a systematic search for English language articles published between January 2006 and March 2016 using the following keywords in various combination: street children, HIV/AIDS knowledge and social integration from the following bibliographic databases: Scopus, ProQuest, JSTOR, ScienceDirect, SpringerLink, EBSCOhost, Sage Publication, Clinical Key, Google Web, and Google Scholar . Results: A total of 10 articles met the inclusion criteria were systematically reviewed. This study reviews the existing quantitative and qualitative literature regarding the HIV/AIDS knowledge of street children in many countries. The study locations were Asia, the Americas, Europe, and Africa. The most determinants associated with HIV/AIDS knowledge among street children are age and sex. In this review, social integration that may be associated with HIV/AIDS knowledge among street children has not been investigated. Conclusion: To the best of the author’s knowledge, this study found that there is no research examining the relationship of social integration with the HIV knowledge among street children. This information may assist in the development of relevant strategies and HIV prevention programs to improve HIV knowledge and decrease risk behaviors among street children.

Keywords: HIV/AIDS knowledge, review, social integration, street children

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Authors: Ridha Zgolli, Hatem Kanfoudi

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Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A 2D numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier-Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density which is expressed as function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term TEM. The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in details. The numerical simulations are in good agreement with the experimental data for steady flow.

Keywords: cavitation, injection nozzle, numerical simulation, k–ω

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Authors: Nai-Chia Chao, Meng-Chi Shih

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Under today’s fast technology and massive data era, the working method start to change. In this study, based under literature meaning of “Co-working” we had implemented the new “Co-working innovation model”. Research concluded that co-working innovation model shall not be limited in co-working space but use under different field when applying multiple art integration stragies. Research show co-working should not be limited in special field or group, should be use or adapt whenever different though or ideas where found, it should be use under different field and plans.

Keywords: arts integration, co-working, children's musical

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Authors: M. Rafiur Rahman, M. Mezbah Uddin, Mohammad Irfan Uddin, M. Moinul Islam

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With a rapid development of offshore renewable energy industry, the research activities in regards of harnessing power from offshore wind and wave energy are increasing day by day. Integration of wind turbines and wave energy converters into one combined semi-submersible platform might be a cost-economy and beneficial option. In this paper, the coupled integrated dynamic analysis in the time domain (TD) of a simplified semi-submersible flap type concept (SFC) is accomplished via state-of-the-art numerical code referred as Simo-Riflex-Aerodyn (SRA). This concept is a combined platform consisting of a semi-submersible floater supporting a 5 MW horizontal axis wind turbine (WT) and three elliptical shaped flap type wave energy converters (WECs) on three pontoons. The main focus is to validate the numerical model of SFC with experimental results and perform the frequency domain (FD) and TD response analysis. The numerical analysis is performed using potential flow theory for hydrodynamics and blade element momentum (BEM) theory for aerodynamics. A variety of environmental conditions encompassing the functional & survival conditions for short-term sea (1-hour simulation) are tested to evaluate the sustainability of the SFC. The numerical analysis is performed in full scale. Finally, the time domain analysis of heave, pitch & surge motions is performed numerically using SRA and compared with the experimental results. Due to the simplification of the model, there are some discrepancies which are discussed in brief.

Keywords: coupled integrated dynamic analysis, SFC, time domain analysis, wave energy converters

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Authors: A. Chellil, A. Nour, S. Lecheb, H.Mechakra, A. Bouderba, H. Kebir

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In this paper, the numerical study for the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor is developed. The use of the composite material for the rotor, offers a good Stability. Numerical calculations on the model develop of three dimensions prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed to determine the vibratory responses due to various excitations.

Keywords: rotor, composite, damage, finite element, numerical

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

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

Keywords: medical decision, medical ontologies, ontologies integration, linked data, knowledge engineering, e-health system

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Authors: Adji Achmad Rinaldo Fernandes

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Path analysis is an analytical technique to study the causal relationship between independent and dependent variables. In this study, the integration of Clusters in the Ward Linkage method was used in a variety of clusters with path analysis. The variables used are character (x₁), capacity (x₂), capital (x₃), collateral (x₄), and condition of economy (x₄) to on time pay (y₂) through the variable willingness to pay (y₁). The purpose of this study was to compare the Ward Linkage method cluster integration in various clusters with path analysis to classify willingness to pay (y₁). The data used are primary data from questionnaires filled out by customers of Bank X, using purposive sampling. The measurement method used is the average score method. The results showed that the Ward linkage method cluster integration with path analysis on 2 clusters is the best method, by comparing the coefficient of determination. Variable character (x₁), capacity (x₂), capital (x₃), collateral (x₄), and condition of economy (x₅) to on time pay (y₂) through willingness to pay (y₁) can be explained by 58.3%, while the remaining 41.7% is explained by variables outside the model.

Keywords: cluster integration, linkage, path analysis, compliant paying behavior

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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

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

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

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