Search results for: Structural analysis.

Authors: Qurban A Memon, Mohammad S. Laghari

Abstract:

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear debris analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self-organizing maps. This is achieved using relationship measurements among corresponding attributes of various measurements for wear debris. Finally, visualization technique is proposed that helps the viewer in understanding and utilizing these relationships that enable accurate diagnostics.

Keywords: Relationship Network, Relationship Measurement, Self-organizing Clusters, Wear Debris Analysis, Kohonen Network

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Authors: Naoki Yamamoto, Jun Murakami, Chiharu Okuma, Yutaro Shigeto, Satoko Saito, Takashi Izumi, Nozomi Hayashida

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Multi-dimensional principal component analysis (PCA) is the extension of the PCA, which is used widely as the dimensionality reduction technique in multivariate data analysis, to handle multi-dimensional data. To calculate the PCA the singular value decomposition (SVD) is commonly employed by the reason of its numerical stability. The multi-dimensional PCA can be calculated by using the higher-order SVD (HOSVD), which is proposed by Lathauwer et al., similarly with the case of ordinary PCA. In this paper, we apply the multi-dimensional PCA to the multi-dimensional medical data including the functional independence measure (FIM) score, and describe the results of experimental analysis.

Keywords: multi-dimensional principal component analysis, higher-order SVD (HOSVD), functional independence measure (FIM), medical data, tensor decomposition

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Authors: Yeo Kyeong Lee, Hae Won Min, Ji Yeon Kang, Hee Sun Kim, Yeong Soo Shin

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In recent years, fire accidents have been steadily increased and the amount of property damage caused by the accidents has gradually raised. Damaging building structure, fire incidents bring about not only such property damage but also strength degradation and member deformation. As a result, the building structure undermines its structural ability. Examining the degradation and the deformation is very important because reusing the building is more economical than reconstruction. Therefore, engineers need to investigate the strength degradation and member deformation well, and make sure that they apply right rehabilitation methods. This study aims at evaluating deformation characteristics of fire damaged and rehabilitated normal strength concrete beams through both experiments and finite element analyses. For the experiments, control beams, fire damaged beams and rehabilitated beams are tested to examine deformation characteristics. Ten test beam specimens with compressive strength of 21MPa are fabricated and main test variables are selected as cover thickness of 40mm and 50mm and fire exposure time of 1 hour or 2 hours. After heating, fire damaged beams are air-recurred for 2 months and rehabilitated beams are repaired with polymeric cement mortar after being removed the fire damaged concrete cover. All beam specimens are tested under four points loading. FE analyses are executed to investigate the effects of main parameters applied to experimental study. Test results show that both maximum load and stiffness of the rehabilitated beams are higher than those of the fire damaged beams. In addition, predicted structural behaviors from the analyses also show good rehabilitation effect and the predicted load-deflection curves are similar to the experimental results. For the further, the proposed analytical method can be used to predict deformation characteristics of fire damaged and rehabilitated concrete beams without suffering from time and cost consuming of experimental process.

Keywords: Fire, Normal strength concrete, Rehabilitation, Reinforced concrete beam.

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Authors: M. Meskinfam , M. S. Sadjadi , H. Jazdarreh

Abstract:

In this study, synthesis of biomemitic patterned nano hydroxyapatite-starch biocomposites using different concentration of starch to evaluate effect of polymer alteration on biocomposites structural properties has been reported. Formation of hydroxyapatite nano particles was confirmed by X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FT-IR). Size and morphology of the samples were characterized using scanning and transmission electron microscopy (SEM and TEM). It seems that by increasing starch content, the more active site of polymer (oxygen atoms) can be provided for interaction with Ca2+ followed by phosphate and hydroxyl group.

Keywords: Biocomposite, Biomimetic, Nano hydroxyapatite, Starch

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Authors: Yiannis Smirlis, Dimitris K. Despotis

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This study performs a comparative analysis of the 21 Greek Universities in terms of their public funding, awarded for covering their operating expenditure. First it introduces a DEA/MCDM model that allocates the fund into four expenditure factors in the most favorable way for each university. Then, it presents a common, consensual assessment model to reallocate the amounts, remaining in the same level of total public budget. From the analysis it derives that a number of universities cannot justify the public funding in terms of their size and operational workload. For them, the sufficient reduction of their public funding amount is estimated as a future target. Due to the lack of precise data for a number of expenditure criteria, the analysis is based on a mixed crisp-ordinal data set.

Keywords: Data envelopment analysis, Greek universities, operating expenditures, ordinal data.

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Authors: P. Bhramara, V. D. Rao, K. V. Sharma , T. K. K. Reddy

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In designing of condensers, the prediction of pressure drop is as important as the prediction of heat transfer coefficient. Modeling of two phase flow, particularly liquid – vapor flow under diabatic conditions inside a horizontal tube using CFD analysis is difficult with the available two phase models in FLUENT due to continuously changing flow patterns. In the present analysis, CFD analysis of two phase flow of refrigerants inside a horizontal tube of inner diameter, 0.0085 m and 1.2 m length is carried out using homogeneous model under adiabatic conditions. The refrigerants considered are R22, R134a and R407C. The analysis is performed at different saturation temperatures and at different flow rates to evaluate the local frictional pressure drop. Using Homogeneous model, average properties are obtained for each of the refrigerants that is considered as single phase pseudo fluid. The so obtained pressure drop data is compared with the separated flow models available in literature.

Keywords: Adiabatic conditions, CFD analysis, Homogeneousmodel and Liquid – Vapor flow.

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Authors: H. Ozbasaran

Abstract:

Lateral torsional buckling is a global buckling mode which should be considered in design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice for calculation ease which can be obtained by using energy method. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. Accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties and loading case, the hardest step is to determine a proper mode function in application of energy method. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for concentrated load at free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: Buckling mode, cantilever, lateral-torsional buckling, I-beam.

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Authors: A. Q. Sobia, M. S. Hamidah, I. Azmi, S. F. A. Rafeeqi

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Fibre-reinforced polymer (FRP) strengthened reinforced concrete (RC) structures are susceptible to intense deterioration when exposed to elevated temperatures, particularly in the incident of fire. FRP has the tendency to lose bond with the substrate due to the low glass transition temperature of epoxy; the key component of FRP matrix.  In the past few decades, various types of high performance cementitious composites (HPCC) were explored for the protection of RC structural members against elevated temperature. However, there is an inadequate information on the influence of elevated temperature on the ultra high performance fibre-reinforced cementitious composites (UHPFRCC) containing ground granulated blast furnace slag (GGBS) as a replacement of high alumina cement (HAC) in conjunction with hybrid fibres (basalt and polypropylene fibres), which could be a prospective fire resisting material for the structural components. The influence of elevated temperatures on the compressive as well as flexural strength of UHPFRCC, made of HAC-GGBS and hybrid fibres, were examined in this study. Besides control sample (without fibres), three other samples, containing 0.5%, 1% and 1.5% of basalt fibres by total weight of mix and 1 kg/m³ of polypropylene fibres, were prepared and tested. Another mix was also prepared with only 1 kg/m³ of polypropylene fibres. Each of the samples were retained at ambient temperature as well as exposed to 400, 700 and 1000 °C followed by testing after 28 and 56 days of conventional curing. Investigation of results disclosed that the use of hybrid fibres significantly helped to improve the ambient temperature compressive and flexural strength of UHPFRCC, which was found to be 80 and 14.3 MPa respectively. However, the optimum residual compressive strength was marked by UHPFRCC-CP (with polypropylene fibres only), equally after both curing days (28 and 56 days), i.e. 41%. In addition, the utmost residual flexural strength, after 28 and 56 days of curing, was marked by UHPFRCC– CP and UHPFRCC– CB2 (1 kg/m³ of PP fibres + 1% of basalt fibres) i.e. 39% and 48.5% respectively.

Keywords: Fibre reinforced polymer materials, ground granulated blast furnace slag, high-alumina cement, hybrid fibres.

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Authors: G. W. Ni, Y. M. Zhang, D. L. Jiang, J. N. Chen, B. Liu

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In order to improve the effect of isolation structure, the principles and behaviours of the base-isolation system are studied, and the types and characteristics of the base-isolation are also discussed. Compared to the traditional aseismatic structures, the base isolation structures decrease the seismic response obviously: the total structural aseismatic value decreases to 1/4-1/32 and the seismic shear stress in the upper structure decreases to 1/14-1/23. In the huge seism, the structure can have an obvious aseismatic effect.

Keywords: Base-isolation, earthquake wave, dynamic response.

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Authors: Hyeondal Jeong, Yoonjung Baek

Abstract:

This research examines the effects of positive psychological capital (or PsyCap) on employee’s outcomes (satisfaction, commitment, organizational citizenship behavior, innovation behavior and individual creativity). This study conducted a meta-analysis of articles published in the Republic of Korea. As a result, positive psychological capital has a positive effect on the behavior of employees. Heterogeneity was identified among the studies included in the analysis and the context factors were analyzed; the study proposes contextual factors such as team tenure. The moderating effect of team tenure was not statistically significant. The implications were discussed based on the analysis results.

Keywords: Positive psychological capital, satisfaction, commitment, OCB, creativity, meta-analysis.

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Authors: J. R. Wang, S. W. Chen, Y. Chiang, W. S. Hsu, J. H. Yang, Y. S. Tseng, C. Shih

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In this research, the HABIT analysis methodology was established for Maanshan nuclear power plant (NPP). The Final Safety Analysis Report (FSAR), reports, and other data were used in this study. To evaluate the control room habitability under the CO₂ storage burst, the HABIT methodology was used to perform this analysis. The HABIT result was below the R.G. 1.78 failure criteria. This indicates that Maanshan NPP habitability can be maintained. Additionally, the sensitivity study of the parameters (wind speed, atmospheric stability classification, air temperature, and control room intake flow rate) was also performed in this research.

Keywords: PWR, HABIT, habitability, Maanshan.

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Authors: Iveta Řepková

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The aim of this paper is to estimate the efficiency of the Slovak commercial banks employing the Data Envelopment Analysis (DEA) window analysis approach during the period 2003-2012. The research is based on unbalanced panel data of the Slovak commercial banks. Undesirable output was included into analysis of banking efficiency. It was found that most efficient banks were Postovabanka, UniCredit Bank and Istrobanka in CCR model and the most efficient banks were Slovenskasporitelna, Istrobanka and UniCredit Bank in BCC model. On contrary, the lowest efficient banks were found Privatbanka and CitiBank. We found that the largest banks in the Slovak banking market were lower efficient than medium-size and small banks. Results of the paper is that during the period 2003-2008 the average efficiency was increasing and then during the period 2010-2011 the average efficiency decreased as a result of financial crisis.

Keywords: Data Envelopment Analysis, efficiency, Slovak banking sector, window analysis.

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Authors: Zhang Yan, Yu Bin

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Principle component analysis is often combined with the state-of-art classification algorithms to recognize human faces. However, principle component analysis can only capture these features contributing to the global characteristics of data because it is a global feature selection algorithm. It misses those features contributing to the local characteristics of data because each principal component only contains some levels of global characteristics of data. In this study, we present a novel face recognition approach using non-negative principal component analysis which is added with the constraint of non-negative to improve data locality and contribute to elucidating latent data structures. Experiments are performed on the Cambridge ORL face database. We demonstrate the strong performances of the algorithm in recognizing human faces in comparison with PCA and NREMF approaches.

Keywords: classification, face recognition, non-negativeprinciple component analysis (NPCA)

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Authors: H. Z. Ulukan, E. Demircioğlu, M. Erol Genevois

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The scope of this paper and the aim of proposed model were to apply monetary Input –Output (I-O) analysis to point out the importance of reusing know-how and other requirements in order to reduce the production costs in a manufacturing process for a laptop computer. I-O approach using the monetary input-output model is employed to demonstrate the impacts of different factors in a manufacturing process. A sensitivity analysis showing the correlation between these different factors is also presented. It is expected that the recommended model would have an advantageous effect in the cost minimization process.

Keywords: Input-Output Analysis, Monetary Input-Output Model, Manufacturing Process, Laptop Computer.

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Authors: Jeeeun Kim, Sungjoo Lee

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This research proposes a methodology for patent-citation-based technology input-output analysis by applying the patent information to input-output analysis developed for the dependencies among different industries. For this analysis, a technology relationship matrix and its components, as well as input and technology inducement coefficients, are constructed using patent information. Then, a technology inducement coefficient is calculated by normalizing the degree of citation from certain IPCs to the different IPCs (International patent classification) or to the same IPCs. Finally, we construct a Dependency Structure Matrix (DSM) based on the technology inducement coefficient to suggest a useful application for this methodology.

Keywords: Technology spillover effect, technology relationship, IO table, technology inducement coefficients, patent analysis, patent citation.

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Authors: Omar GACI, Stefan BALEV, Antoine DUTOT

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In this paper we introduce the notion of protein interaction network. This is a graph whose vertices are the protein-s amino acids and whose edges are the interactions between them. Using a graph theory approach, we observe that according to their structural roles, the nodes interact differently. By leading a community structure detection, we confirm this specific behavior and describe thecommunities composition to finally propose a new approach to fold a protein interaction network.

Keywords: interaction network, protein structure, community structure detection.

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Authors: Chunling Cong, Chris.P.Tsokos

Abstract:

The objective of the present research manuscript is to perform parametric, nonparametric, and decision tree analysis to evaluate two treatments that are being used for breast cancer patients. Our study is based on utilizing real data which was initially used in “Tamoxifen with or without breast irradiation in women of 50 years of age or older with early breast cancer" [1], and the data is supplied to us by N.A. Ibrahim “Decision tree for competing risks survival probability in breast cancer study" [2]. We agree upon certain aspects of our findings with the published results. However, in this manuscript, we focus on relapse time of breast cancer patients instead of survival time and parametric analysis instead of semi-parametric decision tree analysis is applied to provide more precise recommendations of effectiveness of the two treatments with respect to reoccurrence of breast cancer.

Keywords: decision tree, breast cancer treatments, parametricanalysis, non-parametric analysis

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Authors: Ana Paula Melchiors Stahlschmidt

Abstract:

This paper discusses the role of music as a ludic activity and constituent element of voice in the construction and consolidation of the relationship of the baby and his/her mother or caretaker, evaluating its implications in his/her psychic structure and constitution as a subject. The work was based on the research developed as part of the author’s doctoral activities carried out from her insertion in a project of the Music Department of Federal University of Rio Grande do Sul - UFRGS, which objective was the development of musical activities with groups of babies from 0 to 24 months old and their caretakers. Observations, video recordings of the meetings, audio testemonies, and evaluation tools applied to group participants were used as instruments for this research. Information was collected on the participation of 195 babies, among which 8 were more focused on through interviews with their mothers or caretakers. These interviews were analyzed based on the referential of French Discourse Analysis, Psychoanalysis, Psychology of Development and Musical Education. The results of the research were complemented by other posterior experiences that the author developed with similar groups, in a context of a private clinic. The information collected allowed the observation of the ludic and structural functions of musical activities, when developed in a structured environment, as well as the importance of the musicality of the mother’s voice to the psychical structuring of the baby, allowing his/her insertion in the language and his/her constitution as a subject.

Keywords: Music and babies, maternal voice, Psychoanalysis and music, Psychology and music.

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Authors: Mevlüt Burak Dalmış, Kemal Yaman

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In this study, flutter characteristics of cantilever rectangular plate structure under incompressible flow regime are investigated by comparing the results of commercial flutter analysis program ZAERO^© with wind tunnel tests conducted in Ankara Wind Tunnel (ART). A rectangular polycarbonate (PC) plate, 5x125x1000 mm in dimensions, is used for both numerical and experimental investigations. Analysis and test results are very compatible with each other. A comparison between two different solution methods (g and k-method) of ZAERO^© is also done. It is seen that, k-method gives closer result than the other one. However, g-method results are on conservative side and it is better to use conservative results namely g-method results. Even if the modal analysis results are used for the flutter analysis for this simple structure, a modal test should be conducted in order to validate the modal analysis results to have accurate flutter analysis results for more complicated structures.

Keywords: Flutter, plate, subsonic flow, wind tunnel.

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Authors: M. Rodionov, Z. Dedovets

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This article discusses ways to implement a differentiated approach to developing academic motivation for mathematical studies which relies on defining the primary structural characteristics of motivation. The following characteristics are considered: features of realization of cognitive activity, meaningmaking characteristics, level of generalization and consistency of knowledge acquired by personal experience. The assessment of the present level of individual student understanding of each component of academic motivation is the basis for defining the relevant educational strategy for its further development.

Keywords: Learning activity, mathematics, motivation, student.

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Authors: Cecilia Perri, Vincenzo Corvello

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The aim of the present study is to investigate consumers' determinants of intention toward the adoption of Smart Grid solutions and technologies. Ajzen's Theory of Planned Behaviour (TPB) model is applied and tested to explain the formation of such adoption intention. An exogenous variable, taking into account the resistance to change of individuals, was added to the basic model. The elicitation study allowed obtaining salient modal beliefs, which were used, with the support of literature, to design the questionnaire. After the screening phase, data collected from the main survey were analysed for evaluating measurement model's reliability and validity. Consistent with the theory, the results of structural equation analysis revealed that attitude, subjective norm, and perceived behavioural control positively, which affected the adoption intention. Specifically, the variable with the highest estimate loading factor was found to be the perceived behavioural control, and, the most important belief related to each construct was determined (e.g., energy saving was observed to be the most significant belief linked with attitude). Further investigation indicated that the added exogenous variable has a negative influence on intention; this finding confirmed partially the hypothesis, since this influence was indirect: such relationship was mediated by attitude. Implications and suggestions for future research are discussed.

Keywords: Adoption of innovation, consumers behaviour, energy management, smart grid, theory of planned behaviour.

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Authors: Zeinab Ghasemi, S. Amirhassan Monadjemi, Abbas Vafaei

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This paper presents a comparative analysis of a new unsupervised PCA-based technique for steel plates texture segmentation towards defect detection. The proposed scheme called Variance Based Component Analysis or VBCA employs PCA for feature extraction, applies a feature reduction algorithm based on variance of eigenpictures and classifies the pixels as defective and normal. While the classic PCA uses a clusterer like Kmeans for pixel clustering, VBCA employs thresholding and some post processing operations to label pixels as defective and normal. The experimental results show that proposed algorithm called VBCA is 12.46% more accurate and 78.85% faster than the classic PCA.

Keywords: Principal Component Analysis; Variance Based Component Analysis; Defect Detection; Texture Segmentation.

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Authors: Vitalice K. Oduol

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The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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Authors: C. M. De Marco Muscat-Fenech, A. M. Grech La Rosa

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Although a lot of importance has been given to resistance analysis for various vessel types, explicit guidelines applied to multihull vessels have not been clearly defined.  The purpose of this investigation is to highlight the importance of the vessel’s layout in terms of three axes, the transverse (separation), the longitudinal (stagger) and the vertical (draught) with respect to resistance analysis. When a vessel has the potential to experience less resistance at a particular range of speeds a vast selection of opportunities are made available for both the commercial and leisure market.

Keywords: Multihull, Reistance, Trimaran.

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Authors: Lorenzo Putzu, Cecilia Di Ruberto

Abstract:

The counting and analysis of blood cells allows the evaluation and diagnosis of a vast number of diseases. In particular, the analysis of white blood cells (WBCs) is a topic of great interest to hematologists. Nowadays the morphological analysis of blood cells is performed manually by skilled operators. This involves numerous drawbacks, such as slowness of the analysis and a nonstandard accuracy, dependent on the operator skills. In literature there are only few examples of automated systems in order to analyze the white blood cells, most of which only partial. This paper presents a complete and fully automatic method for white blood cells identification from microscopic images. The proposed method firstly individuates white blood cells from which, subsequently, nucleus and cytoplasm are extracted. The whole work has been developed using MATLAB environment, in particular the Image Processing Toolbox.

Keywords: Automatic detection, Biomedical image processing, Segmentation, White blood cell analysis.

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Authors: T. Watanabe

Abstract:

Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: Combustion, analysis, sodium, droplet.

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Authors: M. K. Pradhan, Mayank Meena, Shubham Sen, Arvind Singh

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In this study, a multi objective optimization for end milling of Al 6061 alloy has been presented to provide better surface quality and higher Material Removal Rate (MRR). The input parameters considered for the analysis are spindle speed, depth of cut and feed. The experiments were planned as per Taguchis design of experiment, with L27 orthogonal array. The Grey Relational Analysis (GRA) has been used for transforming multiple quality responses into a single response and the weights of the each performance characteristics are determined by employing the Principal Component Analysis (PCA), so that their relative importance can be properly and objectively described. The results reveal that Taguchi based G-PCA can effectively acquire the optimal combination of cutting parameters.

Keywords: Material Removal Rate, Surface Roughness, Taguchi Method, Grey Relational Analysis, Principal Component Analysis.

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Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

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In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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Authors: E. Rahmathulla Noufal

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Investigating the dynamic responses of high rise structures under the effect of siesmic ground motion is extremely important for the proper analysis and design of multitoried structures. Since the presence of infilled walls strongly influences the behaviour of frame systems in multistoried buildings, there is an increased need for developing guidelines for the analysis and design of infilled frames under the effect of dynamic loads for safe and proper design of buildings. In this manuscript, we evaluate the natural frequencies and natural periods of single bay single storey frames considering the effect of infill walls by using the Eigen value analysis and validating with SAP 2000 (free vibration analysis). Various parameters obtained from the diagonal strut model followed for the free vibration analysis is then compared with the Finite Element model, where infill is modeled as shell elements (four noded). We also evaluated the effect of various parameters on the natural periods of vibration obtained by free vibration analysis in SAP 2000 comparing them with those obtained by the empirical expressions presented in I.S. 1893(Part I)- 2002.

Keywords: Infilled frame, eigen value analysis, free vibration analysis, diagonal strut model, finite element model, SAP 2000, natural period.

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

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A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: Eigenvalue analysis, microgrid, modal analysis, voltage stability.

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