Search results for: oscillometric method

Authors: Bianca A. Szasz, Keiichi Okuyama

Abstract:

As the human race will continue to explore the space by creating new space transportation means and sending them to other planets, the enhance of atmospheric reentry study is crucial. In this context, an analysis of mass recession rate of ablative materials for thermal shields of reentry spacecrafts is important to be carried out. The paper describes a new estimation method for calculating the mass recession of an ablator system made of carbon fiber reinforced plastic materials. This method is based on Arrhenius equation for low temperatures and, for high temperatures, on a theory applied for the recession phenomenon of carbon fiber reinforced plastic materials, theory which takes into account the presence of the resin inside the materials. The space mission of USERS spacecraft is considered as a case study.

Keywords: Ablator system, mass recession, spacecraft, atmospheric reentry.

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Authors: K. Petcharat, Y. Areepong, S. Sukparungsri, G. Mititelu

Abstract:

These paper, we approximate the average run length (ARL) for CUSUM chart when observation are an exponential first order moving average sequence (EMA1). We used Gauss-Legendre numerical scheme for integral equations (IE) method for approximate ARL0 and ARL1, where ARL in control and out of control, respectively. We compared the results from IE method and exact solution such that the two methods perform good agreement.

Keywords: Cumulative Sum Chart, Moving Average Observation, Average Run Length, Numerical Approximations.

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

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Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: Group decision making, intuitionistic fuzzy entropy measure, intuitionistic fuzzy set, vendor selection VIKOR.

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Authors: Mohamed K. Metwally, Sherif H. El-Gohary, Kyung Min Byun, Seung Moo Han, Soo Yeol Lee, Min Hyoung Cho, Gon Khang, Jinsung Cho, Tae-Seong Kim

Abstract:

Photoacoustic imaging (PAI) is a non-invasive and non-ionizing imaging modality that combines the absorption contrast of light with ultrasound resolution. Laser is used to deposit optical energy into a target (i.e., optical fluence). Consequently, the target temperature rises, and then thermal expansion occurs that leads to generating a PA signal. In general, most image reconstruction algorithms for PAI assume uniform fluence within an imaging object. However, it is known that optical fluence distribution within the object is non-uniform. This could affect the reconstruction of PA images. In this study, we have investigated the influence of optical fluence distribution on PA back-propagation imaging using finite element method. The uniform fluence was simulated as a triangular waveform within the object of interest. The non-uniform fluence distribution was estimated by solving light propagation within a tissue model via Monte Carlo method. The results show that the PA signal in the case of non-uniform fluence is wider than the uniform case by 23%. The frequency spectrum of the PA signal due to the non-uniform fluence has missed some high frequency components in comparison to the uniform case. Consequently, the reconstructed image with the non-uniform fluence exhibits a strong smoothing effect.

Keywords: Finite Element Method, Fluence Distribution, Monte Carlo Method, Photoacoustic Imaging.

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Authors: Yang Zhou, Kangfeng Zheng, Wei Ni, Ren Ping Liu

Abstract:

Software-defined networking (SDN) provides a solution for scalable network framework with decoupled control and data plane. However, this architecture also induces a particular distributed denial-of-service (DDoS) attack that can affect or even overwhelm the SDN network. DDoS attack detection problem has to date been mostly researched as entropy comparison problem. However, this problem lacks the utilization of SDN, and the results are not accurate. In this paper, we propose a DDoS attack detection method, which interprets DDoS detection as a signature matching problem and is formulated as Earth Mover’s Distance (EMD) model. Considering the feasibility and accuracy, we further propose to define the cost function of EMD to be a generalized Kullback-Leibler divergence. Simulation results show that our proposed method can detect DDoS attacks by comparing EMD values with the ones computed in the case without attacks. Moreover, our method can significantly increase the true positive rate of detection.

Keywords: DDoS detection, EMD, relative entropy, SDN.

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Authors: S. Ghorbani, N. I. Polushin

Abstract:

The machinability of workpieces (AISI 1045 Steel, AA2024 aluminum alloy, A48-class30 gray cast iron) in turning operation has been carried out using different types of cutting tool (conventional, cutting tool with holes in toolholder and cutting tool filled up with composite material) under dry conditions on a turning machine at different stages of spindle speed (630-1000 rpm), feed rate (0.05-0.075 mm/rev), depth of cut (0.05-0.15 mm) and tool overhang (41-65 mm). Experimentation was performed as per Taguchi’s orthogonal array. To evaluate the relative importance of factors affecting surface roughness the single decision tree (SDT), Decision tree forest (DTF) and Group method of data handling (GMDH) were applied.

Keywords: Decision Tree Forest, GMDH, surface roughness, taguchi method, turning process.

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Authors: Sudipta Majumdar

Abstract:

This paper presents a method for identification of a linear time invariant (LTI) autonomous all pole system using singular value decomposition. The novelty of this paper is two fold: First, MUSIC algorithm for estimating complex frequencies from real measurements is proposed. Secondly, using the proposed algorithm, we can identify the coefficients of differential equation that determines the LTI system by switching off our input signal. For this purpose, we need only to switch off the input, apply our complex MUSIC algorithm and determine the coefficients as symmetric polynomials in the complex frequencies. This method can be applied to unstable system and has higher resolution as compared to time series solution when, noisy data are used. The classical performance bound, Cramer Rao bound (CRB), has been used as a basis for performance comparison of the proposed method for multiple poles estimation in noisy exponential signal.

Keywords: MUSIC algorithm, Cramer Rao bound, frequency estimation.

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Authors: Mahdi Nouri

Abstract:

In this paper we introduce an efficient solution method for the Eigen-decomposition of bisymmetric and per symmetric matrices of symmetric structures. Here we decompose adjacency and Laplacian matrices of symmetric structures to submatrices with low dimension for fast and easy calculation of eigenvalues and eigenvectors. Examples are included to show the efficiency of the method.

Keywords: Graphs theory, Eigensolution, adjacency and Laplacian matrix, Canonical forms, bisymmetric, per symmetric.

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Authors: C. Ardil

Abstract:

This paper introduces a new method for multiplecriteria decision making (MCDM) that avoids order reversal and ensures consistency in decision-making. The proposed method involves range targeting of benefit and cost criteria vectors for range normalization of the initial decision matrix. The Reference Linear Combination (RLC) is used to avoid the rank reversal problem. The preference order generated from the target score matrix does not require relative comparisons between alternatives but relies on a chosen reference solution point after transforming the original decision matrix into an MCDM problem by specifying the minimum and maximum bounds of each criterion. The efficiency and applicability of the proposed RLC method were demonstrated in the selection of commercial passenger aircraft. 

Keywords: Aircraft selection, reference linear combination (RLC), multiple criteria decision-making, MCDM

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Authors: S. Kotsiantis, E. Koumanakos, D. Tzelepis, V. Tampakas

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This paper explores the effectiveness of machine learning techniques in detecting firms that issue fraudulent financial statements (FFS) and deals with the identification of factors associated to FFS. To this end, a number of experiments have been conducted using representative learning algorithms, which were trained using a data set of 164 fraud and non-fraud Greek firms in the recent period 2001-2002. The decision of which particular method to choose is a complicated problem. A good alternative to choosing only one method is to create a hybrid forecasting system incorporating a number of possible solution methods as components (an ensemble of classifiers). For this purpose, we have implemented a hybrid decision support system that combines the representative algorithms using a stacking variant methodology and achieves better performance than any examined simple and ensemble method. To sum up, this study indicates that the investigation of financial information can be used in the identification of FFS and underline the importance of financial ratios.

Keywords: Machine learning, stacking, classifier.

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Authors: Düzgün Akmaz, Hüseyin Erişti

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In the last few years, harmonics have been occurred with the increasing use of nonlinear loads, and these harmonics have been an ever increasing problem for the line systems. This situation importantly affects the quality of power and gives large losses to the network. An efficient way to solve these problems is providing harmonic compensation through parallel active power filters. Many methods can be used in the control systems of the parallel active power filters which provide the compensation. These methods efficiently affect the performance of the active power filters. For this reason, the chosen control method is significant. In this study, Fourier analysis (FA) control method and synchronous reference frame (SRF) control method are discussed. These control methods are designed for both eliminate harmonics and perform reactive power compensation in MATLAB/Simulink pack program and are tested. The results have been compared for each two methods.

Keywords: Harmonics, Harmonic compensation, Parallel active power filters, Power quality.

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Authors: Gábor Kovács

Abstract:

Requirement for pole-changing motors emerged at the very early times of asynchronous motor design. Different solutions have been elaborated and some of them are generally used. An alternative is the so called 3 Y/3 Y pole-changing winding. This paper deals with high power application of this solution. A complete and comprehensive study is introduced, including features and design guidelines. The method presented in this paper is especially suitable for pole numbers being close to each other. The study also reveals that the method is more advantageous then the existing solutions for high power motors with 1:3 pole ratio. Using this motor, a new and complete drive supply system has been proposed as most appropriate arrangement of high power main naval propulsion drive. Further, the method makes possible to extend the pole ratio to 1:6, 1:9, 1:12, etc. At the end, the proposal is further extended to the here so far missing 1:4, 1:5, 1:7 etc. pole ratios. A complete proposal for the theoretically infinite range has been given in this way.

Keywords: Induction motor, pole changing 3Y/3Y, pole phase modulation, pole changing 1:3, 1:4, 1:5, 1:6.

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Authors: M. Najafi, F. Rahimi Dehgolan

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method.

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Authors: Tainchi Lu, Chochih Lin

Abstract:

With a rapid growth in 3D graphics technology over the last few years, people are desired to see more flexible reacting motions of a biped in animations. In particular, it is impossible to anticipate all reacting motions of a biped while facing a perturbation. In this paper, we propose a three-level tracking method for animating a 3D humanoid character. First, we take the laws of physics into account to attach physical attributes, such as mass, gravity, friction, collision, contact, and torque, to bones and joints of a character. The next step is to employ PD controller to follow a reference motion as closely as possible. Once the character cannot tolerate a strong perturbation to prevent itself from falling down, we are capable of tracking a desirable falling-down action to avoid any falling condition inaccuracy. From the experimental results, we demonstrate the effectiveness and flexibility of the proposed method in comparison with conventional data-driven approaches.

Keywords: Character Animation, Forward Dynamics, Motion Tracking, PD Control.

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Authors: Veljko Jeremic, Milica Kostic-Stankovic, Aleksandar Markovic, Milan Martic

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Evaluating the efficiency of decision making units has been frequently elaborated on in numerous publications. In this paper, the theoretical framework for a novel method of Distance Based Analysis (DBA) is presented. In addition, the method is performed on a sample of the ARWU’s top 54 Universities of the United States; the findings of which clearly demonstrate that the best ranked Universities are far from also being the most efficient.

Keywords: Evaluating Efficiency, Distance Based Analysis, Ranking of Universities, ARWU.

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Authors: Yasusi Kanada

Abstract:

When printing a plate (or dish) by an FDM 3D printer, the process normally requires support material, which causes several problems. This paper proposes a method for forming thin plates without using wasteful support material. This method requires several extraordinary parameter values when slicing plates. The experiments show that the plates can, for the most part, be successfully formed using a conventional slicer and a 3D printer; however, seams between layers spoil them and the quality of printed objects strongly depends on the slicer.

Keywords: Fused deposition modeling (FDM), 3D printing, Support-less, Layer seam, Slicer.

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Authors: Satyendra Pratap Singh, S. P. Singh

Abstract:

This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: Gravitational Search Algorithm (GSA), Law of Motion, Law of Gravity, Observability, Phasor Measurement Unit.

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Authors: Amin Aghatabar Roodbary, Mohammad Hassan Bastani

Abstract:

One of the defects of stepped frequency radar systems is their sensitivity to target motion. In such systems, target motion causes range cell shift, false peaks, Signal to Noise Ratio (SNR) reduction and range profile spreading because of power spectrum interference of each range cell in adjacent range cells which induces distortion in High Resolution Range Profile (HRRP) and disrupt target recognition process. Thus Target Motion Parameters (TMPs) effects compensation should be employed. In this paper, such a method for estimating TMPs (velocity and acceleration) and consequently eliminating or suppressing the unwanted effects on HRRP based on entropy minimization has been proposed. This method is carried out in two major steps: in the first step, a discrete search method has been utilized over the whole acceleration-velocity lattice network, in a specific interval seeking to find a less-accurate minimum point of the entropy function. Then in the second step, a 1-D search over velocity is done in locus of the minimum for several constant acceleration lines, in order to enhance the accuracy of the minimum point found in the first step. The provided simulation results demonstrate the effectiveness of the proposed method.

Keywords: ATR, HRRP, motion compensation, SFW, TMP.

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Authors: C. Kalamani, K. Paramasivam

Abstract:

Test data compression is an efficient method for reducing the test application cost. The problem of reducing test data has been addressed by researchers in three different aspects: Test Data Compression, Built-in-Self-Test (BIST) and Test set compaction. The latter two methods are capable of enhancing fault coverage with cost of hardware overhead. The drawback of the conventional methods is that they are capable of reducing the test storage and test power but when test data have redundant length of runs, no additional compression method is followed. This paper presents a modified Run Length Coding (RLC) technique with Multilevel Selective Huffman Coding (MLSHC) technique to reduce test data volume, test pattern delivery time and power dissipation in scan test applications where redundant length of runs is encountered then the preceding run symbol is replaced with tiny codeword. Experimental results show that the presented method not only improves the test data compression but also reduces the overall test data volume compared to recent schemes. Experiments for the six largest ISCAS-98 benchmarks show that our method outperforms most known techniques.

Keywords: Modified run length coding, multilevel selective Huffman coding, built-in-self-test modified selective Huffman coding, automatic test equipment.

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Authors: Mitsuyuki Kawakami, Kimihiro Yamanaka

Abstract:

The top-heavy demographic of low birth-rate and longer lifespan is a growing social problem, and one of its expected effects will be a shortage of young workers and a growing reliance on a workforce of middle-aged and older people. However, the environment of today's industrial workplace is not particularly suited to middle-aged and older workers, one notable problem being temperature control. Higher temperatures can cause health problems such as heat stroke, and the number of cases increases sharply in people over 65. Moreover, in conditions above 33°C, older people can develop circulatory system disorders, and also have a higher chance of suffering a fatal heart attack. We therefore propose a new method for controlling temperature in the indoor workplace. In this study two different verification experiments were conducted, with the proposed temperature control method being tested in cargo containers and conventional houses. The method's effectiveness was apparent in measurements of temperature and electricity consumption

Keywords: CO2 reduction, Energy saving, Temperature control

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Authors: G.H. Farrahi, S.A. Faghidian, D.J. Smith

Abstract:

A thin layer on the component surface can be found with high tensile residual stresses, due to turning operations, which can dangerously affect the fatigue performance of the component. In this paper an analytical approach is presented to reconstruct the residual stress field from a limited incomplete set of measurements. Airy stress function is used as the primary unknown to directly solve the equilibrium equations and satisfying the boundary conditions. In this new method there exists the flexibility to impose the physical conditions that govern the behavior of residual stress to achieve a meaningful complete stress field. The analysis is also coupled to a least squares approximation and a regularization method to provide stability of the inverse problem. The power of this new method is then demonstrated by analyzing some experimental measurements and achieving a good agreement between the model prediction and the results obtained from residual stress measurement.

Keywords: Residual stress, Limited measurements, Inverse problems, Turning process.

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Authors: G. Korotcenkov, B. K. Cho, L. B. Gulina, V. P. Tolstoy

Abstract:

The effect of SnO2 surface modification by Ag nanoclusters, synthesized by SILD method, on the operating characteristics of thin film gas sensors was studied and models for the promotional role of Ag additives were discussed. It was found that mentioned above approach can be used for improvement both the sensitivity and the rate of response of the SnO2-based gas sensors to CO and H2. At the same time, the presence of the Ag clusters on the surface of SnO2 depressed the sensor response to ozone.

Keywords: Ag nanoparticles, deposition, characterization, gas sensors, optimization.

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Authors: Inseok Yeo, Tae-Ho Song

Abstract:

To practically apply vacuum insulation panels (VIPs) to buildings or home appliances, VIPs have demanded long-term lifespan with outstanding insulation performance. Service lives of VIPs enveloped with Al-foil and three-layer Al-metallized envelope are calculated. For Al-foil envelope, the service life is longer but edge conduction is too large compared with the Al-metallized envelope. To increase service life even more, the proposed double enveloping method and metal-barrier-added enveloping method are further analyzed. The service lives of the VIP to employ two enveloping methods are calculated. Also, pressure increase and thermal insulation performance characteristics are investigated. For the metalbarrier- added enveloping method, effective thermal conductivity increase with time is close to that of Al-foil envelope, especially, for getter-inserted VIPs. For double enveloping method, if water vapor is perfectly adsorbed, the effect of service life enhancement becomes much greater. From these methods, the VIP can be guaranteed for service life of more than 20 years.

Keywords: Vacuum insulation panels, Service life, Double enveloping, Metal-barrier-added enveloping, Edge conduction.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: Hidemi Ogasawara, Kiyoshi Akama, Hiroshi Mabuchi

Abstract:

The purpose of this paper is to propose a framework for constructing correct parallel processing programs based on Equivalent Transformation Framework (ETF). ETF regards computation as In the framework, a problem-s domain knowledge and a query are described in definite clauses, and computation is regarded as transformation of the definite clauses. Its meaning is defined by a model of the set of definite clauses, and the transformation rules generated must preserve meaning. We have proposed a parallel processing method based on “specialization", a part of operation in the transformations, which resembles substitution in logic programming. The method requires “Memo-tree", a history of specialization to maintain correctness. In this paper we proposes the new method for the specialization-base parallel processing without Memo-tree.

Keywords: Parallel processing, Program correctness, Equivalent transformation, Specializer generation rule

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Authors: R. Fan, Q. Wan, H. Chen, Y.L. Liu, Y.P. Liu

Abstract:

This paper considers a robust recovery of sparse frequencies from partial phase-only measurements. With the proposed method, sparse frequencies can be reconstructed, which makes full use of the sparse distribution in the Fourier representation of the complex-valued time signal. Simulation experiments illustrate the proposed method-s advantages over conventional methods in both noiseless and additive white Gaussian noise cases.

Keywords: Sparse signal recovery, phase-only measurements, Compressive sensing, convex relaxation.

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Authors: F. I. Belheouane, M. Bensaibi

Abstract:

The seismic feedback experiences in Algeria have shown higher percentage of damages for non-code conforming reinforced concrete (RC) buildings. Furthermore, the vulnerability of these buildings was further aggravated due to presence of many factors (e.g. weak the seismic capacity of these buildings, shorts columns, Pounding effect, etc.). Consequently Seismic risk assessments were carried out on populations of buildings to identify the buildings most likely to undergo losses during an earthquake. The results of such studies are important in the mitigation of losses under future seismic events as they allow strengthening intervention and disaster management plans to be drawn up. Within this paper, the state of the existing structures is assessed using "the vulnerability index" method. This method allows the classification of RC constructions taking into account both, structural and non structural parameters, considered to be ones of the main parameters governing the vulnerability of the structure. Based on seismic feedback from past earthquakes DPM (damage probability matrices) were developed too.

Keywords: Seismic vulnerability, Reinforced concrete buildings, Earthquake, DPM, Algeria.

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Authors: A. S. Kipcak, P. Gurses, E. Moroydor Derun, S. Piskin

Abstract:

Borate minerals have attracted considerable attention in the past years due to their structural chemistry and mechanical properties in several industries. Recently, increasing attention has been paid to the use of; synthetically produced magnesium borates as catalysts reinforcing material for plastics, the conversion of hydrocarbons, electro-conductive treating agent, anti-wear and anti-corrosion materials. Magnesium borates can be synthesized by several methods such as; hydrothermal and solid-state (thermal) processes. In this study the hydrothermal production method was applied at the modest temperature of 80C along with convenient crystal growth. Using MgCl2.6H2O, H3BO3, and NaOH as starting materials, 30, 60, 120, 240 minutes of reaction times were studied. After all, the crystal structure and the morphology of the products were examined by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). As a result the forms of Admontite and Mcallisterite minerals were synthesized.

Keywords: FT-IR, hydrothermal method, magnesium borates, XRD.

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Authors: E. B. Jo, J. H. Lee, J. Y. Park, S. M. Kim

Abstract:

In this study, we present an advanced detection technique for mass type breast cancer based on texture information of organs. The proposed method detects the cancer areas in three stages. In the first stage, the midpoints of mass area are determined based on AHE (Adaptive Histogram Equalization). In the second stage, we set the threshold coefficient of homogeneity by using MLE (Maximum Likelihood Estimation) to compute the uniformity of texture. Finally, mass type cancer tissues are extracted from the original image. As a result, it was observed that the proposed method shows an improved detection performance on dense breast tissues of Korean women compared with the existing methods. It is expected that the proposed method may provide additional diagnostic information for detection of mass-type breast cancer.

Keywords: Mass Type Breast Cancer, Mammography, Maximum Likelihood Estimation (MLE), Ranklets, SVM

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Authors: Autcha Araveeporn

Abstract:

The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.

Keywords: Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.

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