Search results for: Discrete Fourier Transform (DFT)

Authors: S. S. Pati, L. Herojit Singh, A. C. Oliveira, V. K. Garg

Abstract:

Chitosan functionalized Fe3O4-Au core shell nanoparticles have been prepared using a two-step wet chemical approach using NaBH4 as reducing agent for formation of Au in ethylene glycol. X-ray diffraction studies shows individual phases of Fe3O4 and Au in the as prepared samples with crystallite size of 5.9 and 11.4 nm respectively. The functionalization of the core-shell nanostructure with Chitosan has been confirmed using Fourier transform infrared spectroscopy along with signatures of octahedral and tetrahedral sites of Fe3O4 below 600cm-1. Mössbauer spectroscopy shows decrease in particle-particle interaction in presence of Au shell (72% sextet) than pure oleic coated Fe3O4 nanoparticles (88% sextet) at room temperature. At 80K, oleic acid coated Fe3O4 shows only sextets whereas the Chitosan functionalized Fe3O4 and Chitosan functionalized Fe3O4@Au core shell show presence of 5 and 11% doublet, respectively.

Keywords: Magnetic nanoparticles, Fe3O4@Au core shell, iron oxide, Au nanoparticles.

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Authors: Labiba Gilani, Asifullah Khan, Anwar M. Mirza

Abstract:

This paper introduces a technique of distortion estimation in image watermarking using Genetic Programming (GP). The distortion is estimated by considering the problem of obtaining a distorted watermarked signal from the original watermarked signal as a function regression problem. This function regression problem is solved using GP, where the original watermarked signal is considered as an independent variable. GP-based distortion estimation scheme is checked for Gaussian attack and Jpeg compression attack. We have used Gaussian attacks of different strengths by changing the standard deviation. JPEG compression attack is also varied by adding various distortions. Experimental results demonstrate that the proposed technique is able to detect the watermark even in the case of strong distortions and is more robust against attacks.

Keywords: Blind Watermarking, Genetic Programming (GP), Fitness Function, Discrete Cosine Transform (DCT).

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Authors: K. Kuntanoo, S. Promkotra, P. Kaewkannetra

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According to synthetic plastics obtained from petroleum cause some environmental problems. Therefore, degradable plastics become widely used and studied for replacing the synthetic plastic waste. A biopolymer of poly hydroxybutyrate-co-hydroxyvalerate (PHBV) is subgroups of a main kind of polyhydroxyalkanoates (PHAs). Naturally, PHBV is hard, brittle and low flexible while natural rubber (NR) is high elastic latex. Then, they are blended and the biodegradation of the blended PHBV and NR films were examined in soil environment. The results showed that the degradation occurs predominantly in the bulk of the samples. The order of biodegradability was shown as follows: PHBV> PHBV/NR> NR. After biodegradation, the blended films were characterized by appearance analysis such as Scanning Electron Microscope (SEM), Fourier transform infrared spectroscopy (FTIR) and Differential Scanning Calorimetry (DSC). It was found that the biodegradation mainly occurred at the polymer surface.

Keywords: Biodegradation, polyhydroxyalkanoates (PHAs), Polyhydroxybutyrate-co-hydroxyvalerate (PHBV), natural rubber (NR).

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Authors: Mbaitiga Zacharie

Abstract:

The objective of the presented work is to implement the Kalman Filter into an application that reduces the influence of the environmental changes over the robot expected to navigate over a terrain of varying friction properties. The Discrete Kalman Filter is used to estimate the robot position, project the estimated current state ahead at time through time update and adjust the projected estimated state by an actual measurement at that time via the measurement update using the data coming from the infrared sensors, ultrasonic sensors and the visual sensor respectively. The navigation test has been performed in a real world environment and has been found to be robust.

Keywords: Kalman filter, sensors fusion, robot navigation.

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Authors: Ahmed A. Helal, Nahla E. Zakzouk, Yasser G. Desouky

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This paper presents a fuzzy logic controlled shunt active power filter used to compensate for harmonic distortion in three-phase four-wire systems. The shunt active filter employs a simple method for the calculation of the reference compensation current based of Fast Fourier Transform. This presented filter is able to operate in both balanced and unbalanced load conditions. A fuzzy logic based current controller strategy is used to regulate the filter current and hence ensure harmonic free supply current. The validity of the presented approach in harmonic mitigation is verified via simulation results of the proposed test system under different loading conditions.

Keywords: Active power filters, Fuzzy logic controller, Power quality

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Manato Ono, Hiromitsu Ogawa, Naohiro Ban, Yoshihisa Ishida

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This paper deals with a design method of a discrete modified Internal Model Control (IMC) for a plant with an integrator and dead time. If there is a load disturbance in the input or output side of the plant, the proposed control system can eliminate the steady-state error caused by it. The disturbance compensator in this method is simple and its order is low regardless of that of a plant. The simulation studies show that the proposed method has superior performance for a load disturbance rejection and robustness.

Keywords: Internal Model Control, Smith Predictor, Dead time, Integrator.

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Authors: M.Ghazvini, S. A. Monadjemi, N. Movahhedinia, K. Jamshidi

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In this article, a method has been offered to classify normal and defective tiles using wavelet transform and artificial neural networks. The proposed algorithm calculates max and min medians as well as the standard deviation and average of detail images obtained from wavelet filters, then comes by feature vectors and attempts to classify the given tile using a Perceptron neural network with a single hidden layer. In this study along with the proposal of using median of optimum points as the basic feature and its comparison with the rest of the statistical features in the wavelet field, the relational advantages of Haar wavelet is investigated. This method has been experimented on a number of various tile designs and in average, it has been valid for over 90% of the cases. Amongst the other advantages, high speed and low calculating load are prominent.

Keywords: Defect detection, tile and ceramic quality inspection, wavelet transform, classification, neural networks, statistical features.

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Authors: Mbaitiga Zacharie

Abstract:

This paper discusses the implementation of the Kalman Filter along with the Global Positioning System (GPS) for indoor robot navigation. Two dimensional coordinates is used for the map building, and refers to the global coordinate which is attached to the reference landmark for position and direction information the robot gets. The Discrete Kalman Filter is used to estimate the robot position, project the estimated current state ahead in time through time update and adjust the projected estimated state by an actual measurement at that time via the measurement update. The navigation test has been performed and has been found to be robust.

Keywords: Global positioning System, kalman filter, robot navigation.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Parekhan M. Jaff

Abstract:

This paper describes the gain and noise performances of discrete Raman amplifier as a function of fiber lengths and the signal input powers for different pump configurations. Simulation has been done by using optisystem 7.0 software simulation at signal wavelength of 1550 nm and a pump wavelength of 1450nm. The results showed that the gain is higher in bidirectional pumping than in counter pumping, the gain changes with increasing the fiber length while the noise figure remain the same for short fiber lengths and the gain saturates differently for different pumping configuration at different fiber lengths and power levels of the signal.

Keywords: Optical Amplifier, Raman Amplifier DiscreteRaman Amplifier (DRA), Wavelength Division Multiplexing(WDM).

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Authors: M.Saleem Khan, Khaled Benkrid

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This paper presents a time control liquids mixing system in the tanks as an application of fuzzy time control discrete model. The system is designed for a wide range of industrial applications. The simulation design of control system has three inputs: volume, viscosity, and selection of product, along with the three external control adjustments for the system calibration or to take over the control of the system autonomously in local or distributed environment. There are four controlling elements: rotatory motor, grinding motor, heating and cooling units, and valves selection, each with time frame limit. The system consists of three controlled variables measurement through its sensing mechanism for feed back control. This design also facilitates the liquids mixing system to grind certain materials in tanks and mix with fluids under required temperature controlled environment to achieve certain viscous level. Design of: fuzzifier, inference engine, rule base, deffuzifiers, and discrete event control system, is discussed. Time control fuzzy rules are formulated, applied and tested using MATLAB simulation for the system.

Keywords: Fuzzy time control, industrial application and timecontrol systems, adjustment of Fuzzy system, liquids mixing system, design of fuzzy time control DEV system.

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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: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

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Mostly the real life signals are time varying in nature. For proper characterization of such signals, time-frequency representation is required. The STFT (short-time Fourier transform) is a classical tool used for this purpose. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local variations. Therefore, it provides an adaptive resolution time-frequency representation of the input. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power. The processing error of the proposed technique is also discussed.

Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational Complexity

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Authors: N. Tugrul, F. T. Senberber, A. S. Kipcak E. Moroydor Derun, S. Piskin

Abstract:

In this research, it is aimed not only microwave synthesis of magnesium borates but also evaluation of magnesium wastes. Synthesis process can be described with the reaction of Mg wastes and boric acid using microwave energy. X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) were applied to synthesized minerals. According to XRD results, magnesium borate hydrate mixtures were obtained as mcallisterite (pdf# = 01-070-1902, Mg₂(B₆O₇(OH)₆)₂.9(H₂O)) at higher crystallinity properties was achieved at the mole ratio raw material 1:1. Also, other kinds of magnesium borate hydrates were obtained at lower crystallinity such as admontite (pdf # = 01-076-0540, MgO(B₂O₃)₃.7(H₂O)), inderite (pdf # = 01-072-2308, 2MgO.3B₂O₃.15(H₂O)) and magnesium borate hydrates (pdf # = 01-076-0539, MgO(B₂O₃)₃.6(H₂O)). FT-IR spectrums indicated that minor changes were seen at the band values of characteristic stretching in each experiment. At the end of experiments it is seen that using microwave energy may contribute positive effects to design of synthesis process such as reducing reaction time and products at higher crystallinity.

Keywords: Magnesium wastes, boric acid, magnesium borate, microwave energy.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

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This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: Leila Samiee, Amir Yadegari, Saeedeh Tasharrofi

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In the work presented here, nitrogen-doped graphene materials were synthesized and used as metal-free electrocatalysts for oxygen reduction reaction (ORR) under alkaline conditions. Paraphenylenediamine was used as N precursor. The N-doped graphene was synthesized under hydrothermal treatment at 200°C. All the materials have been characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Transmission electron microscopy (TEM) and X-ray photo-electron spectroscopy (XPS). Moreover, for electrochemical evaluation of samples, Rotating Disk electrode (RDE) and Cyclic Voltammetry techniques (CV) were employed. The resulting material exhibits an outstanding catalytic activity for the oxygen reduction reaction (ORR) as well as excellent resistance towards methanol crossover effects, indicating their promising potential as ORR electrocatalysts for alkaline fuel cells.

Keywords: Alkaline fuel cell, graphene, metal-free catalyst, paraphenylenediamine.

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Authors: Maxat Bokambayev, Bella Tussupova, Aisha Mamyrova, Erlan Izbasarov

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Optimization of business processes in trading companies is reviewed in the report. There is the presentation of the “Wholesale Customer Order Handling Process” business process model applicable for small and medium businesses. It is proposed to apply the algorithm for automation of the customer order processing which will significantly reduce labor costs and time expenditures and increase the profitability of companies. An optimized business process is an element of the information system of accounting of spare parts trading network activity. The considered algorithm may find application in the trading industry as well.

Keywords: Business processes, discrete-event simulation.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: S. Jalilzadeh, A. Kimiyaghalam, A. Ashouri

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This paper presents a mathematical model and a methodology to analyze the losses in transmission expansion planning (TEP) under uncertainty in demand. The methodology is based on discrete particle swarm optimization (DPSO). DPSO is a useful and powerful stochastic evolutionary algorithm to solve the large-scale, discrete and nonlinear optimization problems like TEP. The effectiveness of the proposed idea is tested on an actual transmission network of the Azerbaijan regional electric company, Iran. The simulation results show that considering the losses even for transmission expansion planning of a network with low load growth is caused that operational costs decreases considerably and the network satisfies the requirement of delivering electric power more reliable to load centers.

Keywords: DPSO, TEP, Uncertainty

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Authors: Jolanta Pulit-Prociak, Olga Długosz, Marcin Banach

Abstract:

The toxicity of bare zinc oxide nanoparticles used as drug carriers may be the result of releasing zinc ions. Thus, zinc oxide nanoparticles modified with galactose were obtained. The process of their formation was conducted in the microwave field. The physicochemical properties of the obtained products were studied. The size and electrokinetic potential were defined by using dynamic light scattering technique. The crystalline properties were assessed by X-ray diffractometry. In order to confirm the formation of the desired products, Fourier-transform infrared spectroscopy was used. Releasing of zinc ions from the prepared products when comparing to the bare oxide was analyzed. It was found out that modification of zinc oxide nanoparticles with galactose limits the releasing of zinc ions which are responsible for the toxic effect of the whole carrier-drug conjugate.

Keywords: Nanomaterials, zinc oxide, drug delivery system, toxicity.

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Authors: G. T. Ramos-Escobedo, E. T. Pecina-Treviño, L. F. Camacho-Ortegon, E. Orrantia-Borunda

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The mineral bioflotation represents a viable alternative for the evaluation of new processes benefit alternative. The adsorption bacteria on minerals surfaces will depend mainly on the type of the microorganism as well as of the studied mineral surface. In the current study, adhesion of S. carnosus on coal was studied. Several methods were used as: DRX, Fourier Transform Infra-Red (FTIR) adhesion isotherms and kinetic. The main goal is to recovery of organic matter by the microflotation process on coal particles with biological reagent (S. carnosus). Adhesion tests revealed that adhesion took place after of 8 h at pH 9. The results suggest that the adhesion of bacteria to solid substrates can be considered an abiotic physicochemical process that is consequently governed by bacterial surface properties such as their specific surface area, hydrophobicity and surface functionalities. The greatest coal fine flotability was of 75%, after 5 min of flotation.

Keywords: Fine Coal, Bacteria, Adhesion, recovery matter organic.

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Authors: N. Tugrul, N. Baran Acarali, A. S. Kipcak, E. Moroydor Derun, S. Piskin

Abstract:

Turkey has 72 % of total world boron reserves on the basis of B2O3.Borates that is a refined form of boron minerals have a wide range of applications. Zinc borates can be used as multifunctional synergistic additives. The most important properties are low solubility in water and high dehydration temperature. Zinc borates dehydrate above 290°C and anhydrous zinc borate has thermal resistance about 400°C. Zinc borates can be synthesized using several methods such as hydrothermal and solid-state processes. In this study, the solid-state method was applied between 500 and 800°C using the starting materials of ZnO and H3BO3 with 1:4 mole ratio. The reaction time was determined as 4 hours after some preliminary experiments. After the synthesis, the crystal structure and the morphology of the products were examined by XRay Diffraction (XRD), Fourier Transform Infrared Spectroscopy (FT-IR) and Raman Spectrometer. As a result the form of ZnB4O7 was synthesized with the highest crystal score at 800°C.

Keywords: Raman, solid-state method, zinc borate, XRD.

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Authors: Thomas O. Olwal, Michael A. van Wyk, Barend J. van Wyk

Abstract:

In this paper we present a soft timing phase estimation (STPE) method for wireless mobile receivers operating in low signal to noise ratios (SNRs). Discrete Polyphase Matched (DPM) filters, a Log-maximum a posterior probability (MAP) and/or a Soft-output Viterbi algorithm (SOVA) are combined to derive a new timing recovery (TR) scheme. We apply this scheme to wireless cellular communication system model that comprises of a raised cosine filter (RCF), a bit-interleaved turbo-coded multi-level modulation (BITMM) scheme and the channel is assumed to be memory-less. Furthermore, no clock signals are transmitted to the receiver contrary to the classical data aided (DA) models. This new model ensures that both the bandwidth and power of the communication system is conserved. However, the computational complexity of ideal turbo synchronization is increased by 50%. Several simulation tests on bit error rate (BER) and block error rate (BLER) versus low SNR reveal that the proposed iterative soft timing recovery (ISTR) scheme outperforms the conventional schemes.

Keywords: discrete polyphase matched filters, maximum likelihood estimators, soft timing phase estimation, wireless mobile systems.

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Authors: G. Çelik Gül, F. Kurtuluş

Abstract:

Rare earths containing complex metal oxides have drawn much attention due to physical, chemical and optical properties which make them feasible in so many areas such as non-linear optical materials and ion exchanger. We have researched a systematic study to obtain rare earth containing zirconium molybdate compound, characterization, investigation of crystal system and calculation of unit cell parameters.  After a successful synthesis of Nd₂Zr₃(MoO₄)₉ which is a member of rare earth metal containing complex oxides family, X-ray diffraction (XRD), High Score Plus/Rietveld refinement analysis, and Fourier Transform Infrared Spectroscopy (FTIR) were completed to determine the crystal structure. Morphological properties and elemental composition were determined by scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis. Thermal properties were observed via Thermogravimetric-differential thermal analysis (TG/DTA).

Keywords: Nd2Zr3(MoO4)9, solid state synthesis, powder x-ray diffraction, zirconium molybdates.

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

Abstract:

There are many kinds of metal borates found not only in nature but also synthesized in the laboratory such as magnesium borates. Due to its excellent properties, as remarkable ceramic materials, they have also application areas in anti-wear and friction reducing additives as well as electro-conductive treating agents. The synthesis of magnesium borate powders can be fulfilled simply with two different methods, hydrothermal and thermal synthesis. Microwave assisted method, also another way of producing magnesium borate, can be classified into thermal synthesis because of using the principles of solid state synthesis. It also contributes producing particles with small size and high purity in nano-size material synthesize. In this study the production of magnesium borates, are aimed using MgCl2.6H2O and H3BO3. The identification of both starting materials and products were made by the equipments of, X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). After several synthesis steps magnesium borates were synthesized and characterized by XRD and FT-IR, as well.

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

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Authors: J. Kala, V. Salajka, P. Hradil

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The main focus of this paper is on the human induced forces. Almost all existing force models for this type of load (defined either in the time or frequency domain) are developed from the assumption of perfect periodicity of the force and are based on force measurements conducted on rigid (i.e. high frequency) surfaces. To verify the different authors conclusions the vertical pressure measurements invoked during the walking was performed, using pressure gauges in various configurations. The obtained forces are analyzed using Fourier transformation. This load is often decisive in the design of footbridges. Design criteria and load models proposed by widely used standards and other researchers were introduced and a comparison was made.

Keywords: Pedestrian action, Experimental analysis, Fourier series, serviceability, cycle loading.

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Authors: J. Kavitha, S. Sowmyayani, P. Arockia Jansi Rani

Abstract:

In this paper, a shot boundary detection method is presented using octagon square search pattern. The color, edge, motion and texture features of each frame are extracted and used in shot boundary detection. The motion feature is extracted using octagon square search pattern. Then, the transition detection method is capable of detecting the shot or non-shot boundaries in the video using the feature weight values. Experimental results are evaluated in TRECVID video test set containing various types of shot transition with lighting effects, object and camera movement within the shots. Further, this paper compares the experimental results of the proposed method with existing methods. It shows that the proposed method outperforms the state-of-art methods for shot boundary detection.

Keywords: Content-based indexing and retrieval, cut transition detection, discrete wavelet transform, shot boundary detection, video source.

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Authors: Shih-Ching Lo

Abstract:

Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

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Authors: Omid A. Zargar

Abstract:

Material damages dynamic analysis is difficult to deal with different material geometry and mechanism. In addition, it is difficult to measure the dynamic behavior of cracks, debond and delamination inside the material. Different simulation methods are developed in recent years for different physical features of mechanical systems like vibration and acoustic. Nonlinear fractures are analyzed and identified for different locations in this paper. The main idea of this work is to perform dynamic analysis on different types of materials (from normal homogeneous material to complex composite laminates). Technical factors like cracks, voids, interfaces and the damages’ locations are evaluated. In this project the modal analysis is performed on different types of materials. The results could be helpful in finding modal frequencies, natural frequencies, Time domain and fast Fourier transform (FFT) in industrial applications.

Keywords: Finite element method, dynamic analysis, vibration and acoustic, composite, crack, delamination.

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