Search results for: Short Time Fourier Transform

Authors: I. F. Fiţigău, F. Peter, C. G. Boeriu

Abstract:

Five lignin samples were fractionated with Acetone/Water mixtures and the obtained fractions were subjected to extensive structural characterization, including Fourier Transform Infrared (FT-IR), Gel permeation Chromatography (GPC) and Phosphorus-31 NMR spectroscopy (31P-NMR). The results showed that for all studied lignins the solubility increases with the increment of the acetone concentration. Wheat straw lignin has the highest solubility in 90/10 (v/v) Acetone/Water mixture, 400 mg lignin being dissolved in 1 mL mixture. The weight average molecular weight of the obtained fractions increased with the increment of acetone concentration and thus with solubility. 31P-NMR analysis based on lignin modification by reactive phospholane into phosphitylated compounds was used to differentiate and quantify the different types of OH groups (aromatic, aliphatic, and carboxylic) found in the fractions obtained with 70/30 (v/v) Acetone/Water mixture.

Keywords: Lignin, fractionation, FT-IR, GPC, 31P-NMR.

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Authors: Young-Seok Choi

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This paper provides a quantitative measure of the time-varying multiunit neuronal spiking activity using an entropy based approach. To verify the status embedded in the neuronal activity of a population of neurons, the discrete wavelet transform (DWT) is used to isolate the inherent spiking activity of MUA. Due to the de-correlating property of DWT, the spiking activity would be preserved while reducing the non-spiking component. By evaluating the entropy of the wavelet coefficients of the de-noised MUA, a multiresolution Shannon entropy (MRSE) of the MUA signal is developed. The proposed entropy was tested in the analysis of both simulated noisy MUA and actual MUA recorded from cortex in rodent model. Simulation and experimental results demonstrate that the dynamics of a population can be quantified by using the proposed entropy.

Keywords: Discrete wavelet transform, Entropy, Multiresolution, Multiunit activity.

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Authors: N. Kh. Gomidze, I. N. Jabnidze, K. A. Makharadze

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The influence of inhomogeneities of plasma and statistical characteristics on the propagation of signal is very actual in wireless communication systems. While propagating in the media, the deformation and evaluation of the signal in time and space take place and on the receiver we get a deformed signal. The present article is dedicated to studying the space-time evolution of rectangular, sinusoidal, exponential and bi-exponential impulses via numerical experiment in the collisional, cold plasma. The presented method is not based on the Fourier-presentation of the signal. Analytically, we have received the general image depicting the space-time evolution of the radio impulse amplitude that gives an opportunity to analyze the concrete results in the case of primary impulse.

Keywords: Collisional, cold plasma, rectangular pulse signal, impulse envelope.

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Authors: Chuan Li, Ming Liang

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Oil debris signal generated from the inductive oil debris monitor (ODM) is useful information for machine condition monitoring but is often spoiled by background noise. To improve the reliability in machine condition monitoring, the high-fidelity signal has to be recovered from the noisy raw data. Considering that the noise components with large amplitude often have higher frequency than that of the oil debris signal, the integral transform is proposed to enhance the detectability of the oil debris signal. To cancel out the baseline wander resulting from the integral transform, the empirical mode decomposition (EMD) method is employed to identify the trend components. An optimal reconstruction strategy including both de-trending and de-noising is presented to detect the oil debris signal with less distortion. The proposed approach is applied to detect the oil debris signal in the raw data collected from an experimental setup. The result demonstrates that this approach is able to detect the weak oil debris signal with acceptable distortion from noisy raw data.

Keywords: Integral transform, empirical mode decomposition, oil debris, signal processing, detection.

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Authors: B.P. Bezruchko, D.A. Smirnov

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Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Keywords: Nonlinear time series analysis, directional couplings, coupled oscillators.

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

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An analytical 4-DOF nonlinear model of a de Laval rotor-stator system based on Energy Principles has been used theoretically and experimentally to investigate fault symptoms in a rotating system. The faults, namely rotor-stator-rub, crack and unbalance are modeled as excitations on the rotor shaft. Mayes steering function is used to simulate the breathing behaviour of the crack. The fault analysis technique is based on waveform signal, orbits and Fast Fourier Transform (FFT) derived from simulated and real measured signals. Simulated and experimental results manifest considerable mutual resemblance of elliptic-shaped orbits and FFT for a same range of test data.

Keywords: A breathing crack, fault, FFT, nonlinear, orbit, rotorstator rub, vibration analysis.

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Authors: Agnieszka Danek, Rafał Pokrzywa

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Approximate tandem repeats in a genomic sequence are two or more contiguous, similar copies of a pattern of nucleotides. They are used in DNA mapping, studying molecular evolution mechanisms, forensic analysis and research in diagnosis of inherited diseases. All their functions are still investigated and not well defined, but increasing biological databases together with tools for identification of these repeats may lead to discovery of their specific role or correlation with particular features. This paper presents a new approach for finding approximate tandem repeats in a given sequence, where the similarity between consecutive repeats is measured using the Hamming distance. It is an enhancement of a method for finding exact tandem repeats in DNA sequences based on the Burrows- Wheeler transform.

Keywords: approximate tandem repeats, Burrows-Wheeler transform, Hamming distance, suffix array

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, L-stable methods, pricing European options, Jump–diffusion model.

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Authors: Nebi Gedik

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The goal of motor image brain computer interface research is to create a link between the central nervous system and a computer or device. The most important signal for brain-computer interface is the electroencephalogram. The aim of this research is to explore a set of effective features from EEG signals, separated into frequency bands, using wave atom sub-bands to discriminate right and left-hand motor imagery signals. Over the transform coefficients, feature vectors are constructed for each frequency range and each transform sub-band, and their classification performances are tested. The method is validated using EEG signals from the BCI competition III dataset IIIa and classifiers such as support vector machine and k-nearest neighbors.

Keywords: motor imagery, EEG, Wave atom transform sub-bands, SVM, k-NN

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Authors: M. Cynthya, V. Prabhawathi, D. Mukesh

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Food contamination occurs during post process handling. This leads to spoilage and growth of pathogenic microorganisms in the food, thereby reducing its shelf life or spreading of food borne diseases. Several methods are tried and one of which is use of antimicrobial packaging. Here, papain, a protease enzyme, is covalently immobilized with the help of glutarldehyde on polyurethane and used as a food wrap to protect food from microbial contamination. Covalent immobilization of papain was achieved at a pH of 7.4; temperature of 4°C; glutaraldehyde concentration of 0.5%; incubation time of 24h; and 50mg of papain. The formation of -C=Nobserved in the Fourier transform infrared spectrum confirmed the immobilization of the enzyme on the polymer. Immobilized enzyme retained higher activity than the native free enzyme. The modified polyurethane showed better reduction of Staphylococcus aureus biofilm than bare polymer film (eight folds reduction in live colonies, two times reduction in protein and 6 times reduction in carbohydrates). The efficacy of this was studied by wrapping it over S. aureus contaminated cottage cheese (paneer) and cheese and stored at a temperature of 4°C for 7days. The modified film reduced the bacterial contamination by eight folds when compared to the bare film. FTIR also indicated reduction in lipids, sugars and proteins in the biofilm.

Keywords: Cheese, Papain, polyurethane, Staphylococcus aureus.

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Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, we propose a new robust and secure system that is based on the combination between two different transforms Discrete wavelet Transform (DWT) and Contourlet Transform (CT). The combined transforms will compensate the drawback of using each transform separately. The proposed algorithm has been designed, implemented and tested successfully. The experimental results showed that selecting the best sub-band for embedding from both transforms will improve the imperceptibility and robustness of the new combined algorithm. The evaluated imperceptibility of the combined DWT-CT algorithm which gave a PSNR value 88.11 and the combination DWT-CT algorithm improves robustness since it produced better robust against Gaussian noise attack. In addition to that, the implemented system shored a successful extraction method to extract watermark efficiently.

Keywords: DWT, CT, Digital Image Watermarking, Copyright Protection.

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Authors: Kemal Tutuncu, Recai Ozcan

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Having done in this study, air-conditioning automation for patisserie shopwindow was designed. In the cooling sector it is quite important to cooling up the air temperature in the shopwindow within short time interval. Otherwise the patisseries inside of the shopwindow will be spoilt in a few days. Additionally the humidity is other important parameter for the patisseries kept in shopwindow. It must be raised up to desired level in a quite short time. Traditional patisserie shopwindows only allow controlling temperature manually. There is no humidity control and humidity is supplied by fans that are directed to the water at the bottom of the shopwindows. In this study, humidity and temperature sensors (SHT11), PIC, AC motor controller, DC motor controller, ultrasonic nebulizer and other electronic circuit members were used to simulate air conditioning automation for patisserie shopwindow in proteus software package. The simulation results showed that temperature and humidity values are adjusted in desired time duration by openloop control technique. Outer and inner temperature and humidity values were used for control mechanism.

Keywords: Air conditioning automation, temperature and humidity, SHT11, AC motor controller, open-loop control.

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Authors: Min Wang , Shuyuan Yang

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The paper presents a method of designing ultrawide band (UWB) pulse array beamformer in the case of nearfield. Firstly the principle of space-time processing of UWB pulse array is discussed. The radical beampattern transform based on spherical coordinates is employed to solve the nearfield beamforming of UWB pulse array. The frequency invariant technology is considered for the frequency dependent beampattern of UWB pulse array. We use a multirate bank scheme of to implement the FI beamformer of UWB pulse array. By using multirate filters in each element channel, it can make the response of the UWB array to avoid distortion in the whole band. The simulation resultes are given to prove the efficiency and feasibility of this method.

Keywords: UWB pulse array, frequency invariant, multiratebank, nearfield beamformer, radical transform

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Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: Dipeng Chen, Qi Li

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Image fusion aims to enhance the perception of a scene by combining important information captured by different sensors. Dual-Tree Complex Wavelet (DT-CWT) has been thouroughly investigated for image fusion, since it takes advantages of approximate shift invariance and direction selectivity. But it can only handle limited direction information. To allow a more flexible directional expansion for images, we propose a novel fusion scheme, referred to as complex contourlet transform (CCT). It successfully incorporates directional filter banks (DFB) into DT-CWT. As a result it efficiently deal with images containing contours and textures, whereas it retains the property of shift invariance. Experimental results demonstrated that the method features high quality fusion performance and can facilitate many image processing applications.

Keywords: Complex contourlet transform, Complex wavelettransform, Fusion.

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Authors: M.Z. Norashikin, M.Z. Ibrahim

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This report shows the performance of composite biodegradable film from chitosan, starch and sawdust fiber. The main objectives of this research are to fabricate and characterize composite biodegradable film in terms of morphology and physical properties. The film was prepared by casting method. Sawdust fiber was used as reinforcing agent and starch as polymer matrix in the casting solution. The morphology of the film was characterized using atomic force microscope (AFM). The result showed that the film has smooth structure. Chemical composition of the film was investigated using Fourier transform infrared (FTIR) where the result revealed present of starch in the film. The thermal properties were characterized using thermal gravimetric analyzer (TGA) and differential scanning calorimetric (DSC) where the results showed that the film has small difference in melting and degradation temperature.

Keywords: Sawdust, composite, film, biodegradable.

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Authors: G. Martemucci, D. Casamassima, A. G. D'Alessandro

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The study aimed to evaluated the reproductive performance response to short term oestrus synchronization during the transition period. One hundred and sixty-five indigenous multiparous non-lactating goats were subdivided into the following six treatment groups for oestrus synchronization: NT control Group (N= 30), Fe-21d, FGA vaginal sponge for 21days+eCG at 19thd; FPe- 11d, FGA 11d + PGF2α and eCG at 9th d; FPe-10d, FGA 10d+ PGF2α and eCG at 8th d; FPe-9d, FGA 9d +PGF2α and eCG at 7thd; PFe-5d, PGF2α at d0 + FGA 5d + eCG at 5thd. The goats were natural mated (1 male/6 females). Fecundity rates (n. births /n. females treated x 100) were statistically higher (P < 0.05) in short term FPe-9d (157.9%), FPe- 11d (115.4%), FPe-10d (111.1%) and PFe-5d (107.7%) groups compared to the NT control Group (66.7%).

Keywords: Goats, oestrus synchronization, short-term protocols.

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Authors: Suheyla Kocaman, Gulnare Ahmetli

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In this study, acrylated soybean oil (AESO) was used as modifying agent for DGEBF-type epoxy resin (ER). AESO was used as a co-matrix in 50 wt % with ER. Composites with eco-friendly natural fillers-banana bark and seashell were prepared. MNA was used as a hardener. Effect of banana peel (BP) and seashell (SSh) fillers on mechanical properties, such as tensile strength, elongation at break, and hardness of M-ERs were investigated. The structure epoxy resins (M-ERs) cured with MNA and sebacic acid (SAc) hardeners were characterized by Fourier transform infrared spectroscopy (FTIR). Tensile test results show that Young’s (elastic) modulus, tensile strength and hardness of SSh particles reinforced with M-ERs were higher than the M-ERs reinforced with banana bark.

Keywords: Biobased composite, epoxy resin, mechanical properties, natural fillers.

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Authors: Sezen Yildirim, Tahir Çetin Akinci, Serhat Seker, Nazmi Ekren

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Ferroresonance is an electrical phenomenon in nonlinear character, which frequently occurs in power system due to transmission line faults and single or more-phase switching on the lines as well as usage of the saturable transformers. In this study, the ferroresonance phenomena are investigated under the modeling of the West Anatolian Electric Power Network of 380 kV in Turkey. The ferroresonance event is observed as a result of removing the loads at the end of the lines. In this sense, two different cases are considered. At first, the switching is applied at 2nd second and the ferroresonance affects are observed between 2nd and 4th seconds in the voltage variations of the phase-R. Hence the ferroresonance and nonferroresonance parts of the overall data are compared with each others using the Fourier transform techniques to show the ferroresonance affects.

Keywords: Ferroresonance, West Anatolian Electric Power System, Power System Modeling, Switching, Spectral Analysis.

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Authors: Jhalique Jane R. Fojas, Rizalinda L. De Leon, Lucille V. Abad

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The characterization of κ-carrageenan could provide a better understanding of its functions in biological, medical and industrial applications. Chemical and physical analyses of carrageenan from seaweeds, Euchema cottonii L., were done to offer information on its properties and the effects of Co-60 γ-irradiation on its thermochemical characteristics. The structural and morphological characteristics of κ-carrageenan were determined using scanning electron microscopy (SEM) while the composition, molecular weight and thermal properties were determined using attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), gel permeation chromatography (GPC), thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC). Further chemical analysis was done using hydrogen-1 nuclear magnetic resonance (1H NMR) and functional characteristics in terms of biocompatibility were evaluated using cytotoxicity test.

Keywords: Biocompatibility, carrageenan, DSC, FTIR, GPC, irradiation, NMR, physicochemical, SEM, TGA.

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Authors: M. Hoseinnezhad, K. Gharanjig

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Two organic dyes comprising carbazole as the electron donors and cyanoacetic acid moieties as the electron acceptors were synthesized. The organic dye was prepared by standard reaction from carbazole as the starting material. To this end, carbazole was reacted with bromobenzene and further oxidation and reacted with cyanoacetic acid. The obtained organic dye was purified and characterized using differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), proton nuclear magnetic resonance (¹HNMR), carbon nuclear magnetic resonance (¹³CNMR) and elemental analysis. The influence of heteroatom on carbazole donors and cyno substitution on the acid acceptor is evidenced by spectral and electrochemical photovoltaic experiments. Finally, light fastness properties for organic dye were investigated.

Keywords: Dye-sensitized solar cells, Indoline dye, nanostructure, oxidation potential, solar energy.

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Authors: Masrour Dowlatabadi, Jalil Shirazi

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In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: G.Vinitha, A.Ramalingam

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TiO2 nanoparticles were synthesized by hydrothermal method at 180°C from TiOSO4 aqueous solution with1m/l concentration. The obtained products were coated with silica by means of a seeded polymerization technique for a coating time of 1440 minutes to obtain well defined TiO2@SiO2 core-shell structure. The uncoated and coated nanoparticles were characterized by using X-Ray diffraction technique (XRD), Fourier Transform Infrared Spectroscopy (FT-IR) to study their physico-chemical properties. Evidence from XRD and FTIR results show that SiO2 is homogenously coated on the surface of titania particles. FTIR spectra show that there exists an interaction between TiO2 and SiO2 and results in the formation of Ti-O-Si chemical bonds at the interface of TiO2 particles and SiO2 coating layer. The non linear optical limiting properties of TiO2 and TiO2@SiO2 nanoparticles dispersed in ethylene glycol were studied at 532nm using 5ns Nd:YAG laser pulses. Three-photon absorption is responsible for optical limiting characteristics in these nanoparticles and it is seen that the optical nonlinearity is enhanced in core-shell structures when compared with single counterparts. This effective three-photon type absorption at this wavelength, is of potential application in fabricating optical limiting devices.

Keywords: hydrothermal method, optical limiting devicesseeded polymerization technique, three-photon type absorption

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Authors: Guo Xiuhua, Sun Tao, Wu Haifeng, He Wen, Liang Zhigang, Zhang Mengxia, Guo Aimin, Wang Wei

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Purpose: To explore the use of Curvelet transform to extract texture features of pulmonary nodules in CT image and support vector machine to establish prediction model of small solitary pulmonary nodules in order to promote the ratio of detection and diagnosis of early-stage lung cancer. Methods: 2461 benign or malignant small solitary pulmonary nodules in CT image from 129 patients were collected. Fourteen Curvelet transform textural features were as parameters to establish support vector machine prediction model. Results: Compared with other methods, using 252 texture features as parameters to establish prediction model is more proper. And the classification consistency, sensitivity and specificity for the model are 81.5%, 93.8% and 38.0% respectively. Conclusion: Based on texture features extracted from Curvelet transform, support vector machine prediction model is sensitive to lung cancer, which can promote the rate of diagnosis for early-stage lung cancer to some extent.

Keywords: CT image, Curvelet transform, Small pulmonary nodules, Support vector machines, Texture extraction.

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Authors: A. Benyahia, M. Zergoug, M. Amir, M. Fodil

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The main objective of this work is to enhance the Pulsed Eddy Current (PEC) response from the aluminum structure using signal processing. Cracks and metal loss in different structures cause changes in PEC response measurements. In this paper, time-frequency analysis is used to represent PEC response, which generates a large quantity of data and reduce the noise due to measurement. Power Spectral Density (PSD) after Wavelet Decomposition (PSD-WD) is proposed for defect detection. The experimental results demonstrate that the cracks in the surface can be extracted satisfactorily by the proposed methods. The validity of the proposed method is discussed.

Keywords: NDT, pulsed eddy current, continuous wavelet transform, Mexican hat wavelet mother, defect detection, power spectral density.

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Authors: Gülşah Çelik Gül, Figen Kurtuluş

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Magnesium containing boron compounds with hexagonal structure have been drawn much attention due to their superconductive nature. The main target of this work is new modified microwave oven by on our own has an ability about passing through a gas in the oven medium for attainment of oxygen-free compounds such as c-BN.  Mg containing boride was synthesized by modified-microwave method under nitrogen atmosphere using amorphous boron and magnesium source in appropriate molar ratio. Microwave oven with oxygen free environment has been modified to aimed to obtain magnesium boride without oxygen. Characterizations were done by powder X-ray diffraction (XRD), and Fourier transform infrared (FTIR) spectroscopy. Mg containing boride, generally named magnesium boride, with amorphous character without oxygen is obtained via designed microwave oven system.

Keywords: Magnesium containing boron compounds, modified microwave synthesis, powder X-ray diffraction, FTIR.

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Authors: Mohammadhosein Rahimi, Mohammad Raouf Hosseini, Mehran Bakhshi, Alireza Baghbanan

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Silver ions (Ag⁺) and their compounds are consequentially toxic to microorganisms, showing biocidal effects on many species of bacteria. Silver-phosphate (or silver orthophosphate) is one of these compounds, which is famous for its antimicrobial effect and catalysis application. In the present study, a green method was presented to synthesis silver-phosphate nanoparticles using Sporosarcina pasteurii. The composition of the biosynthesized nanoparticles was identified as Ag₃PO₄ using X-ray Diffraction (XRD) and Energy Dispersive Spectroscopy (EDS). Also, Fourier Transform Infrared (FTIR) spectroscopy showed that Ag₃PO₄ nanoparticles was synthesized in the presence of biosurfactants, enzymes, and proteins. In addition, UV-Vis adsorption of the produced colloidal suspension approved the results of XRD and FTIR analyses. Finally, Transmission Electron Microscope (TEM) images indicated that the size of the nanoparticles was about 20 nm.

Keywords: Bacteria, biosynthesis, silver-phosphate, Sporosarcina pasteurii, nanoparticle.

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Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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Authors: J. Ruiz-Pinales, J. J. Acosta-Reyes, A. Salazar-Garibay, R. Jaime-Rivas

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In this paper, we present a new method for incorporating global shift invariance in support vector machines. Unlike other approaches which incorporate a feature extraction stage, we first scale the image and then classify it by using the modified support vector machines classifier. Shift invariance is achieved by replacing dot products between patterns used by the SVM classifier with the maximum cross-correlation value between them. Unlike the normal approach, in which the patterns are treated as vectors, in our approach the patterns are treated as matrices (or images). Crosscorrelation is computed by using computationally efficient techniques such as the fast Fourier transform. The method has been tested on the ORL face database. The tests indicate that this method can improve the recognition rate of an SVM classifier.

Keywords: Face recognition, support vector machines, shiftinvariance, image registration.

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Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

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We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

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