Search results for: Fourier Spectral method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8429

Search results for: Fourier Spectral method

7649 Two Stage Control Method Using a Disturbance Observer and a Kalman Filter

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

Abstract:

This paper describes the two stage control using a disturbance observer and a Kalman filter. The system feedback uses the estimated state when it controls the speed. After the change-over point, its feedback uses the controlled plant output when it controls the position. To change the system continually, a change-over point has to be determined pertinently, and the controlled plant input has to be adjusted by the addition of the appropriate value. The proposed method has noise-reduction effect. It changes the system continually, even if the controlled plant identification has the error. Although the conventional method needs a speed sensor, the proposed method does not need it. The proposed method has a superior robustness compared with the conventional two stage control.

Keywords: Disturbance observer, kalman filter, optimal control, two stage control.

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7648 Emotion Recognition Using Neural Network: A Comparative Study

Authors: Nermine Ahmed Hendy, Hania Farag

Abstract:

Emotion recognition is an important research field that finds lots of applications nowadays. This work emphasizes on recognizing different emotions from speech signal. The extracted features are related to statistics of pitch, formants, and energy contours, as well as spectral, perceptual and temporal features, jitter, and shimmer. The Artificial Neural Networks (ANN) was chosen as the classifier. Working on finding a robust and fast ANN classifier suitable for different real life application is our concern. Several experiments were carried out on different ANN to investigate the different factors that impact the classification success rate. Using a database containing 7 different emotions, it will be shown that with a proper and careful adjustment of features format, training data sorting, number of features selected and even the ANN type and architecture used, a success rate of 85% or even more can be achieved without increasing the system complicity and the computation time

Keywords: Classification, emotion recognition, features extraction, feature selection, neural network

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7647 Projective Synchronization of a Class of Fractional-Order Chaotic Systems

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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7646 Application of Fuzzy Logic in Fault Diagnosis in Transformers using Dissolved Gas based on Different Standards

Authors: Rahmatollah Hooshmand, Mahdi Banejad

Abstract:

One of the problems in fault diagnosis of transformer based on dissolved gas, is lack of matching the result of fault diagnosis of different standards with the real world. In this paper, the result of the different standards is analyzed using fuzzy and the result is compared with the empirical test. The comparison between the suggested method and existing methods indicate the capability of the suggested method in on-line fault diagnosis of the transformers. In addition, in some cases the existing standards are not able to diagnose the fault. In theses cases, the presented method has the potential of diagnosing the fault. The information of three transformers is used to the show the capability of the suggested method in diagnosing the fault. The results validate the capability of the presented method in fault diagnosis of the transformer.

Keywords: Fault Diagnosis of Transformer, Dissolved Gas, Fuzzy Logic.

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7645 The Analogue of a Property of Pisot Numbers in Fields of Formal Power Series

Authors: Wiem Gadri

Abstract:

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral characteristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, Formal power series, Minimal polynomial degree.

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7644 Effect of Castration on CLA in Meat Goats

Authors: P. Paengkoum, T. Phonmun, S. Paengkoum

Abstract:

Twenty four male Thai native × Anglo-Nubian crossbred goats were randomly allocated to receive four treatments. The experiment was conducted for four months and slaughtered that the Longissimus dorsi muscle was collected for fatty acid analysis. The results conclude that either castrated method or ages had no significantly different on monounsaturated fatty acid (MUFA) (P>0.05) except erucic acid (C22:1n9). Interaction between castrated method and ages had significantly different in MUFA (P<0.01). Although the effect of castration method and age are not difference on fatty acid composition, it contributed to known that difference castration method and age (surgical and budizzo) no effect on accumulation fatty acid in meat goats.

Keywords: Castration, goat, CLA, meat.

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7643 Preliminary Study on Fixture Layout Optimization Using Element Strain Energy

Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The objective of positioning the fixture elements in the fixture is to make the workpiece stiff, so that geometric errors in the manufacturing process can be reduced. Most of the work for optimal fixture layout used the minimization of the sum of the nodal deflection normal to the surface as objective function. All deflections in other direction have been neglected. We propose a new method for fixture layout optimization in this paper, which uses the element strain energy. The deformations in all the directions have been considered in this way. The objective function in this method is to minimize the sum of square of element strain energy. Strain energy and stiffness are inversely proportional to each other. The optimization problem is solved by the sequential quadratic programming method. Three different kinds of case studies are presented, and results are compared with the method using nodal deflections as objective function to verify the propose method.

Keywords: Fixture layout, optimization, strain energy, quadratic programming.

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7642 Significant Role Analysis of Transmission Control Protocols in 4G Cellular Systems

Authors: Ghassan A. Abed, Bayan M. Sabbar

Abstract:

The society of 3rd Generation Partnership Project (3GPP) is completed developing Long Term Evolution Advanced (LTE-Advanced) systems as a standard 4G cellular system. This generation goals to produce conditions for a new radio-access technology geared to higher data rates, low latency, and better spectral efficiency. LTE-Advanced is an evolutionary step in the continuing development of LTE where the description in this article is based on LTE release 10. This paper provides a model of the traffic links of 4G system represented by LTE-Advanced system with the effect of the Transmission Control Protocols (TCP) and Stream Control Transmission Protocol (SCTP) in term of throughput and packet loss. Furthermore, the article presents the investigation and the analysis the behavior of SCTP and TCP variants over the 4G cellular systems. The traffic model and the scenario of the simulation developed using the network simulator NS-2 using different TCP source variants.

Keywords: LTE-Advanced, LTE, SCTP, TCP, 4G, NS-2.

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7641 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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7640 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, element-free Galerkin, moving least squares, meshless methods.

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7639 High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation

Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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7638 Modern Method for Solving Pure Integer Programming Models

Authors: G. Shojatalab

Abstract:

In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.

Keywords: Integer, Programming, Operation Research, Variables of decision.

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7637 Level Set and Morphological Operation Techniques in Application of Dental Image Segmentation

Authors: Abdolvahab Ehsani Rad, Mohd Shafry Mohd Rahim, Alireza Norouzi

Abstract:

Medical image analysis is one of the great effects of computer image processing. There are several processes to analysis the medical images which the segmentation process is one of the challenging and most important step. In this paper the segmentation method proposed in order to segment the dental radiograph images. Thresholding method has been applied to simplify the images and to morphologically open binary image technique performed to eliminate the unnecessary regions on images. Furthermore, horizontal and vertical integral projection techniques used to extract the each individual tooth from radiograph images. Segmentation process has been done by applying the level set method on each extracted images. Nevertheless, the experiments results by 90% accuracy demonstrate that proposed method achieves high accuracy and promising result.

Keywords: Integral production, level set method, morphological operation, segmentation.

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7636 A Reasoning Method of Cyber-Attack Attribution Based on Threat Intelligence

Authors: Li Qiang, Yang Ze-Ming, Liu Bao-Xu, Jiang Zheng-Wei

Abstract:

With the increasing complexity of cyberspace security, the cyber-attack attribution has become an important challenge of the security protection systems. The difficult points of cyber-attack attribution were forced on the problems of huge data handling and key data missing. According to this situation, this paper presented a reasoning method of cyber-attack attribution based on threat intelligence. The method utilizes the intrusion kill chain model and Bayesian network to build attack chain and evidence chain of cyber-attack on threat intelligence platform through data calculation, analysis and reasoning. Then, we used a number of cyber-attack events which we have observed and analyzed to test the reasoning method and demo system, the result of testing indicates that the reasoning method can provide certain help in cyber-attack attribution.

Keywords: Reasoning, Bayesian networks, cyber-attack attribution, kill chain, threat intelligence.

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7635 Approximation of Sturm-Liouville Problems by Exponentially Weighted Legendre-Gauss Tau Method

Authors: Mohamed K. El Daou

Abstract:

We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

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7634 Price Quoting Method for Contract Manufacturer

Authors: S. Homrossukon, W. Parinyasart

Abstract:

This is an applied research to propose the method for price quotation for a contract electronics manufacturer. It has had a precise price quoting method but such method could not quickly provide a result as the customer required. This reduces the ability of company to compete in this kind of business. In this case, the cause of long time quotation process was analyzed. A lot of product features have been demanded by customer. By checking routine processes, it was found that high fraction of quoting time was used for production time estimating which has effected to the manufacturing or production cost. Then the historical data of products including types, number of components, assembling method, and their assembling time were used to analyze the key components affecting to production time. The price quoting model then was proposed. The implementation of proposed model was able to remarkably reduce quoting time with an acceptable required precision.

Keywords: Price quoting, Contract manufacturer, Stepwise technique, Best subset technique.

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7633 Stabilization of Rotational Motion of Spacecrafts Using Quantized Two Torque Inputs Based on Random Dither

Authors: Yusuke Kuramitsu, Tomoaki Hashimoto, Hirokazu Tahara

Abstract:

The control problem of underactuated spacecrafts has attracted a considerable amount of interest. The control method for a spacecraft equipped with less than three control torques is useful when one of the three control torques had failed. On the other hand, the quantized control of systems is one of the important research topics in recent years. The random dither quantization method that transforms a given continuous signal to a discrete signal by adding artificial random noise to the continuous signal before quantization has also attracted a considerable amount of interest. The objective of this study is to develop the control method based on random dither quantization method for stabilizing the rotational motion of a rigid spacecraft with two control inputs. In this paper, the effectiveness of random dither quantization control method for the stabilization of rotational motion of spacecrafts with two torque inputs is verified by numerical simulations.

Keywords: Spacecraft control, quantized control, nonlinear control, random dither method.

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7632 Dialect and Gender Variations in the Place and Manner of Articulation of the Korean Fricatives

Authors: Kyung-Im Han

Abstract:

This study examines dialect and gender variations in the place and manner of articulation between the two Korean fricatives, /s/ and /s’/, as produced by speakers of the Daegu and Jeju dialects. The acoustic parameters of center of gravity and skewness for the place of articulation, and the rise time and the amplitude rise slope for the manner of articulation were measured. The study results revealed a gender effect, but no dialect effect, for the center of gravity and the skewness. No main effect for either the gender or dialect was found for the rise time and the amplitude rise slope. These findings indicated that, with regard to the place of articulation, Korean fricative sound differences are a gender distinction, not a dialectal one.

Keywords: Dialect, gender, Korean fricative, manner of articulation, place of articulation, spectral moments.

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7631 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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7630 Performance of the Strong Stability Method in the Univariate Classical Risk Model

Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

Abstract:

In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: Markov Chain, regenerative processes, risk models, ruin probability, strong stability.

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7629 The Optimization of Copper Sulfate and Tincalconite Molar Ratios on the Hydrothermal Synthesis of Copper Borates

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

Abstract:

In this research, copper borates are synthesized by the reaction of copper sulfate pentahydrate (CuSO4.5H2O) and tincalconite (Na2O4B7.10H2O). The experimental parameters are selected as 80oC reaction temperature and 60 of reaction time. The effect of mole ratio of CuSO4.5H2O to Na2O4B7.5H2O is studied. For the identification analyses X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) techniques are used. At the end of the experiments, synthesized copper borate is matched with the powder diffraction file of “00-001-0472” [Cu(BO2)2] and characteristic vibrations between B and O atoms are seen. The proper crystals are obtained at the mole ratio of 3:1. This study showed that simplified synthesis process is suitable for the production of copper borate minerals.

Keywords: Hydrothermal synthesis, copper borates, copper sulfate, tincalconite.

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7628 Synthesis, Investigation, DFT Study and Biological Activity of Zirconium (IV) Complexes

Authors: Salem El-t. Ashoor, Ibtisam M. Ediab

Abstract:

Zirconium diamine and triamine complexes can possess biological activities. These complexes were synthesised via the reaction of equimolar quantities of 1,10-phenanthroline {NC3H3(C6H2)NC3H3} (L1) or 4-4-amino phenazone {ONC6H5(NH)CH(NH2} (L2) or diphenyl carbizon {HNNCO(NH)2(C6H5)} (L3) with a Zirconium Salt {ZrOCl2} in a 1:1 ratio to form complexes [{NC3H3(C6H2)NC3H3}ZrOCl2}] [ZrOCl2L1], [{(O2NC6H4(NH)(NH2)}ZrOCl2] [ZrOCl2L2] and [{HNNCO(NH)2(C6H5)ZrOCl2}] [ZrOCl2L3] respectively. They were characterised using Fourier Transform Infrared (FT-IR) and UV-Visible spectroscopy. Also a variable temperature study of these complexes was completed, using UV-Visible spectroscopy to observe electronic transitions under temperature control. Also a DFT study was done on these complexes via the information from FT-IR and UV-Visible spectroscopy.

These complexes were found to show different inhibition to the growth of bacterial strains of Bacillus spp. & Klebsiella spp. & E. coli & Proteus spp. & Pseudomona spp. at different concentrations (0.001, 0.2 and 1M). For better understanding these complexes were examined by using a Density Functional Theory (DFT) calculation.

Keywords: (1:10-phenanthroline) (L1), 4-4-amino phenazone (L2), diphenyl carbizon (L3), DFT study, antibacterial.

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7627 An Analytical Method for Solving General Riccati Equation

Authors: Y. Pala, M. O. Ertas

Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.

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7626 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method

Authors: Nisha Goyal, R.K. Gupta

Abstract:

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,

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7625 Computer Aided Classification of Architectural Distortion in Mammograms Using Texture Features

Authors: Birmohan Singh, V. K. Jain

Abstract:

Computer aided diagnosis systems provide vital opinion to radiologists in the detection of early signs of breast cancer from mammogram images. Architectural distortions, masses and microcalcifications are the major abnormalities. In this paper, a computer aided diagnosis system has been proposed for distinguishing abnormal mammograms with architectural distortion from normal mammogram. Four types of texture features GLCM texture, GLRLM texture, fractal texture and spectral texture features for the regions of suspicion are extracted. Support vector machine has been used as classifier in this study. The proposed system yielded an overall sensitivity of 96.47% and an accuracy of 96% for mammogram images collected from digital database for screening mammography database.

Keywords: Architecture Distortion, GLCM Texture features, GLRLM Texture Features, Mammograms, Support Vector Machine.

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7624 On the Differential Geometry of the Curves in Minkowski Space-Time II

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut

Abstract:

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.

Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.

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7623 Periodic Solutions for Some Strongly Nonlinear Oscillators by He's Energy Balance Method

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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7622 Solving 94-bit ECDLP with 70 Computers in Parallel

Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

Abstract:

Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.

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7621 Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation

Authors: J. H. Park, T. H. Lee, S. M. Lee, H. Y. Jung

Abstract:

In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.

Keywords: Chaotic systems, synchronization, Lyapunov method, simulation.

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7620 Impact of Weather Conditions on Generalized Frequency Division Multiplexing over Gamma Gamma Channel

Authors: Muhammad Sameer Ahmed, Piotr Remlein, Tansal Gucluoglu

Abstract:

The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

Keywords: Free space optics, generalized frequency division multiplexing, weather conditions, gamma gamma distribution.

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