**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4236

# Search results for: Taylor series algorithm

##### 4236 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm

**Authors:**
U. C. Amadi,
N. A. Udoh

**Abstract:**

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

**Keywords:**
Ying Buzu Shu,
nonlinear boundary problem,
Taylor series algorithm,
infinite series.

##### 4235 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method

**Authors:**
Chinwendu. B. Eleje,
Udechukwu P. Egbuhuzor

**Abstract:**

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

**Keywords:**
Newton Raphson method,
non-linear boundary value problem,
Taylor series approximation,
Michaelis-Menten equation.

##### 4234 A New Floating Point Implementation of Base 2 Logarithm

**Authors:**
Ahmed M. Mansour,
Ali M. El-Sawy,
Ahmed T Sayed

**Abstract:**

Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving insights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

**Keywords:**
Logarithms,
log2,
floor,
iterative,
CORDIC,
Taylor series.

##### 4233 Experimental Investigations of a Modified Taylor-Couette Flow

**Authors:**
A. Esmael,
A. El Shrif

**Abstract:**

In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

**Keywords:**
Hydrodynamic Instability,
Modified Taylor-Couette
Flow,
Turbulence,
Taylor vortices.

##### 4232 An IM-COH Algorithm Neural Network Optimization with Cuckoo Search Algorithm for Time Series Samples

**Authors:**
Wullapa Wongsinlatam

**Abstract:**

**Keywords:**
Artificial neural networks,
back propagation
algorithm,
time series,
local minima problem,
metaheuristic
optimization.

##### 4231 Retail Strategy to Reduce Waste Keeping High Profit Utilizing Taylor's Law in Point-of-Sales Data

**Authors:**
Gen Sakoda,
Hideki Takayasu,
Misako Takayasu

**Abstract:**

Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.

**Keywords:**
Food waste reduction,
particle filter,
point of sales,
sustainable development goals,
Taylor's Law,
time series analysis.

##### 4230 Correction of Infrared Data for Electrical Components on a Board

**Authors:**
Seong-Ho Song,
Ki-Seob Kim,
Seop-Hyeong Park,
Seon-Woo Lee

**Abstract:**

**Keywords:**
Infrared camera,
Temperature Data compensation,
Environmental Ambient Temperature,
Electric Component

##### 4229 Investigation on Performance of Change Point Algorithm in Time Series Dynamical Regimes and Effect of Data Characteristics

**Authors:**
Farhad Asadi,
Mohammad Javad Mollakazemi

**Abstract:**

In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reflected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system.

**Keywords:**
Time series,
fluctuation in statistical characteristics,
optimal learning.

##### 4228 Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing

**Authors:**
Changhong Guo,
Shaomei Fang,
Yong He

**Abstract:**

**Keywords:**
European option pricing,
fractional Black-Scholes
equations,
fractional G-Brownian motion,
Taylor’s series of fractional
order,
uncertain volatility.

##### 4227 Efficient Spectral Analysis of Quasi Stationary Time Series

**Authors:**
Khalid M. Aamir,
Mohammad A. Maud

**Abstract:**

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

**Keywords:**
Power Spectral Density (PSD),
quasi-stationarytime series,
short time Fourier Transform,
Sliding window DFT.

##### 4226 Influence of Parameters of Modeling and Data Distribution for Optimal Condition on Locally Weighted Projection Regression Method

**Authors:**
Farhad Asadi,
Mohammad Javad Mollakazemi,
Aref Ghafouri

**Abstract:**

Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

**Keywords:**
Local nonlinear estimation,
LWPR algorithm,
Online training method.

##### 4225 SDVAR Algorithm for Detecting Fraud in Telecommunications

**Authors:**
Fatimah Almah Saaid,
Darfiana Nur,
Robert King

**Abstract:**

**Keywords:**
Telecommunications Fraud,
SDVAR Algorithm,
Multivariate
time series,
Vector Autoregressive,
Change points.

##### 4224 Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule

**Authors:**
Reza Moosavi Mohseni,
Wenjun Zhang,
Jiling Cao

**Abstract:**

**Keywords:**
Chaos theory,
GMM estimator,
Lyapunov Exponent,
Monetary System,
Taylor Rule.

##### 4223 A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation

**Authors:**
Ashvin Gopaul,
Jayrani Cheeneebash,
Kamleshsing Baurhoo

**Abstract:**

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

**Keywords:**
Chebyshev Pseudospectral collocation method,
convection-diffusion equation,
restrictive Taylor approximation.

##### 4222 Fast and Accuracy Control Chart Pattern Recognition using a New cluster-k-Nearest Neighbor

**Authors:**
Samir Brahim Belhaouari

**Abstract:**

**Keywords:**
Pattern recognition,
Time series,
k-Nearest Neighbor,
k-means cluster,
Gaussian Mixture Model,
Classification

##### 4221 Hybrid TOA/AOA Schemes for Mobile Location in Cellular Communication Systems

**Authors:**
Chien-Sheng Chen,
Szu-Lin Su,
Chuan-Der Lu

**Abstract:**

Wireless location is to determine the mobile station (MS) location in a wireless cellular communications system. When fewer base stations (BSs) may be available for location purposes or the measurements with large errors in non-line-of-sight (NLOS) environments, it is necessary to integrate all available heterogeneous measurements to achieve high location accuracy. This paper illustrates a hybrid proposed schemes that combine time of arrival (TOA) at three BSs and angle of arrival (AOA) information at the serving BS to give a location estimate of the MS. The proposed schemes mitigate the NLOS effect simply by the weighted sum of the intersections between three TOA circles and the AOA line without requiring a priori information about the NLOS error. Simulation results show that the proposed methods can achieve better accuracy when compare with Taylor series algorithm (TSA) and the hybrid lines of position algorithm (HLOP).

**Keywords:**
Time of arrival (TOA),
angle of arrival (AOA),
non-line-of-sight (NLOS).

##### 4220 Rear Separation in a Rotating Fluid at Moderate Taylor Numbers

**Authors:**
S. Damodaran,
T. V. S.Sekhar

**Abstract:**

**Keywords:**
Navier_Stokes equations,
Taylor number,
Reynolds number,
Higher order compact scheme,
Rotating Fluid.

##### 4219 An efficient Activity Network Reduction Algorithm based on the Label Correcting Tracing Algorithm

**Authors:**
Weng Ming Chu

**Abstract:**

**Keywords:**
Series/Parallel network,
Stochastic network,
Network
reduction,
Interdictive Graph,
Complexity Index.

##### 4218 Series-Parallel Systems Reliability Optimization Using Genetic Algorithm and Statistical Analysis

**Authors:**
Essa Abrahim Abdulgader Saleem,
Thien-My Dao

**Abstract:**

The main objective of this paper is to optimize series-parallel system reliability using Genetic Algorithm (GA) and statistical analysis; considering system reliability constraints which involve the redundant numbers of selected components, total cost, and total weight. To perform this work, firstly the mathematical model which maximizes system reliability subject to maximum system cost and maximum system weight constraints is presented; secondly, a statistical analysis is used to optimize GA parameters, and thirdly GA is used to optimize series-parallel systems reliability. The objective is to determine the strategy choosing the redundancy level for each subsystem to maximize the overall system reliability subject to total cost and total weight constraints. Finally, the series-parallel system case study reliability optimization results are showed, and comparisons with the other previous results are presented to demonstrate the performance of our GA.

**Keywords:**
Genetic algorithm,
optimization,
reliability,
statistical analysis.

##### 4217 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

**Authors:**
Rashidah Omar,
Suzeini Abdul Halim,
Aini Janteng

**Abstract:**

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function *f *ϵ* A *is said to be bi-univalent in the open unit disk *D* if both *f *and *f ^{-1}* are univalent in

*D*. The symbol

*A*denotes the class of all analytic functions

*f*in

*D*and it is normalized by the conditions

*f*(0) =

*f’*(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function

*f*is subordinate to an analytic function

*g*if there is an analytic function

*w*defined on

*D*with

*w*(0) = 0 and |

*w*(z)| < 1 satisfying

*f*(

*z*) =

*g*[

*w*(

*z*)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

**Keywords:**
Analytic functions,
bi-univalent functions,
Hohlov operator,
subordination.

##### 4216 Implementation of Neural Network Based Electricity Load Forecasting

**Authors:**
Myint Myint Yi,
Khin Sandar Linn,
Marlar Kyaw

**Abstract:**

**Keywords:**
Neural network,
Load forecast,
Time series,
wavelettransform.

##### 4215 A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream

**Authors:**
M. A. Koroma,
Z. Chuangyi,
A. F.,
Kamara,
A. M. H. Conteh

**Abstract:**

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

**Keywords:**
Modified Laplace decomposition algorithm,
Boundary
layer equation,
Padé approximant,
Numerical solution.

##### 4214 Application of Extreme Learning Machine Method for Time Series Analysis

**Authors:**
Rampal Singh,
S. Balasundaram

**Abstract:**

**Keywords:**
Chaotic time series,
Extreme learning machine,
Generalization performance.

##### 4213 Applying a Noise Reduction Method to Reveal Chaos in the River Flow Time Series

**Authors:**
Mohammad H. Fattahi

**Abstract:**

Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

**Keywords:**
Chaotic behavior,
wavelet,
noise reduction,
river flow.

##### 4212 Application of Fourier Series Based Learning Control on Mechatronic Systems

**Authors:**
Sandra Baßler,
Peter Dünow,
Mathias Marquardt

**Abstract:**

**Keywords:**
Climbing stairs,
FSBLC,
ILC,
Service robot.

##### 4211 Forecasting US Dollar/Euro Exchange Rate with Genetic Fuzzy Predictor

**Authors:**
R. Mechgoug,
A. Titaouine

**Abstract:**

Fuzzy systems have been successfully used for exchange rate forecasting. However, fuzzy system is very confusing and complex to be designed by an expert, as there is a large set of parameters (fuzzy knowledge base) that must be selected, it is not a simple task to select the appropriate fuzzy knowledge base for an exchange rate forecasting. The researchers often look the effect of fuzzy knowledge base on the performances of fuzzy system forecasting. This paper proposes a genetic fuzzy predictor to forecast the future value of daily US Dollar/Euro exchange rate time’s series. A range of methodologies based on a set of fuzzy predictor’s which allow the forecasting of the same time series, but with a different fuzzy partition. Each fuzzy predictor is built from two stages, where each stage is performed by a real genetic algorithm.

**Keywords:**
Foreign exchange rate,
time series forecasting,
Fuzzy System,
and Genetic Algorithm.

##### 4210 Two States Mapping Based Neural Network Model for Decreasing of Prediction Residual Error

**Authors:**
Insung Jung,
lockjo Koo,
Gi-Nam Wang

**Abstract:**

The objective of this paper is to design a model of human vital sign prediction for decreasing prediction error by using two states mapping based time series neural network BP (back-propagation) model. Normally, lot of industries has been applying the neural network model by training them in a supervised manner with the error back-propagation algorithm for time series prediction systems. However, it still has a residual error between real value and prediction output. Therefore, we designed two states of neural network model for compensation of residual error which is possible to use in the prevention of sudden death and metabolic syndrome disease such as hypertension disease and obesity. We found that most of simulations cases were satisfied by the two states mapping based time series prediction model compared to normal BP. In particular, small sample size of times series were more accurate than the standard MLP model. We expect that this algorithm can be available to sudden death prevention and monitoring AGENT system in a ubiquitous homecare environment.

**Keywords:**
Neural network,
U-healthcare,
prediction,
timeseries,
computer aided prediction.

##### 4209 Computational Intelligence Hybrid Learning Approach to Time Series Forecasting

**Authors:**
Chunshien Li,
Jhao-Wun Hu,
Tai-Wei Chiang,
Tsunghan Wu

**Abstract:**

**Keywords:**
forecasting,
hybrid learning (HL),
Neuro-FuzzySystem (NFS),
particle swarm optimization (PSO),
recursiveleast-squares estimator (RLSE),
time series

##### 4208 Computable Function Representations Using Effective Chebyshev Polynomial

**Authors:**
Mohammed A. Abutheraa,
David Lester

**Abstract:**

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

**Keywords:**
Approximation Theory,
Chebyshev Polynomial,
Computable Functions,
Computable Real Arithmetic,
Integration,
Numerical Analysis.

##### 4207 Optimal Allocation of FACTS Devices for ATC Enhancement Using Bees Algorithm

**Authors:**
R.Mohamad Idris,
A.Khairuddin,
M.W.Mustafa

**Abstract:**

In this paper, a novel method using Bees Algorithm is proposed to determine the optimal allocation of FACTS devices for maximizing the Available Transfer Capability (ATC) of power transactions between source and sink areas in the deregulated power system. The algorithm simultaneously searches the FACTS location, FACTS parameters and FACTS types. Two types of FACTS are simulated in this study namely Thyristor Controlled Series Compensator (TCSC) and Static Var Compensator (SVC). A Repeated Power Flow with FACTS devices including ATC is used to evaluate the feasible ATC value within real and reactive power generation limits, line thermal limits, voltage limits and FACTS operation limits. An IEEE30 bus system is used to demonstrate the effectiveness of the algorithm as an optimization tool to enhance ATC. A Genetic Algorithm technique is used for validation purposes. The results clearly indicate that the introduction of FACTS devices in a right combination of location and parameters could enhance ATC and Bees Algorithm can be efficiently used for this kind of nonlinear integer optimization.

**Keywords:**
ATC,
Bees Algorithm,
TCSC,
SVC