Search results for: Function tuner method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 9447

Search results for: Function tuner method

9357 Two Area Power Systems Economic Dispatch Problem Solving Considering Transmission Capacity Constraints

Authors: M. Zarei, A. Roozegar, R. Kazemzadeh, J.M. Kauffmann

Abstract:

This paper describes an efficient and practical method for economic dispatch problem in one and two area electrical power systems with considering the constraint of the tie transmission line capacity constraint. Direct search method (DSM) is used with some equality and inequality constraints of the production units with any kind of fuel cost function. By this method, it is possible to use several inequality constraints without having difficulty for complex cost functions or in the case of unavailability of the cost function derivative. To minimize the number of total iterations in searching, process multi-level convergence is incorporated in the DSM. Enhanced direct search method (EDSM) for two area power system will be investigated. The initial calculation step size that causes less iterations and then less calculation time is presented. Effect of the transmission tie line capacity, between areas, on economic dispatch problem and on total generation cost will be studied; line compensation and active power with reactive power dispatch are proposed to overcome the high generation costs for this multi-area system.

Keywords: Economic dispatch, Power System Operation, Direct Search Method, Transmission Capacity Constraint.

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9356 Assessing the Function of Light and Colorin Architectural View

Authors: Gholam Hossein Naseri, Manucher Tamizi

Abstract:

Light is one of the most important qualitative and symbolic factors and has a special position in architecture and urban development in regard to practical function. The main function of light, either natural or artificial, is lighting up the environment and the constructional forms which is called lighting. However, light is used to redefine the urban spaces by architectural genius with regard to three aesthetic, conceptual and symbolic factors. In architecture and urban development, light has a function beyond lighting up the environment, and the designers consider it as one of the basic components. The present research aims at studying the function of light and color in architectural view and their effects in buildings.

Keywords: Architectural View , Color , Light

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9355 Input Variable Selection for RBFN-based Electric Utility's CO2 Emissions Forecasting

Authors: I. Falconett, K. Nagasaka

Abstract:

This study investigates the performance of radial basis function networks (RBFN) in forecasting the monthly CO2 emissions of an electric power utility. We also propose a method for input variable selection. This method is based on identifying the general relationships between groups of input candidates and the output. The effect that each input has on the forecasting error is examined by removing all inputs except the variable to be investigated from its group, calculating the networks parameter and performing the forecast. Finally, the new forecasting error is compared with the reference model. Eight input variables were identified as the most relevant, which is significantly less than our reference model with 30 input variables. The simulation results demonstrate that the model with the 8 inputs selected using the method introduced in this study performs as accurate as the reference model, while also being the most parsimonious.

Keywords: Correlation analysis, CO2 emissions forecasting, electric power utility, radial basis function networks.

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9354 Fault Detection and Isolation using RBF Networks for Polymer Electrolyte Membrane Fuel Cell

Authors: Mahanijah Md Kamal., Dingli Yu

Abstract:

This paper presents a new method of fault detection and isolation (FDI) for polymer electrolyte membrane (PEM) fuel cell (FC) dynamic systems under an open-loop scheme. This method uses a radial basis function (RBF) neural network to perform fault identification, classification and isolation. The novelty is that the RBF model of independent mode is used to predict the future outputs of the FC stack. One actuator fault, one component fault and three sensor faults have been introduced to the PEMFC systems experience faults between -7% to +10% of fault size in real-time operation. To validate the results, a benchmark model developed by Michigan University is used in the simulation to investigate the effect of these five faults. The developed independent RBF model is tested on MATLAB R2009a/Simulink environment. The simulation results confirm the effectiveness of the proposed method for FDI under an open-loop condition. By using this method, the RBF networks able to detect and isolate all five faults accordingly and accurately.

Keywords: Polymer electrolyte membrane fuel cell, radial basis function neural networks, fault detection, fault isolation.

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9353 Measurement of CES Production Functions Considering Energy as an Input

Authors: Donglan Zha, Jiansong Si

Abstract:

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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9352 Aircraft Supplier Selection Process with Fuzzy Proximity Measure Method using Multiple Criteria Group Decision Making Analysis

Authors: C. Ardil

Abstract:

Being effective in every organizational activity has become necessary due to the escalating level of competition in all areas of corporate life. In the context of supply chain management, aircraft supplier selection is currently one of the most crucial activities. It is possible to choose the best aircraft supplier and deliver efficiency in terms of cost, quality, delivery time, economic status, and institutionalization if a systematic supplier selection approach is used. In this study, an effective multiple criteria decision-making methodology, proximity measure method (PMM), is used within a fuzzy environment based on the vague structure of the real working environment. The best appropriate aircraft suppliers are identified and ranked after the proposed multiple criteria decision making technique is used in a real-life scenario.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, proximity measure method, Minkowski distance family function, Hausdorff distance function, PMM, MCDM

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9351 Order Reduction using Modified Pole Clustering and Pade Approximations

Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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9350 Calculus Logarithmic Function for Image Encryption

Authors: Adil AL-Rammahi

Abstract:

When we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

Keywords: Linear Systems, Image Encryption, Calculus.

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9349 The Method of Evaluation Artery Diameter from Ultrasound Video

Authors: U. Rubins, Z. Marcinkevics, K.Volceka

Abstract:

The cardiovascular system has become the most important subject of clinical research, particularly measurement of arterial blood flow. Therefore correct determination of arterial diameter is crucial. We propose a novel, semi-automatic method for artery lumen detection. The method is based on Gaussian probability function. Usability of our proposed method was assessed by analyzing ultrasound B-mode CFA video sequences acquired from eleven healthy volunteers. The correlation coefficient between the manual and semi-automatic measurement of arterial diameter was 0.996. Our proposed method for detecting artery boundary is novel and accurate enough for the measurement of artery diameter.

Keywords: Ultrasound, boundary detection, artery diameter, curve fitting.

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9348 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

Authors: F. Castillo, J. Arellano, S. Sánchez

Abstract:

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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9347 Regional Stability Analysis of Rotor-Ball Bearing and Rotor- Roller Bearing Systems Considering Switching Phenomena

Authors: Jafar Abbaszadeh Chekan, Kaveh Merat, Hassan Zohoor

Abstract:

In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.

Keywords: Stability analysis, Rotor-rolling bearing systems, Switching systems, Multiple Lyapunov Function Method

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9346 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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9345 A Study for Carbonation Degree on Concrete using a Phenolphthalein Indicator and Fourier-Transform Infrared Spectroscopy

Authors: Ho Jae Lee, Do Gyeum Kim, Jang Hwa Lee, Myoung Suk Cho

Abstract:

A concrete structure is designed and constructed for its purpose of use, and is expected to maintain its function for the target durable years from when it was planned. Nevertheless, as time elapses the structure gradually deteriorates and then eventually degrades to the point where the structure cannot exert the function for which it was planned. The performance of concrete that is able to maintain the level of the performance required over the designed period of use as it has less deterioration caused by the elapse of time under the designed condition is referred to as Durability. There are a number of causes of durability degradation, but especially chloride damage, carbonation, freeze-thaw, etc are the main causes. In this study, carbonation, one of the main causes of deterioration of the durability of a concrete structure, was investigated via a microstructure analysis technique. The method for the measurement of carbonation was studied using the existing indicator method, and the method of measuring the progress of carbonation in a quantitative manner was simultaneously studied using a FT-IR (Fourier-Transform Infrared) Spectrometer along with the microstructure analysis technique.

Keywords: Concrete, Carbonation, Microsturcture, FT-IR

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9344 Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method

Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

Abstract:

In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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9343 Evaluation of a Surrogate Based Method for Global Optimization

Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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9342 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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9341 Self-Organizing Map Network for Wheeled Robot Movement Optimization

Authors: Boguslaw Schreyer

Abstract:

The paper investigates the application of the Kohonen’s Self-Organizing Map (SOM) to the wheeled robot starting and braking dynamic states. In securing wheeled robot stability as well as minimum starting and braking time, it is important to ensure correct torque distribution as well as proper slope of braking and driving moments. In this paper, a correct movement distribution has been formulated, securing optimum adhesion coefficient and good transversal stability of a wheeled robot. A neural tuner has been proposed to secure the above properties, although most of the attention is attached to the SOM network application. If the delay of the torque application or torque release is not negligible, it is important to change the rising and falling slopes of the torque. The road/surface condition is also paramount in robot dynamic states control. As the road conditions may randomly change in time, application of the SOM network has been suggested in order to classify the actual road conditions.

Keywords: SOM network, torque distribution, torque slope, wheeled robots.

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9340 A Case Study to Assess the Validity of Function Points

Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

Abstract:

Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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9339 Selective Minterms Based Tabular Method for BDD Manipulations

Authors: P. W. C. Prasad, A. Assi, M. Raseen, A. Harb

Abstract:

The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBDD parameters, such as best variable order, number of nodes etc. Experimental results on benchmarks are given for this technique.

Keywords: Tabular Method, Binary Decision Diagram, BDD Manipulation, Boolean Function.

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9338 Dynamic Analysis by a Family of Time Marching Procedures Based On Numerically Computed Green’s Functions

Authors: Delfim Soares Jr.

Abstract:

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically computed, taking into account the generalized-α method and subcycling techniques. As it is discussed and illustrated along the text, the proposed procedure is efficient and accurate, providing a very attractive time marching technique. 

Keywords: Dynamics, Time-Marching, Green’s Function, Generalized-α Method, Subcycling.

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9337 Characteristic Function in Estimation of Probability Distribution Moments

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

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9336 Non-Convex Multi Objective Economic Dispatch Using Ramp Rate Biogeography Based Optimization

Authors: Susanta Kumar Gachhayat, S. K. Dash

Abstract:

Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances.

Keywords: Economic load dispatch, Biogeography based optimization, Ramp rate biogeography based optimization, Valve Point loading, Moderate random particle swarm optimization method, Weight improved particle swarm optimization method

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9335 A Neural Network Based Facial Expression Analysis using Gabor Wavelets

Authors: Praseeda Lekshmi.V, Dr.M.Sasikumar

Abstract:

Facial expression analysis is rapidly becoming an area of intense interest in computer science and human-computer interaction design communities. The most expressive way humans display emotions is through facial expressions. In this paper we present a method to analyze facial expression from images by applying Gabor wavelet transform (GWT) and Discrete Cosine Transform (DCT) on face images. Radial Basis Function (RBF) Network is used to classify the facial expressions. As a second stage, the images are preprocessed to enhance the edge details and non uniform down sampling is done to reduce the computational complexity and processing time. Our method reliably works even with faces, which carry heavy expressions.

Keywords: Face Expression, Radial Basis Function, GaborWavelet Transform, Human Computer Interaction.

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9334 Fixture Layout Optimization Using Element Strain Energy and Genetic Algorithm

Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The stiffness of the workpiece is very important to reduce the errors in manufacturing process. The high stiffness of the workpiece can be achieved by optimal positioning of fixture elements in the fixture. The minimization of the sum of the nodal deflection normal to the surface is used as objective function in previous research. The deflection in other direction has been neglected. The 3-2-1 fixturing principle is not valid for metal sheets due to its flexible nature. We propose a new fixture layout optimization method N-3-2-1 for metal sheets that uses the strain energy of the finite elements. This method combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of all the element strain energy. By using the concept of element strain energy, the deformations in all the directions have been considered. Strain energy and stiffness are inversely proportional to each other. So, lower the value of strain energy, higher will be the stiffness. Two different kinds of case studies are presented. The case studies are solved for both objective functions; element strain energy and nodal deflection. The result are compared to verify the propose method.

Keywords: Fixture layout, optimization, fixturing element, genetic algorithm.

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9333 A Distance Function for Data with Missing Values and Its Application

Authors: Loai AbdAllah, Ilan Shimshoni

Abstract:

Missing values in data are common in real world applications. Since the performance of many data mining algorithms depend critically on it being given a good metric over the input space, we decided in this paper to define a distance function for unlabeled datasets with missing values. We use the Bhattacharyya distance, which measures the similarity of two probability distributions, to define our new distance function. According to this distance, the distance between two points without missing attributes values is simply the Mahalanobis distance. When on the other hand there is a missing value of one of the coordinates, the distance is computed according to the distribution of the missing coordinate. Our distance is general and can be used as part of any algorithm that computes the distance between data points. Because its performance depends strongly on the chosen distance measure, we opted for the k nearest neighbor classifier to evaluate its ability to accurately reflect object similarity. We experimented on standard numerical datasets from the UCI repository from different fields. On these datasets we simulated missing values and compared the performance of the kNN classifier using our distance to other three basic methods. Our  experiments show that kNN using our distance function outperforms the kNN using other methods. Moreover, the runtime performance of our method is only slightly higher than the other methods.

Keywords: Missing values, Distance metric, Bhattacharyya distance.

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9332 Capsule-substrate Adhesion in the Presence of Osmosis by the Immersed Interface Method

Authors: P.G. Jayathilake, B.C. Khoo, Zhijun Tan

Abstract:

A two-dimensional thin-walled capsule of a flexible semi-permeable membrane is adhered onto a rigid planar substrate under adhesive forces (derived from a potential function) in the presence of osmosis across the membrane. The capsule is immersed in a hypotonic and diluted binary solution of a non-electrolyte solute. The Stokes flow problem is solved by the immersed interface method (IIM) with equal viscosities for the enclosed and surrounding fluid of the capsule. The numerical results obtained are verified against two simplified theoretical solutions and the agreements are good. The osmotic inflation of the adhered capsule is studied as a function of the solute concentration field, hydraulic conductivity, and the initial capsule shape. Our findings indicate that the contact length shrinks in dimension as capsule inflates in the hypotonic medium, and the equilibrium contact length does not depend on the hydraulic conductivity of the membrane and the initial shape of the capsule.

Keywords: Capsule-substrate adhesion, Fluid mechanics, Immersed interface method, Osmosis, Mass transfer.

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9331 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.

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9330 Computation of Probability Coefficients using Binary Decision Diagram and their Application in Test Vector Generation

Authors: Ashutosh Kumar Singh, Anand Mohan

Abstract:

This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of n variable function have been developed. It is shown that for n ≥ 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.

Keywords: Binary Decision Diagrams, Spectral Coefficients, Fault detection

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9329 An Improved Learning Algorithm based on the Conjugate Gradient Method for Back Propagation Neural Networks

Authors: N. M. Nawi, M. R. Ransing, R. S. Ransing

Abstract:

The conjugate gradient optimization algorithm usually used for nonlinear least squares is presented and is combined with the modified back propagation algorithm yielding a new fast training multilayer perceptron (MLP) algorithm (CGFR/AG). The approaches presented in the paper consist of three steps: (1) Modification on standard back propagation algorithm by introducing gain variation term of the activation function, (2) Calculating the gradient descent on error with respect to the weights and gains values and (3) the determination of the new search direction by exploiting the information calculated by gradient descent in step (2) as well as the previous search direction. The proposed method improved the training efficiency of back propagation algorithm by adaptively modifying the initial search direction. Performance of the proposed method is demonstrated by comparing to the conjugate gradient algorithm from neural network toolbox for the chosen benchmark. The results show that the number of iterations required by the proposed method to converge is less than 20% of what is required by the standard conjugate gradient and neural network toolbox algorithm.

Keywords: Back-propagation, activation function, conjugategradient, search direction, gain variation.

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9328 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong

Abstract:

The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.

Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.

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