Search results for: Fitness Functions
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1191

Search results for: Fitness Functions

1101 Development of Condition Monitoring System with Control Functions for Wind Turbines

Authors: Joon-Young Park, Beom-Joo Kim, Jae-Kyung Lee

Abstract:

As an effort to promote wind power industry in Korea, Korea South-East Power Corporation has been developing 22MW YeungHeung wind farm consisting of nine 2 to 3MW wind turbines supplied by three manufacturers. To maximize its availability and reliability and to solve the difficulty of operating three kinds of SCADA systems, Korea Electric Power Corporation has been developing a condition monitoring system integrated with control functions. This paper presents the developed condition monitoring system and its application to YeungHeung wind test bed, and the design of its control functions.

Keywords: condition monitoring, control function, reliability, wind turbine

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1100 On Symmetry Analysis and Exact Wave Solutions of New Modified Novikov Equation

Authors: Anupma Bansal, R. K. Gupta

Abstract:

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.

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1099 Univalence of an Integral Operator Defined by Generalized Operators

Authors: Salma Faraj Ramadan, Maslina Darus

Abstract:

In this paper we define generalized differential operators from some well-known operators on the class A of analytic functions in the unit disk U = {z ∈ C : |z| < 1}. New classes containing these operators are investigated. Also univalence of integral operator is considered.

Keywords: Univalent functions, integral operators, differential operators.

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1098 Measurement and Evaluation of Outdoor Lighting Environment at Night in Residential Community in China: A Case Study of Hangzhou

Authors: Jiantao Weng, Yujie Zhao

Abstract:

With the improvement of living quality and demand for nighttime activities in China, the current situation of outdoor lighting environment at night needs to be assessed. Lighting environment at night plays an important role to guarantee night safety. Two typical residential communities in Hangzhou were selected. A comprehensive test method of outdoor lighting environment at night was established. The road, fitness area, landscape, playground and entrance were included. Field measurements and questionnaires were conducted in these two residential communities. The characteristics of residents’ habits and the subjective evaluation on different aspects of outdoor lighting environment at night were collected via questionnaire. A safety evaluation system on the outdoor lighting environment at night in the residential community was established. The results show that there is a big difference in illumination in different areas. The lighting uniformities of roads cannot meet the requirement of lighting standard in China. Residents pay more attention to the lighting environment of the fitness area and road than others. This study can provide guidance for the design and management of outdoor lighting environment at night.

Keywords: Residential community, lighting environment, night, field measurement.

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1097 Attribute Selection for Preference Functions in Engineering Design

Authors: Ali E. Abbas

Abstract:

Industrial Engineering is a broad multidisciplinary field with intersections and applications in numerous areas. When designing a product, it is important to determine the appropriate attributes of value and the preference function for which the product is optimized. This paper provides some guidelines on appropriate selection of attributes for preference and value functions for engineering design.

Keywords: Decision analysis, engineering design, direct vs. indirect values.

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1096 Efficient Pipelined Hardware Implementation of RIPEMD-160 Hash Function

Authors: H. E. Michail, V. N. Thanasoulis, G. A. Panagiotakopoulos, A. P. Kakarountas, C. E. Goutis

Abstract:

In this paper an efficient implementation of Ripemd- 160 hash function is presented. Hash functions are a special family of cryptographic algorithms, which is used in technological applications with requirements for security, confidentiality and validity. Applications like PKI, IPSec, DSA, MAC-s incorporate hash functions and are used widely today. The Ripemd-160 is emanated from the necessity for existence of very strong algorithms in cryptanalysis. The proposed hardware implementation can be synthesized easily for a variety of FPGA and ASIC technologies. Simulation results, using commercial tools, verified the efficiency of the implementation in terms of performance and throughput. Special care has been taken so that the proposed implementation doesn-t introduce extra design complexity; while in parallel functionality was kept to the required levels.

Keywords: Hardware implementation, hash functions, Ripemd-160, security.

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1095 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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1094 Design Systems and the Need for a Usability Method: Assessing the Fitness of Components and Interaction Patterns in Design Systems Using Atmosphere Methodology

Authors: P. Johansson, S. Mardh

Abstract:

The present study proposes a usability test method, Atmosphere, to assess the fitness of components and interaction patterns of design systems. The method covers the user’s perception of the components of the system, the efficiency of the logic of the interaction patterns, perceived ease of use as well as the user’s understanding of the intended outcome of interactions. These aspects are assessed by combining measures of first impression, visual affordance and expectancy. The method was applied to a design system developed for the design of an electronic health record system. The study was conducted involving 15 healthcare personnel. It could be concluded that the Atmosphere method provides tangible data that enable human-computer interaction practitioners to analyze and categorize components and patterns based on perceived usability, success rate of identifying interactive components and success rate of understanding components and interaction patterns intended outcome.

Keywords: atomic design, atmosphere methodology, design system, expectancy testing, first impression testing, usability testing, visual affordance testing

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1093 Problem-based Learning Approach to Human Computer Interaction

Authors: Oon-Seng Tan

Abstract:

Human Computer Interaction (HCI) has been an emerging field that draws in the experts from various fields to enhance the application of computer programs and the ease of computer users. HCI has much to do with learning and cognition and an emerging approach to learning and problem-solving is problembased learning (PBL). The processes of PBL involve important cognitive functions in the various stages. This paper will illustrate how closely related fields to HCI, PBL and cognitive psychology can benefit from informing each other through analysing various cognitive functions. Several cognitive functions from cognitive function disc (CFD) would be presented and discussed in relation to human-computer interface. This paper concludes with the implications of bridging the gaps amongst these disciplines.

Keywords: problem-based learning, human computerinteraction, cognitive psychology, Cognitive Function Disc (CFD)

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1092 Evolutionary Algorithms for Learning Primitive Fuzzy Behaviors and Behavior Coordination in Multi-Objective Optimization Problems

Authors: Li Shoutao, Gordon Lee

Abstract:

Evolutionary robotics is concerned with the design of intelligent systems with life-like properties by means of simulated evolution. Approaches in evolutionary robotics can be categorized according to the control structures that represent the behavior and the parameters of the controller that undergo adaptation. The basic idea is to automatically synthesize behaviors that enable the robot to perform useful tasks in complex environments. The evolutionary algorithm searches through the space of parameterized controllers that map sensory perceptions to control actions, thus realizing a specific robotic behavior. Further, the evolutionary algorithm maintains and improves a population of candidate behaviors by means of selection, recombination and mutation. A fitness function evaluates the performance of the resulting behavior according to the robot-s task or mission. In this paper, the focus is in the use of genetic algorithms to solve a multi-objective optimization problem representing robot behaviors; in particular, the A-Compander Law is employed in selecting the weight of each objective during the optimization process. Results using an adaptive fitness function show that this approach can efficiently react to complex tasks under variable environments.

Keywords: adaptive fuzzy neural inference, evolutionary tuning

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1091 An Application of Differential Subordination to Analytic Functions

Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

Abstract:

the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction

Keywords: function, Differential subordination, Multiplier transformation.

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1090 Generational PipeLined Genetic Algorithm (PLGA)using Stochastic Selection

Authors: Malay K. Pakhira, Rajat K. De

Abstract:

In this paper, a pipelined version of genetic algorithm, called PLGA, and a corresponding hardware platform are described. The basic operations of conventional GA (CGA) are made pipelined using an appropriate selection scheme. The selection operator, used here, is stochastic in nature and is called SA-selection. This helps maintaining the basic generational nature of the proposed pipelined GA (PLGA). A number of benchmark problems are used to compare the performances of conventional roulette-wheel selection and the SA-selection. These include unimodal and multimodal functions with dimensionality varying from very small to very large. It is seen that the SA-selection scheme is giving comparable performances with respect to the classical roulette-wheel selection scheme, for all the instances, when quality of solutions and rate of convergence are considered. The speedups obtained by PLGA for different benchmarks are found to be significant. It is shown that a complete hardware pipeline can be developed using the proposed scheme, if parallel evaluation of the fitness expression is possible. In this connection a low-cost but very fast hardware evaluation unit is described. Results of simulation experiments show that in a pipelined hardware environment, PLGA will be much faster than CGA. In terms of efficiency, PLGA is found to outperform parallel GA (PGA) also.

Keywords: Hardware evaluation, Hardware pipeline, Optimization, Pipelined genetic algorithm, SA-selection.

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1089 Solving Weighted Number of Operation Plus Processing Time Due-Date Assignment, Weighted Scheduling and Process Planning Integration Problem Using Genetic and Simulated Annealing Search Methods

Authors: Halil Ibrahim Demir, Caner Erden, Mumtaz Ipek, Ozer Uygun

Abstract:

Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of these three important functions are not adequately addressed. Here, the integration of these three important functions is studied by using genetic, random-genetic hybrid, simulated annealing, random-simulated annealing hybrid and random search techniques. As well, the importance of the integration of these three functions and the power of meta-heuristics and of hybrid heuristics are studied.

Keywords: Process planning, weighted scheduling, weighted due-date assignment, genetic search, simulated annealing, hybrid meta-heuristics.

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1088 A Sandwich-type Theorem with Applications to Univalent Functions

Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

Abstract:

In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.

Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.

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1087 Design of an Augmented Automatic Choosing Control by Lyapunov Functions Using Gradient Optimization Automatic Choosing Functions

Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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1086 Adaptive and Personalizing Learning Sequence Using Modified Roulette Wheel Selection Algorithm

Authors: Melvin A. Ballera

Abstract:

Prior literature in the field of adaptive and personalized learning sequence in e-learning have proposed and implemented various mechanisms to improve the learning process such as individualization and personalization, but complex to implement due to expensive algorithmic programming and need of extensive and prior data. The main objective of personalizing learning sequence is to maximize learning by dynamically selecting the closest teaching operation in order to achieve the learning competency of learner. In this paper, a revolutionary technique has been proposed and tested to perform individualization and personalization using modified reversed roulette wheel selection algorithm that runs at O(n). The technique is simpler to implement and is algorithmically less expensive compared to other revolutionary algorithms since it collects the dynamic real time performance matrix such as examinations, reviews, and study to form the RWSA single numerical fitness value. Results show that the implemented system is capable of recommending new learning sequences that lessens time of study based on student's prior knowledge and real performance matrix.

Keywords: E-learning, fitness value, personalized learning sequence, reversed roulette wheel selection algorithms.

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1085 Stochastic Modeling for Parameters of Modified Car-Following Model in Area-Based Traffic Flow

Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

Abstract:

The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: Area-based traffic, car-following model, micro-simulation, stochastic modeling.

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1084 A Laser Point Interaction System Integrating Mouse Functions

Authors: Ching-Sheng Wang, Lun-Ping Hung, Sheng-Yu Peng, Li-Chieh Cheng

Abstract:

The computer has become an essential tool in modern life, and the combined use of a computer with a projector is very common in teaching and presentations. However, as typical computer operating devices involve a mouse or keyboard, when making presentations, users often need to stay near the computer to execute functions such as changing pages, writing, and drawing, thus, making the operation time-consuming, and reducing interactions with the audience. This paper proposes a laser pointer interaction system able to simulate mouse functions in order that users need not remain near the computer, but can directly use laser pointer operations from at a distance. It can effectively reduce the users- time spent by the computer, allowing for greater interactions with the audience.

Keywords: laser pointer, presentation, interaction, mousefunction

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1083 Modeling and Identification of Hammerstein System by using Triangular Basis Functions

Authors: K. Elleuch, A. Chaari

Abstract:

This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functions for the description of the static nonlinear block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters. The proposed approach has been efficiently tested on academic examples of simulation.

Keywords: Identification, Hammerstein model, Piecewisenonlinear characteristic, Dead-zone nonlinearity, Triangular basisfunctions, Singular Values Decomposition

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1082 Solving Process Planning and Scheduling with Number of Operation Plus Processing Time Due-Date Assignment Concurrently Using a Genetic Search

Authors: Halil Ibrahim Demir, Alper Goksu, Onur Canpolat, Caner Erden, Melek Nur

Abstract:

Traditionally process planning, scheduling and due date assignment are performed sequentially and separately. High interrelation between these functions makes integration very useful. Although there are numerous works on integrated process planning and scheduling and many works on scheduling with due date assignment, there are only a few works on the integration of these three functions. Here we tested the different integration levels of these three functions and found a fully integrated version as the best. We applied genetic search and random search and genetic search was found better compared to the random search. We penalized all earliness, tardiness and due date related costs. Since all these three terms are all undesired, it is better to penalize all of them.

Keywords: Process planning, scheduling, due-date assignment, genetic algorithm, random search.

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1081 Utilizing Analytic Hierarchy Process to Analyze Consumers- Purchase Evaluation Factors of Smartphones

Authors: Yi-Chung Hu, Yu-Lin Liao

Abstract:

Due to the fast development of technology, the competition of technological products is turbulent; therefore, it is important to understand the market trend, consumers- demand and preferences. As the smartphones are prevalent, the main purpose of this paper is to utilize Analytic Hierarchy Process (AHP) to analyze consumer-s purchase evaluation factors of smartphones. Through the AHP expert questionnaire, the smartphones- main functions are classified as “user interface", “mobile commerce functions", “hardware and software specifications", “entertainment functions" and “appearance and design", five aspects to analyze the weights. Then four evaluation criteria are evaluated under each aspect to rank the weights. Based on an analysis of data shows that consumers consider when purchase factors are “hardware and software specifications", “user interface", “appearance and design", “mobile commerce functions" and “entertainment functions" in sequence. The “hardware and software specifications" aspect obtains the weight of 33.18%; it is the most important factor that consumers are taken into account. In addition, the most important evaluation criteria are central processing unit, operating system, touch screen, and battery function in sequence. The results of the study can be adopted as reference data for mobile phone manufacturers in the future on the design and marketing strategy to satisfy the voice of customer.

Keywords: Analytic Hierarchy Process (AHP), evaluation criteria, purchase evaluation factors, smartphone.

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1080 Moment Generating Functions of Observed Gaps between Hypopnea Using Saddlepoint Approximations

Authors: Nur Zakiah Mohd Saat, Abdul Aziz Jemain

Abstract:

Saddlepoint approximations is one of the tools to obtain an expressions for densities and distribution functions. We approximate the densities of the observed gaps between the hypopnea events using the Huzurbazar saddlepoint approximation. We demonstrate the density of a maximum likelihood estimator in exponential families.

Keywords: Exponential, maximum likehood estimators, observed gap, Saddlepoint approximations.

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1079 Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions

Authors: Vitalice K. Oduol

Abstract:

The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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1078 An Advanced Nelder Mead Simplex Method for Clustering of Gene Expression Data

Authors: M. Pandi, K. Premalatha

Abstract:

The DNA microarray technology concurrently monitors the expression levels of thousands of genes during significant biological processes and across the related samples. The better understanding of functional genomics is obtained by extracting the patterns hidden in gene expression data. It is handled by clustering which reveals natural structures and identify interesting patterns in the underlying data. In the proposed work clustering gene expression data is done through an Advanced Nelder Mead (ANM) algorithm. Nelder Mead (NM) method is a method designed for optimization process. In Nelder Mead method, the vertices of a triangle are considered as the solutions. Many operations are performed on this triangle to obtain a better result. In the proposed work, the operations like reflection and expansion is eliminated and a new operation called spread-out is introduced. The spread-out operation will increase the global search area and thus provides a better result on optimization. The spread-out operation will give three points and the best among these three points will be used to replace the worst point. The experiment results are analyzed with optimization benchmark test functions and gene expression benchmark datasets. The results show that ANM outperforms NM in both benchmarks.

Keywords: Spread out, simplex, multi-minima, fitness function, optimization, search area, monocyte, solution, genomes.

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1077 Database Development and Discrimination Algorithms for Membrane Protein Functions

Authors: M. Michael Gromiha, Y. Yabuki, K. Imai, P. Horton, K. Fukui

Abstract:

We have developed a database for membrane protein functions, which has more than 3000 experimental data on functionally important amino acid residues in membrane proteins along with sequence, structure and literature information. Further, we have proposed different methods for identifying membrane proteins based on their functions: (i) discrimination of membrane transport proteins from other globular and membrane proteins and classifying them into channels/pores, electrochemical and active transporters, and (ii) β-signal for the insertion of mitochondrial β-barrel outer membrane proteins and potential targets. Our method showed an accuracy of 82% in discriminating transport proteins and 68% to classify them into three different transporters. In addition, we have identified a motif for targeting β-signal and potential candidates for mitochondrial β-barrel membrane proteins. Our methods can be used as effective tools for genome-wide annotations.

Keywords: Membrane proteins, database, transporters, discrimination, β-signal.

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1076 Characteristics of Cognitive Functions among Polish Adolescence with Spelling Disorders

Authors: Izabela Pietras

Abstract:

The level of visual abilities, language, memory processes and intellectual functioning development affects the quality of a written text. The following analysis will present the results of diagnostic tests indicating the most common criterion for a group and stating whether a person has been diagnosed with having cognitive developmental level below the group-s average or not.The study-s aim is to determine whether there are specific patterns of cognitive deficits, which can be distinguished among the group of young people with spelling disorders.

Keywords: cognitive deficits, cognitive functions, spellingdisorders

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1075 Effect of Architecture and Operating Conditions of Vehicle on Bulb Lifetime in Automotive

Authors: Hatice Özbek, Caner Çil, Ahmet Rodoplu

Abstract:

Automotive lighting is the leading function in the configuration of vehicle architecture. Especially headlights and taillights from external lighting functions are among the structures that determine the stylistic character of the vehicle. At the same time, the fact that lighting functions are related to many other functions brings along difficulties in design. Customers expect maximum quality from the vehicle. In these circumstances, it is necessary to make designs that aim to keep the performance of bulbs with limited working lives at the highest level. With this study, the factors that influence the working lives of filament lamps were examined and bulb explosions that can occur sooner than anticipated in the future were prevented while the vehicle was still in the design phase by determining the relations with electrical, dynamical and static variables. Especially the filaments of the bulbs used in the front lighting of the vehicle are deformed in a shorter time due to the high voltage requirement. In addition to this, rear lighting lamps vibrate as a result of the tailgate opening and closing and cause the filaments to be exposed to high stress. With this study, the findings that cause bulb explosions were evaluated. Among the most important findings: 1. The structure of the cables to the lighting functions of the vehicle and the effect of the voltage values are drawn; 2. The effect of the vibration to bulb throughout the life of the vehicle; 3 The effect of the loads carried to bulb while the vehicle doors are opened and closed. At the end of the study, the maximum performance was established in the bulb lifetimes with the optimum changes made in the vehicle architecture based on the findings obtained.

Keywords: Vehicle architecture, automotive lighting functions, filament lamps, bulb lifetime.

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1074 Certain Conditions for Strongly Starlike and Strongly Convex Functions

Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

Abstract:

In the present paper, we investigate a differential subordination involving multiplier transformation related to a sector in the open unit disk E = {z : |z| < 1}. As special cases to our main result, certain sufficient conditions for strongly starlike and strongly convex functions are obtained.

Keywords: Analytic function, Multiplier transformation, Strongly starlike function, Strongly convex function.

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1073 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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1072 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

Authors: M. Zarebnia, N. Aliniya

Abstract:

In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method

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