Search results for: Tangent search method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8603

Search results for: Tangent search method

8183 Cross-Industry Innovations – Systematic Identification and Adaption

Authors: Niklas Echterhoff, Benjamin Amshoff, Jürgen Gausemeier

Abstract:

Due to today-s fierce competition, companies have to be proactive creators of the future by effectively developing innovations. Especially radical innovations allow high profit margins – but they also entail high risks. One possibility to realize radical innovations and reduce the risk of failure is cross-industry innovation (CII). CII brings together problems and solution ideas from different industries. However, there is a lack of systematic ways towards CII. Bridging this gap, the present paper provides a systematic approach towards planned CII. Starting with the analysis of potentials, the definition of promising search strategies is crucial. Subsequently, identified solution ideas need to be assessed. For the most promising ones, the adaption process has to be systematically planned – regarding the risk affinity of a company. The introduced method is explained on a project from the furniture industry.

Keywords: Analogy building, cross-industry innovations, knowledge transfer, solution adaption.

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8182 Convergence Analysis of the Generalized Alternating Two-Stage Method

Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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8181 Analysis of Distribution of Thrust, Torque and Efficiency of a Constant Chord, Constant Pitch C.R.P. Fan by H.E.S. Method

Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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8180 An Optimal Load Shedding Approach for Distribution Networks with DGs considering Capacity Deficiency Modelling of Bulked Power Supply

Authors: A. R. Malekpour, A.R. Seifi

Abstract:

This paper discusses a genetic algorithm (GA) based optimal load shedding that can apply for electrical distribution networks with and without dispersed generators (DG). Also, the proposed method has the ability for considering constant and variable capacity deficiency caused by unscheduled outages in the bulked generation and transmission system of bulked power supply. The genetic algorithm (GA) is employed to search for the optimal load shedding strategy in distribution networks considering DGs in two cases of constant and variable modelling of bulked power supply of distribution networks. Electrical power distribution systems have a radial network and unidirectional power flows. With the advent of dispersed generations, the electrical distribution system has a locally looped network and bidirectional power flows. Therefore, installed DG in the electrical distribution systems can cause operational problems and impact on existing operational schemes. Introduction of DGs in electrical distribution systems has introduced many new issues in operational and planning level. Load shedding as one of operational issue has no exempt. The objective is to minimize the sum of curtailed load and also system losses within the frame-work of system operational and security constraints. The proposed method is tested on a radial distribution system with 33 load points for more practical applications.

Keywords: DG, Load shedding, Optimization, Capacity Deficiency Modelling.

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8179 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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8178 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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8177 Active Vibration Control of Flexible Beam using Differential Evolution Optimisation

Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

Abstract:

This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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8176 Feature Selection for Web Page Classification Using Swarm Optimization

Authors: B. Leela Devi, A. Sankar

Abstract:

The web’s increased popularity has included a huge amount of information, due to which automated web page classification systems are essential to improve search engines’ performance. Web pages have many features like HTML or XML tags, hyperlinks, URLs and text contents which can be considered during an automated classification process. It is known that Webpage classification is enhanced by hyperlinks as it reflects Web page linkages. The aim of this study is to reduce the number of features to be used to improve the accuracy of the classification of web pages. In this paper, a novel feature selection method using an improved Particle Swarm Optimization (PSO) using principle of evolution is proposed. The extracted features were tested on the WebKB dataset using a parallel Neural Network to reduce the computational cost.

Keywords: Web page classification, WebKB Dataset, Term Frequency-Inverse Document Frequency (TF-IDF), Particle Swarm Optimization (PSO).

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8175 The Homotopy Analysis Method for Solving Discontinued Problems Arising in Nanotechnology

Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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8174 Dynamic Routing to Multiple Destinations in IP Networks using Hybrid Genetic Algorithm (DRHGA)

Authors: K. Vijayalakshmi, S. Radhakrishnan

Abstract:

In this paper we have proposed a novel dynamic least cost multicast routing protocol using hybrid genetic algorithm for IP networks. Our protocol finds the multicast tree with minimum cost subject to delay, degree, and bandwidth constraints. The proposed protocol has the following features: i. Heuristic local search function has been devised and embedded with normal genetic operation to increase the speed and to get the optimized tree, ii. It is efficient to handle the dynamic situation arises due to either change in the multicast group membership or node / link failure, iii. Two different crossover and mutation probabilities have been used for maintaining the diversity of solution and quick convergence. The simulation results have shown that our proposed protocol generates dynamic multicast tree with lower cost. Results have also shown that the proposed algorithm has better convergence rate, better dynamic request success rate and less execution time than other existing algorithms. Effects of degree and delay constraints have also been analyzed for the multicast tree interns of search success rate.

Keywords: Dynamic Group membership change, Hybrid Genetic Algorithm, Link / node failure, QoS Parameters.

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8173 Oncogene Identification using Filter based Approaches between Various Cancer Types in Lung

Authors: Michael Netzer, Michael Seger, Mahesh Visvanathan, Bernhard Pfeifer, Gerald H. Lushington, Christian Baumgartner

Abstract:

Lung cancer accounts for the most cancer related deaths for men as well as for women. The identification of cancer associated genes and the related pathways are essential to provide an important possibility in the prevention of many types of cancer. In this work two filter approaches, namely the information gain and the biomarker identifier (BMI) are used for the identification of different types of small-cell and non-small-cell lung cancer. A new method to determine the BMI thresholds is proposed to prioritize genes (i.e., primary, secondary and tertiary) using a k-means clustering approach. Sets of key genes were identified that can be found in several pathways. It turned out that the modified BMI is well suited for microarray data and therefore BMI is proposed as a powerful tool for the search for new and so far undiscovered genes related to cancer.

Keywords: lung cancer, micro arrays, data mining, feature selection.

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8172 Prediction of Air-Water Two-Phase Frictional Pressure Drop Using Artificial Neural Network

Authors: H. B. Mehta, Vipul M. Patel, Jyotirmay Banerjee

Abstract:

The present paper discusses the prediction of gas-liquid two-phase frictional pressure drop in a 2.12 mm horizontal circular minichannel using Artificial Neural Network (ANN). The experimental results are obtained with air as gas phase and water as liquid phase. The superficial gas velocity is kept in the range of 0.0236 m/s to 0.4722 m/s while the values of 0.0944 m/s, 0.1416 m/s and 0.1889 m/s are considered for superficial liquid velocity. The experimental results are predicted using different Artificial Neural Network (ANN) models. Networks used for prediction are radial basis, generalised regression, linear layer, cascade forward back propagation, feed forward back propagation, feed forward distributed time delay, layer recurrent, and Elman back propagation. Transfer functions used for networks are Linear (PURELIN), Logistic sigmoid (LOGSIG), tangent sigmoid (TANSIG) and Gaussian RBF. Combination of networks and transfer functions give different possible neural network models. These models are compared for Mean Absolute Relative Deviation (MARD) and Mean Relative Deviation (MRD) to identify the best predictive model of ANN.

Keywords: Minichannel, Two-Phase Flow, Frictional Pressure Drop, ANN, MARD, MRD.

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8171 Adomian Method for Second-order Fuzzy Differential Equation

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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8170 Multilevel Arnoldi-Tikhonov Regularization Methods for Large-Scale Linear Ill-Posed Systems

Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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8169 EML-Estimation of Multivariate t Copulas with Heuristic Optimization

Authors: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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8168 Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities

Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: structured variational inequalities, proximal point method, global convergence

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8167 A Method for Improving Dental Crown Fit-Increasing the Robustness

Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

Abstract:

The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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8166 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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8165 Authenticity of Ecuadorian Commercial Honeys

Authors: Elisabetta Schievano, Valentina Zuccato, Claudia Finotello, Patricia Vit

Abstract:

Control of honey frauds is needed in Ecuador to protect bee keepers and consumers because simple syrups and new syrups with eucalyptus are sold as genuine honeys. Authenticity of Ecuadorian commercial honeys was tested with a vortex emulsion consisting on one volume of honey:water (1:1) dilution, and two volumes of diethyl ether. This method allows a separation of phases in one minute to discriminate genuine honeys that form three phase and fake honeys that form two phases; 34 of the 42 honeys analyzed from five provinces of Ecuador were genuine. This was confirmed with 1H NMR spectra of honey dilutions in deuterated water with an enhanced amino acid region with signals for proline, phenylalanine and tyrosine. Classic quality indicators were also tested with this method (sugars, HMF), indicators of fermentation (ethanol, acetic acid), and residues of citric acid used in the syrup manufacture. One of the honeys gave a false positive for genuine, being an admixture of genuine honey with added syrup, evident for the high sucrose. Sensory analysis was the final confirmation to recognize the honey groups studied here, namely honey produced in combs by Apis mellifera, fake honey, and honey produced in cerumen pots by Geotrigona, Melipona, and Scaptotrigona. Chloroform extractions of honey were also done to search lipophilic additives in NMR spectra. This is a valuable contribution to protect honey consumers, and to develop the beekeeping industry in Ecuador.

Keywords: Fake, genuine, honey, 1H NMR, Ecuador.

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8164 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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8163 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method

Authors: Caihong Su

Abstract:

Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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8162 Variational Iteration Method for the Solution of Boundary Value Problems

Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.

Abstract:

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.

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8161 Low Resolution Single Neural Network Based Face Recognition

Authors: Jahan Zeb, Muhammad Younus Javed, Usman Qayyum

Abstract:

This research paper deals with the implementation of face recognition using neural network (recognition classifier) on low-resolution images. The proposed system contains two parts, preprocessing and face classification. The preprocessing part converts original images into blurry image using average filter and equalizes the histogram of those image (lighting normalization). The bi-cubic interpolation function is applied onto equalized image to get resized image. The resized image is actually low-resolution image providing faster processing for training and testing. The preprocessed image becomes the input to neural network classifier, which uses back-propagation algorithm to recognize the familiar faces. The crux of proposed algorithm is its beauty to use single neural network as classifier, which produces straightforward approach towards face recognition. The single neural network consists of three layers with Log sigmoid, Hyperbolic tangent sigmoid and Linear transfer function respectively. The training function, which is incorporated in our work, is Gradient descent with momentum (adaptive learning rate) back propagation. The proposed algorithm was trained on ORL (Olivetti Research Laboratory) database with 5 training images. The empirical results provide the accuracy of 94.50%, 93.00% and 90.25% for 20, 30 and 40 subjects respectively, with time delay of 0.0934 sec per image.

Keywords: Average filtering, Bicubic Interpolation, Neurons, vectorization.

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8160 Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation

Authors: G.Hariharan, K.Kannan

Abstract:

In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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8159 Dynamics of Marital Status and Information Search through Consumer Generated Media: An Exploratory Study

Authors: Shivakumar Krishnamurti, Ruchi Agarwal

Abstract:

The study examines the influence of marital status on consumers of products and services using blogs as a source of information. A pre-designed questionnaire was used to collect the primary data from the respondents (experiences). Data were collected from one hundred and eighty seven respondents residing in and around the Emirates of Sharjah and Dubai of the United Arab Emirates. The collected data was analyzed with the help of statistical tools such as averages, percentages, factor analysis, Student’s t-test and Structural Equation Modelling Technique. Objectives of the study are to know the reasons how married and unmarried or single consumers of products and services are motivated to use blogs as a source of information, to know whether the consumers of products and services irrespective of their marital status share their views and experiences with other bloggers and to know the respondents’ future intentions towards blogging. The study revealed the following: Majority of the respondents have the motivation to blog because they are willing to receive comments on what they post about services, convenience of blogs to search for information about services and products, by blogging respondents share information on the symptoms of a disease/ disorder that may be experienced by someone, helps to share information about ready to cook mix products and are keen to spend more time blogging in the future.

Keywords: Blog, consumer, information, marital status.

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8158 A Method for Measurement and Evaluation of Drape of Textiles

Authors: L. Fridrichova, R. Knížek, V. Bajzík

Abstract:

Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: Drape, drape shape, automated drape meter.

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8157 Seat Assignment Model for Student Admissions Process at Saudi Higher Education Institutions

Authors: Mohammed Salem Alzahrani

Abstract:

In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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8156 Transesterification of Jojoba Oil-Wax Using Microwave Technique

Authors: Labiba I. Hussein, Maher Z. Elsabee, Eid A. Ismail, Hala F. Naguib, Hilda A. Aziz, Moataz A. Elsawy

Abstract:

Jojoba oil-wax is extracted from the seeds of the jojoba (Simmondsia chinensis Link Schneider), a perennial shrub that grows in semi desert areas in Egypt and in some parts of the world. The main uses of jojoba oil-wax are in the cosmetics and pharmaceutical industry, but new uses could arise related to the search of new energetic crops. This paper summarizes a process to convert the jojoba oil-wax to biodiesel by transesterification with ethanol and a series of aliphatic alcohols using a more economic and energy saving method in a domestic microwave. The effect of time and power of the microwave on the extent of the transesterification using ethanol and other aliphatic alcohols has been studied. The separation of the alkyl esters from the fatty alcohols rich fraction has been done in a single crystallization step at low temperature (−18°C) from low boiling point petroleum ether. Gas chromatography has been used to follow up the transesterification process. All products have been characterized by spectral analysis.

Keywords: Jojoba oil, transesterification, microwave, gas chromatography jojoba esters, Jojoba alcohol.

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8155 A Dual Method for Solving General Convex Quadratic Programs

Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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8154 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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