Search results for: Generalized differential quadrature method
7939 On Fuzzy Weakly-Closed Sets
Authors: J. Mahanta, P.K. Das
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A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
Keywords: Fuzzy weakly-closed set, fuzzy weakly-closed space, fuzzy weakly-compactness, MSC: 54A40, 54D30.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17767938 Analytical solution of Gas Flow Through a Micro-Nano Porous Media by Homotopy Perturbation method
Authors: Jamal Amani Rad, Kourosh Parand
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In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which have previously been applied. The results of homotopy perturbation method are of high accuracy and the method is very effective and succinct.Keywords: Unsteady gas equation, Homotopy perturbation method(HPM), Porous medium, Nonlinear ODE
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18887937 Electrical Field Around the Overhead Transmission Lines
Authors: S.S. Razavipour, M. Jahangiri, H. Sadeghipoor
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In this paper, the computation of the electrical field distribution around AC high-voltage lines is demonstrated. The advantages and disadvantages of two different methods are described to evaluate the electrical field quantity. The first method is a seminumerical method using the laws of electrostatic techniques to simulate the two-dimensional electric field under the high-voltage overhead line. The second method which will be discussed is the finite element method (FEM) using specific boundary conditions to compute the two- dimensional electric field distributions in an efficient way.
Keywords: Electrical field, unloaded transmission lines, finite element method, electrostatic images technique.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 83697936 A Finite Point Method Based on Directional Derivatives for Diffusion Equation
Authors: Guixia Lv, Longjun Shen
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This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13527935 Unsteady Heat and Mass Transfer in MHD Flow of Nanofluids over Stretching Sheet with a Non-Uniform Heat Source/Sink
Authors: Bandaris Shankar, Yohannes Yirga
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In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.
Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 32237934 A Method for Quality Inspection of Motors by Detecting Abnormal Sound
Authors: Tadatsugu Kitamoto
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Recently, a quality of motors is inspected by human ears. In this paper, I propose two systems using a method of speech recognition for automation of the inspection. The first system is based on a method of linear processing which uses K-means and Nearest Neighbor method, and the second is based on a method of non-linear processing which uses neural networks. I used motor sounds in these systems, and I successfully recognize 86.67% of motor sounds in the linear processing system and 97.78% in the non-linear processing system.Keywords: Acoustical diagnosis, Neural networks, K-means, Short-time Fourier transformation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17017933 Proposal for a Ultra Low Voltage NAND gate to withstand Power Analysis Attacks
Authors: Omid Mirmotahari, Yngvar Berg
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In this paper we promote the Ultra Low Voltage (ULV) NAND gate to replace either partly or entirely the encryption block of a design to withstand power analysis attack.
Keywords: Differential Power Analysis (DPA), Low Voltage (LV), Ultra Low Voltage (ULV), Floating-Gate (FG), supply current analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19557932 A New Approach for Mobile Agent Security
Authors: R. Haghighat far, H. Yarahmadi
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A mobile agent is a software which performs an action autonomously and independently as a person or an organizations assistance. Mobile agents are used for searching information, retrieval information, filtering, intruder recognition in networks, and so on. One of the important issues of mobile agent is their security. It must consider different security issues in effective and secured usage of mobile agent. One of those issues is the integrity-s protection of mobile agents. In this paper, the advantages and disadvantages of each method, after reviewing the existing methods, is examined. Regarding to this matter that each method has its own advantage or disadvantage, it seems that by combining these methods, one can reach to a better method for protecting the integrity of mobile agents. Therefore, this method is provided in this paper and then is evaluated in terms of existing method. Finally, this method is simulated and its results are the sign of improving the possibility of integrity-s protection of mobile agents.Keywords: Integrity, Mobile Agent, Security.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17597931 A New Model for Discovering XML Association Rules from XML Documents
Authors: R. AliMohammadzadeh, M. Rahgozar, A. Zarnani
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The inherent flexibilities of XML in both structure and semantics makes mining from XML data a complex task with more challenges compared to traditional association rule mining in relational databases. In this paper, we propose a new model for the effective extraction of generalized association rules form a XML document collection. We directly use frequent subtree mining techniques in the discovery process and do not ignore the tree structure of data in the final rules. The frequent subtrees based on the user provided support are split to complement subtrees to form the rules. We explain our model within multi-steps from data preparation to rule generation.Keywords: XML, Data Mining, Association Rule Mining.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16317930 A First Course in Numerical Methods with “Mathematica“
Authors: Andrei A. Kolyshkin
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In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.Keywords: Numerical methods, "Mathematica", e-learning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36717929 A Formatting Method for Transforming XML Data into HTML
Authors: Zhe JIN, Motomichi TOYAMA
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In this paper, we propose a fixed formatting method of PPX(Pretty Printer for XML). PPX is a query language for XML database which has extensive formatting capability that produces HTML as the result of a query. The fixed formatting method is to completely specify the combination of variables and layout specification operators within the layout expression of the GENERATE clause of PPX. In the experiment, a quick comparison shows that PPX requires far less description compared to XSLT or XQuery programs doing the same tasks.
Keywords: PPX, XML, HTML, XSLT, XQuery, fixed formatting method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13647928 Advances on LuGre Friction Model
Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane
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LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.
Keywords: Hysteresis, LuGre model, operator, (strong) consistency.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27127927 Containment/Penetration Analysis for the Protection of Aircraft Engine External Configuration and Nuclear Power Plant Structures
Authors: Dong Wook Lee, Adrian Mistreanu
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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.
Keywords: Computer Aided Engineering, CAE, containment analysis, Finite Element Analysis, FEA, impact analysis, penetration analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5397926 Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers
Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian
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The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.Keywords: Fuzzy number linear programming, rankingfunction, simplex method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 35287925 Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method
Authors: Mohamed Hafid, Marcel Lacroix
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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.Keywords: Melting furnace, inverse heat transfer, enthalpy method, Levenberg–Marquardt Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13187924 Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA
Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita
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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.Keywords: Dynamic response, Nonlinear impact response, Finite Element analysis, Numerical analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17207923 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem
Authors: Talaat S. El-Danaf
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In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20107922 Increased Signal to Noise Ratio in P300 Potentials by the Method of Coherent Self-Averaging in BCI Systems
Authors: Ricardo Espinosa
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The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise
Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21447921 Nullity of t-Tupple Graphs
Authors: Khidir R. Sharaf, Didar A. Ali
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The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs,
Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.
Keywords: Graph theory, Graph spectra, Nullity of graphs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19177920 An Optimized Design of Non-uniform Filterbank
Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena
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The tree structured approach of non-uniform filterbank (NUFB) is normally used in perfect reconstruction (PR). The PR is not always feasible due to certain limitations, i.e, constraints in selecting design parameters, design complexity and some times output is severely affected by aliasing error if necessary and sufficient conditions of PR is not satisfied perfectly. Therefore, there has been generalized interest of researchers to go for near perfect reconstruction (NPR). In this proposed work, an optimized tree structure technique is used for the design of NPR non-uniform filterbank. Window functions of Blackman family are used to design the prototype FIR filter. A single variable linear optimization is used to minimize the amplitude distortion. The main feature of the proposed design is its simplicity with linear phase property.Keywords: Tree structure, NUFB, QMF, NPR.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17387919 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation
Authors: Minghui Wang, Juntao Zhang
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An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.
Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16067918 Magnetohydrodynamic Maxwell Nanofluids Flow over a Stretching Surface through a Porous Medium: Effects of Non-Linear Thermal Radiation, Convective Boundary Conditions and Heat Generation/Absorption
Authors: Sameh E. Ahmed, Ramadan A. Mohamed, Abd Elraheem M. Aly, Mahmoud S. Soliman
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In this paper, an enhancement of the heat transfer using non-Newtonian nanofluids by magnetohydrodynamic (MHD) mixed convection along stretching sheets embedded in an isotropic porous medium is investigated. Case of the Maxwell nanofluids is studied using the two phase mathematical model of nanofluids and the Darcy model is applied for the porous medium. Important effects are taken into account, namely, non-linear thermal radiation, convective boundary conditions, electromagnetic force and presence of the heat source/sink. Suitable similarity transformations are used to convert the governing equations to a system of ordinary differential equations then it is solved numerically using a fourth order Runge-Kutta method with shooting technique. The main results of the study revealed that the velocity profiles are decreasing functions of the Darcy number, the Deborah number and the magnetic field parameter. Also, the increase in the non-linear radiation parameters causes an enhancement in the local Nusselt number.
Keywords: MHD, nanofluids, stretching surface, non-linear thermal radiation, convective condition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9627917 Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification
Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai
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This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14677916 Modified Levenberg-Marquardt Method for Neural Networks Training
Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi
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In this paper a modification on Levenberg-Marquardt algorithm for MLP neural network learning is proposed. The proposed algorithm has good convergence. This method reduces the amount of oscillation in learning procedure. An example is given to show usefulness of this method. Finally a simulation verifies the results of proposed method.
Keywords: Levenberg-Marquardt, modification, neural network, variable learning rate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 50497915 Derivative Spectrophotometry Applied to the Determination of Triprolidine Hydrochloride and Pseudoephedrine Hydrochloride in Tablets and Dissolution Testing
Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj
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A spectrophotometric method was developed for simultaneous quantification of pseudoephedrine hydrochloride (PSE) triprolidine hydrochloride (TRI) using second derivative method (zero-crossing technique). The second derivative amplitudes of PSE and TRI were measured at 271 and 321 nm, respectively. The calibration curves were linear in the range of 200 to 1,000 g/ml for PSE and 10 to 50 g/ml for TRI. The method was validated for specificity, accuracy, precision, limit of detection and limit of quantitation. The proposed method was applied to the assaying and dissolution of PSE and TRI in commercial tablets without any chemical separation. The results were compared with those obtained by the official USP31 method and statistical tests showed that there is no significant between the methods at 95% confidence level. The proposed method is simple, rapid and suitable for the routine quality control application. KeywordsTriprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.
Keywords: Triprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22517914 Terminal Wiener Index for Graph Structures
Authors: J. Baskar Babujee, J. Senbagamalar,
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The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i Keywords:
Graph,
Degree,
Distance,
Pendent vertex,
Wiener index,
Tree.
7913 Parameters Identification of Mathematical Model of the Fission Yeast Cell Cycle Control Using Evolutionary Strategy
Authors: A. Ghaffari, A. S. Mostafavi
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Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, mitosis and cell division. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks that control the activities of cyclin-dependent kinases (CDK). The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. In this paper, an innovative approach has been proposed that uses genetic algorithms to mine a set of behavior data output by a biological system in order to determine the kinetic parameters of the system. In our approach, the machine learning method is integrated with the framework of existent biological information in a wiring diagram so that its findings are expressed in a form of system dynamic behavior. By numerical simulations it has been illustrated that the model is consistent with experiments and successfully shown that such application of genetic algorithms will highly improve the performance of mathematical model of the cell division cycle to simulate such a complicated bio-system.Keywords: Cell cycle, Cyclin-dependent kinase, Fission yeast, Genetic algorithms, Mathematical modeling, Wiring diagram
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15077912 Statistical Properties and Performance of Ecological Indices Based On Relative Abundances
Authors: Gebriel M. Shamia
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The Improved Generalized Diversity Index (IGDI) has been proposed as a tool that can be used to identify areas that have high conservation value and measure the ecological condition of an area. IGDI is based on the species relative abundances. This paper is concerned with particular attention is given to comparisons involving the MacArthur model of species abundances. The properties and performance of various species indices were assessed. Both IGDI and species richness increased with sampling area according to a power function. IGDI were also found to be acceptable ecological indicators of conditions and consistently outperformed coefficient of conservatism indices.Keywords: Statistical ecology, MacArthur model, Functional Diversity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20287911 An Efficient Method for Load−Flow Solution of Radial Distribution Networks
Authors: Smarajit Ghosh , Karma Sonam Sherpa
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This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.
Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 57077910 Simplex Method for Fuzzy Variable Linear Programming Problems
Authors: S.H. Nasseri, E. Ardil
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Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.
Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3351