Search results for: Sinc Numerical Methods
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5997

Search results for: Sinc Numerical Methods

4257 PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays

Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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4256 Production of High-Content Fructo-Oligosaccharides

Authors: C. Nobre, C. C. Castro, A.-L. Hantson, J. A. Teixeira, L. R. Rodrigues, G. De Weireld

Abstract:

Fructo-oligosaccharides (FOS) are produced from sucrose by Aureobasidium pullulans in yields between 40-60% (w/w). To increase the amount of FOS it is necessary to remove the small, non-prebiotic sugars, present. Two methods for producing high-purity FOS have been developed: the use of microorganisms able to consume small saccharides; and the use of continuous chromatography to separate sugars: simulated moving bed (SMB). It is herein proposed the combination of both methods. The aim of this study is to optimize the composition of the fermentative broth (in terms of salts and sugars) that will be further purified by SMB. A yield of 0.63 gFOS.gSucrose^-1 was obtained with A. pullulans using low amounts of salts in the initial fermentative broth. By removing the small sugars, Saccharomyces cerevisiae and Zymomonas mobilis increased the percentage of FOS from around 56.0% to 83% (w/w) in average, losing only 10% (w/w) of FOS during the recovery process.

Keywords: Fructo-oligosaccharides, microbial treatment, Saccharomyces cerevisiae, Zymomonas mobilis.

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4255 Application of Smooth Ergodic Hidden Markov Model in Text to Speech Systems

Authors: Armin Ghayoori, Faramarz Hendessi, Asrar Sheikh

Abstract:

In developing a text-to-speech system, it is well known that the accuracy of information extracted from a text is crucial to produce high quality synthesized speech. In this paper, a new scheme for converting text into its equivalent phonetic spelling is introduced and developed. This method is applicable to many applications in text to speech converting systems and has many advantages over other methods. The proposed method can also complement the other methods with a purpose of improving their performance. The proposed method is a probabilistic model and is based on Smooth Ergodic Hidden Markov Model. This model can be considered as an extension to HMM. The proposed method is applied to Persian language and its accuracy in converting text to speech phonetics is evaluated using simulations.

Keywords: Hidden Markov Models, text, synthesis.

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4254 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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4253 Make Up Flash: Web Application for the Improvement of Physical Appearance in Images Based on Recognition Methods

Authors: Stefania Arguelles Reyes, Octavio José Salcedo Parra, Alberto Acosta López

Abstract:

This paper presents a web application for the improvement of images through recognition. The web application is based on the analysis of picture-based recognition methods that allow an improvement on the physical appearance of people posting in social networks. The basis relies on the study of tools that can correct or improve some features of the face, with the help of a wide collection of user images taken as reference to build a facial profile. Automatic facial profiling can be achieved with a deeper study of the Object Detection Library. It was possible to improve the initial images with the help of MATLAB and its filtering functions. The user can have a direct interaction with the program and manually adjust his preferences.

Keywords: Application, MATLAB, make up, model, recognition.

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4252 Hydrothermal Alteration Zones Identification Based on Remote Sensing Data in the Mahin Area, West of Qazvin Province, Iran

Authors: R. Nouri, M.R. Jafari, M. Arain., F. Feizi

Abstract:

The Mahin area is a part of Tarom- Hashtjin zone that located in west of Qazvin province in northwest of Iran. Many copper and base metals ore deposits are hosted by this zone. High potential localities identification in this area is very necessary. The objective of this research, is finding hydrothermal alteration zones by remote sensing methods and best processing technique of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data. Different methods such as band ratio, Principal Component Analysis (PCA), Minimum Noise Fraction (MNF) and Least Square Fit (LS-Fit) were used for mapping hydrothermal alteration zones.

Keywords: Hydrothermal alteration, Iran, Mahin, Remote sensing

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4251 HOPF Bifurcation of a Predator-prey Model with Time Delay and Habitat Complexity

Authors: Li Hongwei

Abstract:

In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as  crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.

Keywords: Predator-prey system, delay, habitat complexity, HOPF bifurcation.

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4250 Allocation of Mobile Units in an Urban Emergency Service System

Authors: Dimitra Alexiou

Abstract:

In an urban area the location allocation of emergency services mobile units, such as ambulances, police patrol cars must be designed so as to achieve a prompt response to demand locations. In this paper the partition of a given urban network into distinct sub-networks is performed such that the vertices in each component are close and simultaneously the sums of the corresponding population in the sub-networks are almost uniform. The objective here is to position appropriately in each sub-network a mobile emergency unit in order to reduce the response time to the demands. A mathematical model in framework of graph theory is developed. In order to clarify the corresponding method a relevant numerical example is presented on a small network.

Keywords: Distances, Emergency Service, Graph Partition, location.

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4249 Measuring of Urban Sustainability in Town Planners Practice

Authors: J. Zagorskas, I. Veteikyte

Abstract:

Physical urban form is recognized to be the media for human transactions. It directly influences the travel demand of people in a specific urban area and the amount of energy used for transportation. Distorted, sprawling form often creates sustainability problems in urban areas. It is declared in EU strategic planning documents that compact urban form and mixed land use pattern must be given the main focus to achieve better sustainability in urban areas, but the methods to measure and compare these characteristics are still not clear. This paper presents the simple methods to measure the spatial characteristics of urban form by analyzing the location and distribution of objects in an urban environment. The extended CA (cellular automata) model is used to simulate urban development scenarios.

Keywords: Cellular automata (CA), Mixed used planning, Spatial analysis, Urban compactness, Geographic information systems (GIS).

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4248 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

Authors: J. Sulaiman, M. Othman, M. K. Hasan

Abstract:

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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4247 Performance Analysis of Genetic Algorithm with kNN and SVM for Feature Selection in Tumor Classification

Authors: C. Gunavathi, K. Premalatha

Abstract:

Tumor classification is a key area of research in the field of bioinformatics. Microarray technology is commonly used in the study of disease diagnosis using gene expression levels. The main drawback of gene expression data is that it contains thousands of genes and a very few samples. Feature selection methods are used to select the informative genes from the microarray. These methods considerably improve the classification accuracy. In the proposed method, Genetic Algorithm (GA) is used for effective feature selection. Informative genes are identified based on the T-Statistics, Signal-to-Noise Ratio (SNR) and F-Test values. The initial candidate solutions of GA are obtained from top-m informative genes. The classification accuracy of k-Nearest Neighbor (kNN) method is used as the fitness function for GA. In this work, kNN and Support Vector Machine (SVM) are used as the classifiers. The experimental results show that the proposed work is suitable for effective feature selection. With the help of the selected genes, GA-kNN method achieves 100% accuracy in 4 datasets and GA-SVM method achieves in 5 out of 10 datasets. The GA with kNN and SVM methods are demonstrated to be an accurate method for microarray based tumor classification.

Keywords: F-Test, Gene Expression, Genetic Algorithm, k- Nearest-Neighbor, Microarray, Signal-to-Noise Ratio, Support Vector Machine, T-statistics, Tumor Classification.

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4246 Buckling Analysis of a Five-walled CNT with Nonlocal Theory

Authors: Alireza Bozorgian, Navid Majdi Nasab, Abdolreza Memari

Abstract:

A continuum model is presented to study vdW interaction on buckling analysis of multi-walled walled carbon nanotube. In previous studies, only the vdW interaction between adjacent two layers was considered and the vdW interaction between the other two layers was neglected. The results show that the vdW interaction cofficients are dependent on the change of interlayer spacing and the radii of tubes. With increase of radii the vdW coefficients approach a constant value. The numerical results show that the effect of vdW interaction on the critical strain for a doublewalled CNT is negligible when the radius is large enough for the both the cases of before and after buckling.

Keywords: Buckling, Carbon nanotube, van der Waals interaction, Multi-walled Carbon nanotube, Critical Strain, Prebuckling Pressure

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4245 Analytical Solutions of Three Dimensional Steady-State Heat Transfer in Rectangular Ribs

Authors: Tao Nie, Weiqiang Liu

Abstract:

In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.

Keywords: variable separation method, analytical solution, rib, heat transfer

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4244 Fuzzy Predictive Pursuit Guidance in the Homing Missiles

Authors: Mustafa Resa Becan, Ahmet Kuzucu

Abstract:

A fuzzy predictive pursuit guidance is proposed as an alternative to the conventional methods. The purpose of this scheme is to obtain a stable and fast guidance. The noise effects must be reduced in homing missile guidance to get an accurate control. An aerodynamic missile model is simulated first and a fuzzy predictive pursuit control algorithm is applied to reduce the noise effects. The performance of this algorithm is compared with the performance of the classical proportional derivative control. Stability analysis of the proposed guidance method is performed and compared with the stability properties of other guidance methods. Simulation results show that the proposed method provides the satisfying performance.

Keywords: Fuzzy, noise effect, predictive, pursuit.

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4243 Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

Authors: K. M. Alsager, N. O. Alshehri

Abstract:

In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

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4242 3D Quantum Numerical Simulation of Horizontal Rectangular Dual Metal Gate\Gate All Around MOSFETs

Authors: M. Khaouani, A. Guen-Bouazza, B. Bouazza, Z. Kourdi

Abstract:

The integrity and issues related to electrostatic performance associated with scaling Si MOSFET bulk sub 10nm channel length promotes research in new device architectures such as SOI, double gate and GAA MOSFET. In this paper, we present some novel characteristic of horizontal rectangular gate\gate all around MOSFETs with dual metal of gate we obtained using SILVACO TCAD tools. We will also exhibit some simulation results we obtained relating to the influence of some parameters variation on our structure, that having a direct impact on their threshold voltage and drain current. In addition, our TFET showed reasonable ION/IOFF ratio of (104) and low drain induced barrier lowering (DIBL) of 39 mV/V.

Keywords: GAA, SILVACO, QUANTUM, MOSFETs.

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4241 Cognitive SATP for Airborne Radar Based on Slow-Time Coding

Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu

Abstract:

Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.

Keywords: Space-time adaptive processing (STAP), signal-to-clutter ratio, slow-time coding.

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4240 Harvesting of Kinetic Energy of the Raindrops

Authors: K. C. R. Perera, B. G. Sampath, V. P. C. Dassanayake, B. M. Hapuwatte.

Abstract:

This paper presents a methodology to harvest the kinetic energy of the raindrops using piezoelectric devices. In the study 1m×1m PVDF (Polyvinylidene fluoride) piezoelectric membrane, which is fixed by the four edges, is considered for the numerical simulation on deformation of the membrane due to the impact of the raindrops. Then according to the drop size of the rain, the simulation is performed classifying the rainfall types into three categories as light stratiform rain, moderate stratiform rain and heavy thundershower. The impact force of the raindrop is dependent on the terminal velocity of the raindrop, which is a function of raindrop diameter. The results were then analyzed to calculate the harvestable energy from the deformation of the piezoelectric membrane.

Keywords: Raindrop, piezoelectricity, deformation, terminal velocity.

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4239 Multimethod Approach to Research in Interlanguage Pragmatics

Authors: Saad Al-Gahtani, Ghassan H Al Shatter

Abstract:

Argument over the use of particular method in interlanguage pragmatics has increased recently. Researchers argued the advantages and disadvantages of each method either natural or elicited. Findings of different studies indicated that the use of one method may not provide enough data to answer all its questions. The current study investigated the validity of using multimethod approach in interlanguage pragmatics to understand the development of requests in Arabic as a second language (Arabic L2). To this end, the study adopted two methods belong to two types of data sources: the institutional discourse (natural data), and the role play (elicited data). Participants were 117 learners of Arabic L2 at the university level, representing four levels (beginners, low-intermediate, highintermediate, and advanced). Results showed that using two or more methods in interlanguage pragmatics affect the size and nature of data.

Keywords: Arabic L2, Development of requests, Interlanguage Pragmatics, Multimethod approach.

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4238 An Efficient Method for Load−Flow Solution of Radial Distribution Networks

Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

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

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4237 Hole Configuration Effect on Turbine Blade Cooling

Authors: A.Hasanpour, M. Farhadi, H.R. Ashorynejad

Abstract:

In this paper a numerical technique is used to predict the metal temperature of a gas turbine vane. The Rising combustor exit temperatures in gas turbine engines necessitate active cooling for the downstream turbine section to avoid thermal failure. This study is performed the solution of external flow, internal convection, and conduction within the metal vane. Also the trade-off between the cooling performances in four different hole shapes and configurations is performed. At first one of the commonly used cooling hole geometry is investigated; cylindrical holes and then two other configurations are simulated. The average temperature magnitude in mid-plan section of each configuration is obtained and finally the lower temperature value is selected such as best arrangement.

Keywords: Forced Convection, Gas Turbine Blade, Hole Configuration

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4236 Application of Genetic Algorithms to Feature Subset Selection in a Farsi OCR

Authors: M. Soryani, N. Rafat

Abstract:

Dealing with hundreds of features in character recognition systems is not unusual. This large number of features leads to the increase of computational workload of recognition process. There have been many methods which try to remove unnecessary or redundant features and reduce feature dimensionality. Besides because of the characteristics of Farsi scripts, it-s not possible to apply other languages algorithms to Farsi directly. In this paper some methods for feature subset selection using genetic algorithms are applied on a Farsi optical character recognition (OCR) system. Experimental results show that application of genetic algorithms (GA) to feature subset selection in a Farsi OCR results in lower computational complexity and enhanced recognition rate.

Keywords: Feature Subset Selection, Genetic Algorithms, Optical Character Recognition.

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4235 Influence of Selected Finishing Technologies on the Roughness Parameters of Stainless Steel Manufactured by Selective Laser Melting Method

Authors: J. Hajnys, M. Pagac, J. Petru, P. Stefek, J. Mesicek, J. Kratochvil

Abstract:

The new progressive method of 3D metal printing SLM (Selective Laser Melting) is increasingly expanded into the normal operation. As a result, greater demands are placed on the surface quality of the parts produced in this way. The article deals with research of selected finishing methods (tumbling, face milling, sandblasting, shot peening and brushing) and their impact on the final surface roughness. The 20 x 20 x 7 mm produced specimens using SLM additive technology on the Renishaw AM400 were subjected to testing of these finishing methods by adjusting various parameters. Surface parameters of roughness Sa, Sz were chosen as the evaluation criteria and profile parameters Ra, Rz were used as additional measurements. Optical measurement of surface roughness was performed on Alicona Infinite Focus 5. An experiment conducted to optimize the surface roughness revealed, as expected, that the best roughness parameters were achieved through a face milling operation. Tumbling is particularly suitable for 3D printing components, as tumbling media are able to reach even complex shapes and, after changing to polishing bodies, achieve a high surface gloss. Surface quality after tumbling depends on the process time. Other methods with satisfactory results are shot peening and tumbling, which should be the focus of further research.

Keywords: Additive manufacturing, selective laser melting, surface roughness, stainless steel.

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4234 Design Optimization for Efficient Erbium-Doped Fiber Amplifiers

Authors: Parekhan M. Aljaff, Banaz O. Rasheed

Abstract:

The exact gain shape profile of erbium doped fiber amplifiers (EDFA`s) are depends on fiber length and Er3 ion densities. This paper optimized several of erbium doped fiber parameters to obtain high performance characteristic at pump wavelengths of λp= 980 nm and λs= 1550 nm for three different pump powers. The maximum gain obtained for pump powers (10, 30 and 50mw) is nearly (19, 30 and 33 dB) at optimizations. The required numerical aperture NA to obtain maximum gain becomes less when pump power increased. The amplifier gain is increase when Er+3doped near the center of the fiber core. The simulation has been done by using optisystem 5.0 software (CAD for Photonics, a license product of a Canadian based company) at 2.5 Gbps.

Keywords: EDFA, Erbium Doped Fiber, optimization OpticalAmplifiers.

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4233 Unsteady Reversed Stagnation-Point Flow over a Flat Plate

Authors: Vai Kuong Sin, Chon Kit Chio

Abstract:

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. ". In this study, we revisit the problem of reversed stagnation-point flow over a flat plate. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. This is no true in neglecting the viscous terms within the total flow field. In particular it is pointed out that for a plate impulsively accelerated from rest to a constant velocity V0 that a similarity solution to the self-similar ODE is obtained which is noteworthy completely analytical.

Keywords: reversed stagnation-point flow, similarity solutions, analytical solution, numerical solution

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4232 New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components

Authors: Xingyuan Qu, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: Delay-dependent stability, time-varying delays, Lyapunov functional, linear matrix inequality (LMI).

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4231 A Neural Approach for Color-Textured Images Segmentation

Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

Abstract:

In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: Segmentation, color-texture, neural networks, fractal, watershed.

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4230 A Sliding Mesh Technique and Compressibility Correction Effects of Two-equation Turbulence Models for a Pintle-Perturbed Flow Analysis

Authors: J. Y. Heo, H. G. Sung

Abstract:

Numerical simulations have been performed for assessment of compressibility correction of two-equation turbulence models suitable for large scale separation flows perturbed by pintle strokes. In order to take into account pintle movement, a sliding mesh method was applied. The chamber pressure, mass flow rate, and thrust have been analyzed, and the response lag and sensitivity at the chamber and nozzle were estimated for a movable pintle. The nozzle performance for pintle reciprocating as its insertion and extraction processes, were analyzed to better understand the dynamic performance of the pintle nozzle.

Keywords: Pintle, sliding mesh, turbulent model, compressibility correction.

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4229 Optimization of Multifunctional Battery Structures for Mars

Authors: James A Foster, Guglielmo S Aglietti

Abstract:

Multifunctional structures are a potentially disruptive technology that allows for significant mass savings on spacecraft. The specific concept addressed herein is that of a multifunctional power structure. In this paper, a parametric optimisation of the design of such a structure that uses commercially available battery cells is presented. Using numerical modelling, it was found that there exists several trade-offs aboutthe conflict between the capacity of the panel and its mechanical properties. It was found that there is no universal optimal location for the cells. Placing them close to the mechanical interfaces increases loading in the mechanically weak cells whereas placing them at the centre of the panel increases the stress inthe panel and reduces the stiffness of the structure.

Keywords: Design Optimization, Multifunctional Structures, Power Storage.

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4228 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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