Search results for: Perturbation Theory for Linear Operators
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3528

Search results for: Perturbation Theory for Linear Operators

1488 Boundary-Element-Based Finite Element Methods for Helmholtz and Maxwell Equations on General Polyhedral Meshes

Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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1487 Estimating an Optimal Neighborhood Size in the Spherical Self-Organizing Feature Map

Authors: Alexandros Leontitsis, Archana P. Sangole

Abstract:

This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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1486 Research Regarding Resistance Characteristics of Biscuits Assortment Using Cone Penetrometer

Authors: G.–A. Constantin, G. Voicu, E.–M. Stefan, P. Tudor, G. Paraschiv, M.–G. Munteanu

Abstract:

In the activity of handling and transport of food products, the products may be subjected to mechanical stresses that may lead to their deterioration by deformation, breaking, or crushing. This is the case for biscuits, regardless of their type (gluten-free or sugary), the addition of ingredients or flour from which they are made. However, gluten-free biscuits have a higher mechanical resistance to breakage or crushing compared to easily shattered sugar biscuits (especially those for children). The paper presents the results of the experimental evaluation of the texture for four varieties of commercial biscuits, using the penetrometer equipped with needle cone at five different additional weights on the cone-rod. The assortments of biscuits tested in the laboratory were Petit Beurre, Picnic, and Maia (all three manufactured by RoStar, Romania) and Sultani diet biscuits, manufactured by Eti Burcak Sultani (Turkey, in packs of 138 g). For the four varieties of biscuits and the five additional weights (50, 77, 100, 150 and 177 g), the experimental data obtained were subjected to regression analysis in the MS Office Excel program, using Velon's relationship (h = a∙ln(t) + b). The regression curves were analysed comparatively in order to identify possible differences and to highlight the variation of the penetration depth h, in relation to the time t. Based on the penetration depth between two-time intervals (every 5 seconds), the curves of variation of the penetration speed in relation to time were then drawn. It was found that Velon's law verifies the experimental data for all assortments of biscuits and for all five additional weights. The correlation coefficient R2 had in most of the analysed cases values over 0.850. The values recorded for the penetration depth were framed, in general, within 45-55 p.u. (penetrometric units) at an additional mass of 50 g, respectively between 155-168 p.u., at an additional mass of 177 g, at Petit Beurre biscuits. For Sultani diet biscuits, the values of the penetration depth were within the limits of 32-35 p.u., at an additional weight of 50 g and between 80-114 p.u., at an additional weight of 177g. The data presented in the paper can be used by both operators on the manufacturing technology flow, as well as by the traders of these food products, in order to establish the most efficient parametric of the working regimes (when packaging and handling).

Keywords: Biscuits resistance/texture, penetration depth, penetration velocity, sharp pin penetrometer.

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1485 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.

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1484 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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1483 Analysis of Electrical Networks Using Phasors: A Bond Graph Approach

Authors: Israel Núñez-Hernández, Peter C. Breedveld, Paul B. T. Weustink, Gilberto Gonzalez-A

Abstract:

This paper proposes a phasor representation of electrical networks by using bond graph methodology. A so-called phasor bond graph is built up by means of two-dimensional bonds, which represent the complex plane. Impedances or admittances are used instead of the standard bond graph elements. A procedure to obtain the steady-state values from a phasor bond graph model is presented. Besides the presentation of a phasor bond graph library in SIDOPS code, also an application example is discussed.

Keywords: Bond graphs, phasor theory, steady-state, complex power, electrical networks.

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1482 Static Study of Piezoelectric Bimorph Beams with Delamination Zone

Authors: A. Zemirline, M. Ouali, A. Mahieddine

Abstract:

The FOSDT (the First Order Shear Deformation Theory) is taking into consideration to study the static behavior of a bimorph beam, with a delamination zone between the upper and the lower layer. The effect of limit conditions and lengths of the delamination zone are presented in this paper, with a PVDF piezoelectric material application. A FEM “Finite Element Method” is used to discretize the beam. In the axial displacement, a displacement field appears in the debonded zone with inverse effect between the upper and the lower layer was observed.

Keywords: Beam, Delamination, Piezoelectricity, Static.

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1481 Building a Trend Based Segmentation Method with SVR Model for Stock Turning Detection

Authors: Jheng-Long Wu, Pei-Chann Chang, Yi-Fang Pan

Abstract:

This research focus on developing a new segmentation method for improving forecasting model which is call trend based segmentation method (TBSM). Generally, the piece-wise linear representation (PLR) can finds some of pair of trading points is well for time series data, but in the complicated stock environment it is not well for stock forecasting because of the stock has more trends of trading. If we consider the trends of trading in stock price for the trading signal which it will improve the precision of forecasting model. Therefore, a TBSM with SVR model used to detect the trading points for various stocks of Taiwanese and America under different trend tendencies. The experimental results show our trading system is more profitable and can be implemented in real time of stock market

Keywords: Trend based segmentation method, support vector machine, turning detection, stock forecasting.

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1480 Effect of Substituent on Titanocene/MMAO Catalyst for Ethylene/1-Hexene Copolymerization

Authors: M. Wannaborworn, B. Jongsomjit, T. Shiono

Abstract:

Copolymerization of ethylene with 1-hexene was carried out using two ansa-fluorenyl titanium derivative complexes. The substituent effect on the catalytic activity, monomer reactivity ratio and polymer property was investigated. It was found that the presence of t-Bu groups on fluorenyl ring exhibited remarkable catalytic activity and produced polymer with high molecular weight. However, these catalysts produce polymer with narrow molecular weight distribution, indicating the characteristic of single-site metallocene catalyst. Based on 13C NMR, we can observe that monomer reactivity ratio was affected by catalyst structure. The rH values of complex 2 were lower than that of complex 1 which might be result from the higher steric hindrance leading to a reduction of 1- hexene insertion step.

Keywords: Constrained geometry catalyst, linear low density polyethylene, copolymerization, reactivity ratio

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1479 Influence Maximization in Dynamic Social Networks and Graphs

Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

Abstract:

Influence and influence diffusion have been studied extensively in social networks. However, most existing literature on this task are limited on static networks, ignoring the fact that the interactions between users change over time. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time is studied. The DM algorithm is an extension of Matrix Influence (MATI) algorithm and solves the Influence Maximization (IM) problem in dynamic networks and is proposed under the Linear Threshold (LT) and Independent Cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: Influence maximization, dynamic social networks, diffusion, social influence.

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1478 Relationship between Food Resources and Brooding Site by Asiatic Houbara (Chlamydotis macqueenii ) in Central Steppe of Iran

Authors: S. Aghainajafi Zadeh, M.R. Hemami., F. Heydari

Abstract:

Knowledge of food resource of the houbara which an endangered species would be a important step toward the preservation of this bird. Adequate study has not been done in this field and therefore the food sources of the houbara during the brooding season was studied in the central steppe of Iran. In order to determine the density of insect in plant communities the pitfall trap was used , positioned in five linear transects divided between plant communities and in two repetitions. The results showed that the among communities there was a significant difference in term of the number beetles and ants ( p= 0.01, F2, 29= 4.66) collectively. Also bush steppe habitat had a higher arthropoda density in comparison with the shrub steppe habitat. Considering that most houbara nests were found in the bush steppe habitat .It seems this habitat provides the most available food supply for the houbara chicks.

Keywords: Asiatic houbara bustard, Brooding season, Food resource

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1477 Investigation on the Stability of Rock Slopes Subjected to Tension Cracks via Limit Analysis

Authors: W. Wu, S. Utili

Abstract:

Based on the kinematic approach of limit analysis, a full set of upper bound solutions for the stability of homogeneous rock slopes subjected to tension cracks are obtained. The generalized Hoek-Brown failure criterion is employed to describe the non-linear strength envelope of rocks. In this paper, critical failure mechanisms are determined for cracks of known depth but unspecified location, cracks of known location but unknown depth, and cracks of unspecified location and depth. It is shown that there is a nearly up to 50% drop in terms of the stability factors for the rock slopes intersected by a tension crack compared with intact ones. Tables and charts of solutions in dimensionless forms are presented for ease of use by practitioners.

Keywords: Hoek-Brown failure criterion, limit analysis, rock slope, tension cracks.

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1476 Equalization Algorithms for MIMO System

Authors: Said Elkassimi, Said Safi, B. Manaut

Abstract:

In recent years, multi-antenna techniques are being considered as a potential solution to increase the flow of future wireless communication systems. The objective of this article is to study the emission and reception system MIMO (Multiple Input Multiple Output), and present the different reception decoding techniques. First we will present the least complex technical, linear receivers such as the zero forcing equalizer (ZF) and minimum mean squared error (MMSE). Then a nonlinear technique called ordered successive cancellation of interferences (OSIC) and the optimal detector based on the maximum likelihood criterion (ML), finally, we simulate the associated decoding algorithms for MIMO system such as ZF, MMSE, OSIC and ML, thus a comparison of performance of these algorithms in MIMO context.

Keywords: Multiple Input Multiple Outputs (MIMO), ZF, MMSE, Ordered Interference Successive Cancellation (OSIC), ML, Interference Successive Cancellation (SIC).

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1475 Why We Are Taller in the Morning than Going to Bed at Night – An in vivo and in vitro Study

Authors: Harcharan Singh Ranu

Abstract:

Intradiscal and intervertebral pressure transducers were developed. They were used to map the pressures in the nucleus and within the annulus of the human spinal segments. Their stressrelaxation were recorded over a period of time for nucleus pressure, applied load, and peripherial strain against time. The results show that for normal discs, pressures in the nucleus are viscoelastic in nature with the applied compressive load. Mechanical strains which develop around the periphery of the vertebral body are also viscoelastic with the applied compressive load. Applied compressive load against time also shows viscoelastic behavior. However, annulus does not respond viscoelastically with the applied load. It showed a linear response to compressive loading.

Keywords: Intradiscal pressure transducer (IDPT), intervertebral pressure transducer (IVPT), mechanical strains of vertebral bone, viscoelasticity of human spinal disc.

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1474 2n Positive Periodic Solutions to n Species Non-autonomous Lotka-Volterra Competition Systems with Harvesting Terms

Authors: Yongkun Li, Kaihong Zhao

Abstract:

By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.

Keywords: Positive periodic solutions, Lotka-Volterra competition system, coincidence degree, harvesting term.

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1473 Comparative Finite Element Simulation of Nonlinear Vibrations and Sensor Output Voltage of Smart Piezolaminated Structures

Authors: Ruediger Schmidt, Thang Duy Vu

Abstract:

Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.

Keywords: Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.

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1472 Application of l1-Norm Minimization Technique to Image Retrieval

Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

Abstract:

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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1471 A Source Point Distribution Scheme for Wave-Body Interaction Problem

Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

Abstract:

A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: Source point distribution, panel method, Rankine source, desingularized algorithm.

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1470 Numerical Simulation and Experimental Validation of the Tire-Road Separation in Quarter-Car Model

Authors: Quy Dang Nguyen, Reza Nakhaie Jazar

Abstract:

The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.

Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.

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1469 Kuehne + Nagel's PharmaChain: IoT-Enabled Product Monitoring Using Radio Frequency Identification

Authors: Rebecca Angeles

Abstract:

This case study features the Kuehne + Nagel PharmaChain solution for ‘cold chain’ pharmaceutical and biologic product shipments with IOT-enabled features for shipment temperature and location tracking. Using the case study method and content analysis, this research project investigates the application of the structurational model of technology theory introduced by Orlikowski in order to interpret the firm’s entry and participation in the IOT-impelled marketplace.

Keywords: Internet of things, IoT, radio frequency identification, supply chain management, business intelligence.

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1468 On the Robust Stability of Homogeneous Perturbed Large-Scale Bilinear Systems with Time Delays and Constrained Inputs

Authors: Chien-Hua Lee, Cheng-Yi Chen

Abstract:

The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.

Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.

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1467 pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

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1466 Iron Doped Biomaterial Calcium Borate: Synthesis and Characterization

Authors: G. Çelik Gül, F. Kurtuluş

Abstract:

Colemanite is the most common borate mineral, and the main source of the boron required by plants, human, and earth. Transition metals exhibit optical and physical properties such as; non-linear optical character, structural diversity, thermal stability, long cycle life and luminescent radiation. The doping of colemanite with a transition metal, bring it very interesting and attractive properties which make them applicable in industry. Iron doped calcium borate was synthesized by conventional solid state method at 1200 °C for 12 h with a systematic pathway. X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy/energy dispersive analyze (SEM/EDS) were used to characterize structural and morphological properties. Also, thermal properties were recorded by thermogravimetric-differential thermal analysis (TG/DTA). 

Keywords: Colemanite, conventional synthesis, powder x-ray diffraction, borates.

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1465 An Improved Algorithm of SPIHT based on the Human Visual Characteristics

Authors: Meng Wang, Qi-rui Han

Abstract:

Because of excellent properties, people has paid more attention to SPIHI algorithm, which is based on the traditional wavelet transformation theory, but it also has its shortcomings. Combined the progress in the present wavelet domain and the human's visual characteristics, we propose an improved algorithm based on human visual characteristics of SPIHT in the base of analysis of SPIHI algorithm. The experiment indicated that the coding speed and quality has been enhanced well compared to the original SPIHT algorithm, moreover improved the quality of the transmission cut off.

Keywords: Lifted wavelet transform, SPIHT, Human Visual Characteristics.

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1464 Enhancement of a 3D Sound Using Psychoacoustics

Authors: Kyosik Koo, Hyungtai Cha

Abstract:

Generally, in order to create 3D sound using binaural systems, we use head related transfer functions (HRTF) including the information of sounds which is arrived to our ears. But it can decline some three-dimensional effects in the area of a cone of confusion between front and back directions, because of the characteristics of HRTF. In this paper, we propose a new method to use psychoacoustics theory that reduces the confusion of sound image localization. In the method, HRTF spectrum characteristic is enhanced by using the energy ratio of the bark band. Informal listening tests show that the proposed method improves the front-back sound localization characteristics much better than the conventional methods

Keywords: HRTF, 3D sound, Psychoacoustics, Localization

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1463 Voltage Stability Enhancement Using Cat Swarm Optimization Algorithm

Authors: P. Suryakumari, P. Kantarao

Abstract:

Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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1462 Advanced ILQ Control for Buck-Converter viaTwo-Degrees of Freedom Servo-System

Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

Abstract:

In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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1461 Improved Tropical Wood Species Recognition System based on Multi-feature Extractor and Classifier

Authors: Marzuki Khalid, RubiyahYusof, AnisSalwaMohdKhairuddin

Abstract:

An automated wood recognition system is designed to classify tropical wood species.The wood features are extracted based on two feature extractors: Basic Grey Level Aura Matrix (BGLAM) technique and statistical properties of pores distribution (SPPD) technique. Due to the nonlinearity of the tropical wood species separation boundaries, a pre classification stage is proposed which consists ofKmeans clusteringand kernel discriminant analysis (KDA). Finally, Linear Discriminant Analysis (LDA) classifier and KNearest Neighbour (KNN) are implemented for comparison purposes. The study involves comparison of the system with and without pre classification using KNN classifier and LDA classifier.The results show that the inclusion of the pre classification stage has improved the accuracy of both the LDA and KNN classifiers by more than 12%.

Keywords: Tropical wood species, nonlinear data, featureextractors, classification

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1460 Stability and Bifurcation Analysis of a Discrete Gompertz Model with Time Delay

Authors: Yingguo Li

Abstract:

In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark- Sacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis.

Keywords: Gompertz system, Neimark-Sacker bifurcation, stability, time delay.

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1459 Optimal Relaxation Parameters for Obtaining Efficient Iterative Methods for the Solution of Electromagnetic Scattering Problems

Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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