Search results for: Quaternion linear functional.

Authors: S. N. Deepa, G. Sugumaran

Abstract:

This paper proposes the novel model order formulation scheme to design a discrete PID controller for higher order linear time invariant discrete systems. Modified PSO (MPSO) based model order formulation technique has used to obtain the successful formulated second order system. PID controller is tuned to meet the desired performance specification by using pole-zero cancellation and proposed design procedures. Proposed PID controller is attached with both higher order system and formulated second order system. System specifications are tabulated and closed loop response is observed for stabilization process. The proposed method is illustrated through numerical examples from literature.

Keywords: Discrete PID controller, Model Order Formulation, Modified Particle Swarm Optimization, Pole-Zero Cancellation

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Authors: Parisa Farzaneh, Azade Harati

Abstract:

Mushrooms or macro-fungi, as an important superfood, contain many bioactive compounds, particularly bio-peptides. In this research, mushroom proteins were extracted by buffer or buffer plus salt (0.15 M), along with ultrasound bath to extract the intercellular protein. As a result, the highest amount of proteins in mushrooms were categorized into albumin. Proteins were also hydrolyzed and changed into peptides through endogenous and exogenous proteases, including gastrointestinal enzymes. The potency of endogenous proteases was also higher in Agaricus bisporus than Terfezia claveryi, as their activity ended at 75 for 15 min. The blanching process, endogenous enzymes, the mixture of gastrointestinal enzymes (pepsin-trypsin-α-chymotrypsin or trypsin- α-chymotrypsin) produced the different antioxidant and antibacterial hydrolysates. The peptide fractions produced with different cut-off ultrafilters also had various levels of radical scavenging, lipid peroxidation inhibition, and antibacterial activities. The bio-peptides with the superior bio-activities (less than 3 kD of T. claveryi) were resistance to various environmental conditions (pH and temperatures). Therefore, they are good options to be added in nutraceutical and pharmaceutical preparations or functional foods, even during processing. 

Keywords: Bio-peptides, mushrooms, gastrointestinal enzymes, bioactivities.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

We study the problem of synthesis of lumped sources control for the objects with distributed parameters on the basis of continuous observation of phase state at given points of object. In the proposed approach the phase state space (phase space) is beforehand somehow partitioned at observable points into given subsets (zones). The synthesizing control actions therewith are taken from the class of piecewise constant functions. The current values of control actions are determined by the subset of phase space that contains the aggregate of current states of object at the observable points (in these states control actions take constant values). In the paper such synthesized control actions are called zone control actions. A technique to obtain optimal values of zone control actions with the use of smooth optimization methods is given. With this aim, the formulas of objective functional gradient in the space of zone control actions are obtained.

Keywords: Feedback control, distributed systems, smooth optimization methods, lumped control synthesis.

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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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Authors: Sean Paulsen, Michael Casey

Abstract:

In this work, we present a self-supervised pretraining framework for transformers on functional Magnetic Resonance Imaging (fMRI) data. First, we pretrain our architecture on two self-supervised tasks simultaneously to teach the model a general understanding of the temporal and spatial dynamics of human auditory cortex during music listening. Our pretraining results are the first to suggest a synergistic effect of multitask training on fMRI data. Second, we finetune the pretrained models and train additional fresh models on a supervised fMRI classification task. We observe significantly improved accuracy on held-out runs with the finetuned models, which demonstrates the ability of our pretraining tasks to facilitate transfer learning. This work contributes to the growing body of literature on transformer architectures for pretraining and transfer learning with fMRI data, and serves as a proof of concept for our pretraining tasks and multitask pretraining on fMRI data.

Keywords: Transfer learning, fMRI, self-supervised, brain decoding, transformer, multitask training.

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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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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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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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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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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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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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Authors: R. Tandlich, S. Hoossein, K. A. Tagwira, M. M. Marais, T. A. Ludwig, R. P. Chidziva, M. N. Munodawafa, W. M. Wrench

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Response to the public health-related emergencies is analysed here for a rural university in South Africa. The structure of the designated emergency plan covers all the phases of the disaster management cycle. The plan contains elements of the vulnerability model and the technocratic model of emergency management. The response structures are vertically and horizontally integrated, while the planning contains elements of scenario-based and functional planning. The available number of medical professionals at the Rhodes University, along with the medical insurance rates, makes the staff and students potentially more medically vulnerable than the South African population. The main improvements of the emergency management are required in the tornado response and the information dissemination during health emergencies. The latter should involve the increased use of social media and e-mails, following the Taylor model of communication. Infrastructure must be improved in the telecommunication sector in the face of unpredictable electricity outages.

Keywords: Public health, Rural university, Taylor model of communication.

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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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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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Authors: Yousra M. Zakaria Helmy, Edward H. Smith

Abstract:

Lake Nasser is one of the largest reservoirs in the world. Over 120 million metric tons of sediments are deposited in its dead storage zone every year. The main objective of the present work was to determine the physical and chemical characteristics of Lake Nasser sediments. The sample had a relatively low surface area of 2.9 m2/g which increased more than 3-fold upon chemical activation. The main chemical elements of the raw sediments were C, O and Si with some traces of Al, Fe and Ca. The organic functional groups for the tested sample included O-H, C=C, C-H and C-O, with indications of Si-O and other metal-C and/or metal-O bonds normally associated with clayey materials. Potentiometric titration of the sample in different ionic strength backgrounds revealed an alkaline material with very strong positive surface charge at pH values just a little less than the pH of zero charge which is ~9. Surface interactions of the sediments with the background electrolyte were significant. An advanced surface complexation model was able to capture these effects, employing a single-site approach to represent protolysis reactions in aqueous solution, and to determine the significant surface species in the pH range of environmental interest.

Keywords: Lake Nasser, sediments, surface characterization

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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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Authors: D. Singh, R. Yousefi, M. Boroushaki

Abstract:

Intelligent deep-drawing is an instrumental research field in sheet metal forming. A set of 28 different experimental data have been employed in this paper, investigating the roles of die radius, punch radius, friction coefficients and drawing ratios for axisymmetric workpieces deep drawing. This paper focuses an evolutionary neural network, specifically, error back propagation in collaboration with genetic algorithm. The neural network encompasses a number of different functional nodes defined through the established principles. The input parameters, i.e., punch radii, die radii, friction coefficients and drawing ratios are set to the network; thereafter, the material outputs at two critical points are accurately calculated. The output of the network is used to establish the best parameters leading to the most uniform thickness in the product via the genetic algorithm. This research achieved satisfactory results based on demonstration of neural networks.

Keywords: Deep-drawing, Neural network, Genetic algorithm, Sheet metal forming.

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Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy

Abstract:

The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.

Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.

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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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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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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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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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Authors: Inês Ramalhete, Hugo Farias, Rui da Silva Pinto

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Adequate housing has been a widely discussed theme in academic circles related to low-cost housing, whereas its physical features are easy to deal with, overcrowding (related to social, cultural and economic aspects) is still ambiguous, particularly regarding the set of indicators that can accurately reflect and measure it. This paper develops research on low-cost housing models for developing countries and what is the best method to embed overcrowding as an important parameter for adaptability. A critical review of international overcrowding indicators and their application in two developing countries, Cape Verde and Angola, is presented. The several rationales and the constraints for an accurate assessment of overcrowding are considered, namely baseline data (statistics), which can induce misjudgments, as well as social and cultural factors (such as personal choices of residents). This paper proposes a way to tackle overcrowding through housing adaptability, considering factors such as physical flexibility, functional ambiguity, and incremental expansion schemes. Moreover, a case-study is presented to establish a framework for the theoretical application of the proposed approach.

Keywords: Adaptive housing, low-cost housing, overcrowding.

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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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Authors: Hafizuddin W. Yussof, Syamsutajri S. Bahri, Adam P. Harvey

Abstract:

Strong anion exchange resins with QN+OH-, have the potential to be developed and employed as heterogeneous catalyst for transesterification, as they are chemically stable to leaching of the functional group. Nine different SIERs (SIER1-9) with QN+OH-were prepared by suspension polymerization of vinylbenzyl chloridedivinylbenzene (VBC-DVB) copolymers in the presence of n-heptane (pore-forming agent). The amine group was successfully grafted into the polymeric resin beads through functionalization with trimethylamine. These SIERs are then used as a catalyst for the transesterification of triacetin with methanol. A set of differential equations that represents the Langmuir-Hinshelwood-Hougen- Watson (LHHW) and Eley-Rideal (ER) models for the transesterification reaction were developed. These kinetic models of LHHW and ER were fitted to the experimental data. Overall, the synthesized ion exchange resin-catalyzed reaction were welldescribed by the Eley-Rideal model compared to LHHW models, with sum of square error (SSE) of 0.742 and 0.996, respectively.

Keywords: Anion exchange resin, Eley-Rideal, Langmuir-Hinshelwood-Hougen-Watson, transesterification.

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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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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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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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Authors: Samy E. Oraby, Ayman M. Alaskari

Abstract:

The importance of machining process in today-s industry requires the establishment of more practical approaches to clearly represent the intimate and severe contact on the tool-chipworkpiece interfaces. Mathematical models are developed using the measured force signals to relate each of the tool-chip friction components on the rake face to the operating cutting parameters in rough turning operation using multilayers coated carbide inserts. Nonlinear modeling proved to have high capability to detect the nonlinear functional variability embedded in the experimental data. While feedrate is found to be the most influential parameter on the friction coefficient and its related force components, both cutting speed and depth of cut are found to have slight influence. Greater deformed chip thickness is found to lower the value of friction coefficient as the sliding length on the tool-chip interface is reduced.

Keywords: Mathematical modeling, Cutting forces, Frictionforces, Friction coefficient and Chip ratio.

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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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