Search results for: Linear Matrix Inequalities (LMI)

Authors: Chong Wang, Kellem M. Soares, Luis E. Kosteski

Abstract:

The problem of toughening in brittle materials reinforced by fibers is complex, involving all of the mechanical properties of fibers, matrix and the fiber/matrix interface, as well as the geometry of the fiber. Development of new numerical methods appropriate to toughening simulation and analysis is necessary. In this work, we have performed simulations and analysis of toughening in brittle matrix reinforced by randomly distributed fibers by means of the discrete elements method. At first, we put forward a mechanical model of toughening contributed by random fibers. Then with a numerical program, we investigated the stress, damage and bridging force in the composite material when a crack appeared in the brittle matrix. From the results obtained, we conclude that: (i) fibers of high strength and low elasticity modulus are beneficial to toughening; (ii) fibers of relatively high elastic modulus compared to the matrix may result in substantial matrix damage due to spalling effect; (iii) employment of high-strength synthetic fibers is a good option for toughening. We expect that the combination of the discrete element method (DEM) with the finite element method (FEM) can increase the versatility and efficiency of the software developed. The present work can guide the design of ceramic composites of high performance through the optimization of the parameters.

Keywords: Bridging stress, discrete element method, fiber reinforced composites, toughening.

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Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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Authors: Nagasamy Venkatesh Dhandapani

Abstract:

The objective of the present study was to develop sustained release oral matrix tablets of anti epileptic drug levetiracetam. The sustained release matrix tablets of levetiracetam were prepared using hydrophilic matrix hydroxypropyl methylcellulose (HPMC) as a release retarding polymer by wet granulation method. Prior to compression, FTIR studies were performed to understand the compatibility between the drug and excipients. The study revealed that there was no chemical interaction between drug and excipients used in the study. The tablets were characterized by physical and chemical parameters and results were found in acceptable limits. In vitro release study was carried out for the tablets using 0.1 N HCl for 2 hours and in phosphate buffer pH 7.4 for remaining time up to 12 hours. The effect of polymer concentration was studied. Different dissolution models were applied to drug release data in order to evaluate release mechanisms and kinetics. The drug release data fit well to zero order kinetics. Drug release mechanism was found as a complex mixture of diffusion, swelling and erosion.

Keywords: Levetiracetam, sustained-release, hydrophilic matrix tablet, HPMC grade K 100 MCR, wet granulation, zero order release kinetics.

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Authors: Yeongyu Choi, Ju H. Park, S. M. Lee, Ho-Youl Jung

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In this paper, an improved method for estimating fundamental matrix is proposed. The method is applied effectively to monocular camera based moving object detection. The method consists of corner points detection, moving object’s motion estimation and fundamental matrix calculation. The corner points are obtained by using Harris corner detector, motions of moving objects is calculated from pyramidal Lucas-Kanade optical flow algorithm. Through epipolar geometry analysis using RANSAC, the fundamental matrix is calculated. In this method, we have improved the performances of moving object detection by using two threshold values that determine inlier or outlier. Through the simulations, we compare the performances with varying the two threshold values.

Keywords: Corner detection, optical flow, epipolar geometry, RANSAC.

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Authors: Qiuyu Dai, Haochong Zhang, Xiangrong Liu

Abstract:

Efficient matrix-vector multiplication with diagonal sparse matrices is pivotal in a multitude of computational domains, ranging from scientific simulations to machine learning workloads. When encoded in the conventional Diagonal (DIA) format, these matrices often induce computational overheads due to extensive zero-padding and non-linear memory accesses, which can hamper the computational throughput, and elevate the usage of precious compute and memory resources beyond necessity. The ’DIA-Adaptive’ approach, a methodological enhancement introduced in this paper, confronts these challenges head-on by leveraging the advanced parallel instruction sets embedded within Machine Learning Units (MLUs). This research presents a thorough analysis of the DIA-Adaptive scheme’s efficacy in optimizing Sparse Matrix-Vector Multiplication (SpMV) operations. The scope of the evaluation extends to a variety of hardware architectures, examining the repercussions of distinct thread allocation strategies and cluster configurations across multiple storage formats. A dedicated computational kernel, intrinsic to the DIA-Adaptive approach, has been meticulously developed to synchronize with the nuanced performance characteristics of MLUs. Empirical results, derived from rigorous experimentation, reveal that the DIA-Adaptive methodology not only diminishes the performance bottlenecks associated with the DIA format but also exhibits pronounced enhancements in execution speed and resource utilization. The analysis delineates a marked improvement in parallelism, showcasing the DIA-Adaptive scheme’s ability to adeptly manage the interplay between storage formats, hardware capabilities, and algorithmic design. The findings suggest that this approach could set a precedent for accelerating SpMV tasks, thereby contributing significantly to the broader domain of high-performance computing and data-intensive applications.

Keywords: Adaptive method, DIA, diagonal sparse matrices, MLU, sparse matrix-vector multiplication.

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Authors: S. M. Lee, J. H. Park, H. Y. Jung

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This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.

Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.

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Authors: P. Subha Karuvelam, M. Rajaram

Abstract:

Brushless DC motors (BLDC) are widely used in industrial areas. The BLDC motors are driven either by indirect ACAC converters or by direct AC-AC converters. Direct AC-AC converters i.e. matrix converters are used in this paper to drive the three phase BLDC motor and it eliminates the bulky DC link energy storage element. A matrix converter converts the AC power supply to an AC voltage of variable amplitude and variable frequency. A control technique is designed to generate the switching pulses for the three phase matrix converter. For the control of speed of the BLDC motor a separate PI controller and Fuzzy Logic Controller (FLC) are designed and a hysteresis current controller is also designed for the control of motor torque. The control schemes are designed and tested separately. The simulation results of both the schemes are compared and contrasted in this paper. The results show that the fuzzy logic control scheme outperforms the PI control scheme in terms of dynamic performance of the BLDC motor. Simulation results are validated with the experimental results.

Keywords: Fuzzy logic controller, matrix converter, permanent magnet brushless DC motor, PI controller.

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Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand

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Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models, on two different real-world electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.

Keywords: EHR, Machine Learning, imputation, laboratory variables, algorithmic bias.

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Authors: N. Parandin, M. A. Fariborzi Araghi

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in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: Distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor.

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Authors: M. M. Qasaymeh, M. A. Khodeir

Abstract:

Subspace channel estimation methods have been studied widely, where the subspace of the covariance matrix is decomposed to separate the signal subspace from noise subspace. The decomposition is normally done by using either the eigenvalue decomposition (EVD) or the singular value decomposition (SVD) of the auto-correlation matrix (ACM). However, the subspace decomposition process is computationally expensive. This paper considers the estimation of the multipath slow frequency hopping (FH) channel using noise space based method. In particular, an efficient method is proposed to estimate the multipath time delays by applying multiple signal classification (MUSIC) algorithm which is based on the null space extracted by the rank revealing LU (RRLU) factorization. As a result, precise information is provided by the RRLU about the numerical null space and the rank, (i.e., important tool in linear algebra). The simulation results demonstrate the effectiveness of the proposed novel method by approximately decreasing the computational complexity to the half as compared with RRQR methods keeping the same performance.

Keywords: Time Delay Estimation, RRLU, RRQR, MUSIC, LS-ESPRIT, LS-ESPRIT, Frequency Hopping.

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Authors: J. Prakash, K. Rajesh

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In this paper we present a new method for coin identification. The proposed method adopts a hybrid scheme using Eigenvalues of covariance matrix, Circular Hough Transform (CHT) and Bresenham-s circle algorithm. The statistical and geometrical properties of the small and large Eigenvalues of the covariance matrix of a set of edge pixels over a connected region of support are explored for the purpose of circular object detection. Sparse matrix technique is used to perform CHT. Since sparse matrices squeeze zero elements and contain only a small number of non-zero elements, they provide an advantage of matrix storage space and computational time. Neighborhood suppression scheme is used to find the valid Hough peaks. The accurate position of the circumference pixels is identified using Raster scan algorithm which uses geometrical symmetry property. After finding circular objects, the proposed method uses the texture on the surface of the coins called texton, which are unique properties of coins, refers to the fundamental micro structure in generic natural images. This method has been tested on several real world images including coin and non-coin images. The performance is also evaluated based on the noise withstanding capability.

Keywords: Circular Hough Transform, Coin detection, Covariance matrix, Eigenvalues, Raster scan Algorithm, Texton.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Mehran Yazdi, Zahra Adelpour, Batoul Bahraini, Yasaman Keshtkar Jahromi

Abstract:

In this paper we use the property of co-occurrence matrix in finding parallel lines in binary pictures for fingerprint identification. In our proposed algorithm, we reduce the noise by filtering the fingerprint images and then transfer the fingerprint images to binary images using a proper threshold. Next, we divide the binary images into some regions having parallel lines in the same direction. The lines in each region have a specific angle that can be used for comparison. This method is simple, performs the comparison step quickly and has a good resistance in the presence of the noise.

Keywords: Parallel lines detection, co-occurrence matrix, fingerprint identification.

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Authors: B. Z. Manuel, H. D. Esmeralda, H. S. Felipe, D. R. Héctor, D. de la Torre Sebastián, R. L. Diego

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Aluminum Matrix Composites reinforced with nanocrystalline Ni3Al carbon-coated intermetallic particles, were synthesized by powder metallurgy. Powder mixture of aluminum with 0.5-volume fraction of reinforcement particles was compacted by spark plasma sintering (SPS) technique and the compared with conventional sintering process. The better results for SPS technique were obtained in 520ºC-5kN-3min.The hardness (70.5±8 HV) and the elastic modulus (95 GPa) were evaluated in function of sintering conditions for SPS technique; it was found that the incorporation of these kind of reinforcement particles in aluminum matrix improve its mechanical properties. The densities were about 94% and 97% of the theoretical density. The carbon coating avoided the interfacial reaction between matrix-particle at high temperature (520°C) without show composition change either intermetallic dissolution.

Keywords: Aluminum matrix composites, Intermetallics Spark plasma sintering.

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Authors: M.Puviyarasan, C.Praveen

Abstract:

In this study, Friction Stir Processing (FSP) a recent grain refinement technique was employed to disperse micron-sized (2 *m) SiCp particles into aluminum alloy AA6063. The feasibility to fabricate bulk composites through FSP was analyzed and experiments were conducted at different traverse speeds and wider volumes of the specimens. Micro structural observation were carried out by employing optical microscopy test of the cross sections in both parallel and perpendicular to the tool traverse direction. Mechanical property including micro hardness was evaluated in detail at various regions on the specimen. The composites had an excellent bonding with aluminum alloy substrate and a significant increase of 30% in the micro hardness value of metal matrix composite (MMC) as to that of the base metal has observed. The observations clearly indicate that SiC particles were uniformly distributed within the aluminum matrix.

Keywords: Friction Stir Processing, Metal matrix composite, Bulk composite.

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Authors: Armando Calabrese, Roberta Costa, Tamara Menichini, Francesco Rosati

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A company CSR commitment, as stated in its Social Report is, actually, perceived by its stakeholders?And in what measure? Moreover, are stakeholders satisfied with the company CSR efforts? Indeed, business returns from Corporate Social Responsibility (CSR) practices, such as company reputation and customer loyalty, depend heavily on how stakeholders perceive the company social conduct. In this paper, we propose a methodology to assess a company CSR commitment based on Global Reporting Initiative (GRI) indicators, Content Analysis and a CSR positioning matrix. We evaluate three aspects of CSR: the company commitment disclosed through its Social Report; the company commitment perceived by its stakeholders; the CSR commitment that stakeholders require to the company. The positioning of the company under study in the CSR matrix is based on the comparison among the three commitment aspects (disclosed, perceived, required) and it allows assessment and development of CSR strategies.

Keywords: Corporate Social Responsibility (CSR), CSR Positioning Matrix, Global Reporting Initiative (GRI), Stakeholder Orientation

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Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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Authors: Tingting Lu, Yonghai Wang, Haiyong Wang, Jiaqi Liu

Abstract:

To satisfy the need of outfield tests of star sensors, a method is put forward to construct the reference attitude benchmark. Firstly, its basic principle is introduced; Then, all the separate conversion matrixes are deduced, which include: the conversion matrix responsible for the transformation from the Earth Centered Inertial frame i to the Earth-centered Earth-fixed frame w according to the time of an atomic clock, the conversion matrix from frame w to the geographic frame t, and the matrix from frame t to the platform frame p, so the attitude matrix of the benchmark platform relative to the frame i can be obtained using all the three matrixes as the multiplicative factors; Next, the attitude matrix of the star sensor relative to frame i is got when the mounting matrix from frame p to the star sensor frame s is calibrated, and the reference attitude angles for star sensor outfield tests can be calculated from the transformation from frame i to frame s; Finally, the computer program is finished to solve the reference attitudes, and the error curves are drawn about the three axis attitude angles whose absolute maximum error is just 0.25ÔÇ│. The analysis on each loop and the final simulating results manifest that the method by precise timing to acquire the absolute reference attitude is feasible for star sensor outfield tests.

Keywords: Atomic time, attitude determination, coordinate conversion, inertial coordinate system, star sensor.

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Authors: A. Perolini

Abstract:

Feature and model selection are in the center of attention of many researches because of their impact on classifiers- performance. Both selections are usually performed separately but recent developments suggest using a combined GA-SVM approach to perform them simultaneously. This approach improves the performance of the classifier identifying the best subset of variables and the optimal parameters- values. Although GA-SVM is an effective method it is computationally expensive, thus a rough method can be considered. The paper investigates a joined approach of Genetic Algorithm and kernel matrix criteria to perform simultaneously feature and model selection for SVM classification problem. The purpose of this research is to improve the classification performance of SVM through an efficient approach, the Kernel Matrix Genetic Algorithm method (KMGA).

Keywords: Feature and model selection, Genetic Algorithms, Support Vector Machines, kernel matrix.

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Authors: M. Mahli, A.I. Che-Ani, M.Z. Abd-Razak. N.M. Tawil, H. Yahaya

Abstract:

Building condition assessment is a critical activity in Malaysia-s Comprehensive Asset Management Model. It is closely related to building performance that impact user-s life and decision making. This study focuses on public primary school, one of the most valuable assets for the country. The assessment was carried out based on CSP1 Matrix in Kuching Division of Sarawak, Malaysia. Based on the matrix used, three main criteria of the buildings has successfully evaluate: the number of defects; schools rating; and total schools rating. The analysis carried out on 24 schools found that the overall 4, 725 defects has been identified. Meanwhile, the overall score obtained was 45, 868 and the overall rating is 9.71, which is at the fair condition. This result has been associated with building age to evaluate its impacts on school buildings condition. The findings proved that building condition is closely related to building age and its support the theory that 'the ageing building has more defect than the new one'.

Keywords: building condition, CSP1 Matrix, assessment, school, Malaysia

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: E. Ansari-Piri, N. Eghbali

Abstract:

Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: Miaomiao Yang, Shouming Zhong

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This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: V.Manikandan, N.Devarajan

Abstract:

The main objective of this work is to provide a fault detection and isolation based on Markov parameters for residual generation and a neural network for fault classification. The diagnostic approach is accomplished in two steps: In step 1, the system is identified using a series of input / output variables through an identification algorithm. In step 2, the fault is diagnosed comparing the Markov parameters of faulty and non faulty systems. The Artificial Neural Network is trained using predetermined faulty conditions serves to classify the unknown fault. In step 1, the identification is done by first formulating a Hankel matrix out of Input/ output variables and then decomposing the matrix via singular value decomposition technique. For identifying the system online sliding window approach is adopted wherein an open slit slides over a subset of 'n' input/output variables. The faults are introduced at arbitrary instances and the identification is carried out in online. Fault residues are extracted making a comparison of the first five Markov parameters of faulty and non faulty systems. The proposed diagnostic approach is illustrated on benchmark problems with encouraging results.

Keywords: Artificial neural network, Fault Diagnosis, Identification, Markov parameters.

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Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

Abstract:

There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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Authors: Yongxin Yuan

Abstract:

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.

Keywords: approximation, generalized reflexive matrix, generalized anti-reflexive matrix, inverse eigenvalue problem.

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

Abstract:

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: Asymptotic relative efficiency, non-linear rank-based, robust, rank estimates, variogram.

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Authors: Ksenija Dumičić, Anita Čeh Časni, Irena Palić

Abstract:

This paper examines economic and Information and Communication Technology (ICT) development influence on recently increasing Internet purchases by individuals for European Union member states. After a growing trend for Internet purchases in EU27 was noticed, all possible regression analysis was applied using nine independent variables in 2011. Finally, two linear regression models were studied in detail. Conducted simple linear regression analysis confirmed the research hypothesis that the Internet purchases in analyzed EU countries is positively correlated with statistically significant variable Gross Domestic Product per capita (GDPpc). Also, analyzed multiple linear regression model with four regressors, showing ICT development level, indicates that ICT development is crucial for explaining the Internet purchases by individuals, confirming the research hypothesis.

Keywords: European Union, Internet purchases, multiple linear regression model, outlier

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