Search results for: matrix approximation

Authors: Zaid Jamal Saeed Almahmoud

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Smart grid is emerging as the future power grid, with smart techniques to optimize power consumption and electricity generation. Minimizing peak power consumption under a fixed delay requirement is a significant problem in the smart grid.For this problem, all appliances must be scheduled within a given finite time duration. We consider the problem of minimizing the peak demand under appliances constraints by scheduling power jobs with uniform release dates and deadlines. As the problem is known to be NP-hard, we analyze the performance of a version of the natural greedy heuristic for solving this problem. Our theoretical analysis and experimental results show that the proposed heuristic outperforms existing methods by providing a better approximation to the optimal solution.

Keywords: peak demand scheduling, approximation algorithms, smart grid, heuristics

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Authors: Anuj Suhag, Rahul Dayal

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Aluminum matrix composites (AMCs) refer to the class of metal matrix composites that are lightweight but high performance aluminum centric material systems. The reinforcement in AMCs could be in the form of continuous/discontinuous fibers, whisker or particulates, in volume fractions. Properties of AMCs can be altered to the requirements of different industrial applications by suitable combinations of matrix, reinforcement and processing route. This work focuses on the fabrication of aluminum alloy (Al6061) matrix composites (AMCs) reinforced with 5 and 3 wt% Al2O3 particulates of 45µm using stir casting route. The aim of the present work is to investigate the effects of process parameters, determined by design of experiments, on microhardness, microstructure, Charpy impact strength, surface roughness and tensile properties of the AMC.

Keywords: aluminium matrix composite, Charpy impact strength test, composite materials, matrix, metal matrix composite, surface roughness, reinforcement

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Authors: Vikram Saini, Lillie Dewan

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This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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Authors: Kai-Sheng Ji, Yi-Feng Lin

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The pervaporation process for solvent and water separation has attracted research attention due to its lower energy consumption compared with conventional distillation processes. The membranes used for the pervaporation approach should exhibit high flux and separation factors. In this study, the ZIF-7 crystal particles were successfully incorporated into chitosan (CS) membranes to form ZIF-7/CS mixed-matrix membranes. The as-prepared ZIF-7/CS mixed-matrix membranes were used to separate mixtures of water/ethanol at 25℃ in the pervaporation process. The mixed-matrix membranes with different ZIF-7 wt% incorporation showed better separation efficiency than the pristine CS membranes because of the smaller pore size of the mixed-matrix membranes. The separation factor and the flux of the ZIF-7/CS membranes clearly exceed the upper limit of the previously reported CS-based and mixed-matrix membranes.

Keywords: pervaporation, chitosan, ZIF-7, memberane separation

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Authors: H. V. Jayaprakash, P. V. Krupakara

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This paper deals with the high corrosion resistance developed by the metal matrix composites when compared with that of matrix alloy by open circuit potential test. Matrix selected is ZA-27 and reinforcement selected is red mud particulates, which is a ceramic material. The composites are prepared using liquid melt metallurgy technique using vortex method. Preheated but uncoated red mud particulates are added to the melt. Metal matrix composites containing 2, 4 and 6 weight percentage of red mud are casted. Matrix was also casted in the same way for comparison. Specimen are fabricated according to ASTM standards. The corrodents used for the tests were 0.025, 0.05 and 0.1 molar sodium hydroxide solutions. They are subjected to Open Circuit Potential studies and weight loss corrosion tests. Corrosion rate was found to be decreased with increase in exposure time in both experiments. Effect of exposure time and presence of increased percentage of reinforcement red mud is discussed in detail.

Keywords: composites, vortex, particulates, red mud

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Nagaraju Jarugu, B. R. Narendra

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This paper focused on boost rectification by Single Phase Matrix Converter with fewer numbers of switches. The conventional matrix converter consists of 4 bidirectional switches, i.e. 8 set of IGBT/MOSFET with anti-parallel diodes. In this proposed matrix converter, only six switches are used. The switch commutation arrangements are also carried out in this work. The SPMC topology has many advantages as a minimal passive device use. It is very flexible and it can be used as a lot of converters. The gate pulses to the switches are provided by the PWM techniques. The duty ratio of the switches based on Pulse Width Modulation (PWM) technique was used to produce the output waveform of the circuit, simply by turning ON and OFF the switches. The simulation results using MATLAB/Simulink were provided to validate the feasibility of this proposed method.

Keywords: single phase matrix converter, reduced switches, AC voltage regulators, boost rectifier operation

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Authors: Boris Melnikov, Ye Zhang, Dmitrii Chaikovskii

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We continue to consider one of the cybernetic methods in computational biology related to the study of DNA chains. Namely, we are considering the problem of reconstructing the not fully filled distance matrix of DNA chains. When applied in a programming context, it is revealed that with a modern computer of average capabilities, creating even a small-sized distance matrix for mitochondrial DNA sequences is quite time-consuming with standard algorithms. As the size of the matrix grows larger, the computational effort required increases significantly, potentially spanning several weeks to months of non-stop computer processing. Hence, calculating the distance matrix on conventional computers is hardly feasible, and supercomputers are usually not available. Therefore, we started publishing our variants of the algorithms for calculating the distance between two DNA chains; then, we published algorithms for restoring partially filled matrices, i.e., the inverse problem of matrix processing. In this paper, we propose an algorithm for restoring the distance matrix for DNA chains, and the primary focus is on enhancing the algorithms that shape the greedy function within the branches and boundaries method framework.

Keywords: DNA chains, distance matrix, optimization problem, restoring algorithm, greedy algorithm, heuristics

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Guillaume Leduc

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In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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Authors: Emine Tuğba Akyüz

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In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: K. Vinutha

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The stress corrosion resistance of ZA-27 / TiO2 metal matrix composites (MMC’s) in high temperature acidic media has been evaluated using an autoclave. The liquid melt metallurgy technique using vortex method was used to fabricate MMC’s. TiO2 particulates of 50-80 µm in size are added to the matrix. ZA-27 containing 2,4,6 weight percentage of TiO2 are prepared. Stress corrosion tests were conducted by weight loss method for different exposure time, normality and temperature of the acidic medium. The corrosion rates of composites were lower to that of matrix ZA-27 alloy under all conditions.

Keywords: autoclave, MMC’s, stress corrosion, vortex method

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Authors: Sarisa Pinkham, Kanyarat Bussaban

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The research aims to approximate the amount of daily rainfall by using a pixel value data approach. The daily rainfall maps from the Thailand Meteorological Department in period of time from January to December 2013 were the data used in this study. The results showed that this approach can approximate the amount of daily rainfall with RMSE=3.343.

Keywords: daily rainfall, image processing, approximation, pixel value data

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Authors: Ratchada Sopakayang, Gerhard A. Holzapfel

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In this study, a new constitutive model is developed to describe the hyperelastic behavior of collagenous tissues with a parallel arrangement of collagen fibers such as ligaments and tendons. The model is formulated using a continuum approach incorporating the structural changes of the main tissue components: collagen fibers, proteoglycan-rich matrix and fiber-matrix interaction. The mechanical contribution of the interaction between the fibers and the matrix is simply expressed by a coupling term. The structural change of the collagen fibers is incorporated in the constitutive model to describe the activation of the fibers under tissue straining. Finally, the constitutive model can easily describe the stress-stretch nonlinearity which occurs when a ligament/tendon is axially stretched. This study shows that the interaction between the fibers and the matrix contributes to the mechanical tissue response. Therefore, the model may lead to a better understanding of the physiological mechanisms of ligaments and tendons under axial loading.

Keywords: constitutive model, fiber-matrix, hyperelasticity, interaction, ligament, tendon

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.

Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter

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Authors: Kourosh Modarresi

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The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry.

Keywords: convex optimization, LASSO, regression, recommender systems, singular value decomposition, low rank approximation

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Authors: Iva Hereitova, Miroslav Svatek, Vit Novacek

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Background and Aim: Autonomic imbalance is one of the complications for immobilized patients in the acute stage after a stroke. The predominance of sympathetic activity significantly increases cardiac activity. The technique of glenohumeral joint approximation may contribute in a non-pharmacological way to the regulation of blood pressure and heart rate in patients in this risk group. The aim of the study was to evaluate the effect of glenohumeral joint approximation on the change in heart rate and blood pressure in immobilized patients in the acute phase after a stroke. Methods: The experimental study bilaterally evaluated heart rate, systolic and diastolic pressure values before and after glenohumeral joint approximation in 40 immobilized participants (72.6 ± 10.2 years) in the acute phase after stroke. The experimental group was compared with 40 healthy participants in the control group (68.6 ± 14.2 years). An SpO2 vital signs monitor and a validated Microlife WatchBP Office blood pressure monitor were used for evaluation. Statistical processing and evaluation were performed in MATLAB R2019 (The Math Works®, Inc., Natick, MA, USA). Results: Approximation of the glenohumeral joint resulted in a statistically significant decrease in systolic and diastolic pressure. An average decrease in systolic pressure for individual groups ranged from 8.2 to 11.3 mmHg (p <0.001). For diastolic pressure, the average decrease ranged from 5.0 - 14.2 mmHg (p <0.001). There was a statistically significant reduction in heart rate (p <0.01) only in patients after ischemic stroke in the inferior cerebral artery. There was the average decrease in heart rate of 3.9 beats per minute (median 4 beats per minute). Conclusion: Approximation of the glenohumeral joint leads to a statistically significant decrease in systolic and diastolic pressure in immobilized patients in the acute phase after stroke.

Keywords: Aproximation technique, Cardiovaskular system, Glenohumeral joint, Stroke

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Authors: Elżbieta Cygan-Bączek, Piotr Wyżga, Sławomir Cygan

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In the presented work, the main goal was to investigate the retention properties, defined as the ability of the matrix material to hold diamond particles in relation to metallized (Ti, Si, Cr, Co, Cu, Ni) and non-metallized diamond crystals. For this purpose, diamond-impregnated specimens were tested for wear rate on abrasive sandstone using a test rig specially designed to simulate tool application conditions. The tests that involved 3- and 2-body abrasion ranked the alloys in different orders. The ability of the matrix to retain diamond crystals was determined using the electron microskopy (SEM, TEM). The specimens were also characterized by X-ray diffraction (XRD) and hardness. The conducted research has shown that Si and Ti metallized diamonds, apart from mechanical jamming in the matrix, are also connected in a metallurgical manner, ensuring the improvement of the retention properties of the matrix material.

Keywords: diamond, metallic-diamond segments, retention, abrasive wear resistance

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Authors: M. E. Turan, H. Zengin, E. Cevik, Y. Sun, Y. Turen, H. Ahlatci

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In this study, the effects of B₄C and SiC particle reinforcements on wear properties of magnesium matrix metal composites produced by pressure infiltration method were investigated. AZ91 (9%Al-1%Zn) magnesium alloy was used as a matrix. AZ91 magnesium alloy was melted under an argon atmosphere. The melt was infiltrated to the particles with an appropriate pressure. Wear tests, hardness tests were performed respectively. Microstructure characterizations were examined by light optical (LOM) and scanning electron microscope (SEM). The results showed that uniform particle distributions were achieved in both B₄C and SiC reinforced composites. Wear behaviors of magnesium matrix metal composites changed as a function of type of particles. SiC reinforced composite has better wear performance and higher hardness than B₄C reinforced composite.

Keywords: magnesium matrix composite, pressure infiltration, SEM, wear

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Authors: Somaye Zare

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The critical beam radius is a significant factor that predicts the behavior of the laser beam in the plasma, so if the laser beam radius is adequately greater in comparison to it, the beam will experience stable focusing on the plasma; otherwise, the beam will diverge after entering into the plasma. In this work, considering the paraxial approximation and moment theories, the localization of a relativistic laser beam in thermal quantum plasma is investigated. Using the dielectric function obtained in the quantum hydrodynamic model, the mathematical equation for the laser beam width parameter is attained and solved numerically by the fourth-order Runge-Kutta method. The results demonstrate that the stouter focusing effect is occurred in the moment theory compared to the paraxial approximation. Besides, similar to the two theories, with increasing Fermi temperature, plasma density, and laser intensity, the oscillation rate of the beam width parameter growths and focusing length reduces which means improving the focusing effect. Furthermore, it is understood that behaviors of the critical laser radius are different in the two theories, in the paraxial approximation, the critical radius after a minimum value is enhanced with increasing laser intensity, but in the moment theory, with increasing laser intensity, the critical radius decreases until it becomes independent of the laser intensity.

Keywords: laser localization, quantum plasma, paraxial approximation, moment theory, quantum hydrodynamic model

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Authors: M. Khajezadeh, M. Saied Fallah Niasar, S. Ali Asli, D. Davani Davari, M. Godarzi, Y. Asgari

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This study aims to explore the joint application of both Boston and Ansoff matrices in the operational development of the product. We conduct deep analysis, by utilizing the Artificial Neural Network, to predict the position of the product in the market while the company is interested in increasing its share. The data are gathered from two industries, called hygiene and detergent. In doing so, the effort is being made by investigating the behavior of top player companies and, recommend strategic orientations. In conclusion, this combination analysis is appropriate for operational development; as well, it plays an important role in providing the position of the product in the market for both hygiene and detergent industries. More importantly, it will elaborate on the company’s strategies to increase its market share related to a combination of the Boston Consulting Group (BCG) Matrix and Ansoff Matrix.

Keywords: artificial neural network, portfolio analysis, BCG matrix, Ansoff matrix

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Authors: Xiaoqian Cheng, Jon Kleppe, Ole Torsæter

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The properties of rocks have effects on efficiency of surfactant. One objective of this study is to analyze the effects of rock properties (permeability, porosity, initial water saturation) on surfactant spontaneous imbibition at laboratory scale. The other objective is to evaluate existing upscaling methods and establish a modified upscaling method. A core is put in a container that is full of surfactant solution. Assume there is no space between the bottom of the core and the container. The core is modelled as a cuboid matrix with a length of 3.5 cm, a width of 3.5 cm, and a height of 5 cm. The initial matrix, brine and oil properties are set as the properties of Ekofisk Field. The simulation results of matrix permeability show that the oil recovery rate has a strong positive linear relationship with matrix permeability. Higher oil recovery is obtained from the matrix with higher permeability. One existing upscaling method is verified by this model. The study on matrix porosity shows that the relationship between oil recovery rate and matrix porosity is a negative power function. However, the relationship between ultimate oil recovery and matrix porosity is a positive power function. The initial water saturation of matrix has negative linear relationships with ultimate oil recovery and enhanced oil recovery. However, the relationship between oil recovery and initial water saturation is more complicated with the imbibition time because of the transition of dominating force from capillary force to gravity force. Modified upscaling methods are established. The work here could be used as a reference for the surfactant application in fractured reservoirs. And the description of the relationships between properties of matrix and the oil recovery rate and ultimate oil recovery helps to improve upscaling methods.

Keywords: initial water saturation, permeability, porosity, surfactant EOR

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Authors: Gak-Gyu Kim, Won Il Jung

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According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Marwane Ben Hcine, Ridha Bouallegue

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The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.

Keywords: LTE, OFDMA, effective SINR, log skew normal approximation

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Authors: Temesgen Takele Kasa

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The main aim of this paper is to suggest one active slip based continuum dislocation approach to matrix dominated MMC plasticity analysis. The approach centered the free energy principles through the continuum behavior of dislocations combined with small strain continuum kinematics. The analytical derivation of this method includes the formulation of one active slip system, the thermodynamic approach of dislocations, determination of free energy, and evolution of dislocations. In addition zero and non-zero energy dissipation analysis of dislocation evolution is also formulated by using varational energy minimization method. In general, this work shows its capability to analyze the plasticity of matrix dominated MMC with inclusions. The proposed method is also found to be capable of handling plasticity of MMC.

Keywords: active slip, continuum dislocation, distortion, dominated, energy dissipation, matrix dominated, plasticity

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Authors: M. Khalfa, H. Khachai, F. Chiker, K. Bougherara, R. Khenata, G. Murtaza, M. Harmel

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A theoretical study of structural, elastic, electronic and thermodynamic properties of Fe2VX, (with X = Al and Ga), were studied by means of the full-relativistic version of the full-potential augmented plane wave plus local orbitals method. For exchange and correlation potential we used both generalized-gradient approximation (GGA) and local-density approximation (LDA). Our calculated ground state properties like as lattice constants, bulk modulus and elastic constants appear more accurate when we employed the GGA rather than the LDA approximation, and these results agree very well with the available experimental and theoretical data. Further, prediction of the thermal effects on some macroscopic properties of Fe2VAl and Fe2VGa are given in this paper using the quasi-harmonic Debye model in which the lattice vibrations are taken into account. We have obtained successfully the variations of the primitive cell volume, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0–40 GPa and 0–1500 K.

Keywords: full Heusler, FP-LAPW, electronic properties, thermal properties

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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Authors: Elham Allahmoradi, Bahman Allahmoradi, Ali Bonyadi Naeini

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Complex systems have many aspects. A variety of methods have been developed to analyze these systems. The most efficient of these methods should not only be simple, but also provide useful and comprehensive information about many aspects of the system. Matrix methods are considered the most commonly methods used to analyze and design systems. Each matrix method can examine a particular aspect of the system. If these methods are combined, managers can access to more comprehensive and broader information about the system. This study was conducted in four steps. In the first step, a process model of a real project has been extracted through IDEF3. In the second step, activity levels have been attained by writing a process model in the form of a design structure matrix (DSM) and sorting it through triangulation algorithm (TA). In the third step, sub-processes have been obtained by writing the process model in the form of an interface structure matrix (ISM) and clustering it through cluster identification algorithm (CIA). In the fourth step, a mixed model has been developed to provide a unified picture of the project structure through the simultaneous presentation of activities and sub-processes. Finally, the paper is completed with a conclusion.

Keywords: integrated definition for process description capture (IDEF3) method, design structure matrix (DSM), interface structure matrix (ism), mixed matrix model, activity level, sub-process

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