Search results for: Linear Quadratic Model

Authors: Manoochehr Gholipoor

Abstract:

The response of growth and yield of rainfed-chickpea to population density should be evaluated based on long-term experiments to include the climate variability. This is achievable just by simulation. In this simulation study, this evaluation was done by running the CYRUS model for long-term daily weather data of five locations in Iran. The tested population densities were 7 to 59 (with interval of 2) stands per square meter. Various functions, including quadratic, segmented, beta, broken linear, and dent-like functions, were tested. Considering root mean square of deviations and linear regression statistics [intercept (a), slope (b), and correlation coefficient (r)] for predicted versus observed variables, the quadratic and broken linear functions appeared to be appropriate for describing the changes in biomass and grain yield, and in harvest index, respectively. Results indicated that in all locations, grain yield tends to show increasing trend with crowding the population, but subsequently decreases. This was also true for biomass in five locations. The harvest index appeared to have plateau state across low population densities, but decreasing trend with more increasing density. The turning point (optimum population density) for grain yield was 30.68 stands per square meter in Isfahan, 30.54 in Shiraz, 31.47 in Kermanshah, 34.85 in Tabriz, and 32.00 in Mashhad. The optimum population density for biomass ranged from 24.6 (in Tabriz) to 35.3 stands per square meter (Mashhad). For harvest index it varied between 35.87 and 40.12 stands per square meter.

Keywords: Rainfed-chickpea, biomass, harvest index, grain yield, simulation.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

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This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Xiang Zhang, David Rey, S. Travis Waller

Abstract:

Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: Parameter calibration, sequential quadratic programming, Stochastic User Equilibrium, traffic assignment, transportation planning.

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Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis

Abstract:

In a particular case of behavioural model reduction by ANNs, a validity domain shortening has been found. In mechanics, as in other domains, the notion of validity domain allows the engineer to choose a valid model for a particular analysis or simulation. In the study of mechanical behaviour for a cantilever beam (using linear and non-linear models), Multi-Layer Perceptron (MLP) Backpropagation (BP) networks have been applied as model reduction technique. This reduced model is constructed to be more efficient than the non-reduced model. Within a less extended domain, the ANN reduced model estimates correctly the non-linear response, with a lower computational cost. It has been found that the neural network model is not able to approximate the linear behaviour while it does approximate the non-linear behaviour very well. The details of the case are provided with an example of the cantilever beam behaviour modelling.

Keywords: artificial neural network, validity domain, cantileverbeam, non-linear behaviour, model reduction.

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Authors: Ahmet Tekcan

Abstract:

In this paper, we derive some algebraic identities on right and left neighbors R(F) and L(F) of an indefinite binary quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant Δ = b2 -4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F.

Keywords: Quadratic form, indefinite form, cycle, proper cycle, right neighbor, left neighbor.

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Authors: Mohd Amaluddin Yusoff

Abstract:

In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to solve the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel.

Keywords: channel equalization filter, Hermite-Rodriguez, pulseshaping filter, quadratic programming.

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Authors: A. Maddi, A. Guessoum, D. Berkani

Abstract:

The purpose of this paper is to provide a practical example to the Linear Quadratic Gaussian (LQG) controller. This method includes a description and some discussion of the discrete Kalman state estimator. One aspect of this optimality is that the estimator incorporates all information that can be provided to it. It processes all available measurements, regardless of their precision, to estimate the current value of the variables of interest, with use of knowledge of the system and measurement device dynamics, the statistical description of the system noises, measurement errors, and uncertainty in the dynamics models. Since the time of its introduction, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. For example, to determine the velocity of an aircraft or sideslip angle, one could use a Doppler radar, the velocity indications of an inertial navigation system, or the relative wind information in the air data system. Rather than ignore any of these outputs, a Kalman filter could be built to combine all of this data and knowledge of the various systems- dynamics to generate an overall best estimate of velocity and sideslip angle.

Keywords: Aircraft motion, Kalman filter, LQG control, Lateral stability, State estimator.

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Authors: Mehdi Nasri, Hossein Nezamabadi-pour, Malihe Maghfoori

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This Paper presents a particle swarm optimization (PSO) method for determining the optimal proportional-integral-derivative (PID) controller parameters, for speed control of a linear brushless DC motor. The proposed approach has superior features, including easy implementation, stable convergence characteristic and good computational efficiency. The brushless DC motor is modelled in Simulink and the PSO algorithm is implemented in MATLAB. Comparing with Genetic Algorithm (GA) and Linear quadratic regulator (LQR) method, the proposed method was more efficient in improving the step response characteristics such as, reducing the steady-states error; rise time, settling time and maximum overshoot in speed control of a linear brushless DC motor.

Keywords: Brushless DC motor, Particle swarm optimization, PID Controller, Optimal control.

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Authors: J. Ritonja

Abstract:

The biochemical technology has been developing extremely fast since the middle of the last century. The main reason for such development represents a requirement for large production of high-quality biologically manufactured products such as pharmaceuticals, foods, and beverages. The impact of the biochemical industry on the world economy is enormous. The great importance of this industry also results in intensive development in scientific disciplines relevant to the development of biochemical technology. In addition to developments in the fields of biology and chemistry, which enable to understand complex biochemical processes, development in the field of control theory and applications is also very important. In the paper, the control for the biochemical reactor for the milk fermentation was studied. During the fermentation process, the biophysical quantities must be precisely controlled to obtain the high-quality product. To control these quantities, the bioreactor’s stirring drive and/or heating system can be used. Available commercial biochemical reactors are equipped with open loop or conventional linear closed loop control system. Due to the outstanding parameters variations and the partial nonlinearity of the biochemical process, the results obtained with these control systems are not satisfactory. To improve the fermentation process, the self-tuning adaptive control system was proposed. The use of the self-tuning adaptive control is suggested because the parameters’ variations of the studied biochemical process are very slow in most cases. To determine the linearized mathematical model of the fermentation process, the recursive least square identification method was used. Based on the obtained mathematical model the linear quadratic regulator was tuned. The parameters’ identification and the controller’s synthesis are executed on-line and adapt the controller’s parameters to the fermentation process’ dynamics during the operation. The use of the proposed combination represents the original solution for the control of the milk fermentation process. The purpose of the paper is to contribute to the progress of the control systems for the biochemical reactors. The proposed adaptive control system was tested thoroughly. From the obtained results it is obvious that the proposed adaptive control system assures much better following of the reference signal as a conventional linear control system with fixed control parameters.

Keywords: Adaptive control, biochemical reactor, linear quadratic regulator, recursive least square identification.

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Authors: Mamoun F. Al-Mistarihi

Abstract:

We have previously introduced an ultrasonic imaging approach that combines harmonic-sensitive pulse sequences with a post-beamforming quadratic kernel derived from a second-order Volterra filter (SOVF). This approach is designed to produce images with high sensitivity to nonlinear oscillations from microbubble ultrasound contrast agents (UCA) while maintaining high levels of noise rejection. In this paper, a two-step algorithm for computing the coefficients of the quadratic kernel leading to reduction of tissue component introduced by motion, maximizing the noise rejection and increases the specificity while optimizing the sensitivity to the UCA is presented. In the first step, quadratic kernels from individual singular modes of the PI data matrix are compared in terms of their ability of maximize the contrast to tissue ratio (CTR). In the second step, quadratic kernels resulting in the highest CTR values are convolved. The imaging results indicate that a signal processing approach to this clinical challenge is feasible.

Keywords: Volterra Filter, Pulse Inversion, Ultrasonic Imaging, Contrast Agent.

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Authors: Y. Fathi, B. Karimi, S. M. J. Mirzapour Al-e-Hashem

Abstract:

Cross-docking includes receiving products supplied by a set of suppliers, unloading them from inbound trucks (ITs) at strip doors, consolidating and handling these products to stack doors based on their destinations, loading them into outbound trucks (OTs); then, delivering these products to customers. An effective assignment of the trucks to the doors would enhance the advantages of the cross-docking (e.g. reduction of the handling costs). This paper addresses the truck-to-door assignment problem in a cross-dock in which assignment of the ITs to the strip doors as well as assignment of the OTs to the stacks doors is determined so that total material handling cost in the cross-dock is minimized. Capacity constraints are applied for the ITs, OTs, strip doors, and stack doors. We develop a Quadratic Programming (QP) to formulate the problem. To solve it, the model is coded in LINGO software to specify the best assignment of the trucks to the doors.

Keywords: Cross-docking, truck-to-door assignment, supply chain, quadratic programming.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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Authors: Shrawan Kumar, D. K. Lobiyal

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In this paper, we propose improved versions of DVHop algorithm as QDV-Hop algorithm and UDV-Hop algorithm for better localization without the need for additional range measurement hardware. The proposed algorithm focuses on third step of DV-Hop, first error terms from estimated distances between unknown node and anchor nodes is separated and then minimized. In the QDV-Hop algorithm, quadratic programming is used to minimize the error to obtain better localization. However, quadratic programming requires a special optimization tool box that increases computational complexity. On the other hand, UDV-Hop algorithm achieves localization accuracy similar to that of QDV-Hop by solving unconstrained optimization problem that results in solving a system of linear equations without much increase in computational complexity. Simulation results show that the performance of our proposed schemes (QDV-Hop and UDV-Hop) is superior to DV-Hop and DV-Hop based algorithms in all considered scenarios.

Keywords: Wireless sensor networks, Error term, DV-Hop algorithm, Localization.

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Authors: Dursun Aydın, Bilgin Senel

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In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

Abstract:

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Musa Demirci, Nazlı Yıldız İkikardeş, Gökhan Soydan, İsmail Naci Cangül

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In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.

Keywords: Elliptic curves over finite fields, rational points, quadratic residue.

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Authors: Yuichi Masukake, Yoshihisa Ishida

Abstract:

In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: Chao Yuan, Bao Guang Tian

Abstract:

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.

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Authors: Aly Farag, Ayman El-Baz, Refaat Mohamed

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In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.

Keywords: Logistic regression model, Expectationmaximization, Segmentation.

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Authors: A. A. Penin, A. S. Sidorenko

Abstract:

A convenient and physically sound mathematical model of the external or I - V characteristic of solar cells generators is presented in this paper. This model is compared with the traditional model of p-n junction. The direct analytical calculation of load regime leads to a quadratic equation, which is importantly to simplify the calculations in the real time.

Keywords: A solar cell generator, I−V characteristic, activetwo-pole.

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Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan

Abstract:

The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.

Keywords: Chaos, Synchronization, Quadratic stability theory, Observer

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

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In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: Liu Zhiyuan, Sun Zongdi, Liu Zhiyuan, Sun Zongdi

Abstract:

Qingdao is a seaside city. Taking into account the characteristics of Qingdao, this article established a multiple linear regression model to analyze the impact of macroeconomic factors on housing prices. We used stepwise regression method to make multiple linear regression analysis, and made statistical analysis of F test values and T test values. According to the analysis results, the model is continuously optimized. Finally, this article obtained the multiple linear regression equation and the influencing factors, and the reliability of the model was verified by F test and T test.

Keywords: Housing prices, multiple linear regression model, macroeconomic factors, Qingdao City.

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Authors: A. Elyousfi, A. Tamtaoui, E. Bouyakhf

Abstract:

The H.264/AVC standard uses an intra prediction, 9 directional modes for 4x4 luma blocks and 8x8 luma blocks, 4 directional modes for 16x16 macroblock and 8x8 chroma blocks, respectively. It means that, for a macroblock, it has to perform 736 different RDO calculation before a best RDO modes is determined. With this Multiple intra-mode prediction, intra coding of H.264/AVC offers a considerably higher improvement in coding efficiency compared to other compression standards, but computational complexity is increased significantly. This paper presents a fast intra prediction algorithm for H.264/AVC intra prediction based a characteristic of homogeneity information. In this study, the gradient prediction method used to predict the homogeneous area and the quadratic prediction function used to predict the nonhomogeneous area. Based on the correlation between the homogeneity and block size, the smaller block is predicted by gradient prediction and quadratic prediction, so the bigger block is predicted by gradient prediction. Experimental results are presented to show that the proposed method reduce the complexity by up to 76.07% maintaining the similar PSNR quality with about 1.94%bit rate increase in average.

Keywords: Intra prediction, H.264/AVC, video coding, encodercomplexity.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

Abstract:

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: Boukhzer Abdenbi, El Bikri Khalid, Benamar Rhali

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In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

Keywords: Non-linear vibration, functionally graded materials, rectangular plates.

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Authors: A. A. Penin

Abstract:

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

Keywords: a solar cell generator, I − V characteristic, p − n junction, approximation

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Authors: Liping Zhou, Liang Bao, Yiqin Lin, Yimin Wei, Qinghua Wu

Abstract:

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Keywords: Quadratic eigenvalue problem, Generalized secondorder Krylov subspace, Generalized second-order Arnoldi process, Projection technique, Refined technique, Restarting.

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