Search results for: eigenvalues of the Jacobian

Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du

Abstract:

The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.

Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)

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Authors: A. M. Nazari, B. Sepehrian, M. Jabari

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In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

Keywords: Householder matrix, nonnegative matrix, Inverse eigenvalue problem.

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Authors: A. Alsaadi, B. Gholami

Abstract:

An effective approach for unbalanced three-phase distribution power flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two matrices–the bus-injection to branch-current matrix and the branch-current to busvoltage matrix– and a simple matrix multiplication are used to obtain power flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or admittance matrix required in the traditional power flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.

Keywords: Distribution power flow, distribution automation system, radial network, unbalanced networks.

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Authors: Omid Borazjani, Mahmoud Roosta, Khodakhast Isapour, Ali Reza Rajabi

Abstract:

This paper presents an application of Artificial Neural Network (ANN) algorithm for improving power system voltage stability. The training data is obtained by solving several normal and abnormal conditions using the Linear Programming technique. The selected objective function gives minimum deviation of the reactive power control variables, which leads to the maximization of minimum Eigen value of load flow Jacobian. The considered reactive power control variables are switchable VAR compensators, OLTC transformers and excitation of generators. The method has been implemented on a modified IEEE 30-bus test system. The results obtain from the test clearly show that the trained neural network is capable of improving the voltage stability in power system with a high level of precision and speed.

Keywords: Artificial Neural Network (ANN), Load Flow, Voltage Stability, Power Systems.

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Jing Li, Guang Zhou

Abstract:

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: Array signal processing, direction-of-arrival, antenna arrays, eigenvalues, eigenvectors.

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Authors: Qiang Niu, Linzhang Lu

Abstract:

Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.

Keywords: Arnoldi process, GMRES, Krylov subspace, systems of linear equations.

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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Authors: G. N. Sekhar, P. G. Siddheshwar, G. Jayalatha, R. Prakash

Abstract:

The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Keywords: Ferroconvection, throughflow, temperature dependent viscosity, magnetic field dependent viscosity.

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Authors: M. Salehi, A. A. Motie Birjandi, F. Namdari

Abstract:

Weak damping of low frequency oscillations is a frequent phenomenon in electrical power systems. These frequencies can be damped by power system stabilizers. Unified power flow controller (UPFC), as one of the most important FACTS devices, can be applied to increase the damping of power system oscillations and the more effect of this controller on increasing the damping of oscillations depends on its proper placement in power systems. In this paper, a technique based on controllability is proposed to select proper location of UPFC and the best input control signal in order to enhance damping of power oscillations. The effectiveness of the proposed technique is demonstrated in IEEE 9 bus power system.

Keywords: Unified power flow controller (UPFC), controllability, small signal analysis, eigenvalues.

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Authors: Jose D. Herrera, Mario A. Rios

Abstract:

This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: Balanced realization, controllability Grammian, electromechanical oscillations, FACTS, Hankel singular values, observability Grammian, POD, PSS.

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Authors: K. Prasertwong, N. Mithulananthan

Abstract:

This paper investigates and compares performance of various conventional and fuzzy logic based controllers at generator locations for oscillation damping. Performance of combination of conventional and fuzzy logic based controllers also studied by comparing overshoot on the active power deviation response for a small disturbance and damping ratio of the critical mode. Fuzzy logic based controllers can not be modeled in the state space form to get the eigenvalues and corresponding damping ratios of various modes of generators and controllers. Hence, a new method based on tracing envelop of time domain waveform is also presented and used in the paper for comparing performance of controllers. The paper also shows that if the fuzzy based controllers designed separately combining them could not lead to a better performance.

Keywords: Automatic voltage regulator, damping ratio, fuzzylogic controller, power system stabilizer.

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Authors: Mario Mastriani, Juliana Gambini

Abstract:

In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loève transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version is the best, with minor Mean Absolute Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to Noise Ratio (PSNR) and better image quality. Finally, new technique was far superior to JPEG and JPEG2000.

Keywords: Fast Cosine Transform, image compression, JPEG, JPEG2000, Karhunen-Loève Transform, zig-zag scan.

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Authors: J. Radojicic, D. Surdilovic, G. Schreck

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The paper considers a novel modular and intrinsically safe redundant robotic system with biologically inspired actuators (pneumatic artificial muscles and rubber bellows actuators). Similarly to the biological systems, the stiffness of the internal parallel modules, representing 2 DOF joints in the serial robotic chains, is controlled by co-activation of opposing redundant actuator groups in the null-space of the module Jacobian, without influencing the actual robot position. The decoupled position/stiffness control allows the realization of variable joint stiffness according to different force-displacement relationships. The variable joint stiffness, as well as limited pneumatic muscle/bellows force ability, ensures internal system safety that is crucial for development of human-friendly robots intended for human-robot collaboration. The initial experiments with the system prototype demonstrate the capabilities of independently, simultaneously controlling both joint (Cartesian) motion and joint stiffness. The paper also presents the possible industrial applications of snake-like robots built using the new modules.

Keywords: bellows actuator, human-robot interaction, hyper redundant robot, pneumatic muscle.

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Authors: A. Pashkevich, A. Klimchik, D. Chablat

Abstract:

The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide family

Keywords: Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

Abstract:

The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm- Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solution of classical Sturm–Liouville problem is presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems.

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Authors: Antoni Ivanov, Nikolay Dandanov, Nicole Christoff, Vladimir Poulkov

Abstract:

Spectrum underutilization has made cognitive radio a promising technology both for current and future telecommunications. This is due to the ability to exploit the unused spectrum in the bands dedicated to other wireless communication systems, and thus, increase their occupancy. The essential function, which allows the cognitive radio device to perceive the occupancy of the spectrum, is spectrum sensing. In this paper, the performance of modern adaptations of the four most widely used spectrum sensing techniques namely, energy detection (ED), cyclostationary feature detection (CSFD), matched filter (MF) and eigenvalues-based detection (EBD) is compared. The implementation has been accomplished through the PlutoSDR hardware platform and the GNU Radio software package in very low Signal-to-Noise Ratio (SNR) conditions. The optimal detection performance of the examined methods in a realistic implementation-oriented model is found for the common relevant parameters (number of observed samples, sensing time and required probability of false alarm).

Keywords: Cognitive radio, dynamic spectrum access, GNU Radio, spectrum sensing.

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Authors: Z. Zainuddin, W. D. Wan Rosli, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, pulping modeling, neural networks, preconditioned conjugate gradient.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: Shiji Hu, Lei Li, Wanting Zhou, Daohong Yang

Abstract:

The data encryption is the foundation of today’s communication. On this basis, to improve the speed of data encryption and decryption is always an important goal for high-speed applications. This paper proposed an elliptic curve crypto processor architecture based on SM2 prime field. Regarding hardware implementation, we optimized the algorithms in different stages of the structure. For modulo operation on finite field, we proposed an optimized improvement of the Karatsuba-Ofman multiplication algorithm and shortened the critical path through the pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between the affine coordinate system and the Jacobi projective coordinate system. In the parallel scheduling point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU (dual-core ARM Cortex-A9).

Keywords: Elliptic curve cryptosystems, SM2, modular multiplication, point multiplication.

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Authors: C. Wan, A. Mita

Abstract:

This paper proposes a novel system for monitoring the health of underground pipelines. Some of these pipelines transport dangerous contents and any damage incurred might have catastrophic consequences. However, most of these damage are unintentional and usually a result of surrounding construction activities. In order to prevent these potential damages, monitoring systems are indispensable. This paper focuses on acoustically recognizing road cutters since they prelude most construction activities in modern cities. Acoustic recognition can be easily achieved by installing a distributed computing sensor network along the pipelines and using smart sensors to “listen" for potential threat; if there is a real threat, raise some form of alarm. For efficient pipeline monitoring, a novel monitoring approach is proposed. Principal Component Analysis (PCA) was studied and applied. Eigenvalues were regarded as the special signature that could characterize a sound sample, and were thus used for the feature vector for sound recognition. The denoising ability of PCA could make it robust to noise interference. One class SVM was used for classifier. On-site experiment results show that the proposed PCA and SVM based acoustic recognition system will be very effective with a low tendency for raising false alarms.

Keywords: One class SVM, pipeline monitoring system, principal component analysis, sound recognition, third party damage.

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Authors: R .Lassoued, M. Guenfoud

Abstract:

An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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Authors: Zia Amjad, Salem S. Alghamdi

Abstract:

The study was conducted at the student educational farm at the College of Food and Agriculture in the Kingdom of Saudi Arabia. The aim of study was to characterize 154 Vicia faba L. accessions using agro-morphological traits based on The International Union for the Protection of New Varieties of Plants (UPOV) and The International Board for Plant Genetic Resources (IBPGR) descriptors. This research is significant as it contributes to the understanding of the genetic diversity and potential yield of V. faba in Saudi Arabia. In the study, 24 agro-morphological characters including 11 quantitative and 13 qualitative were observed for genetic variation. All the results were analyzed using multivariate analysis i.e., principal component analysis (PCA). First, six principal components (PC) had eigenvalues greater than one; accounted for 72% of available V. faba genetic diversity. However, first three components revealed more than 10% of genetic diversity each i.e., 22.36%, 15.86% and 10.89% respectively. PCA distributed the V. faba accessions into different groups based on their performance for the characters under observation. PC-1, which represented 22.36% of the genetic diversity, was positively associated with stipule spot pigmentation, intensity of streaks, pod degree of curvature and to some extent with 100 seed weight. PC-2 covered 15.86 of the genetic diversity and showed positive association for average seed weight per plant, pod length, number of seeds per plant, 100 seed weight, stipule spot pigmentation, intensity of streaks (same as in PC-1) and to some extent for pod degree of curvature and number of pods per plant. PC-3 revealed 10.89% of genetic diversity and expressed positive association for number of pods per plant and number of leaflets per plant. This study contributes to the understanding of the genetic diversity and potential yield of V. faba in the Kingdom of Saudi Arabia. By establishing a core collection of V. faba, the research provides a valuable resource for future conservation and utilization of this crop worldwide.

Keywords: Agro-morphological characterization, genetic diversity, core collection, PCA, Vicia faba L.

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