Derivation of Floquet Eigenvectors Displacement for Optimal Design of LC Tank Pulsed Bias Oscillators

The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES ANDAPPLICATIONS

In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of Sturm-Liouville problems of ordinary differential equations.

A Construction of Multi-Sender Authentication Codes from Eigenvalues and Eigenvectors of the Matrix Over Finite Fields

We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.

Eigenvectors of Permutation Matrices

The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.

A Unified Algebraic Technique for Eigenvalues and Eigenvectors in Quaternionic and Split Quaternionic Mechanics

This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.

Floquet Eigenvectors Theory of Pulsed Bias Phase and Quadrature Harmonic Oscillators

The paper presents an analytical derivation of Floquet eigenvalues and eigenvectors for a class of harmonic phase and quadrature oscillators. The derivation refers in particular to systems modeled by two parallel RLC resonators with pulsed energy restoring. Pulsed energy restoring is obtained through parallel current generators with an impulsive characteristic triggered by the resonators voltages. In performing calculation the initial hypothesis of the existence of stable oscillation is only made, then it is verified when both oscillation amplitude and eigenvalues/eigenvectors are deduced from symmetry conditions on oscillator space state. A detailed determination of the first eigenvector is obtained. Remaining eigenvectors are hence calculated with realistic approximations. Since Floquet eigenvectors are acknowledged to give the correct decomposition of noise perturbations superimposed to the oscillator space state along its limit cycle, an analytical and compact model of their behavior highlights the unique phase noise properties of this class of oscillators.

Time Eigenvectors and Their Applications

Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are discussed.

On Monotone Eigenvectors of a Max-<i>T </i>Fuzzy Matrix

The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.

IMPROVING EIGENVECTORS IN ARNOLDI'S METHOD

The Ritz vectors obtained by Arnoldi’s method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the efficiency of Arnoldi type algorithms, we propose a strategy that uses Ritz values obtained from an m-dimensional Krylov subspace but chooses modified approximate eigenvectors in an (m + 1)-dimensional Krylov subspace. Residual norm of each new approximate eigenpair is minimal over the span of the Ritz vector and the (m+1)th basis vector, which is available when the m-step Arnoldi process is run. The resulting modi- fied m-step Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m + 1)-step one. Based on this strategy, we present a modified m-step restarted Arnoldi algorithm. Numerical examples show that the modified m-step restarted algorithm and its version with Chebyshev acceleration are often considerably more efficient than the standard (m+ 1)-step restarted ones.

CONVERGENCE OF ALGORITHMS FOR FINDING EIGENVECTORS

In this paper we give a rigorous analysis of convergence of algorithms for finding eigenvectors of a real symmetric matrix. The algorithms are deterministic and our methods are very intuitive.

Nondegeneracy of eigenvectors and singular vector tuples of tensors

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.

DGMRES Method Augmented with Eigenvectors for Computing the Drazin-inverse Solution of Singular Linear Systems

The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting.But the restarting often slows down the convergence and DGMRES often stagnates.We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R.Morgan in[R.Morgan,A restarted GMRES method augmented with eigenvectors,SIAM J.Matrix Anal.Appl.,16:1154-1171,1995.We derive the implementation of this method and present some numerical examples to show the advantages of this method.

Semi-regularized Hermitian and Skew-Hermitian Splitting Preconditioning for Saddle-Point Linear Systems

In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the saddle-point linear system.By carefully selecting two different regularization matrices,two kinds of SHSS preconditioners are proposed to accelerate the convergence rates of the Krylov subspace iteration methods.Theoretical analysis about the eigenvalue distribution demonstrates that the proposed SHSS preconditioners can make the eigenvalues of the corresponding preconditioned matrices be clustered around 1 and uniformly bounded away from 0.The eigenvector distribution and the upper bound on the degree of the minimal polynomial of the SHSS-preconditioned matrices indicate that the SHSS-preconditioned Krylov subspace iterative methods can converge to the true solution within finite steps in exact arithmetic.In addition,the numerical example derived from the optimal control problem shows that the SHSS preconditioners can significantly improve the convergence speeds of the Krylov subspace iteration methods,and their convergence rates are independent of the discrete mesh size.

Measuring I/O-Production in Digital Economy

According to OECD standards(United Nations,2008),“productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input use”.This ratio indicates how efficiently production inputs,such as labour and capital,are being used in an economy to produce a given level of outputs.Productivity stays aside the main aggregates of national accounts,as the national income(a proxy of GDP),the total output and the circulating capital.Assume the existence of a Leontief-type national Input-Output Table with the vector of total output and the vector of intermediate inputs,situated on its right and lower border.In this paper a measure of capital productivity is proposed.It is called the productiveness,and results from the solution of a boundary value problem,elaborated for Input-Output Tables,involving the vector of total output and the vector of intermediate inputs.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

A Simplified Approach for Interpreting Principal Component Images

Principal component transformation is a standard technique for multi-dimensional data analysis. The purpose of the present article is to elucidate the procedure for interpreting PC images. The discussion focuses on logically explaining how the negative/positive PC eigenvectors (loadings) in combination with strong reflection/absorption spectral behavior at different pixels affect the DN values in the output PC images. It is an explanatory article so that fuller potential of the PCT applications can be realized.

Sizing of STATCOM to Enhance Voltage Stability of Power Systems for Normal and Contingency Cases

The electric power infrastructure that has served huge loads for so long is rapidly running up against many limitations. Out of many challenges it is to operate the power system in secure manner so that the operation constraints are fulfilled under both normal and contingent conditions. Smart grid technology offers valuable techniques that can be deployed within the very near future or which are already deployed nowadays. Flexible AC Transmission Systems (FACTS) devices have been introduced to solve various power system problems. In literature, most of the methods proposed for sizing the FACTS devices only consider the normal operating conditions of power systems. Consequently, some transmission lines are heavily loaded in contingency case and the system voltage stability becomes a power transfer-limiting factor. This paper presents a technique for determining the proper rating/size of FACTS devices, namely the Static Synchronous Compensator (STATCOM), while considering contingency cases. The paper also verifies that the weakest bus determined by eigenvalue and eigenvectors method is the best location for STATCOM. The rating of STATCOM is specified according to the required reactive power needed to improve voltage stability under normal and contingency cases. Two case system studies are investigated: a simple 5-bus system and the IEEE 14-bus system. The obtained results verify that the rating of STATCOM can be determined according to the worst contingency case, and through proper control it can still be effective for normal and other contingency cases.

Development of basic technique to improve seismic response accuracy of tributary area-based lumped-mass stick models

Although a detailed finite element(FE) model provides more precise results, a lumped-mass stick(LMS) model is preferred because of its simplicity and rapid computational time. However, the reliability of LMS models has been questioned especially for structures dominated by higher modes and seismic inputs. Normally, the natural frequencies and dynamic responses of a LMS model based on tributary area mass consideration are different from the results of the FE model. This study proposes a basic updating technique to overcome these discrepancies; the technique employs the identical modal response, D(t), to the detailed FE model. The parameter D(t) is a time variable function in the dynamic response composition and it depends on frequency and damping ratio for each mode, independent of the structure's mode shapes. The identical response D(t) for each mode is obtained from the frequency adaptive LMS model; the adaptive LMS model which can provide identical modal frequencies as the detailed FE model. Theoretical backgrounds and formulations of the updating technique are proposed. To validate the updating technique, two types of structures(a symmetric straight column and an unsymmetric T-shaped structure) are considered. From the seismic response results including base shear and base moment, the updating technique considerably improves the seismic response accuracy of the tributary area-based LMS model.

Linear Prolate Functions for Signal Extrapolation with Time Shift

We propose a low complexity iterative algorithm for band limited signal extrapolation. The extrapolation method is based on the decomposition of finite segments of the signal via truncated series of real-valued linear prolate functions. Our theoretical derivation shows that given a truncated series (up to a selectable value) of prolate functions, it is possible to extrapolate the band limited function elsewhere if each extrapolated portion of the function is subject only to moderate truncation errors that we quantify in this paper. The effects of different sources of errors have been analyzed via extensive simulations. We have investigated a property of the signal decomposition formula based on linear prolate functions whereby the integration interval does not need to be symmetric with respect to the origin while time-shifted prolate functions are used in the series.

The Solution of the Eigenvector Problem in Synchrotron Radiation Based Anomalous Small-Angle X-Ray Scattering

In the last three decades Synchrotron radiation became an indispensable experimental tool for chemical and structural analysis of nano-scaled properties in solid state physics, chemistry, materials science and life science thereby rendering the explanation of the macroscopic behavior of the materials and systems under investigation. Especially the techniques known as Anomalous Small-Angle X-ray Scattering provide deep insight into the materials structural architecture according to the different chemical components on lengths scales starting just above the atomic scale (≈1 nm) up to several 100 nm. The techniques sensitivity to the different chemical components makes use of the energy dependence of the atomic scattering factors, which are different for all chemical elements, thereby disentangling the nanostructure of the different chemical components by the signature of the elemental X-ray absorption edges i.e. by employing synchrotron radiation. The paper wants to focus on the application of an algorithm from linear algebra in the field of synchrotron radiation. It provides a closer look to the algebraic prerequisites, which govern the system of linear equations established by these experimental techniques and its solution by solving the eigenvector problem. The pair correlation functions of the so-called basic scattering functions are expressed as a linear combination of eigenvectors.