In recent years Singular Spectrum Analysis (SSA), a relatively novel but powerful technique in time series analysis, has been developed and applied to many practical problems across different fields. In this paper we review recent developments in the theoretical and methodological aspects of the SSA from the perspective of analyzing and forecasting economic and financial time series, and also r...

For a linearized system such as ]c/]t 5 Mc, singular vector analysis can be used to find patterns that give the largest or smallest ratios between the sizes of Mc and c. Such analyses have applications to a wide range of atmosphere–ocean problems. The resulting singular vectors, however, depend on the norm used to measure the sizes of Mc and c, as noted in various applications. This causes comp...

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, Nucl. Instrum Methods Phys. Res. B 184, 337 (2001); Z. Siwy, Europhys. Lett. 60, 349 (2002)]. Here, the ion current r...

In this study, singular vector analysis was performed for the period from 1856 to 2003 using the latest Zebiak–Cane model version LDEO5. The singular vector, representing the optimal growth pattern of initial perturbations/errors, was obtained by perturbing the constructed tangent linear model of the Zebiak–Cane model. Variations in the singular vector and singular value, as a function of initi...

We consider computing the singular value decomposition of a bidiagonal matrix B. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accuracy, the singular values and singular vectors of B will be determined to much higher accuracy t...

The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A → Ã = A+1A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A → Ã = D∗AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or Ã, in contras...

An important element in a model of non-singular string cosmology is a phase in which classical corrections saturate the growth of curvature in a deSitter-like phase with a linearly growing dilaton (an ‘algebraic fixed point’). As the form of the classical corrections is not well known, here we look for evidence, based on a suggested symmetry of the action, scale factor duality and on conformal ...

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...

The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the correspondig solution of the Bernoulli-Euler beam.The problem of convergence is related to a Singular Perturbation Problem. The main tool in solving this problem is a weak version of a lower bound for hyperbolic polynomials.