[2] Apparently Fourier did not possess the inner-product expression for (concrete) Fourier coefficients when he first proposed that functions are expressible in Fourier series. This understandably weakened his claim. Worse, at the time, notions of convergence and even the notion of function were amorphous, so that the sense(s) in which a function might be represented by a Fourier series could n...

In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if A generates a polynomially bounded n-times integrated group whose spectrum set σ(A) = {iλk; k ∈ Z} is discrete and satisfies ∑ 1 |λk|δ k < ∞ (n and l nonnegative integers), then there exists projectors (Pk)k∈Z∗ such that ∑ Pkx = x (x ∈ D(A)), where δk = min ( |λk+1−λk| 2 , ...

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative CayleyHamilton’s theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it h...

In this paper we present a method that combines evolution strategies (ES) and standard optimization algorithms to solve the problem of fitting line profiles of stellar spectra. This method provides a reliable decomposition and a reduction in computing time over conventional algorithms. Using a stellar spectrum as input, we implemented an evolution strategy to find an approximation of the contin...

Non-stationary trend in R-R interval series is considered as a main factor that could highly influence the evaluation of spectral analysis. It is suggested to remove trends in order to obtain reliable results. In this study, three detrending methods, the smoothness prior approach, the wavelet and the empirical mode decomposition, were compared on artificial R-R interval series with four types o...

Interpretation of subsurface geology is greatly enhanced by 3-D seismic data, and this accounts for its ubiquity in today’s search for hydrocarbons. Seismic interpretation has two fundamental disciplines at its core: seismic geomorphology and seismic stratigraphy. Plan views allow the explorationist to apply principles of geomorphology, based on analogies with modern sedimentary systems, to int...

In this paper, we consider the time averaged distribution of discrete time quantum walks on the glued trees. In order to analyze the walks on the glued trees, we consider a reduction to the walks on path graphs. Using a spectral analysis of the Jacobi matrices defined by the corresponding random walks on the path graphs, we have a spectral decomposition of the time evolution operator of the qua...

A joint speech signal enhancement based on singular value decomposition filter after spectral subtraction (SSVD) is proposed in this paper. The residual noise after spectral subtraction, which results for audible musical noise, is reduced further by SVD filter. The matrix size in spectral domain can be reduced half, and larger step-length adopted by SVD filter in spectral domain leads to lower ...