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Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this same approach to time-independent PDE of the form Lu = f, where L is an elliptic differential operator. Numerical results demonstrate the effectiveness of this approach for Poisson's equation and the Helmholtz equation in two dimensions. [ABSTRACT FROM AUTHOR]

Spectral analysis is a particularly valuable method for seeking dependences expressed as lags between different magnitudes. Its use in this article was first determined by the search for maximum objectivity in the observation of time series. The possibility of applying it to a large number of series was then examined. This twin requirement resulted from a desire to avoid the criticism generally levelled at statistical studies concerning cyclical movements of the economy. Spectral analysis is based on the theory of stochastic processes. It starts with the core hypothesis that a given time series consists of a large number of sinusoidal components with different frequencies (univariate spectral analysis). It makes it possible to divide a particular category of records into a set of oscillations of different frequencies and then to show the links between the components with the same frequency in the various series examined (cross-spectral or bivariate spectral analysis). It has had limited applications in cliometrics to date. It is used here to determine the frequency of GDP series of several OECD countries. A reminder of the method (I) is followed by successive examination of the various series chosen, the treatment of these series and the results of spectral analysis (II). It is then possible as a conclusion to show the prospects of this type of approach and to synthesise a completely new major result for understanding economic dynamics in the nineteenth and twentieth centuries, that is to say the existence of a single intermediate cycle with 15 to 20-year frequency that calls into question or even partially contradicts previous work on economic cycles. [ABSTRACT FROM AUTHOR]

In this paper necessary and sufficient conditions are stated for the Craig-Sakamoto equation det(I - sA - tB) = det(I - sA) det(I - tB), for all scalars s, t. Moreover, spectral properties for A and B are investigated. [ABSTRACT FROM AUTHOR]

The article focuses on the types of waves including impulse waves, spherical waves, and sine waves. It states that the analysis of waves by wave type, which is best solved by modern high speed computers, is a complex mathematical process. It says that the bandwidth of the spectrum is the measure of the dissimilarity between a prism and a light wave, and that larger bandwidth means greater conjugate wave and dissimilarity.

An encyclopedia entry for "spectroscopy" is presented. One type of spectroscopy is magnetic resonance spectroscopy (MRS) which is a dynamic evaluation of brain neurochemistry. Changes in cerebral energy metabolism and pH are shown by changes in phosphorus permit information. MRS can be used to evaluate patients with intractable epilepsy before surgery.

A definition for time-resolve fluorometry is presented. It refers to an instrumental design for collecting emission at a certain time interval after the pulsed excitation and for improving the detection sensitivity by means of a temporal rejection of background.

A definition of the term "Matrix-assisted Laser Desorption/Ionization Mass Spectrometry," is presented. It refers to the second most commonly used method for ionization of biomolecules in mass spectrometry. The use of ultraviolet laser pulse in the ionization and desorption of intact molecular ions is observed in the method.

A definition of the term "High Resolution Mass Spectrometry is presented. It refers to the separation and analysis of chemical compounds based on their fragmentation, ionization and migration in response to a charge field. The advances in sensitivity, resolution and data analysis allow for femtomole quantities of proteins to be identified and for post-translational modifications to be detected and mapped in the sequence.