The art of fitting p-mode spectra: Part II. Leakage and noise covariance matrices

In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using 'Maximum Likelihood Estimators'. In this article, hereafter Part II, we show how to use the theory developed in Part I for fitting real data. We introduce 4 new diagnostics in helioseismology: the $(m,\nu)$ echelle diagramme, the cross echelle diagramme, the inter echelle diagramme, and the ratio cross spectrum. These diagnostics are extremely powerful to visualize and understand the covariance matrices of the Fourier spectra, and also to find bugs in the data analysis code. These diagrammes can also be used to derive quantitative information on the mode leakage and noise covariance matrices. Numerous examples using the LOI/SOHO and GONG data are given.Comment: 17 pages with tex and ps files, submitted to A&A, [email protected]

The art of fitting p-mode spectra: Part I. Maximum Likelihood Estimation

In this article we present our state of the art of fitting helioseismic p-mode spectra. We give a step by step recipe for fitting the spectra: statistics of the spectra both for spatially unresolved and resolved data, the use of Maximum Likelihood estimates, the statistics of the p-mode parameters, the use of Monte-Carlo simulation and the significance of fitted parameters. The recipe is applied to synthetic low-resolution data, similar to those of the LOI, using Monte-Carlo simulations. For such spatially resolved data, the statistics of the Fourier spectrum is assumed to be a multi-normal distribution; the statistics of the power spectrum is \emph{not} a $\chi^{2}$ with 2 degrees of freedom. Results for $l=1$ shows that all parameters describing the p modes can be obtained without bias and with minimum variance provided that the leakage matrix is known. Systematic errors due to an imperfect knowledge of the leakage matrix are derived for all the p-mode parameters.Comment: 13 pages, ps file gzipped. Submitted to A&

Characterization of solar-cycle induced frequency shift of medium- and high-degree acoustic modes

Although it is well known that the solar acoustic mode frequency increases as the solar activity increases, the mechanism behind it is still unknown. Mode frequencies with 20 < l < 900 obtained by applying spherical harmonic decomposition to MDI full-disk observations were used. First, the dependence of solar acoustic mode frequency with solar activity was examined and evidence of a quadratic relation was found indicating a saturation effect at high solar activity. Then, the frequency dependence of frequency differences between the activity minimum and maximum was analyzed. The frequency shift scaled by the normalized mode inertia follows a simple power law where the exponent for the p modes decreases by 37% for modes with frequency larger than 2.5 mHz.Comment: Proceedings of GONG-SoHO 24: A new era of seismology of the sun and solar-like star

Condutividade elétrica do solo, tópicos e equipamentos.

bitstream/CNPDIA-2010/12613/1/DOC43-2009.pd

Programa em linguagem JAVA para comunicação serial.

bitstream/CNPDIA-2010/12672/1/CT109-2009.pd

Renunciation of Right and Remission of Debt in Comparative and Israeli Law

Renunciation and remission are not comprehensively treated in recent Israeli legislation. And although the legislature has referred to these terms in the course of its legislation, they are nowhere defined. Therefore, in order to examine the terms under discussion, we shall follow a comparative approach.\u27 In so doing, we shall also look to Jewish law. We will focus on the question of whether we are concerned with 1) a unilateral or bilateral act and 2) upon the issue of what approach would be most suitable for future legislation. We shall conduct our study in the light of the historical development of Israeli law by examining the Mejelle, Jewish law, English law, as well as other legal systems

On the choice of parameters in solar structure inversion

The observed solar p-mode frequencies provide a powerful diagnostic of the internal structure of the Sun and permit us to test in considerable detail the physics used in the theory of stellar structure. Amongst the most commonly used techniques for inverting such helioseismic data are two implementations of the optimally localized averages (OLA) method, namely the Subtractive Optimally Localized Averages (SOLA) and Multiplicative Optimally Localized Averages (MOLA). Both are controlled by a number of parameters, the proper choice of which is very important for a reliable inference of the solar internal structure. Here we make a detailed analysis of the influence of each parameter on the solution and indicate how to arrive at an optimal set of parameters for a given data set.Comment: 14 pages, 15 figures. Accepted for publication on MNRA