Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Regularization Methods for Ill-Posed Problems in Multiple Hilbert Scales

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases convergence is proved and orders and optimal orders of convergence are shown.Comment: 32 pages, 2 figure

A solid-state high harmonic generation spectrometer with cryogenic cooling

Solid-state high harmonic generation spectroscopy (sHHG) is a promising technique for studying electronic structure, symmetry, and dynamics in condensed matter systems. Here, we report on the implementation of an advanced sHHG spectrometer based on a vacuum chamber and closed-cycle helium cryostat. Using an in situ temperature probe, it is demonstrated that the sample interaction region retains cryogenic temperature during the application of high-intensity femtosecond laser pulses that generate high harmonics. The presented implementation opens the door for temperature-dependent sHHG measurements down to few Kelvin, which makes sHHG spectroscopy a new tool for studying phases of matter that emerge at low temperatures, which is particularly interesting for highly correlated materials

S3 guidelines for intensive care in cardiac surgery patients: hemodynamic monitoring and cardiocirculary system

Hemodynamic monitoring and adequate volume-therapy, as well as the treatment with positive inotropic drugs and vasopressors are the basic principles of the postoperative intensive care treatment of patient after cardiothoracic surgery. The goal of these S3 guidelines is to evaluate the recommendations in regard to evidence based medicine and to define therapy goals for monitoring and therapy. In context with the clinical situation the evaluation of the different hemodynamic parameters allows the development of a therapeutic concept and the definition of goal criteria to evaluate the effect of treatment

Detailed spectral and morphological analysis of the shell type SNR RCW 86

Aims: We aim for an understanding of the morphological and spectral properties of the supernova remnant RCW~86 and for insights into the production mechanism leading to the RCW~86 very high-energy gamma-ray emission. Methods: We analyzed High Energy Spectroscopic System data that had increased sensitivity compared to the observations presented in the RCW~86 H.E.S.S. discovery publication. Studies of the morphological correlation between the 0.5-1~keV X-ray band, the 2-5~keV X-ray band, radio, and gamma-ray emissions have been performed as well as broadband modeling of the spectral energy distribution with two different emission models. Results:We present the first conclusive evidence that the TeV gamma-ray emission region is shell-like based on our morphological studies. The comparison with 2-5~keV X-ray data reveals a correlation with the 0.4-50~TeV gamma-ray emission.The spectrum of RCW~86 is best described by a power law with an exponential cutoff at $E_{cut}=(3.5\pm 1.2_{stat})$ TeV and a spectral index of $\Gamma$~$1.6\pm 0.2$. A static leptonic one-zone model adequately describes the measured spectral energy distribution of RCW~86, with the resultant total kinetic energy of the electrons above 1 GeV being equivalent to $\sim$0.1\% of the initial kinetic energy of a Type I a supernova explosion. When using a hadronic model, a magnetic field of $B$~100$\mu$G is needed to represent the measured data. Although this is comparable to formerly published estimates, a standard E$^{-2}$ spectrum for the proton distribution cannot describe the gamma-ray data. Instead, a spectral index of $\Gamma_p$~1.7 would be required, which implies that ~$7\times 10^{49}/n_{cm^{-3}}$erg has been transferred into high-energy protons with the effective density $n_{cm^{-3}}=n/ 1$ cm^-3. This is about 10\% of the kinetic energy of a typical Type Ia supernova under the assumption of a density of 1~cm^-3.Comment: accepted for publication by A&