Orthonormal wavelets and shift invariant generalized multiresolution analyses

All wavelets can be associated to a multiresolution-like structure, i.e. an increasing sequence of subspaces of . We consider the interaction of a wavelet and the shift operator in terms of which of the subspaces in this multiresolution-like structure are invariant under the shift operator. This action defines the notion of the shift invariance property of order . In this paper we show that wavelets of all levels of shift invariance exist, first for the classic case of dilation by 2, and then for arbitrary integral dilation factors.

     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

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Ohne Zusammenfassung     

A Diagnostic Method for Time Resolved Spatial Profile Measurements of Proton and Impurity Density and Temperature

A new diagnostic technique, based on elastic scattering of neutral atoms off the plasma ions, is proposed and analyzed. Space and time resolved measurements of the number densities and temperatures of the various components of the plasma are possible by energy analysis of the scattered neutral atoms. The ability to resolve ions of different masses is limited by ion thermal motion and the energy and angular dependence of the scattering cross sections. In hydrogenic plasmas with impurities, the scattering by the impurities is easily resolvable from the scattering of protons, even when the individual impurity contributions cannot be separately resolved. Detected particle count rates are calculated for a conceputal system for a tokamak plasma (n ~ 1013 cm-3, Ti ~ 300 eV). Time resolution of ~ 10 ms with spatial resolution of a few cm are predicted.