Comment on "Bounding and approximating parabolas for the spectrum of Heisenberg spin systems" by Schmidt, Schnack and Luban

Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill a weak homogenity condition. Moreover, the extremal values of the exact spectrum of various HSS which were studied numerically were found to lie on approximate parabolas, named rotational bands, which could be obtained by a shift of the boundary parabolas. In view of this, it has been claimed that the rotational band structure (RBS) of the energy spectrum is a general behavior of HSSs. Furthermore, since the approximate parabolas are very close to the true boundaries of the spectrum for the examples discussed, it has been claimed that the methods allow to predict the detailed shape of the spectrum and related properties for a general HSS. In this comment I will show by means of examples that the RBS hypothesis is not valid for general HSSs. In particular, weak homogenity is neither a necessary nor a sufficient condition for a HSS to exhibit a spectrum with RBS.Comment: Comments on the work of Schmidt et al, Europhys. Lett. 55, 105 (2001), cond-mat/0101228 (for the reply see cond-mat/0111581). To be published in Europhys. Let

Simulation of Thematic Mapper performance as a function of sensor scanning parameters

The investigation and results of the Thematic Mapper Instrument Performance Study are described. The Thematic Mapper is the advanced multispectral scanner initially planned for the Earth Observation Satellite and now planned for LANDSAT D. The use of existing digital airborne scanner data obtained with the Modular Multispectral Scanner (M2S) at Bendix provided an opportunity to simulate the effects of variation of design parameters of the Thematic Mapper. Analysis and processing of this data on the Bendix Multispectral Data Analysis System were used to empirically determine categorization performance on data generated with variations of the sampling period and scan overlap parameters of the Thematic Mapper. The Bendix M2S data, with a 2.5 milliradian instantaneous field of view and a spatial resolution (pixel size) of 10-m from 13,000 ft altitude, allowed a direct simulation of Thematic Mapper data with a 30-m resolution. The flight data chosen were obtained on 30 June 1973 over agricultural test sites in Indiana

Initiating the effective unification of black hole horizon area and entropy quantization with quasi-normal modes

Black hole (BH) quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In this specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and non-strictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, this work exemplifies a series of imperative corrections that eventually permits a BH's horizon area spectrum to be generalized from strictly thermal to non-strictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the identified results are significant because quasi-normal modes (QNM) and "effective states" characterize the transitions between the established levels of the non-strictly thermal spectrum.Comment: 23 pages, review paper. Final version to appear in Advances in High Energy Physic

Balance training of the equilibrium organ and its effect on flight strategy

An experimental program was conducted with the pendular platform of the Oto-Rhino-Laryngology Clinic, which was developed for the investigation of disturbances of the equilibrium. The equilibrium sense of the glider pilot was emphasized. Results are presented

A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern

We propose an extension of the 3-3-1 model with an additional symmetry group $Z_{2}\times Z_{4} \times U(1)_{L_g}$ and an extended scalar sector. To our best knowledge this is the first example of a renormalizable 3-3-1 model, which allows explanation of the SM fermion mass hierarchy by a sequential loop suppression: tree-level top and exotic fermion masses, 1-loop bottom, charm, tau and muon masses; 2-loop masses for the light up, down, strange quarks as well as for the electron. The light active neutrino masses are generated from a combination of linear and inverse seesaw mechanisms at two loop level. The model also has viable fermionic and scalar dark matter candidates.Comment: 35 pages, 4 figures. Version accepted for publication in JHE