A counterexample to the first Zassenhaus conjecture

Hans J. Zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group G there exists a unit a in the rational group algebra of G such that a−1· u · a = ±g for some g ∈ G. We disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply. Our smallest example is a metabelian group of order 27·32·5·72·192 whose integral group ring contains a unit of order 7 · 19 which, in the rational group algebra, is not conjugate to any element of the form ±g

Use of high-resolution measurements for the retrieval of temperature and gas-concentration profiles from outgoing infrared spectra in the presence of cirrus clouds

We explore ways in which high-spectral-resolution measurements can aid in the retrieval of atmospheric temperature and gas-concentration profiles from outgoing infrared spectra when optically thin cirrus clouds are present. Simulated outgoing spectra that contain cirrus are fitted with spectra that do not contain cirrus, and the residuals are examined. For those lines with weighting functions that peak near the same altitude as the thin cirrus, unique features are observed in the residuals. These unique features are highly sensitive to the resolution of the instrumental line shape. For thin cirrus these residual features are narrow (≤0.1 cm-1), so high spectral resolution is required for unambiguous observation. The magnitudes of these unique features are larger than the noise of modern instruments. The sensitivities of these features to cloud height and cloud optical depth are also discussed. Our sensitivity studies show that, when the errors in the estimation of temperature profiles are not large, the dominant contribution to the residuals is the misinterpretation of cirrus. An analysis that focuses on information content is also presented. An understanding of the magnitude of the effect and of its dependence on spectral resolution as well as on spectral region is important for retrieving spacecraft data and for the design of future infrared instruments for forecasting weather and monitoring greenhouse gases

Alfven wave scattering and the secondary to primary ratio

The cosmic ray abundances have traditionally been used to determine the elemental and isotopic nature of galactic ray sources and average measures of propagation conditions. Detailed studies of the physics of propagation are usually paired with relatively straightforward estimates of the secondary-to-primary (S/P) ratios. In the work reported here, calculations of elemental abundances are paired with a more careful treatment of the propagation process. It is shown that the physics of propagation does indeed leave specific traces of Galactic structure in cosmic ray abundances

A Passage in Ecclesiasticus.

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On the Modular Isomorphism Problem for groups of class 3

We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new approach to derive properties of the lower central series of a finite $p$-group from the structure of the associated modular group algebra. Finally, we study the class of so-called $p$-obelisks which are highlighted by recent computer-aided investigations of the problem.Comment: 24 page