Remark on integrable Hamiltonian systems

An extension ton degrees of freedom of the fact is established that forn=1 the time and the energy constant are canonically conjugate variables. This extension is useful in some cases to get action-angle variables from the general solution of a given integrable Hamiltonian system. As an example the Delaunay variables are proved to be canonical.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

New faunal and isotopic evidence on the late Weichselian—Holocene oceanographic changes in the Norwegian Sea

Downcore studies of planktonic and benthonic foraminifera and δ¹⁸O and δ¹³C in the planktonic foraminifer Neogloboquadrina pachyderma (sin.) in two piston cores from the southern part of the Norwegian Sea suggest large changes in the oceanic circulation pattern at the end of oxygenisotope stage 2 and in the early part of stage 1. Prior to oxygen-isotope Termination IA (16,000–13,000 yr B.P.), an isolated watermass with lower oxygen content and temperature warmer than today existed below a low salinity ice-covered surface layer in the Norwegian Sea. Close to Termination IA, well-oxygenated deep water, probably with positive temperatures, was introduced. This deep water, which must have had physical and/or chemical parameters different from those of present deep water in the Norwegian Sea, could have been introduced from the North Atlantic or been formed within the basin by another mechanism than that which forms the present deep water of the Norwegian Sea. A seasonal ice cover in the southern part of the Norwegian Sea is proposed for the period between Termination IA and the beginning of IB (close to 10,000 yr B.P.). The present situation, with strong influx of warm Atlantic surface-water and deep-water formation by surface cooling, was established at Termination IB.     

Ferdinand Steinhauser — 80 Jahre

Ohne Zusammenfassung     

A Mathematical View of Weights-of-Evidence,Conditional Independence,and Logistic Regression in Terms of Markov Random Fields

New light is shed on mathematical methods of potential modeling from the point of view of Markov random fields. In particular, weights-of-evidence and logistic regression models are discussed in terms of graphical models possessing Markov properties, where the notion of conditional independence is essential, and will be related to log-linear models. While weights-of-evidence with respect to indicator predictor variables and logistic regression with unrestricted predictor variables model conditional probabilities of an indicator random target variable, the subject of log-linear models is the joint probability of random variables. The relationship to log-linear models leads to a likelihood ratio test of conditional independence, rendering an omnibus test of conditional independence restricted by a normality assumption obsolete. Moreover, it reveals a hierarchy of methods comprising weights-of-evidence, logistic regression without interaction terms, and logistic regression including interaction terms, where each former method is a special case of the consecutive latter method. The assumptions of conditional independence of all predictor variables given the target variable lead to logistic regression without interaction terms. Violations of conditional independence are compensated exactly by corresponding interaction terms, no cumbersome approximate corrections are needed. Thus, including interaction terms into logistic regression models is an appropriate means to account for lacking conditional independence. Logistic regression exempts from the burden to worry about lack of conditional independence. Eventually, the relationship to log-linear models renders logistic regression with indicator predictor variables optimum for discrete predictor variables. Weights-of-evidence applies for indicator predictor variables only, logistic regression applies without restrictions of the type of predictor variables and approximates the proper distribution in the general case.     

Sweden

Four invertebrate and one fish species (Cerastoderma edule, Mya arenaria, Arenicola marina, Crangon crangon, Solea solea) from a single area of the German Wadden sea were investigated for concentrations of ten organochlorine pollutants in 1976. PCB concentrations (wet tissue basis) were predominating with 10–200 ng g^?1, while p,p′-DDD, dieldrin, α-HCH, γ-HCH and p,p′-DDE generally ranged between 1 and 10 ng g^?1. Values of α-endosulfan were even lower; p,p′-DDT, endrin and heptachlor epoxide could not be detected. Residue levels in shrimps were close to the lower range of values which have been found in this species from other areas of the North Sea since 1974. The patterns of residue concentrations in the five aquatic species were remarkably different indicating species- and compound-specific bioaccumulation. Trophic level and lipid content were shown to be responsible for PCB concentrations increasing from bivalves to fish.     

Aromatic components of coal: relation of distribution pattern to rank

Aromatic distribution patterns have been evaluated for a series of twenty-four German high volatile bituminous B to low volatile bituminous coals of Upper Carboniferous Westphalian C-, B- and A-ages using high performance liquid chromatography and glass capillary gas chromatography. The study concentrates on dicyclic and tricyclic aromatic hydrocarbons most of which have been identified by combined gas chromatography-mass spectrometry. The distribution patterns of the methylhomologs of naphthalene and phenanthrene are strongly controlled by rank. A sudden increase of individual isomer ratios at 0.9% Rm coincides with an abrupt shift of the sporinite fluorescence colour from yellow towards red. A recently developed aromatics-derived maturity parameter, the Methylphenanthrene Index (MPI), correlated well with the vitrinite reflectance data over the whole rank range. Deviations have been attributed to variations of maceral composition or migration phenomena. The influence of artificial thermal alteration (350 and 400dgC) on the aromatic distribution pattern of coal is described.