Discrimination distance bounds and statistical applications

Summary Bounds are obtained for the Kullback-Leibler discrimination distance between two random vectorsX andY. IfX is a sequence of independent random variables whose densities have similar tail behavior andY=AX, whereA is an invertible matrix, then the bounds are a product of terms depending onA andX separately. We apply these bounds to obtain the best possible rate of convergence for any estimator of the parameters of an autoregressive process with innovations in the domain of attraction of a stable law. We provide a general theorem establishing the link between total variation proximity of measures and the rate of convergence of statistical estimates to complete the exposition for this application.     

Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

A generalized Stefan problem in several space variables

A multidimensional, multiphase problem of Stefan type, involving quasilinear parabolic equations and nonlinear boundary conditions is considered. Regularization techniques and monotonicity methods are exploited. Existence and uniqueness of a weak solution to the problem, as well as continuous and monotone dependence of the solution upon data are shown.     

Quantification of PCB by dechlorination to biphenyl

Summary Since polychlorinated biphenyls (PCB) are widespread biologically active contaminants in the environment, the need of a sensitive, rapid and simple screening-method for control purposes is obvious. The dechlorination of PCB to biphenyl with LiAlH₄ and subsequent quantification by HPLC and UV detection may fulfil these requirements. Results achieved with this dechlorination method are compared with those obtained by packed-column or capillary-column gas chromatography and EC detection.

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Bestimmung von PCB durch Dechlorierung zu Biphenyl

Zusammenfassung Das ubiquitäre Vorkommen von polychlorierten Biphenylen (PCB) als Kontaminantien in unserer Umwelt erfordert eine empfindliche, rasche und einfache Screening-Methode. Dechlorierung der PCB mit LiAlH₄ zu Biphenyl und anschließende Quantifizierung mittels HPLC und UV-Detektion erfüllt diese Forderungen. Analysenresultate der beschriebenen Dechlorierungsmethode werden verglichen mit Resultaten der Gas-Chromatographie an gepackten Säulen und Capillarsäulen mit EC-Detektion.

     

Primary reactions of sucrose thermal degradation

Thermal degradation of sucrose at 185 °C in a closed glassware and presence of air was studied with the help of GC/MS after acetylation of reaction products. Also model compounds were used to support the mechanism of thermolysis. Goal was to identify all the primary reactions of the process. It was observed that already after 5 min of treatment, two glucopyranose isomers were formed as products of sucrose glycosidic bond splitting. The furanose structure is probably transformed to anhydrofructoses, as 2,6-anhydrofructose was identified among the degradation products in much smaller amount than -glucose. At longer thermolysis times some diastereoisomers of sucrose, anhydrosucroses, and anhydroderivatives of monosaccharides were identified as minor products of parallel primary and secondary reaction. After 30 min at 185 °C there was no sucrose present in the reaction mixture, but some new products with longer retention times (RT) occurred. Also isomers of levoglucosan were observed after 1 h of treatment. This indicates that splitting of glycosidic bond is the most prominent primary reaction. The dehydration towards anhydrosucroses seams to be a minor primary reaction and might proceed via configuration changes on the pyranose ring.