Classification of generic 3-dimensional Lagrangian singularities with (Z2) l -symmetries

The paper provides the complete list of local models forZ ₂ ^l -invariant generic germs of Lagrangian submanifolds of dimension ≦3. Classification is done directly for genrating functions of Lagrangian submanifolds and contains both elementary singularities and non-elementary ones with continuous moduli. The results demonstrate, in particular, that in contrast to the non-equivariant case the classification of equivariant Lagrangian singularities is not subordinated to the classification of symmetric functions up to the right equivariant equivalences.     

Intramolecular silyl migration in the singlet oxygenation of 2-methyl-5-trimethylsilylfuran

Tetraphenylporphyrin-sensitized photooxygenation of 2-methyl-5-trimethylsilylfuran ($\text{4}$) affords quantitatively trimethylsilyl 2-oxo-4-pentenoate ($\text{5}$), presumably via intramolecular Baeyer-Villiger rearrangement of the intermediary dioxirane ($\text{3a}$).     

The second order optical potential for theπd system at the threshold

The second order optical potential for thed system is derived in the framework of the Watson formalism and applied to the calculation of the 1s-state energy shift of the atom and thed scattering lengtha _d . The results are in good agreement with those of the Faddeev type calculations.The authors wish to thank V. B. Belyaev, R. Mach, M. G. Sapozhnikov and R. A. Eramzhyan for stimulating discussions and helpful advice.     

The effect of chain structure on the annealing and deformation behaviour of polymers

Summary In a tensile test ductile thermoplastics may give either uniform deformation or necking. Recently it has been found that those giving uniform deformation either, are known to have extended chain configurations in solution, or have chemical formulae with linear structures and relatively few flexible bonds. The observed differences in behaviour can be predicted from a viscosity retarded rubber elasticity model in which a constant related to chain flexibility is introduced, which quantifies the strain hardening of the material. It is argued that the early development of strain hardening generally interferes with the localization of plastic strain in shear bands or crazes (as well as in a neck) and correlates with the stress cracking performance of high density polythenes.There is now also some evidence that polymers with extended chain configurations have small values ofcp (the change in specific heat atTg) and that this figure has an apparent correlation with draw ratio for different polymers.In the case of P.V.C. however it is possible to cause a changeover from the normal necking behaviour to uniform deformation by quenching the hot material in ice water. This process is believed to eliminate a structure which develops slowly in P.V.C. and most other thermoplastics when they are annealed at temperatures near toTg. The elimination of this structure during yielding causes strain softening and also promotes plastic strain localisation.This physical ageing or annealing process is still not well understood. It almost certainly includes free volume effects but recent studies have shown that a redistribution of rotational isomers also occurs. These observation, if correct, have fundamental implications for the physics of glassy polymers.

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Zusammenfassung Beim Zug-Test erfolgt bei dehnbaren Thermoplasten entweder eine gleichmäßige Deformation oder eine Einschnürung. Erstere tritt auf bei Vorliegen ausgestreckter Kettenkonfigurationen in Lösung oder bei Makromolekülen linearer Struktur und relativ unbiegsamer Bindungen. Die beobachteten Unterschiede wurden anhand eines ViskositätsModells mit verminderter Gummi-Elastizität unter Zugrundelegung von Literaturdaten diskutiert. Die Kettensteifheit wird rechnerisch durch Einfügung einer Konstanten berücksichtigt; sie steht in Konkurrenz mit der Lokalisierung der plastischen Dehnung und korreliert mit dem Auftreten einer Spannungsriß-Bildung im Polyäthylen hoher Dichte. Es wird darauf hingewiesen, daß sich die spezifische Wärme von Polymeren mit ausgedehnter Kettenkonfiguration beiTg nur wenig ändert; dieser Effekt steht mit dem Dehnungsverhältnis verschiedener Polymerer in Einklang.Bei PVC kann jedoch durch Abschrecken des heißen Materials in Eiswasser ein Übergang vom normalen Einschnürungsverhalten zu einer gleichmäßigen Deformation erzielt werden; dieser Effekt ist durch die Unterdrückung einer speziellen Struktur bedingt und kann auch bei der Temperung anderer thermoplastischer Polymerer nahe beiTg auftreten.Die sich bei der physikalischen Alterung und bei der Temperung abspielenden Vorgänge lassen sich noch nicht erklären. Sie umfassen sicherlich Effekte des freien Volumens und die Rückverteilung von Rotations-Isomeren. Beobachtungen dieser Art sind von grundsätzlicher Bedeutung für die Physik glasartiger Polymerer.

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Dedicated to Prof. Dr. Rehage on the occasion of his 60th birthday.

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With 22 figures and 2 tables     

The Synthesis of Unusual Organic Molecules Using Cyclic Peroxides. New synthetic methods (3)

The photodecarboxylation of malonyl peroxides into α-lactones^[1] and the thermal conversion of the 1,4-endo-peroxide 4,5-epoxy-3,6-epidioxy-1-cyclohexene into the novel benzene trioxide^[2] are two recent examples of the potential of cyclic peroxides in the synthesis of unusual organic molecules. The former transformation entails a fragmentation, the latter a rearrangement process. Most reported examples fall into one of these two gross reaction types. Of the numerous examples that have been reported in the literature during the last two decades, only those shall be focused on that lead to unusual compounds or constitute efficient syntheses of known compounds, in order to stress the convenience of cyclic peroxides in the synthesis of organic compounds.     

Synthetically attractive indolization processes and newer methods for the preparation of selectively substituted indoles

The synthetically interesting processes available for indolization reactions are discussed and illustrated in tabular form and particular emphasis is placed on the more recent methods.     

Internal molecular disorder in the nematic and smectic phases of thermotropic liquid crystals studied by NMR SPDE experiments

The recently developed NMR SPDE experiment is shown to provide a new and particularly convenient technique for probing the conformational dynamics of mesogens in thermotropic liquid crystals. Measurements have been made in the nematic and smectic phases of the 4,4′-di-n-alkoxyazoxybenzenes. It is shown for the first time that the internal disorder of the alkyl end chains is intimately related to the molecular organization of these mesophases.     

Preparative uv-laser photochemistry of the azoalkane spiro(2,3-diazabicyclo [2.2.1]hept-2-ene-7′,1-cyclopropane): Trapping of the 1,4-Diradical 2-(3-Cyclopentenyl) ethyl by Molecular Oxygen

Photo-extrusion of nitrogen from the azoalkane 1 in the presence of molecular oxygen gave besides the hydrocarbons 3 and 5, the endoperoxide 10 and hydroperoxide 11, the former via trapping of the 1,4-diradical 4 by triplet oxygen, the latter by ene-reaction-6f hydrocarbon 5 with singlet oxygen.