Extension to velocity dependent gauge transformations

In previous papers it was shown that in phase space a generator of gauge transformations for a singular Lagrangian \(L(q,\dot q)\) is given byG[ε^α]=ε _k ^α φ _α ^k (q,p,t) where φ _α ^k are first class constraints andG is subjected to a stationarity condition. A non-trivial extension from velocity (or momentum) independent gauge transformations to velocity dependent ones is realized, by replacing gauge functions ε^α(t) with momentum dependent functions ε^α(q,p,t), as long asG satisfies the stationarity condition. Inversely, it is proved in a classical framework that, within velocity dependent gauge transformations, all generators of gauge transformations can be expressed in terms of the linear combinations of φ _α ^k .     

Fluorescence high-performance liquid chromatography of arachidonic, eicosapentaenoic and some other higher fatty acids in ovary of several fishes

Summary A highly sensitive and selective fluorescence high-performance liquid chromatography using 9-anthryl-diazomethane as a pre-labelling reagent was applied to the simultaneous microanalysis of arachidonic and eicosapentaenoic acids, and some other higher fatty acids at nanogram level in ovary of several tropical adult fishes taken at Rabaul of New Britain. An existing tendency of arachidonic and eicosapentaenoic acids as precursor of prostaglandins in the generative organ of the fishes, has been revealed.

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Fluorescenz-HPLC von Arachidonsäure, Eicosapentansäure und einigen anderen höheren Fettsäuren im Ovarium verschiedener Fischarten

     

The synthesis of pyrazolo[3,4-d]pyridazines. Photochemical cyclization to pyrazolo[3,4-d]pyridazin-4(5H)-ones with subsequent functionalization

The synthesis of 1,3-disubstituted and 1,3,5-trisubstituted 1H-pyrazolo[3,4-d]pyridazin-4(5H)-ones is conveniently performed by photochemical cyclization. Functionalization of the former compounds leading to the formation of 1,4-disubstituted and 1,3,4-trisubstituted 1H-pyrazolo[3,4-d]pyridazines is smoothly effected through pertinent nucleophilic substitutions.