Mathematical theory of invariant interaction Lagrangians

The problem of determining all possibleG-invariant interaction Lagrangians for a given system of physical fields and their derivatives, whereG is a Lie subgroup of the general linear groupGL _n (R), is discussed, and a method for a complete solution of this problem by means of certain jet structures is outlined.Talk given at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

A theory of generally invariant lagrangians for the metric fields. II

The second-order generally invariant Lagrangians for the metric fields on anyn-dimensional manifold are studied as certain special coordinate functions on a space of jets. The number of independent Lagrangians of this type is determined. The dimensionsn=3 andn=4 are examined in detail with the help of a computer.     

On generalized invariant transformations

The notion of generalized invariant transformations of variational problems in Lagrangian formulation is discussed in the framework of the variational theory in fibred manifolds. Necessary and sufficient conditions for generators of one-parameter groups of such transformations are derived, completing thus some previous results of A. Trautman on the theory of transformations.     

The structure of the Euler-Lagrange mapping

The purpose of this paper is to review properties of the Euler-Lagrange mapping in the higher order variational theory on fibred manifolds. We present basic theorems on the kernel of the Euler-Lagrange mapping, describing variationally trivial Lagrangians, and its image, characterizing variational source forms. We discuss invariance properties of Lagrangians and Euler-Lagrange forms, and the Noether’s theory. The text was submitted by the author in English.     

Molekulare Mechanismen der hydrolytischen Enzymwirkung. 4. Mitt.: Die Struktur des aktiven Zentrums und der Reaktionsmechanismus

Ohne Zusammenfassung     

The determination of the specific heat of a liquid in an electric calorimeter

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The determination of the specific heat of a liquid in an electric calorimeter

     

Variational Sequences in Mechanics on Grassmann Fibrations

Extension of the variational sequence theory in mechanics to the first order Grassmann fibrations of 1-dimensional submanifolds is presented. The correspondence with the variational theory of parameter-invariant problems on manifolds is discussed in terms of the theory of jets (slit tangent bundles) and contact elements. In particular, the Helmholtz expressions for parameter-invariant variational problems, measuring local variationality of differential forms and differential equations, are given in the canonical and adapted coordinates. The methods can easily be extended to higher order variational problems.     

Stabilization of polystyrene by styrylquinoline containing methacrylates

Abstract

The thermostability of polysterene with/without new styrylquinoline containing methacrylic fragments has been described in the present work. Polystyrene and copolymers based on styrene and new methacrylic styrylquinoline containing monomers were synthesized by free radical thermoinitiated polymerization in the presence of 2,2′-azobisisobutyronitrile (1?wt%) as initiator at inert atmosphere. The impact of 2-[2-(4-methoxyphenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М1), 2-(2-phenylethenyl)quinolin-8-yl 2-methylpropyl-2-enoate (М2), 2-[2-(4-nitrophenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М3) on thermal stability of polystyrene was investigated. The thermostability of polystyrene and copolymers ST:M1, ST:M2, ST:M3 were studied by dynamic thermograviametric analysis. It was shown that destruction of polystyrene with corresponding units M1-M2 starts at 41–42°С higher, than reference polystyrene.     

Isomerization of an imine intermediate in a reductive amination reaction over metal catalysts

The reductive amination reaction of acetone by cyclohexylamine over hydrogenation metal catalysts was investigated. The study is focused on the formation of side products in the reaction. It was verified that the formation of amines having unusual combinations of alkyls is caused by the metal-catalyzed rearrangement of the double bond around the nitrogen atom in an imine intermediate and consequent reactions of the isomeric imine. It was found that the isomerization reactions occur over virtually all of the hydrogenation catalysts studied, while their respective activities for the imine isomerization decreases in the order Ni = Co > Ru > Pt = Rh > Pd.