This collection contains survey articles dealing with the following
topics: The Mach principle and its role in the general theory of
relativity, the modern conception of the vacuum, new methods in the
theory of Lie group representations, the coherent state method and
its applica tion to physical problems, and the Newman-Penrose
method and its application to problems in general relativity
theory. v CONTENTS On the Problem of Singularity in the De Sitter
Model . . . . . . . . . . . . . . . . . . . . . . . . . . 1 v. K.
Mal'tsev and M. A. Markov On the Integral Formulation of the Mach
Principle in a Conformally Flat Space . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 v. K. Mal'tsev and M. A. Markov Canonical Transformations and the
Theory of Representations of Lie Groups . 25 A. N. Leznov, I. A.
Malkin, and V. I. Man'ko The Newman-Penrose Method in the Theory of
General Relativity. 73 V. P. Frolov vii ON THE PROBLEM OF
SINGULARITY IN THE DE SITTER MODEL V. K. Mal'tsev and M. A. Markov
The de Sitter solution in no way corresponds to the case of a world
without matter, but corresponds rather to a world in which all
matter is concentrated on the surface r = IT /2 which could proba
bly be proved by taking the limit from a volume distri bution of
matter to a surface distribution 1]."
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