By M. Hazewinkel (auth.), M. Hazewinkel (eds.)

"The booklet of the English version of the** Soviet Encyclopaedia of****Mathematics** is a vital occasion. I checked out a number of entries in my very own box of algebra and located the articles authoritative, good geared up, and lucidly written. The volumes can be of serious support to an individual drawn to Mathematics."**K. Hirsch, Professor Emeritus, Queen Mary university, London**

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"Not a textual content to learn from hide to hide (though one is tempted?), yet a desirable and helpful reference publication, which could be on each library's cabinets. hugely recommended."**Mathematik, Vol.35, 1988**

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If A is a symmetric operator with a dense domain of definition DA, its connected components of regular values will be the upper and the lower half-plane. ': A· x =Xx}, while the deficiency numbers n + =dimD; and n _ =dimD -;, where A· is the adjoint operator, are called the (positive and negative) deficiency indices of the operator A. e. DA' is the direct sum of DA, Di and D - i. Thus, if n + = n - =0, the operator A is self-adjoint; otherwise the deficiency subspace of a symmetric operator characterizes the extent of its deviation from a self-adjoint operator.

One says that a variable y is varied for a formula A in a given deduction if y is free in A and if the deduction under consideration involves an application of the rule of 'Vintroduction into the conclusion of an implication (or the 3-introduction into a premise), in which the quantifier over y is introduced, and the premise of the application depends on A in the proof under consideration. A deduction theorem for traditional predicate calculus may now be rendered more precise as follows: Iff,A I-B, thenfl-('VYt "'YnA:::> B), where y I, .

Analytic space). The theory of deformasubgroups with non-trivial identities have been tions originated with the problem of classification of all described (see also Group calculus). possible pairwise non-isomorphic complex structures on References a given differentiable real manifold. : Universal algebra, Reidel, 1981. idea (which must be credited to B. : The theory ofgroups, 1-2, Chelsea, 1955-1956 (translated from the Russian). : Combinatorial structures. The idea was made precise by the following group theory: presentations ofgroups in terms ofgenerators and relations, Interscience, 1966.