In this paper we introduce and study a type of Cayley graph – subnormal graph. We prove that 2-arc transitive is normal or cover complete bipartite $\mathbf{K}_{p^d,p^d}$ with $p$ prime. Then obtain generic method for constructing half-symmetric (namely edge but not arc transitive) graphs.

The Cauchy dual subnormality problem (for short, CDSP) asks whether the of a $2$-isometry is subnormal. In this paper, we address for cyclic $2$-isometries. view some recent developments in operator theory on function spaces

Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...

Selimeyer, E., Bhettay, E., Truswell, A. S., Meyers, 0. L., and Hansen, J. D. L. (1972). Archives of Disease in Childhood, 47, 429. Lymphocyte transformation in malnourished children. In vitro lymphocyte stimulation with phytohaemagglutinin gave subnormal transformation values in children with proteincalorie malnutrition. It is suggested that impaired cell-mediated immunity may be one important...

Planning Requirements for the Hospital for the Mentally Subnormal. By Guv Aldis, A.R.I.B.A., A.A., Dipl. {Published by Sir Isaac Pitman & Sons Ltd-, 80s.) The architectural ideas developed at Little Plumstead have set the standard for the whole country; and during the last ten years Little Plumstead designs have been copied or have been the prototype of all good new buildings in psychiatric hos...

(we.ht the circumstances of their study. y*al nomenclature in England underIvji1 a change with the passing of the ntal Health Act, 1959. This not only changed "mental deficiency" into "mental subnormality" and did away with the terms "idiot", "imbecile" and "feeble-minded" (roughly replacing the first two by the severely subnormal and the last by the subnormal), but it "cured" those previously ...

Subnormal operators arise naturally in complex function theory, differential geometry, potential theory, and approximation theory, and their study has rich applications in many areas of applied sciences as well as in pure mathematics. We discuss here some research problems concerning the structure of such operators: subnormal operators with finite-rank self-commutator, connections with quadratu...