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## Complex manifolds and unitary representations

### Several Complex Variables II Maryland 1970 (1971-01-01) 185: 242-287 , January 01, 1971

## Linear representation of a class of projective planes in a four dimensional projective space

### Annali di Matematica Pura ed Applicata (1971-12-01) 88: 9-31 , December 01, 1971

### Summary

The theory of linear representations of projective planes developed by Bruck and one of the authors (Bose) in two earlier papers [J. Algebra*1 (1964), pp. 85–102* and*4 (1966), pp. 117–172*] can be further extended by generalizing the concept of incidence adopted there. A linear representation is obtained for a class of non-Desarguesian projective planes illustrating this concept of generalized incidence. It is shown that in the finite case, the planes represented by the new construction are derived planes in the sense defined by Ostrom [Trans. Amer. Math Soc.*111 (1964), pp. 1–18*] and Albert [Boletin Soc. Mat. Mex,*11 (1966), pp, 1–13*] of the dual of translation planes which can be represented in a 4-space by the Bose-Bruck construction. An analogous interpretation is possible for the infinite case.

## Naum Il'ich Akhiezer (on his seventieth birthday)

### Ukrainian Mathematical Journal (1971-05-01) 23: 305-306 , May 01, 1971

## Bayeslösungen bei mehrstufigen Tests

### Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete (1971-06-01) 19: 123-166 , June 01, 1971

## Transformee de Hilbert dans le cas de plusieurs variables (noyaux impairs)

### Intégrales Singulières (1971-01-01) 204: 26-28 , January 01, 1971

## Segal algebras on abelian groups

### L1-Algebras and Segal Algebras (1971-01-01) 231: 85-94 , January 01, 1971

## The Multipliers for Commutative H*-Algebras

### An Introduction to the Theory of Multipliers (1971-01-01) 175: 61-65 , January 01, 1971

An *H*-algebra* is a Banach algebra *A* with involution* which is a Hilbert space under a scalar product <·,·> such that a)
$$\left\| x \right\| = \sqrt {\left\langle {x,x} \right\rangle }$$
, that is, the Hilbert space norm agrees with the Banach algebra norm, b)
$$\left\| {{x^*}} \right\| = \left\| x \right\|$$
c) *x** *x* ≠ 0 if *x* ≠ 0 and d) <*x y*,*z*> = <*y*, *x** *z*> for all *x*, *y*, *z*∈*A*. The standard example of an *H**-algebra is the algebra *L*_{2}(*G*) for a compact group *G* with the usual convolution multiplication and scalar product. A general discussion of *H**-algebras can be found in Loomis [1] and Naimark [1].

## Deformations De Modules

### Complexe Cotangent et Déformations I (1971-01-01) 239: 225-262 , January 01, 1971

## The solid state physical theory of cytochrome oxidase kinetics. Inhibition of second order rate constant, and second to first order kinetic shift with increasing oxygen, predicted from electron injection and trapping

### The bulletin of mathematical biophysics (1971-12-01) 33: 579-588 , December 01, 1971

Conduction of electrons through the solid protein cytochrome oxidase particle in accord with Ohm's law, driven by the difference in electrode potentials of two substrates which exchange electrons with the two sides of the enzyme particle, was previously shown to explain the inhibitory effect of cytochrome*c* on the first order rate constant, and to predict the low semiconduction activation energy of dried cytochrome oxidase. If the solid conduction path in the cytochrome oxidase particle shows electron injection from sites of electron exchange with substrate, and shows trapping of conduction electrons by reversible O_{2} complexes, then one may also predict that the first order kinetics observed as high O_{2} concentrations will change to second order kinetics at lower O_{2} concentrations, as observed by Gibson and Wharton. One may also predict quantitatively the inhibitory effect of increasing O_{2} concentrations on the second order rate constant as observed by Gibson and Wharton. The same concept of electron trapping by O_{2} complexes provides a possible reason for the unusually low semiconduction activation energy of cytochrome oxidase.