258 RECORDS OF PROCEEDINGS AT MEETINGS

Operators which commute with translations: B. L. D. Thorp.Internal points of convex sets: E. 0. Thorpe.The singularities of the fractional integrals of real and of complex

index of an analytic function: R. Wilson.

RECORDS OF PROCEEDINGS AT MEETINGS

SESSION NOVEMBER, 1962—JUNE, 1963.

Thursday, 21 March, 1963.

Dr. M. L. CARTWRIGHT, President, in the Chair.

There were present about 65 members and visitors.The minutes of the last meeting were read and confirmed.Messrs. P. J. Kelly and S. R. Mukhoti were elected members of the

Society.Messrs. A. Baker and A. Sein were elected associate members of the

Society.Mr. S. J. Bernau, Miss M. A. T. Haughton, Messrs. G. C. Morris, W. A.

Sutherland and T. Yamanaka were nominated for membership of theSociety.

Messrs. G. M. Anderson, A. F. Beardon and D. H. Parsons were admittedinto the Society.

Professor P. ErdOs gave a lecture on " Problems and results in settheory".

The following papers were taken as read:—(i) Convergence of recurring series with general order recurrence

relations: (ii) Two-parameter eigenvalue problems in differen-tial equations: F. M. Arscott.

Rational approximations to certain algebraic numbers: A. Baker.On the convergence of Cotes' quadrature formulae: W. Barrett.On fundamental geometric properties of line-sets: A. S. Besicovitch.Continuity and perfect operators: T. K. Boehme.Integrals involving hypergeometric functions: R. G. Buschman.On local continuity mappings: A. K. Chaudhuri.Graph union and chromatic number: G. A. Dirac.Topological operations on the class of continuous images of all

snake-like continua: L. Fearnley.A congruence property of Euler's ^-functions: H. Gupta.Note on parametrization of the four-dimensional real symplectic

group: J. Kronsbein and T. A. Welton.On a theorem of Beck and Putnam: C. A. McCarthy.On the scalar transport equation: J. B. McLeod.

RECORDS OF PROCEEDINGS AT MEETINGS 259

Preharmonic functions: B. H. Murdoch.The convolution of linear functional: J. S. Pyra.The inverse Laplace transforms of the product: F. M. Ragab.On the continuity of multiplication in right i/*-algebras: M.

Rajagopalan.Convexity in Wald's statistical metric spaces: F. Rhodes.Conformally euclidean spaces of class one: R. N. Sen.Topologies in free algebras: S. Swierczykowski.Marginal subgroup properties of outer commutator words: R. F.

Turner-Smith,(i) Diffeomorphiams of 4-manifolds: (ii) On simply-connectal

4-manifolds: C. T. C. Wall.

RECORDS OF PROCEEDINGS AT MEETINGS

SESSION NOVEMBER, 1962—JUNE, 1963

Thursday, 18 April, 1963

Dr. M. L. CARTWRIGHT, President, in the Chair

There were present 43 members and visitors.The minutes of the last meeting were read and confirmed.Mr. S. J. Bernau, Miss M. A. T. Houghton and Messrs. S. M. Mazhar,

G. C. Morris, K. R. Mount, W. A. Sutherland and T. Yamanaka wereelected members of the Society.

Messrs. J. C. Ault, R. S. Azad, N. T. Bloomer, A. J. Ellis, I. E. Farquhar,H. Goldenberg, D. Harding, R. Hart, R. E. Harte, B. K. Kelly, N. Romilly,E. H. Sondheimer, R. S. Taylor, A. Weinmann, and D. J. White werenominated for membership of the Society.

Messrs. S. Kounias and P. M. Lee were nominated for associatemembership of the Society.

Mr. K. Lucas was admitted into the Society.Professor L. Nachbin gave a lecture on "Approximation theory for

continuous and differentiable real functions '.The following papers were taken as read:—

Finitely presented groups with word problems of arbitrary degreesof insolubility: C. H. J. Clapham.

On the spectrum of a second order differential equation: J. H. E.Cohn.

Two uniqueness theorems associated with parabolic differentialoperators: D. E. Edmunds.