An algebraic characterization of certain orthonormal systems

An Algebraic Characterization of Certain Orthonormal Systems1

Smith Homotopy Groups of Certain Algebraic Systems

We shall describe an algebraic scheme giving rise to a group P2 that can be identified as the second homotopy group when the elements entering the scheme are suitably interpreted. We consider particularly the group p2(X) associated with an abstract local group X. Let G be a groupoid.I We denote by it(g) and i,(g) the leftand rightidentities of elements g in G. We call g closed if iK(g) = ir(g) ...

ALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)

We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.

ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

Systems of Orthogonal Polynomials on Certain Algebraic Curves