In this note we assume that all rings have identities and denote by R a commutative ring. All R-algebras considered are assumed to be finitely generated faithful R-modules. An R-algebra Λ is said to be semi-simple ([5]), if any finitely ‘generated Λ-module is (Λ, R)-projective.

Let X(t) = X(t,ω), – ∞ < t < ∞, be a stationary stochastic process with

and the continuous covariance function

where F(x) is the spectral distribution function.

Let be a solvable group of order g. Let p be a prime and let g = pa g′ with (p,g′) = 1. In [4] we have tried to find sufficient conditions for to possess an irreducible character of p-defect 0, that is, a character whose degree is divisible by pa.

Let D be the unit disk {z: | z | < l} in the complex plane C with boundary ∂D and closure and denote by R the image of the canonical embedding r → r + iO of the real line into C. The symbol ε will be used throughout to denote a complex parameter; the unit disk in the complex ε-plane will be denoted by Dp.

Our object in this paper is to prove the following result.

THEOREM. Let G be a finite group satisfying the following conditions:

• (*) G has subgroups L1, L2 such that L1 ≃ SL(2, q1), L2 ≃ SL(2, q2), [L1 L2] = 1, , where j is an involution, and |C(j): L1L2| = 2.

• (**) where n2 = 1,

Let G be a connected Lie group and H a closed subgroup with Lie algebra such that in the Lie algebra g of G there exists a subspace m with (subspace direct sum) and In this case the corresponding manifold M = G/H is called a reductive homogeneous space and (g,) (or (G,H)) a reductive pair. In this paper we shall show how to construct invariant pseudo-Riemannian connections on suitable reductive homogeneous spaces M which make M into an Einstein manifold.

In this paper we treat the problem of determining the rate of growth of entire functions which are solutions of first order algebraic differential equations whose coefficients are arbitrary entire functions (i.e. equations of the form Ω(z, y, dy/dz) = 0, where Ω(z, y, dy/dz) = is a polynomial in y and dy/dz, whose coefficients fkJ(z) are entire functions).

Le but de cette communication est de prouver que la solution u(t, x) faible non négative dans (0,T]=En de l’équation

possède la limite presque partout dans En si t converge vers zéro, ainsi qu’elle représentable sous la forme d’une intégrale de la solution fondamentale faible de (1) par rapport à une mesure non négative. Ces problèmes ont été traités par M. Kato et M. Krzyzanski (voir [7] et [8]) pour les solutions au sens classiques. Nos démonstrations sont basées sur les méthodes utilisées dans leurs travaux.

The following is a well-known result due to A.P. Calderon [2], asserting the existence of non-tangential limits of multiply harmonic functions.

Let E be a totally disconnected compact set in the complex z-plane and let G be the complementary domain of E with respect to the extended z-plane. Consider a domain in G whose relative boundary consists of at most a countable number of analytic curves clustering nowhere in G. Such a domain is called a subregion in G.

Throughout this paper F denotes a field complete with respect to a discrete valuation, kF the residue field of F, K/F a finite Galois extension with Galois group G = G(K/F). The ring of integers 0K of K contains the (unique) prime ideal ; the collection of ideals n for all integers n are ambiguous ideals i.e. G-modules.

Let D be the unit disk, C the unit circle, and f a continuous function from D into the Riemann sphere W. We say that f is normal if f is uniformly continuous with respect to the non-Euclidean hyperbolic metric in D and the chordal metric in W.

Let denote a non-compact parabolic Riemann surface, and let be compact and such that each frontier point of D is contained in a continuum that is also contained in D.

Let there be given a compact topological manifold Mn. If Mn admits a “triangulation” it is known that the fundamental invariants, namely the connectivities of Mn over fields, the Betti numbers and torsion coefficients over Z of the singular homology groups of Mn, are finite and calculable. However it is not known that a “triangulation” of Mn always exists when n > 3.