In this paper, we consider the relationship between the cohomologies of the basic differential forms and the transverse holonomy groupoid of a foliation. Applications to minimal models are given.

We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.

Dealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.

For two-bridge knots, the authors give necessary conditions on coefficients of Alexander polynomials.

Any unital *-endomorphism of a type II1-factor is implemented by isometries of a Cuntz algebra outside the factor. If the Jones index of the range of the *-endomorphism is an integer and the algebras act on the standard space, the Jones index must agree with the number of the generators of the Cuntz algebra. We also study (outer) conjugacy of *-endomorphisms using Cuntz algebras.

Rates of convergence to normality of O(N-½) are obtained for a standardized sum of m random variables selected at random from a finite set of N random variables in two cases. In the first case, the sum is randomly normed and the variables are not restricted to being independent. The second case is an alternative proof of a result due to von Bahr, which deals with independent variables. Both results derive from a rate obtained by Höglund in the case of sampling from a finite population.

Let f be analytic in D = {z: |z| < 1} with f(0) = f′(0)−1=0. For γ > 0, the largest α (γ) and β(γ) are found such that . The results solve the inclusion problem for convex and starlike functions defined in a sector.

In this paper we consider the Plateau problem for surfaces of annular type bounded by a pair of convex, non-compact curves in parallel planes. We prove that for certain symmetric boundaries there are solutions to the non-compact Plateau problems (Theorem B). Except for boundaries consisting of a pair of parallel straight lines, these are the first known examples.

In this paper we show that a bialgebraic context which arises from a duality in a fairly general way must arise from a duality between categories of modules. To show this, we give an elementary proof of Mitchell's Embedding Theorem for prevarieties.

We study cosine and sine Fourier transforms defined by F(t):= (2/π) and (t):= (2/π), where f is L1-integrable over[0, ∞]. We also assume than F are locally absolutely continuous over [0, ∞). In particular, this is the case if both f(x) and xf(x) are (L1-integrable over [0, ∞). Motivated by the inversion formulas, we consider the partial integras Sν (f, x):= and ν(f, x):= , the modified partial integrals uν (f, x):= sν(f, x) - F(ν)(sin νx)/x and ũν(f, x):= ν(f, x) + (ν) (cos νx)/x, where ν > 0. We give necessary and sufficient conditions for(L1 [0, ∞)-convergence of uν (f) and ũν (f) as well as for the L1 [0, X]-convergence of sν (f) and ν(f) to f as ν← ∞, where 0 < X < ∞ is fixed. On the other hand, in certain cases we conclude that sν(f) and ν(f) cannot belong to (L1 [0,∞). Conequently, it makes no sense to speak of their (L1 [0, ∞)-convergence as ν ← ∞.

As an intermediate tool, we use the Cesàro means of Fourier transforms. Then we prove Tauberian type results and apply Sidon type inequalities in order to obtain Tauberian conditions of Hardy-Karamata kind.

We extend these results to the complex Fourier transform defined by G(t):= , where g is L1- integrable over (−∞, ∞).