Università degli Studi di Trieste, Dipartimento di Matematica e Informatica
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We present some existence and multiplicity results for positive solutions to the Dirichlet problem associated with; under suitable conditions on the nonlinearity g(u)and thew eight function a(x): The assumptions considered are related to classical theorems about positive solutions to a sublinear elliptic equation due to Brezis-Oswald and Brown-Hess.
We use Fink’s identity to obtain new identities related to
generalizations of Steffensen’s inequality. Ostrowski-type inequalities
related to these generalizations are also given. Using inequalities for
the Cebysev functional we obtain bounds for these identities. Further,
we use these identities to obtain new generalizations of Steffensen’s inequality for n-convex functions. Finally, we use these generalizations to
construct a linear functional that aenerates exvonentiallv convex functions.
In this note we present a notion of fundamental scheme for
Cohen-Macaulay, order I, irreducible congruences of lines. We show
that such a congruence is formed by the k-secant lines to its fundamental
scheme for a number k that we call the secant, index of the congruence.
if the fundamental scheme X is a smooth connected variety in FN, then
k = (N — l)/(c — 1) (where c is the codimension of X) and X comes
equipped with a special tangency divisor cut out by a virtual hypersurface of degree k — 2 (to be precise, linearly equivalent to a section by
an hypersurface of degree (k — 2) without being cut by one). This is
explained in the main theorem of this paper. This theorem is followed
by a complete classification of known locally Cohen-Macaulay order 1
congruences of lines with smooth fundamental scheme. To conclude we
remark that according to Zak’s classification of Severi Varieties and
Hartshome conjecture for low codimension varieties, this classification