We discuss several notions of first and second-order differentiability for integral functionats on a Hilbert space. Mathematics Subject Classification (1991). 49J52.

Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets C for which the distance function dC is continuously differentiable everywhere on an open “tube” of uniform thickness around C. Here a corresponding local theory is developed for the property of dC being continuously differentiable outside of C on some neighborhood of a point x ∈ C. This is shown to be equ...

In the authorship verification problem, we are given examples of the writing of a single author and are asked to determine if given long texts were or were not written by this author. We present a new learning-based method for adducing the “depth of difference” between two example sets and offer evidence that this method solves the authorship verification problem with very high accuracy. The un...

Let 9TC be an re-dimensional differentiable manifold of class Ck, k = l, • • • , oo, w (as usual O" means analytic, and we use the conventions * ±m= and w + w=w for integers m). An automorphism of 9TC is a one-to-one map of 911 onto itself which is of class C* and is nonsingular. Now let 9TC be given a Riemannian structure, i.e. a positive definite covariant tensor field of rank two, and su...

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting depends smoothly on the dynamical system itself.

the objective of this article is to derive the necessary optimality conditions, known as pontryagin's minimum principle, for fuzzy optimal control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its $alpha$-level sets.