Let X be a WCG Banach space admitting a Ck-Fréchet smooth norm. Then X admits an equivalent norm which is simultaneously C1-Fréchet smooth, LUR, and a uniform limit of Ck-Fréchet smooth norms. If X = C([0, α]), where α is an ordinal, then the same conclusion holds true with k =∞.

Let F (X) and A(X) be respectively the free topological group and the free Abelian topological group on a Tychonoff space X. For every natural number n we denote by Fn(X) (An(X)) the subset of F (X) (A(X)) consisting of all words of reduced length ≤ n. It is well known that if a space X is not discrete, then neither F (X) nor A(X) is Fréchet-Urysohn, and hence first countable. On the other hand...

We present the first results showing that the Fréchet distance between non-flat surfaces can be approximated within a constant factor in polynomial time. Computing the Fréchet distance for surfaces is a surprisingly hard problem. It is not known whether it is computable, it has been shown to be NP-hard, and the only known algorithm computes the Fréchet distance for flat surfaces (Buchin et al.)...

Although the GEV distribution is the most used generalization of the Fréchet model, other distributions has been proposed in the literature. De Gusmão [2] proposed a three parameter generalized inverse Weibull distribution in which includes the Fréchet distribution. Krishna et al. [3] proposed the MarshallOlkin Fréchet distribution. Barreto-Souza et al. [4] discussed some results for beta Fréch...

We present the first results showing that the Fréchet distance between non-flat surfaces can be approximated within a constant factor in polynomial time. Computing the Fréchet distance for surfaces is a surprisingly hard problem. It is not known whether it is computable, it has been shown to be NP-hard, and the only known algorithm computes the Fréchet distance for flat surfaces (Buchin et al.)...

Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and...

This paper reviews Fréchet sensitivity analysis for partial differential equations with variations in distributed parameters. The Fréchet derivative provides a linear map between parametric variations and the linearized response of the solution. We propose a methodology based on representations of the Fréchet derivative operator to find those variations that lead to the largest changes to the s...

Computing Fréchet distance between two curves takes roughly quadratic time. In this paper, we show that for curves with long edges the Fréchet distance computations become easier. Let P and Q be two polygonal curves in R with n and m vertices, respectively. We prove four main results for the case when all edges of both curves are long compared to the Fréchet distance between them: (1) a linear-...

In this paper we present approximate algorithms for matching two polygonal curves with respect to the Fréchet distance. We define a discrete version of the Fréchet distance as a distance measure between polygonal curves and show that this discrete version is bounded by the continuous version of the Fréchet distance. For the task of matching with respect to the discrete Fréchet distance, we deve...