Starting with the motivating example of Stone’s representation theorem that allows one to represent Boolean algebras as subalgebras of the poweralgebra of a sufficiently large set, we ask the question of whether it is possible to generalize this to a relationship between lattice theory and topology. This can be done by considering special lattices called locales, which are, in a sense, a suitab...

Recent theoretical studies of the adaptation of DNA sequences assume that the distribution of fitness effects among new beneficial mutations is exponential. This has been justified by using extreme value theory and, in particular, by assuming that the distribution of fitnesses belongs to the Gumbel domain of attraction. However, extreme value theory shows that two other domains of attraction ar...

A study is made of differentiability of the metric projection P onto a closed convex subset K of a Hubert space H. When K has nonempty interior, the Gateaux or Fréchet smoothness of its boundary can be related with some precision to Gateaux or Fréchet differentiability properties of P. For instance, combining results in §3 with earlier work of R. D. Holmes shows that K has a C2 boundary if and ...

Fréchet’s classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Fréchet embedding is Bourgain’s embedding [4]. The authors have recently shown [2] that for every ε > 0 any n-point metric space contains a subset of size at least n1−ε which embeds into `2 with distortion O ( log(2/ε) ε ) . The embedding used in [2] is no...

The processing and analysis of trajectories are the core of many location-based applications and services, while trajectory similarity is an essential concept regularly used. To address the time-consuming problem of similarity query, an efficient algorithm based on Fréchet distance called Ordered Coverage Judge (OCJ) is proposed, which could realize the filtering query with a given Fréchet dist...

We give a complete characterization of those f : [0, 1] → X (where X is a Banach space which admits an equivalent Fréchet smooth norm) which allow an equivalent C 2 parametrization. For X = R, a characterization is well-known. However, even in the case X = R 2 , several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved.

— We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also pro...

and Applied Analysis 3 Here, R󸀠(κ)∗R(κ) is the Fréchet derivative of the residual operatorR(κ)with respect to κ, and the forcing termpoints in the descent direction of the least squares cost; t is the artificial iteration time, and C is a conveniently chosen constant. The Fréchet derivative can be calculated efficiently using the adjoint formulation (see [9, 12]). Numerically discretizing, we a...

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.