‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

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...

Let X = lp, p ∈ (2,+∞). We construct a function f : X → R which has Lipschitz Fréchet derivative on X but is not a d.c. function.

We investigate several extension properties of Fréchet differentiable functions defined on closed sets for o-minimal expansions of real closed fields.

— 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...

We present the analytic foundation of a unified B-D-F extension functor Extr on the category of noncommutative smooth algebras, for any Fréchet operator ideal ^ . Combining the techniques devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth algebras and Fréchet operator ideals. A key notion involved is r-smoothness, which is verified for the algebras of smooth functio...