Search results for "parable"

On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces

2007

We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.

Comparing weak versions of separability

2012

Our aim is to investigate spaces with sigma-discrete and meager dense sets, as well as selective versions of these properties. We construct numerous examples to point out the differences between these classes while answering questions of Tkachuk [30], Hutchinson [17] and the authors of [8].

Countable connected spaces and bunches of arcs in R3

2006

Abstract We investigate the images (also called quotients) of countable connected bunches of arcs in R 3 , obtained by shrinking the arcs to points (see Section 2 for definitions of new terms). First, we give an intrinsic description of such images among T 1 -spaces: they are precisely countable and weakly first countable spaces. Moreover, an image is first countable if and only if it can be represented as a quotient of another bunch with its projection hereditarily quotient (Theorem 2.7). Applying this result we see, for instance, that two classical countable connected T 2 -spaces—the Bing space [R.H. Bing, A connected countable Hausdorff space, Proc. Amer. Math. Soc. 4 (1953) 474], and th…

Almost disjoint families of countable sets and separable complementation properties

2012

We study the separable complementation property (SCP) and its natural variations in Banach spaces of continuous functions over compacta $K_{\mathcal A}$ induced by almost disjoint families ${\mathcal A}$ of countable subsets of uncountable sets. For these spaces, we prove among others that $C(K_{\mathcal A})$ has the controlled variant of the separable complementation property if and only if $C(K_{\mathcal A})$ is Lindel\"of in the weak topology if and only if $K_{\mathcal A}$ is monolithic. We give an example of ${\mathcal A}$ for which $C(K_{\mathcal A})$ has the SCP, while $K_{\mathcal A}$ is not monolithic and an example of a space $C(K_{\mathcal A})$ with controlled and continuous SCP …

Multi-Locus Phylogenetic Analyses of the Almadablennius Clade Reveals Inconsistencies with the Present Taxonomy of Blenniid Fishes

2022

We used a multi-locus phylogenetic approach (i.e., combining both mitochondrial and nuclear DNA fragments) to address some long-standing taxonomic inconsistencies within the diverse fish clade of Combtooth Blennies (Blenniidae—unranked clade Almadablennius). The obtained phylogenetic trees revealed some major inconsistencies in the current taxonomy of Parablennini, such as the paraphyletic status of the Salaria and Parablennius genera, casting some doubt regarding their actual phylogenetic relationship. Furthermore, a scarce-to-absent genetic differentiation was observed among the three species belonging to the genus Chasmodes. This study provides an updated taxonomy and phylogeny of the fo…

Refus d'application de la notion de faute séparable du dirigeant par le juge pénal : annexe

2018

"Sipensamos en espacios de perpetración, no hay nada comparable al Valle de los Caídos". Conversación con Francisco Ferrándiz

2021

Comment on `Critical scalar field collapse in AdS$_3$: an analytical approach'

2014

We comment on the derivation of an analytical solution presented in arXiv:1309.1629, show that it belongs to a family of separable solutions previously constructed in arXiv:gr-qc/0109002, and question its relevance to critical collapse.

Finite-range separable pairing interaction within the new N3LO DFT approach

2011

For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N3LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N3LO energy …

On identification of separable kernel systems

1979

An identification procedure for special separable kernel systems is presented. The suitable definition of adequateness of a signal leads to a systematic treatment of the choice of inputs for identification.