Search results for "Frame"
showing 10 items of 1767 documents
Distributions Frames and bases
2018
In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal D$ of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frame, Riesz basis and orthonormal basis. A motivation for this study comes from the Gel'fand-Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain $\mathcal D$ which acts like an orthonormal basis of the Hilbert space $\mathcal H$. The correspond…
Frames and representing systems in Fréchet spaces and their duals
2014
[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.
Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces
2016
Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every \(\omega \)-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrodinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.
PIP-Space Valued Reproducing Pairs of Measurable Functions
2019
We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space Z : = Z ( X , μ ), where ( X , μ ) is a measure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbert spaces; (ii) Y is a Hilbert space, but Z is a pip-space; (iii) Y and Z are both pip-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space Y. Examples are presented for each case.
Synergetic effect of host-guest chemistry and spin crossover in 3D Hofmann-like metal-organic frameworks [Fe(bpac)M(CN)4] (M=Pt, Pd, Ni).
2012
The synthesis and characterization of a series of three-dimensional (3D) Hofmann-like clathrate porous metal-organic framework (MOF) materials [Fe(bpac)M(CN) 4] (M=Pt, Pd, and Ni; bpac=bis(4-pyridyl)acetylene) that exhibit spin-crossover behavior is reported. The rigid bpac ligand is longer than the previously used azopyridine and pyrazine and has been selected with the aim to improve both the spin-crossover properties and the porosity of the corresponding porous coordination polymers (PCPs). The 3D network is composed of successive {Fe[M(CN) 4]} n planar layers bridged by the bis-monodentate bpac ligand linked in the apical positions of the iron center. The large void between the layers, w…
Zebrafish as a Model to Evaluate a CRISPR/Cas9-Based Exon Excision Approach as a Future Treatment Option for EYS-Associated Retinitis Pigmentosa
2021
Retinitis pigmentosa (RP) is an inherited retinal disease (IRD) with an overall prevalence of 1 in 4000 individuals. Mutations in EYS (Eyes shut homolog) are among the most frequent causes of non-syndromic autosomal recessively inherited RP and act via a loss-of-function mechanism. In light of the recent successes for other IRDs, we investigated the therapeutic potential of exon skipping for EYS-associated RP. CRISPR/Cas9 was employed to generate zebrafish from which the region encompassing the orthologous exons 37-41 of human EYS (eys exons 40-44) was excised from the genome. The excision of these exons was predicted to maintain the open reading frame and to result in the removal of exactl…
Governance models of coopetition and innovation: the case of Spanish firms
2016
Although numerous studies show that cooperation relates strongly to obtaining benefits in business innovation, few researchers have considered the role of competition in this relationship. Nevertheless, it is expected that firms can boost their innovation if they cooperate with competitors and with intermediaries. The aim of this study was to observe whether coopeting firms achieve high degrees of innovation. To accomplish this aim, we used a sample of innovative firms from the region of Valencia (Spain). The chosen region has specific structural characteristics, which are discussed later. Although the sampled firms compete with one another, they also collaborate with each other and with in…
Receiving water quality assessment: comparison between simplified and detailed integrated urban modelling approaches
2010
Urban water quality management often requires use of numerical models allowing the evaluation of the cause–effect relationship between the input(s) (i.e. rainfall, pollutant concentrations on catchment surface and in sewer system) and the resulting water quality response. The conventional approach to the system (i.e. sewer system, wastewater treatment plant and receiving water body), considering each component separately, does not enable optimisation of the whole system. However, recent gains in understanding and modelling make it possible to represent the system as a whole and optimise its overall performance. Indeed, integrated urban drainage modelling is of growing interest for tools to …
Corresponsabilità e cura educativa dei genitori nello “zero-sei”: un’esperienza di ricerca e formazione attraversata dalla pandemia
2022
This paper focuses on early childhood educators as possible facilitators of educational co-responsibility with families and, therefore, of inclusive educating communities, in line with the PNRR. A research-training with educators from Palermo, which began before the pandemic and was then reformulated, is presented. For this research, a questionnaire was administered in 2019 to investigate three areas from which, according to the literature, obstacles to an effective educational alliance often arise: educators’ understanding of current family education, what educators think parents to be and ideas of co-responsibility. In 2022, an online questionnaire similar to the first was administered, a…
Quality assurance and assessment frameworks of Italian Biosystems Engineering studies
2010
In Italy the tools for quality assurance and assessment frameworks of all University studies are established by the D.M. (Law) of the Ministry of Education, University and Research n. 544 of the 31st October 2007, dealing with the requirements that Universities must have every year in order to offer degree study programs. Moreover, the accreditation procedure is established by the Law of the Italian Ministry of Work and Welfare n. 166 of the 25th May 2001, by which each Italian Regional administration can recognise the proposal and organisation of teaching activities (e.g. higher education) or guidance ones, funded by public resources, to public and/or private bodies (e.g. Universities). Th…