1,201 research outputs found
Collectivity, distributivity, and the interpretation of numerical expressions in child and adult language
No full textSentences containing plural numerical expressions (e.g., two boys) can give rise to two interpretations (collective and distributive), arising from the fact that their representation admits of a part-whole structure. We present the results of a series of experiments designed to explore children’s understanding of this distinction and its implications for the acquisition of linguistic expressions with number words. We show that preschoolers access both interpretations, indicating that they have the requisite linguistic and conceptual machinery to generate the corresponding representations. Furthermore, they can shift their interpretation in response to structural and lexical manipulations. However, they are not fully adult-like: unlike adults, they are drawn to the distributive interpretation, and are not yet fully aware of the lexical semantics of each and together, which should favor one or another interpretation. This research bridges a gap between a well-established body of work in cognitive psychology on the acquisition of number words and more recent work investigating children’s knowledge of the syntactic and semantic properties of sentences featuring numerical expressions.Peer reviewe
A functional analytic approach to homogenization problems
No full textWe plan to illustrate a functional analytic approach to analyze homogenization problems, which has already been developed for singular perturbation problems in bounded domains with small holes (cf. e.g., Lanza de Cristoforis (Comput Methods Funct Theory 2:1– 27, 2002), Lanza de Cristoforis (Analysis (Munich) 28:63–93, 2008), Lanza de Cristoforis (Complex Var Elliptic Equ 55:269–303, 2010) Lanza de Cristoforis (Rev Mat Comput 25:369–412, 2012)). In the frame of linearized elastostatics and of the Stokes equations, we mention Dalla Riva and Lanza de Cristoforis (Complex Var Elliptic Equ 55:771–794, 2010; Complex Anal Oper Theory 5:811–833, 2011), and Dalla Riva (Complex Var Elliptic Equ 58:231–257, 2013). Later on, such an approach has been exploited for the analysis of problems in unbounded perforated domains with a fixed periodic structure, for example in Lanza de Cristoforis and Musolino (Complex Var Elliptic Equ 58:511–536, 2013; Commun Pure Appl Anal 13:2509–2542, 2014; Math Methods Appl Sci 35:334–349, 2012). Instead, here we consider the case where also the size of the periodicity cell tends to zero. The results in this chapter are based on the work of Lanza de Cristoforis and Musolino (Two-parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach, Typewritten manuscript, 2014)
Problemi di perturbazione singolare e di omogeneizzazione in un dominio periodicamente perforato. Un approccio funzionale analitco
No full textAsymptotic behavior of generalized capacities with applications to eigenvalue perturbations: The higher dimensional case
No full textWe provide a full series expansion of a generalization of the so-called u-capacity related to the Dirichlet-Laplacian in dimension three and higher, extending the results of Abatangelo et al. (2021); Abatangelo, Lena and Musolino (2022) dealing with the planar case. We apply the result in order to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain of the eigenvalue problem. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
A Functional Analytic Approach for a Singularly Perturbed Dirichlet Problem for the Laplace Operator in a Periodically Perforated Domain
No full textWe consider a sufficiently regular bounded open connected subset of such that and such that \mathbb{R}^n \setminus \cl\Omega is connected. Then we choose a point . If is a small positive real number, then we define the periodically perforated domain T(\epsilon) \equiv \mathbb{R}^n\setminus \cup_{z \in \mathbb{Z}^n}\cl(w+\epsilon \Omega +z). For each small positive , we introduce a particular Dirichlet problem for the Laplace operator in the set . More precisely, we consider a Dirichlet condition on the boundary of the set , and we denote the unique periodic solution of this problem by . Then we show that (suitable restrictions of) can be continued real analytically in the parameter around
Singular perturbation and homogenization problems in a periodically perforated domain. A functional analytic approach (Tesi di dottorato, Università degli Studi di Padova, Italia)
No full textReal analytic families of harmonic functions in a domain with a small hole
No full textLet . Let and be open bounded connected subsets of containing the origin. Let be such that contains the closure of for all . Then, for a fixed we consider a Dirichlet problem for the Laplace operator in the perforated domain . We denote by the corresponding solution. If and , then we know that under suitable regularity assumptions there exist and a real analytic operator from to such that for all . Thus it is natural to ask what happens to the equality for negative. We show a general result on continuation properties of some particular real analytic families of harmonic functions in domains with a small hole and we prove that the validity of the equality for negative depends on the parity of the dimension
Domain Perturbation for the Solution of a Periodic Dirichlet Problem
No full textWe prove that the solution of the periodic Dirichlet problem for the Laplace equation depends real analytically on a suitable parametrization of the shape of the domain, on the periodicity parameters, and on the Dirichlet datum
Perturbation analysis of the effective conductivity of a periodic composite
No full textWe consider the effective conductivity λeff of a periodic two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. Then we study the behavior of λeff upon perturbation of the shape of the inclusions, of the periodicity structure, and of the conductivity of each material
Sintesi e funzionalizzazione di molecole piattaforma da risorse rinnovabili impiegando carbonati organici
No full textIl termine bioraffineria abbraccia tutti i processi basati sulla biomassa che sono studiati come alternativi ai relativi processi/prodotti legati alla raffineria.1 La biomassa è una risorsa molto attraente in quanto fonte di carbonio ampiamente diffusa e a basso costo che include proteine, acidi grassi, lipidi e carboidrati. Tra i componenti della biomassa, i carboidrati ne costituiscono il 75% e rappresentano i composti più promettenti e di maggiore interesse. Le molecole provenienti dalla digestione e frammentazione della biomassa possono essere – a loro volta - funzionalizzate al fine di ottenere una vasta gamma di prodotti e sono per questo definite molecole piattaforma. Nel 2004, il Dipartimento dell'Energia degli Stati Uniti (DOE) ha pubblicato un elenco di molecole piattaforma derivate da risorse rinnovabili considerate di particolare interesse per lo sviluppo della bioraffineria.2 Il D-sorbitolo, l’isosorbitolo e 2,5-idrossimetilfurfurale (HMF) occupano una posizione di rilievo in questa lista dal momento che incorporano tutte le caratteristiche desiderate di una molecola piattaforma. Negli ultimi anni lo studio della reattività del sorbitolo con i dialchil carbonati ha permesso di mettere a punto una strategia sintetica green dell’isosorbide e della sua funzionalizzazione.3 Il dimetil carbonato si è inoltre dimostrato un ottimo solvente per la sintesi dell’HMF. Studi recenti sull’alchilazione del relativo composto ridotto 2,5-diidrossimetilfurano (BHMF) in condizioni blande hanno permesso la sintesi di una libreria di bis(alcossi)furani (Figura 1).4 I derivati dell’isosorbitolo (dimetil isosorbitolo e bis(metossicarbonil)isosorbitolo) e dell’HMF (Bis(idrossimetil)furano, bis(alcossimetil)furano) hanno numerose potenziali applicazioni come solventi green, monomeri per bioplastiche e additivi per carburanti.
Riferimenti
1. R. J. Van Putten, J. C. van der Waal, et al. Chem. Rev. 2013, 113, 1499.
2. T. Werpy, G. Petersen. U.S. Department of Energy, 2004; Vol. I.
3. F. Aricò, A. S. Aldoshin, P. Tundo, ChemSusChem 2017, 10, 53; F. Aricò, P. Tundo, Beilstein J. Org. Chem. 2016, 12, 2256.
4. M. Musolino, J. Andraos, F. Aricò, ChemistrySelect 2018, 3, 2359; M. Musolino, M. J. Ginés-Molina, R. Moreno-Tost, F. Aricò, ACS Sustainable Chem. Eng. 2019, asap artic
- …
