On universal Banach spaces of density continuum

We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).

Catalogue of the type material of Neriidae (Diptera, Schizophora) in the collection of the Museum fur Naturkunde Berlin, Germany

The Diptera collection of the Natural History Museum Berlin holds one of the most important collections of Neriidae. In this paper, the type specimens (holotypes, lectotypes, paratypes, paralectotypes, syntypes) of this historical collection are listed. 28 species-group taxa are dealt with. A lectotype designation is made for the species Brachantichir purpusianus Enderlein, 1922 in order to fix the identity of the name. Holotypes are recognized by monotypy of the species Chaetomeristes bullatus Enderlein, 1922; Chaetomeristes peruanus Enderlein, 1922; Derocephalus angusticollis Enderlein, 1922; Glyphidops limbatus Enderlein, 1922; Longina abdominalis Wiedemann, 1830; Loxozus clavicornis Enderlein, 1922; Oncopsia mexicana Enderlein, 1922; Paranerius fibulatus Enderlein, 1922; Telostylinus dahli Enderlein, 1922; Telostylus latibrachium Enderlein, 1922; and Telostylinus luridus Enderlein, 1922. Syntypes are labelled and listed for Brachantichir robusta Enderlein, 1922; Nerius terebratus Enderlein, 1922; Odontoloxozus punctulatus Enderlein, 1922; Telostylinus apicalis Enderlein, 1922; Telostylinus obscuratus Enderlein, 1922; and Telostylinus ornatipennis Enderlein, 1922. The account concludes with geographic and taxonomic summaries; an appendix listing the abbreviations, localities, and collectors cited in the text; and a bibliography. ((c) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hypoellipticity in spaces of ultradistributions-Study of a model case

In this work we study C (a)-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hormander's condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.