Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

The practice of book illustration: Three examples by Norah Borges

This article focuses on three different examples of book illustration carried out by Norah Borges in the 1930s and 1940s (Canciones de mar y tierra by Concha Méndez, Platero y yo by Juan Ramón Jiménez, and Paul et Virginie by Bernardin de Saint-Pierre). Its purpose is twofold: to show how illustrations can shape our reading of texts and to examine how the artist's work can be assimilated to a current of neorromanticismo in Spanish letters dating back to the pre-Civil War period. Her work might serve as an illustration of what Ramón Gómez de la Serna termed the cursi bueno, a marginalized reaction to the dehumanization of art that speaks of sentiment, domesticity and, in women's case, of repressed longing.

Virtual Engineering Centre - Examples of Virtual Prototyping and Multidisciplinary Design Optimization

The requirement for the use of Virtual Engineering, encompassing the construction of Virtual Prototypes using Multidisciplinary Design Optimisation, for the development of future aerospace platforms and systems is discussed. Some of the activities at the Virtual Engineering Centre, a University of Liverpool initiative, are described and a number of case studies involving a range of applications of Virtual Engineering illustrated.

A defeasible reasoning model of inductive concept learning from examples and communication

This paper introduces a logical model of inductive generalization, and specifically of the machine learning task of inductive concept learning (ICL). We argue that some inductive processes, like ICL, can be seen as a form of defeasible reasoning. We define a consequence relation characterizing which hypotheses can be induced from given sets of examples, and study its properties, showing they correspond to a rather well-behaved non-monotonic logic. We will also show that with the addition of a preference relation on inductive theories we can characterize the inductive bias of ICL algorithms. The second part of the paper shows how this logical characterization of inductive generalization can be integrated with another form of non-monotonic reasoning (argumentation), to define a model of multiagent ICL. This integration allows two or more agents to learn, in a consistent way, both from induction and from arguments used in the communication between them. We show that the inductive theories achieved by multiagent induction plus argumentation are sound, i.e. they are precisely the same as the inductive theories built by a single agent with all data. © 2012 Elsevier B.V.