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.