Numerical aspects of nonlinear Schrodinger equations in the presence of caustics

The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schrodinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point singularity for which several results have been proven rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed.Comment: 20 pages. To appear in Math. Mod. Meth. Appl. Sc

Governance in Spanish Savings Banks. A Historical Perspective

During the previous three decades, mutual financial firms have been experiencing a process of demutualization, and some of the non-for-profit banks have become publicly listed companies. Hence, the persistence of the Spanish Savings Banks constitutes an interesting case study. In line with recent literature, this paper attempts to reach a better understanding of the factors that have contributed to the persistence of these entities in the long run and to the maintenance of a very specific model of corporate governance. Regulatory influences, politics and political institutions have proved to be key elements of a model which has proved capable of delivering successful outcomes in increasingly competitive conditions. Nonetheless, the financial crisis would seem to have exacerbated the stresses and strains within this model and, in combination with the pressure of increasingly globalized markets, the Spanish Savings Banks find themselves in a new scenario.corporate governance; stakeholder regime; savings banks

The diversity of organisational forms in banking: France, Italy and Spain 1900-2000

This paper examines, from a historical perspective, the gradual entrance into the market of mutual and not for profit banks (specifically cooperative banks and savings banks), their continually increasing competitiveness with traded banks in France, Italy and Spain. In all three countries, these institutions played an important role in the retail banking sector. Special attention will be devoted to analysing the different models of adjustment adopted by the banking systems in the south of Europe in the wake of the deregulating process undertaken in the last quarter of the twentieth century. In summary, then, this paper is an attempt to identify the historical factors responsible for the persistence, or disappearance, of certain idiosyncratic aspects of the banking system in each country, together with the various adjustments produced in each case.banks, savings banks, co-operative banks, comparative banking systems, France, Spain, Italy

A generalization of Ohkawa's theorem

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.Comment: 13 pages; consequences in motivic homotopy theory have been adde

Organisational change and the computerisation of British and Spanish savings banks, 1965-1985

In this article we explore organisational changes associated with the automation of financial intermediaries in Spain and the UK. This international comparison looks at the evolution of the same organisational form in two distinct competitive environments. Changes in regulation and technological developments (particularly applications of information technology) are said to be responsible for enhancing competitiveness of retail finance. Archival research on the evolution of savings banks helps to ascertain how, prior to competitive changes taking place, participants in bank markets had to develop capabilities to compete