Unitary rotation and gyration of pixellated images on rectangular screens

In the two space dimensions of screens in optical sy stems, rotations, gyrations, and fractional Fourier transformations form the Fourier subgroup of the symplectic group of linear canonical transformations: U(2) F $\subset$ Sp(4,R). Here we study the action of this Fourier group on pixellated images within generic rectangular $N_x$ $\times$ $N_y$ screens; its elements here compose properly and act unitarily, i.e., without loss of information.Comment: 7 pages, 5 figure

A Simple Dynamic Model of Credit and Aggregate Demand

The purpose of the paper is to present a tractable model of an old topic which is becoming more important in macroeconomics: the link between financial structure and economic activity.Aggregate Demand, Fiscal Policy, Monetary Policy, moral hazard, adverse selection, suuply of credit, reserves.

How does financial theory apply to catastrophe-linked derivatives? En empirical test of several princing models

The paper focuses on the PCS Catastrophe Insurance Option Contracts and empirically tests the degree of agreement between their real quotes and the standard fmancial theory. The highest possible precision is incorporated since the real quotes are perfectly synchronized and the bid-ask spread is always considered. A static setting is assumed and the main topics of arbitrage, hedging and portfolio choice are involved in the analysis. Three significant conclusions are reached. First, the catastrophe derivatives may be very often priced by arbitrage methods, and the paper provides some examples of practical strategies that were available in the market. Second, hedging arguments also yield adequate criteria to price the derivatives and some real examples are provided as well. Third, in a variance aversion context many agents could be interested in selling derivatives to invest the money in stocks and bonds. These strategies show a suitable level in the variance for any desired expected return. Furthermore, the methodology here applied seems to be quite general and may be useful to price other derivative securities. Simple assumptions on the underlying asset behavior are the only required conditions

Thermodynamics, transition dynamics, and texturing in polymer-dispersed liquid crystals with mesogens exhibiting a direct isotropic/smectic-A transition

Experimental and modeling/simulation studies of phase equilibrium and growth morphologies of novel polymer-dispersed liquid crystal (PDLC) mixtures of PS (polystyrene) and liquid crystals that exhibit a direct isotropic/smectic-A (lamellar) mesophase transition were performed for PS/10CB (decyl- cyanobiphenyl) and PS/12CB (dodecyl-cyanobiphenyl). Partial phase diagrams were determined using polarized optical microscopy (POM) and differential scanning calorimetry (DSC) for different compositions of both materials, determining both phase separation (liquid/liquid demixing) and phase ordering (isotropic/smectic-A transition) temperatures. The Flory-Huggins theory of isotropic mixing and Maier-Saupe-McMillan theory for smectic-A liquid crystalline ordering were used to computationally determine phase diagrams for both systems, showing good agreement with the experimental results. In addition to thermodynamic observations, growth morphology relations were found depending on phase transition sequence, quench rate, and material composition. Three stages of liquid crystal-rich domain growth morphology were observed: spherical macroscale domain growth ("stage I"), highly anisotropic domain growth ("stage II"), and sub-micron spheroid domain growth ("stage III"). Nano-scale structure of spheroidal and spherocylindrical morphologies were then determined via two-dimensional simulation of a high-order Landau-de Gennes model. Morphologies observed during stage II growth are typical of di- rect isotropic/smectic-A phase transitions, such as highly anisotropic "batonnets" and filaments. These morphologies, which are found to be persistent in direct isotropic/smectic-A PDLCs, could provide new functionality and applications for these functional materials.Comment: First Revision, 21 pages, 11 figures, submitted to Macromolecules as an article 17JUL200