Rigorous diffraction theory applied to microlenses

Diffraction of random tilings: some rigorous results

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar random tilings based on solvable dimer models. This article also contains a summary of the measure the...

Diffraction Theory

Rough set theory applied to lattice theory

In this paper, we intend to study a connection between rough sets and lattice theory. We introduce the concepts of upper and lower rough ideals (filters) in a lattice. Then, we offer some of their properties with regard to prime ideals (filters), the set of all fixed points, compact elements, and homomorphisms. 2012 Elsevier Inc. All rights reserved.

Semigroup Theory Applied to Options

Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some condition...

Constraint Theory applied to Proteins

In this article we review how constraint theory can be applied to proteins to give useful information about the rigid and flexible regions. This approach includes all the constraints in a biomolecule that are important at room temperature. A rigid region decomposition determines the rigid regions (both stressed and unstressed) and the flexible regions that separate them. Such a rigid region dec...