First-return integrals

Properties of first-return integrals of real functions defined on the unit interval are explored. In particular, first-return integrals are shown to be continuous but not absolutely continuous.     

Bass-Tits minimization of automata, quotients of trees and diameters

Let X be a tree and let G=Aut(X), Bass and Tits have given an algorithm to construct the ‘ultimate quotient’ of X by G starting with any quotient of X, an ‘edge-indexed’ graph. Using a sequence of integers that we compute at consecutive steps of the Bass-Tits (BT) algorithm, we give a lower bound on the diameter of the ultimate quotient of a tree by its automorphism group. For a tree X with finite quotient, this gives a lower bound on the minimum number of generators of a uniform X-lattice whose quotient graph coincides with G?X. This also gives a criterion to determine if the ultimate quotient of a tree is infinite. We construct an edge-indexed graph (A,i) for a deterministic finite state automaton and show that the BT algorithm for computing the ultimate quotient of (A,i) coincides with state minimizing algorithm for finite state automata. We obtain a lower bound on the minimum number of states of the minimized automaton. This gives a new proof that language for the word problem in a finitely generated group is regular if and only if the group is finite, and a new proof that the language of the membership problem for a subgroup is regular if and only if the subgroup has finite index.     

A cryogenic underground observatory for rare events: CUORE, an update

CUORE is a proposed tightly packed array of 1000 TeO₂ bolometers, each being a cube 5 cm on a side with a mass of 750 g. The array consists of 25 vertical towers, arranged in a square of 5 towers by 5 towers, each containing ten layers of four crystals. The design of the detector is optimized for ultralow-background searches for neutrinoless double beta decay of ¹³⁰Te (33.8% abundance), cold dark matter, solar axions, and rare nuclear decays. A preliminary experiment involving 20 crystals of various sizes (MIBETA) has been completed, and a single CUORE tower is being constructed as a smaller scale experiment called CUORICINO. The expected performance and sensitivity, based on Monte Carlo simulations and extrapolations of present results, are reported.     

Free boundary enclosure in a three-dimensional filtration problem

We give a lower and an upper estimate for the level of a fluid filtrating through a porous, homogeneous and three-dimensional dam with variable cross-section.     

High energy radiation fluences in the ISS-USLab: Ion discrimination and particle abundances

The ALTEA (Anomalous Long Term Effects on Astronauts) detector was used to characterize the radiation environment inside the USLab of the International Space Station (ISS), where it measured the abundances of ions from Be to Fe. We compare the ALTEA results with Alteino results obtained in the PIRS module of the Russian segment of the ISS, and normalize to the high energy Si abundances given by Simpson. These are the first particle spectral measurements, which include ions up to Fe, performed in the USLab. The small differences observed between those made inside the USLab and the Simpson abundances can be attributed to the transport through the spacecraft hull. However, the low abundance of Fe cannot be attributed to only this process.     

Preparation and photoactivity of nanostructured anatase, rutile and brookite TiO2 thin films

Photoactive films consisting of pure anatase, brookite or rutile TiO2 were prepared by dip coating from water dispersions obtained by using TiCl4 as the precursor under similar mild experimental conditions.     

Highly anisotropic Dirac cones in epitaxial graphene modulated by an island superlattice

We present a new method to engineer the charge carrier mobility and its directional asymmetry in epitaxial graphene by using metal cluster superlattices self-assembled onto the moiré pattern formed by graphene on Ir(111). Angle-resolved photoemission spectroscopy reveals threefold symmetry in the band structure associated with strong renormalization of the electron group velocity close to the Dirac point giving rise to highly anisotropic Dirac cones. We further find that the cluster superlattice also affects the spectral-weight distribution of the carbon bands as well as the electronic gaps between graphene states.     

Using a factored dual in augmented Lagrangian methods for semidefinite programming

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further use the approximate maximum of the augmented Lagrangian with the aim of improving the convergence rate of alternating direction augmented Lagrangian frameworks. Numerical results are reported, showing the benefits of the approach.