Multilinear Calderón-Zygmund Theory

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.     

Microscopic model for thin film spreading

A microscopic, driven lattice gas model is proposed for the dynamics and spatiotemporal fluctuations of the precursor film observed in spreading experiments. Matter is transported both by holes and particles, and the distribution of each can be described by driven diffusion with a moving boundary. This picture leads to a stochastic partial differential equation for the shape of the boundary. Explicit analytic results are obtained which agree with the simulations of the lattice gas.     

Origin of the asymmetric magnetization reversal behavior in exchange-biased systems: competing anisotropies

The magnetization reversal in exchange-biased ferromagnetic-antiferromagnetic (FM-AFM) bilayers is investigated. Different reversal pathways on each branch of the hysteresis loop, i.e., asymmetry, are obtained both experimentally and theoretically when the magnetic field is applied at certain angles from the anisotropy direction. The range of angles and the magnitude of this asymmetry are determined by the ratio between the FM anisotropy and the interfacial FM-AFM exchange anisotropy. The occurrence of asymmetry is linked with the appearance of irreversibility, i.e., finite coercivity, as well as with the maximum of exchange bias, increasing for larger anisotropy ratios. Our results indicate that asymmetric hysteresis loops are intrinsic to exchange-biased systems and the competition between anisotropies determines the asymmetric behavior of the magnetization reversal.     

Consistent discretization and loop quantum geometry

We apply the "consistent discretization" approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism constraint to reduce its space of solutions and the constraint is preserved exactly under the discrete evolution. One ends up with a theory that has as physical space what is usually considered the kinematical space of loop quantum geometry, given by diffeomorphism invariant spin networks endowed with appropriate rigorously defined diffeomorphism invariant measures and inner products. The dynamics can be implemented as a unitary transformation and the problem of time explicitly solved or at least reduced to a numerical problem. We exhibit the technique explicitly in (2+1)-dimensional gravity.     

10 kHz detection of CO2 at 4.5 microm by using tunable diode-laser-based difference-frequency generation

A compact, high-speed tunable, diode-laser-based mid-infrared (MIR) laser source has been developed for absorption spectroscopy of CO2 at rates up to 10 kHz. Radiation at 4.5 microm with a mode-hop-free tuning range of 80 GHz is generated by difference-frequency mixing the 860 nm output of a distributed-feedback diode laser with the 1064 nm output of a diode-pumped Nd:YAG laser in a periodically poled lithium niobate crystal. MIR absorption spectroscopy of CO2 with a detection limit of 44 ppm m at 10 kHz is demonstrated in a C2H4-air laminar diffusion flame and in the exhaust of a liquid-fueled model gas-turbine combustor.     

A novel sulfonamidoglycosylation of glycals

[reaction: see text] The sulfonamidoglycosylation of benzylated glycals using a catalytic amount of triphenylphosphine hydrobromide proceeded in a highly stereoselective fashion to give the beta anomers with good to high yields. This process was demonstrated with d-galactal and d-glucal. Two of the new N-2-(deoxyglycosyl)sulfonamides were tested as inhibitors of tumor cell growth in vitro and showed antiproliferative properties in the micromolar range.     

Biomimetic synthesis of biatractylolide and biepiasterolide

[reaction: see text] The biomimetic synthesis of the bisesquiterpenoids biatractylolide 1 and biepiasterolide 2 is reported.     

Finite element approximation of spectral problems with Neumann boundary conditions on curved domains

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain in the framework of the abstract spectral approximation theory.

     

Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.