Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C

We study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms. This generalises work of Coleman, and is a first step in an ongoing project to extend the cohomological approach to classicality to higher-dimensional Shimura varieties.     

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.     

Efficient synthesis of the core structure of muraymycin and caprazamycin nucleoside antibiotics based on a stereochemically revised sulfur ylide reaction

The reaction of protected uridine 5′-aldehydes with sulfur ylides has been reinvestigated. Further transformation of the resulting epoxide product provided a compound of which a single crystal for X-ray diffraction was obtained. As a consequence from the elucidated structure, the stereochemical configuration of the epoxide furnished by the sulfur ylide reaction was revised. Based on these results, an efficient synthesis of the core structure of the naturally occurring muraymycin and caprazamycin nucleoside antibiotics was developed.     

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.     

The thermodynamic limit of quantum Coulomb systems Part I. General theory

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems.In this first part, we consider a general real-valued function E defined on all bounded open sets of R³. Our aim is to give sufficient conditions such that E has a thermodynamic limit. This means that the limit E(Ωn)|Ωn|⁻¹ exists for all ‘regular enough’ sequence Ωn with growing volume, |Ωn|→∞, and is independent of the considered sequence.The sufficient conditions presented in our work all have a clear physical interpretation. In the next paper, we show that the free energies of many different quantum Coulomb systems satisfy these assumptions, hence have a thermodynamic limit.     

Quantum chemical DFT study of 4-azatricyclo [5.2.2.02,6] undecane-3,5,8-trione

Fourier-transform-Raman and infrared spectrum of 4-azatricyclo [5.2.2.0^2,6] undecane-3,5,8-trione were recorded and analyzed. The vibrational wavenumbers were examined theoretically using the Gaussian03 set of quantum chemistry codes, and the normal modes were assigned by potential energy distribution (PED) calculations. The first hyperpolarizability, predicted infrared intensities and Raman activities are reported. The calculated first hyperpolarizability is comparable with reported values of similar structures which makes this compound an attractive object for future studies of nonlinear optics. Optimized geometrical parameters of the compound are in agreement with similar reported structures. The red shift of the NH stretching wavenumber in the infrared spectrum from the computational wavenumber indicates the weakening of NH bond.     

La somme des chiffres des carrés

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.