On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

Structural relaxation time for various liquids

The structural relaxation time for series of various liquids (alkanes, aliphatic alcohols, and diols) are calculated from published data on the shear viscosity and the heat of evaporation per unit volume. Liquids having a 3D H-bond network (diols) are characterized by relaxation times one to two orders of magnitudes longer than those typical of liquids without such a network (alkanes and aliphatic alcohols).     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.     

Two-Variable Identities in Groups and Lie Algebras

We study two-variable Engel-like relations and identities characterizing finite-dimensional solvable Lie algebras and, conjecturally, finite solvable groups and introduce some invariants of finite groups associated with such relations. Bibliography: 29 titles.     

A tight-binding study of LUMO states in ellipsoidal silicon nanocrystals

In this paper we report on tight-binding calculations of lowest unoccupied molecular orbitals states for silicon ellipsoidal nanocrystals. The electronic structure has been calculated for different nanocrystal shapes either keeping constant or varying the number of silicon atoms. We have found that changing the ellipsoid aspect ratio a non-obvious energy level structure is obtained. The implications for the infrared optical transitions and their relationship with the polarization of the radiation involved are discussed.     

The structure of CeAlO3 by Rietveld refinement of X-ray powder diffraction data

The room temperature structure of perovskite CeAlO₃ has been reinvestigated by X-ray powder diffraction. The Rietveld refinement has confirmed the tetragonal symmetry; but revealed a super cell, a=5.32489(6) Å and c=7.58976(10) Å, with the space group I4/mcm. In CeAlO₃, the distortion from the ideal cubic perovskite is caused by the cooperative tilting of the AlO₆ octahedra around the primitive cubic [001]_p-axis.     

On a new calcium vanadate: synthesis, structure and Li insertion behavior

A synthetic form of the mineral hewettite was prepared via a new route in aqueous medium, starting either from the crystalline compound Li_1.1V₃O₈, or from its amorphous precursor. The anhydrous, crystalline derivative Ca_0.5V₃O₈ was obtained by heating the synthetic hewettite at 250°C under dynamic vacuum. The diffraction studies show that the 2D structure of Ca_0.5V₃O₈ involves the same V₃O₈ layers as in the hewettite or in Li_1+αV₃O₈. The stacking of the layers is similar to that in the metahewettite. A structural model is proposed, where the Ca²⁺ ions occupy octahedral sites in the interlayer space. The electrochemical behavior of Ca_0.5V₃O₈ vs. lithium insertion is presented. It is original and reveals particularly good performances in terms of stability during cycling at C/5 rate. The homologues obtained with Mg or Ba, instead of Ca, are briefly presented.