Asymptotic behavior of coupled Euler-Bernoulli beams with pointwise dissipation

Examples of coupled Euler-Bernoulli beams with pointwise dissipation are considered. Exponential decay of energy is shown independently of the support of the pointwise dissipation.     

Band gap and band offsets of GaNAsBi lattice matched to GaAs substrate

In this paper, we calculate the band gap and the band discontinuities of a GaN _y AsBi _x structure lattice matched to GaAs substrate using the conduction and the valence band anticrossing models at the same time. The results obtained show a good agreement with experiment. The nitrogen and the bismuth concentrations leading to a wavelength emission of 1.55 μm have been determined (x = 3.5%, y = 2%). This structure shows a good electron confinement resulting in a high characteristic temperature.     

The repulsive Coulomb barrier along a dissociation path of the BeC(2-)(4) dianion

We present ab initio calculations of the repulsive Coulomb barrier for several geometrically stable isomers of the BeC(2-)(4) dianion. We describe how the deformation of certain isomers can account for the experimental Coulomb explosion images of the dianion. For the most stable linear isomer, C(-)(2)BeC(-)(2), we examined the electron tunneling process along the dissociation path to obtain C(-)(2) plus BeC(-)(2). We found the crossing point for autodetachment to be R(c)(dis)= 3.25 A. R(dis) is the bond length between C(-)(2) and BeC(-)(2); at this point, the electron tunneling energy is equal to the maximum of the repulsive Coulomb barrier. In the framework of the Wenzel-Kramer-Brioullin theory, the electron-loss lifetime of the metastable C(-)(2)BeC(-)(2) dianion at the equilibrium geometry, R(dis) = 1.64 A, was estimated to be about 5 ms. This lower limit is in agreement with the experimental results in which the BeC(2-)(4) dianion has a lifetime much longer than 5 micros.     

Finite size scaling for the atomic Shannon-information entropy

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.     

The mixing advantage is less than 2

Corresponding to n independent non-negative random variables X ₁,...,X _n , are values M ₁,...,M _n , where each M _i is the expected value of the maximum of n independent copies of X _i . We obtain an upper bound for the expected value of the maximum of X ₁,...,X _n in terms of M ₁,...,M _n . This inequality is sharp in the sense that the random variables can be chosen so that the bound is approached arbitrarily closely. We also present related comparison results.      

Invariance principle for biased bootstrap random walks

Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is built, from the original sequence, according to a cellular automata rule. Equipped with these two sequences, we construct two more according to the same cellular automata rule. The construction is repeated a fixed number of times yielding an infinite array ($\{?K,\dots ,K\}\times \mathbb{N}$) of (dependent) Bernoulli random variables. Taking partial sums of these sequences, we obtain a $(2K+1)$-dimensional process whose increments belong to the state space ${\{?1,1\}}^{2K+1}$.The aim of the paper is to study the long term behaviour of this process. In particular, we establish transience/recurrence properties and prove an invariance principle. The limiting behaviour of these processes depends strongly on the direction of the iteration, and exhibits few surprising features. This work is motivated by an earlier investigation (see Collevecchio et al. (2015)), in which the starting sequence is symmetric, and by the related work Ferrari et al. (2000).     

An XPS,ISS and ESR Comparative Study of Eight-Coordination of Copper (II) Ions in the CuTho Compounds

In this study, we attempted to clarify the coordination state and the distribution of copper (II) ions in the CuThO compounds prepared by coprecipitation, by using several physico-chemical techniques in particular, X-Ray Photoelectron Spectroscopy (XPS).

For atomic ratios Cu/Th ≤ 0.25, the copper (II) species are mainly located near the thoria surface. The Cu2p_3/2 level shows a chemical shift towards the lower binding energy compared to Cu²⁺ ions in CuO and also a net decrease in the intensity of the satellite peak, characteristic of copper (11). A relation between these observations and the covalent character o f Cuzt- 02- bond i s esta- blished. Eightfold coordination of copper (11) i n the thoria lattice i s evident. These conclusions are in good agreement with Electron Spin Resonance (ESR) results.

For a higher atomic ratio (Cu/Th > 0.25), a formation o f copper oxide crystallites i s observed on the thoria surface.     

Investigations on the structure of 4-methyldihydro-1,3,4-benzotriazepin-5-ones. Tautomer reassignment

The tautomerism of 4-methyldihydro-1,3,4-benzotriazepin-5-ones (2,3) is re-investigated by means of X-ray diffraction and quantum chemical calculations. The data revealed that the model compound (2a) exists in the amidrazone 1,4-dihydro tautomeric form (A), but not in the alternate 3,4-dihydro tautomer (B) as was previously reported.     

Decay rates at low and high frequencies for a plate equation with feedback concentrated in interior curves

In this paper we study the stabilization of plate vibrations by means of piezoelectric actuators. In this situation the geometric control condition of Bardos, Lebeau and Rauch [6] is not satisfied. We prove that we have exponential stability for the low frequencies but not for the high frequencies. We give an explicit decay rate for regular initial data at high frequencies while clarifying the behavior of the constant which intervenes in this estimation there function of the frequency of cut n. The method used is based on some trace regularity which reduces stability to some observability inequalities for the corresponding undamped problem. Moreover, we show numerically at low frequencies, that the optimal location of the actuator is the center of the domain Ω. Research supported by the RIP program of Oberwolfach Institut and by the Tunisian Ministry for Scientific Research and Technology (MRST) under Grant 02/UR/15-01. Research supported by the RIP program of Oberwolfach Institut. (Received: September 17, 2003; revised: February 26, 2004)