Controlling the ratchet effect for cold atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.     

On Sums of Products of Bernoulli Variables and Random Permutations

Let {X _k } _k1 be independent Bernoulli random variables with parameters p _k . We study the distribution of the number or runs of length 2: that is . Let S=lim _n S _n . For the particular case p _k =1/(k+B), B being given, we show that the distribution of S is a Beta mixture of Poisson distributions. When B=0 this is a Poisson(1) distribution. For the particular case p _k =p for all k we obtain the generating function of S _n and the limiting distribution of S _n for .     

Alkaloids from the stem bark of Turraeanthus africanus (Meliaceae)

Fractionation of the methanol extract of the stem bark of Turraeanthus africanus led to the isolation of two new alkaloids designated turraeanthin A and B, together with two known alkaloids. The structures of the new alkaloids were elucidated by means of spectroscopic analysis and characterized as 10-O-demethyl-17-O-methyl isoarnottianamide and 11-demethoxyl-12-methoxyl oxynitidine respectively.     

Fast and accurate modeling of molecular atomization energies with machine learning

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr?dinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross validation over more than seven thousand organic molecules yields a mean absolute error of ～10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.     

Design guidelines of 1-3 piezoelectric composites dedicated to ultrasound imaging transducers, based on frequency band-gap considerations

Periodic piezoelectric composites are widely used for imaging applications such as biomedical imaging or nondestructive evaluation. In this paper such structures are considered as phononic crystals, and their properties are investigated with respect to periodicity. This approach is based on the investigation of band gaps, that strongly depend on the properties of the considered composites (geometry, size, nature of materials). It is motivated by the fact that band gaps in principle allow one to excite the thickness mode without exciting other parasitic propagating waves. The used plane-wave-expansion method has already been applied to periodic piezoelectric composites, but, in contrast to previous approaches, not only waves propagating in the symmetry plane of the composite are considered, but also waves propagating with a nonzero angle of incidence with this plane. The method is applied to a representative 1-3 connectivity piezocomposite in order to demonstrate its potentialities for design purposes. The evolution of band gaps is explored with respect to the wave vector component parallel to piezoelectric transducer-rod axis. All bulk waves that contribute to the setting up of plate modes in the vicinity of the thickness mode are found and identified.     

Son of the linear search problem

I wish to find something which is located on a certain road. I start at a point on the road, but I do not know in which direction the object sought is to be found. Somehow, I must incorporate in my way of searching the possibility that it is either to the right or to the left. Thus, I must search first to the right, and then to the left, and then to the right again until it is found. What is a good way of conducting this search, and what is a bad way? This general problem can be phrased in many ways mathematically, some of which are answered in the papers in the bibliography. In this paper, we consider three well-known assumptions concerning thea priori guesses for the probability distribution on where the object is located. These concern uniform distribution on an interval, triangular distribution around the original point, and normal distribution about that point. The uniform distribution has a simple answer. For the triangular distribution, we obtain qualitative results and calculate approximate values for the turning points.     

Electrochemical polymerization of aromatic amines: IR,XPS and PMT study of thin film formation on a Pt electrode

Films resulting from the anodic oxidation of various monosubstituted aromatic amines have been grafted on Pt electrodes in a CH₃CN?NaClO₄-pyridine medium. An in situ polaromicrotribometric study of changes occurring on the electrode surface during polarization indicates that these deposits have a stable friction coefficient of 1.3f_o. Their analysis by multiple-reflection IR spectroscopy and by X-ray photoelectron spectroscopy shows that these films are organic polymers of emeraldine basic structure and that they probably result from the coupling of electrochemically formed NH^. radicals with the monomer. These films are homogeneous, very adherent, thermally stable and free of ionic impurities. In the dry state they display a conductivity of 5×10^?13 Ω^?1 cm^?1 which is characteristic of insulators.     

Caustics for inner and outer billiards

With a plane closed convex curve,T, we associate two area preserving twist maps: the (classical) inner billiard inT and the outer billiard in the exterior ofT. The invariant circles of these twist maps correspond to certain plane curves: the inner and the outer caustics ofT. We investigate how the shape ofT determines the possible location of caustics, establish the existence of open regions which are free of caustics, and estimate fro below the size of these regions in terms of the geometry ofT.Partially supported by NSF.Partially supported by NSF Grant DMS 9017995.     

Perturbation des produits infinis et applications

Sans résumé Les auteurs remercient l'Institut de recherche d'été de la Société Mathématiques du Canada, le CNR, DIGES du Québec et la Fondation Fleischer pour leur appui. An erratum to this article is available at .