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.     

Synthesis and investigation of barium titanate nanoparticles covered with silica shell

Matrix isolation of ferroelectric BaTiO₃ nanoparticles was executed by formation of protective silica shell (via hydrolysis and polycondensation of tetraethyl orthosilicate) on particles of precursor—barium titanyl oxalate. Synthesized BaTiO₃–SiO₂ composites have been characterized by IR spectroscopy, XRD, TEM, DTA/DTG methods.     

The reduction of gold nanoparticles in the surface layer of modified silica

Silicas with deposited hydridepolysiloxane layers were used for the in situ preparation of gold nanoparticles by the reduction of metal ions from a solution of chloroauric acid. The metal-containing silicas obtained were characterized by X-ray powder diffraction, transmission electron microscopy, and UV, IR, and laser correlation spectroscopy.     

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.     

Standardness of automorphisms of transposition of intervals and fluxes on surfaces

In this article we shall prove a new necessary and sufficient condition for automorphisms to be standard, from which we shall deduce the standardness of an automorphism of transposition of intervals with respect to any continuous Borel invariant ergodic measure, and the standardness of the flux of the class C¹ on a two-dimensional compact variety with a finite number of stationary points and separatrices, with respect to any Borel invariant ergodic measure whose carrier contains an open set.Translated from Matematicheskie Zametki, Vol. 20, No. 4, pp. 479–488, October, 1976.     

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.     

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.