Embedding by pseudo atoms,and the topologically determined one-electronic energy levels

It is shown that the embedding of covalent clusters with the help of pseudo atoms and thefullerene electronic structure of amorphous carbon can be studied by the same formalism. Tight-binding model calculations were done for silicon clusters. It was found that the covalent clusters often have topologically determined energy levels that are cleared out from the spectrum in the presence of embedding.     

Existence of strong solutions for Itô's stochastic equations via approximations

Summary Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on any probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ^d and in domains in ^d are considered.Research supported by the Hungarian National Foundation of Scientific Research No. 2990.Supported in part by NSF Grant DMS-9302516     

On the almost sure central limit theorem and domains of attraction

We give necessary and sufficient criteria for a sequence (X _n) of i.i.d. r.v.'s to satisfy the a.s. central limit theorem, i.e.,

Molecular structure and ring distortions of p-dichlorobenzene as determined by electron diffraction

The molecular structure of p-dichlorobenzene in the vapour phase has been studied by electron diffraction. Least-squares refinement of a model with D_2h symmetry has led to the accurate determination of the small deviations of the benzene ring from D_6h symmetry caused by the chlorine substituents. The most appreciable effect is an increase from 120° to 121.6 ± 0.2° of the internal angle at the ipso carbon, associated with a shortening of the distance between the two ipso atoms. A less pronounced effect is a shortening of the C-C bonds that originate from the ipso carbons as compared to the central C-C bonds (r_g = 139.0 ± 0.3 pm vs. 139.5 ± 0.4 pm). Other bond distances are r_g (C-Cl) - 173.0 ± 0.4 pm and r_g (C-H) = 109.4 ± 1.0 pm. The observed ring distortions are in agreement with those obtained by low-temperature X-ray crystallography on three different crystal phases of p-dichlorobenzene. They are also consistent with those obtained for chloro-benzene by gas-phase electron diffraction and by NMR spectroscopy in a nematic solvent. The r_s structure of chlorobenzene obtained in a recent study by micro-wave spectroscopy is shown to need revision, as far as the ipso region of the ring is concerned.     

The electronic structure of nonpolyhex carbon nanotubes

Generalizing the folding method to any periodic two-dimensional planar carbon structures we have calculated the corresponding electronic structures in the framework of the one orbital one site tight-binding (Bloch-Hückel) method by solving the eigenvalue problems in a numerical way. We discussed the metallic or the nonmetallic behavior of the nanotubes by applying the folding vectors of parameters (m, n). We extended the topological coordinate method to two-dimensional periodic planar structures as well. Nearly regular hexagonal, pentagonal, and heptagonal polygons were obtained. The curvatures of the final relaxed structures can be read from the sizes of the polygons. Thus relying only on the topological information we could describe the shape of the tubular structures and their conductivity behaviors.     

Molecular structure of aniline in the gaseous phase: A concerted study by electron diffraction and ab initio molecular orbital calculations

The molecular structure of free aniline has been investigated by gas-phase electron diffraction and ab initio MO calculations at the HF and MP2 levels of theory, using the 6-31G^*(6D) basis set. Least-squares refinement of a model withC _s symmetry, with constraints from MP2 calculations, has led to an accurate determination of the C-C-C angle at theipso position of the benzene ring, =119.0±0.2 (where the uncertainty represents total error). This parameter provides information on the extent of the interaction between the nitrogen lone pair and the system of the benzene ring, and could not be determined accurately by microwave spectroscopy. The angles at theortho, meta, andpara positions of the ring are 120.3±0.1, 120.7±0.1, and 119.0±0.3, respectively. Important bond distances are r _g(C-C)=1.398±0.003 å andr _g(C-N) =1.407±0.003 å. The effective dihedral angle between the H-N-H plane and the ring plane, averaged over the large-amplitude inversion motion of the amino group, is ¦¦=44±4. The equilibrium dihedral angle is calculated to be 41.8 at the HF level and 43.6 at the MP2 level, in agreement with far-infrared spectroscopic information. The MO calculations predict that the differencer(C_ortho-C_meta) -r(C_ipso-C_ortho) is 0.008–0.009 å. They also indicate that the nitrogen atom is displaced from the ring plane, on the side opposite to the amino hydrogens. The displacement is 0.049 å at the HF level and 0.072 å at the MP2 level. The two calculations, however, yield very different patterns for the minute deviations from planarity of the ring carbons.     

Polar effect in the reaction of CH3O with HBr

The discharge flow method with laser induced fluorescence detection of CH₃O was applied to determine the rate constant, k ₁, for the reaction CH₃O + HBr → products (1) k ₁ (298 K) = (8.41 ± 0.80(1σ)) 10¹¹ cm³ mol^-1 s^-1. The unusually large k ₁ value was explained by the polar nature of the transition state of the reaction. This revised version was published online in June 2006 with corrections to the Cover Date.     

Exchangeable random variables and the subsequence principle

Summary Call a sequence {X _n } of r.v.'s -exchangeable if on the same probability space there exists an exchangeable sequence {Y _n } such thatP(|X _n –Y _n |) for alln. We prove that any tight sequence {X _n } defined on a rich enough probability space contains -exchangeable subsequences for every >0. The distribution of the approximating exchangeable sequences is also described in terms of {X _n }. Our results give a convenient way to prove limit theorems for subsequences of general r.v. sequences. In particular, they provide a simplified way to prove the subsequence theorems of Aldous [1] and lead also to various extensions.