Indium-catalyzed construction of polycyclic aromatic hydrocarbon skeletons via dehydration

Polycyclic aromatic compounds can be synthesized from 2-benzylic- or 2-allylbenzaldehydes using a catalytic amount of In(III) or Re(I) complexes. By using this method, polycyclic aza-aromatic compounds can also be prepared efficiently. In these reactions, only water is formed as a side product.     

Polymorphism of 4-Fluorophenylpyruvic Acid Studied by X-Ray Crystallography and Vibrational Spectroscopy

Two polymorphic forms (I and II) of 4-fluorophenylpyruvic acid (F-PPA) were obtained by crystallization from different solvents, showing a melting point at 163.2 and 171.0 °C. Crystal structures of polymorphs I and II were determined by X-ray crystallography. IR and Raman spectra of the two polymorphs were measured and the spectral characteristics were compared with those of phenylpyruvic acid. the two polymorphs show similar molecular and crystal structures to each other, except for the molecular geometries of the enol and the carboxylic acid moieties. Distinct IR spectral differences which result from the crystal field splitting were observed between the two polymorphs.     

On a duality for crossed products of C1-algebras

Let $\text{U}$ be a C¹-algebra, and G be a locally compact abelian group. Suppose α is a continuous action of G on $\text{U}$. Then there exists a continuous action $\text{}\text{?}$ga of the dual group $\text{G}\text{?}$ of G on the C¹-crossed product by α such that the C¹-crossed product is isomorphic to the tensor product and the C¹-algebra of all compact operators on L²(G).     

Some results on odd factors of graphs

A {1, 3, …,2n ? 1}-factor of a graph G is defined to be a spanning subgraph of G, each degree of whose vertices is one of {1, 3, …, 2n ? 1}, where n is a positive integer. In this paper, we give a sufficient condition for a graph to have a {1, 3, …, 2n ? 1}-factor.     

Coupling of numerical Green''s matrix and boundary integral equations for the elastodynamic analysis of inhomogeneous bodies on an elastic half-space

A coupled system of integral equations (of the domain and boundary types) is formulated for the elastodynamic response analysis of a locally inhomogeneous body on a homogeneous elastic half-space. The method uses the fundamental solution for homogeneous elastostatics in the inhomogeneous domain owing to the lack of a fundamental solution in inhomogeneous elastodynamics.

The integral representation of displacements in the inhomogeneous domain is formulated with the help of this elastostatic fundamental solution by considering the term induced by the inhomogeneity of materials and the acceleration term as the body force term. Then the Green's matrix is obtained numerically from this integral representation and combined with the ordinary boundary integral equations, which are valid in the exterior homogeneous half-space.

Some numerical examples show the efficiency and the versatility of this coupled method.     

Statistical properties of the dynamic dichromatic laser speckle

The statistical properties of dynamic elongated speckle patterns produced in the far-field diffraction region by a moving diffuse object under illumination of the dichromatic laser beam are experimentally investigated by means of a correlation method. The experimental results show that the correlation length of the normalized autocorrelation function of time-varying dichromatic speckle intensity fluctuations depends strongly on the fibrous radial structure of elongated speckle patterns. The qualitative discussions are given for the experimental results.     

Laser Stark spectroscopy of the ν4 band of CH3C15N: Fermi resonance with 3ν83

Laser Stark spectra for the ν₄ band of CH₃C¹⁵N have been measured by using CO₂ and N₂O lasers. Almost 650 resonances have been assigned to about 140 ro-vibrational transitions with J′ ≤ 34 and K ≤ 11. An anomaly of the rotational structure around K = 7 has been proved to be due to a Fermi interaction by analyzing each K subband separately. Observed data have been fitted to a model which includes ν₄-3ν₈³ Fermi coupling by the method of least squares. The standard deviation of observed from calculated frequencies is 4.6 MHz. Molecular constants derived are also listed.