Photochemically promoted transition metal-free cross-coupling of acylsilanes with organoboronic esters

Intermolecular carbon-carbon bond formation between acylsilanes and organoboronic esters was achieved by photoirradiation under almost neutral, transition metal-free conditions. In this reaction, siloxycarbenes generated by photoisomerization of acylsilanes reacted with boronic esters to give the formal B-C bond insertion intermediates, which underwent unique rearrangement to afford the cyclic α-alkoxyboronic esters. Acidic treatment of the resulting crude products under air furnished the cross-coupled ketones in good yields.     

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).     

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.     

On a problem of Sakai in unbounded derivations

Let A_θ be the irrational rotation algebra. Then there exist non approximately bounded pregenerators δ_i(i = 1, 2) of A_θ with the same domain such that given a ¹-derivation δ of A_θ with D(δ) = D(δ_i), there exist (k,l)∈$\text{R}$² and an approximately bounded ¹-derivation δ₃of A_θ such that δ = kδ₁ + lδ₂ + δ₃, which can be considered as a solution of a problem of Sakai for two dimensional space quantizations.     

Holographic interferometry using a reference wave with a sinusoidally modulated amplitude

A method of holographic interferometry which uses an amplitude-modulated reference wave is proposed for investigating vibration phases. Sinusoidal amplitude modulation of a reference wave yields hologram fringes which are characterized by a function J²₁(α)cos²Δ, where α and Δ are related to vibration amplitudes and phases on object points, respectively. The resultant fringes indicate that vibration amplitude information and phase information are stored separately. The phase information of the vibration is easily obtained as brightness variations of the fringes, independently of the amplitude information.