Reaction of silyl ketene acetals with epoxides: a new method for the synthesis of γ-butanolides

Titanium tetrachloride promoted reaction of silyl ketene acetals with epoxides, followed by acidic work-up, affords butanolides in moderate/good yields. With epihalohydrins the reaction is regioselective and occurs at the less substituted end of the epoxide; the γ-haloalkyl-γ-butanolides thus obtained can be further transformed into various products.     

A new technique for obtaining the activation energy distribution of a relaxing system

This paper describes a robust and fast fitting procedure applicable for relaxing processes that cannot be understood as a discrete sum of single processes but require an activation energy distribution. The method is based on a set of closed-form expressions that allow the computation of the relaxation parameters directly from the isochronal curves obtained experimentally. The usefulness of this method is checked by analyzing the isochronal curves given by a theoretical energy distribution and the magnetic disaccommodation spectra observed in yttrium iron garnet (YIG) samples. PACS 02.60.Ed; 75.60.Lr; 75.50.Gg     

Dihydropyridine-based MCRs. New reaction pathways in the interaction with ethyl glyoxalate and non-aromatic amines

The Lewis acid-catalyzed interaction of dihydropyridines with ethyl glyoxalate and primary aliphatic amines yields, depending on the reaction conditions, bicyclic aminals or rearranged tetrahydropyridines in one-pot multicomponent reactions.     

Equilibrated thermodesorption studies of adsorption of n-hexane and n-heptane on zeolites Y, ZSM-5 and ZSM-11

Gravimetric measurements of thermodesorption of n-hexane and n-heptane were performed under quasi-equilibrium conditions. Differential thermodesorption profiles for ZSM-5 and ZSM-11 showed two peaks, but for Y zeolites, only one thermodesorption peak was observed. A model function, derived from the Langmiur adsorption model, was fitted to the experimental data, and the model parameters (the adsorption entropy and enthalpy) were estimated. The two-step desorption profiles observed for ZSM-5 and ZSM-11 were attributed to the commensurate freezing effect, i.e. a transition in the adsorbed phase resulting in ordering of the adsorbed molecules in the zeolite channels. The results observed for ZSM-11 indicate that the zigzag channels typical for ZSM-5 micropore system are not necessary for this transition to occur.     

Characterization of Cds clusters in zeolite-A grown in alkaline solution

CdS clusters were synthesized in A type zeolite by reaction in alkaline aqueous solution at temperatures from 30 to 70 °C. The optical properties of the samples were studied by diffuse reflectance and photoluminescence spectroscopy. Their crystalline structure and morphology were studied by X-ray diffraction and by transmission and scanning electron microscopy. We found that at lower temperatures the CdS clusters are encapsulated in the zeolite cages. We compared the properties of these clusters with those encapsulated in the cages of zeolites X and Y, prepared by similar methods. CdS clusters smaller than the CdS exciton diameter are also formed outside the cages in the zeolite matrix. The size of these clusters increases with temperature producing a red-shift of the absorption edge in the optical absorption spectra.     

Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

Limits of tangents and minimality of complex links

We show that the complex link of a large class of space germs (X,x₀) is characterized by its “simplicity”, among the Milnor fibres of functions with isolated singularity on X. This amounts to the minimality of the Milnor number, whenever this number is defined. Such a phenomenon has been first pointed out in case (X,x₀) is an isolated hypersurface singularity, by Teissier (Cycles évanescents, sections planes et conditions de Whitney, in: Singularités à Cargèse 1972, Asterisque, Nos. 7 et 8, Soc. Math. France, Paris, 1973, pp. 285-362).     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -