Synthesis of stable azomethine ylides by the rearrangement of 1,3-dipolar cycloadducts of 3,4-dihydroisoquinoline-2-oxides with DMAD

1-Aryl-6,7-dimethoxy-1,2,3,4-tetrahydroisoquinolines were prepared according to a one-pot procedure involving the reaction of 2-(3,4-dimethoxyphenyl)-ethylamine with aromatic aldehydes in TFA at reflux. The tetrahydroisoquinolines were treated with H₂O₂-WO₄²⁻ in methanol at room temperature to give the corresponding 3,4-dihydroisoquinoline-2-oxides. Treatment of these cyclic nitrones with DMAD in toluene at room temperature gave the corresponding isoxazolo[3,2-a]isoquinolines. These compounds were heated in toluene at reflux to give the corresponding ylides in high yields (Method A). The effect of the substituents on the rate of the rearrangement of such compounds prompted us to discuss a new mechanism involving consecutive C-C bond heterolysis and 1,3-sigmatropic shift. A one-pot reaction involving the treatment of the nitrones with equimolar amounts of DMAD in refluxing toluene also gave the ylides (Method B). The structures of the prepared compounds were elucidated by spectral means and elemental analyses.     

Complexation of Ni (II) and Zn(II) ions by 3-(1-naphthyI)-2-mercaptopropenoic acid

The complexation equilibria between Ni(II) and Zn(II) metal ions with 3-(1-naphthyl)-2-mercaptopropenoic acid (H₂NMP) were studied by glass electrode potentiometry, at 25 °C and 1.0 mol·dm^–3 in NaClO₄ as constant ionic medium in 50% (v/v) water-ethanol solutions. Formation constants for the complexes Ni(NMP), Ni(NMP) ₂ ^2– , Zn(NMP) and Zn(NMP) ₂ ^2– , refined by the MINIGLASS program, are reported.     

Brownian confinement and pinning in a Poissonian potential. II

Summary We continue our study ofd-dimensional Brownian motion in a soft repulsive Poissonian potential over a long time interval [0,t]. We prove here a pinning effect: for typical configuratons, with probability tending to 1 ast tends to , the particle gets trapped close to locations of near minima of certain variational problems. These locations lie at distances growing almost linearly witht from the origin, and the particle gets pinned within distance smaller than any positive power oft of one such location. In dimension 1, we can push further our estimates and show that in a suitable sense, the particle gets trapped with high probability, within time t and within distance (logt)²⁺ from a suitable location at distance of ordert/(logt)³ from the origin.This article was processed by the author using the LATEX style filepljour1m from Springer-Verlag     

Processes of flats induced by higher dimensional processes III

Stationary processes of k-flats in ^d can be thought of as point processes on the Grassmannian _k ^d of k-dimensional subspaces of ^d . If such a process is sampled by a (d–k+ j)-dimensional space F, it induces a process of j-flats in F. In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1<k<d–1 and j=0,...,2[r/2]–1, where r is the rank of the manifold _k ^d . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

A note on “small representations of finite distributive lattices as congruence lattices”

G. Grätzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a small lattice L, that is, a lattice L with O(n ² ) elements. G. Grätzer, I. Rival, and N. Zaguia proved that, for any <2, O(n ² ) can not be improved to O(n ). In this note we show that the theorem about small representation can be improved further to get a more delicate result.     

On spectral properties ofq-oscillator operators

The property of self-adjointness of the operatorQ =a ₊ +a _- in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases when this operator is bounded. Generalized eigenvectors are expressed in terms ofq-Hermite polynomials. If the operatorQ is unbounded, then its closure is not self-adjoint. However, in this case, admits self-adjoint extensions. Deficiency subspaces are one-dimensional. These subspaces are explicitly found.     

The algebra of directed complexes

The theory of directed complexes is a higher-dimensional generalisation of the theory of directed graphs. In a directed graph, the simple directed paths form a subset of the free category which they generate; if the graph has no directed cycles, then the simple directed paths constitute the entire category. Generalising this, in a directed complex there is a class of split subsets which is contained in and generates a free -category; when a simple loop-freeness condition is satisfied, the split sets constitute the entire -category. The class of directed complexes is closed under the natural product and join constructions. The free -categories generated by directed complexes include the important examples associated to cubes and simplexes.     

Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

Preparation of 1,1,1,3,3-pentafluoropropane (HFC-245fa) by using a SbF5-attached catalyst

In this report, a simple process for preparing HFC-245fa through the reaction of 1,1,1,3,3-pentachloropropane (PCP) and anhydrous HF via two-step vapor-phase catalytic fluorination is described. The antimony pentafluoride catalyst was supported on inert porous materials to improve the catalytic activity. The resulting process catalyst not only exhibited high catalytic activity and excellent thermo-stability, but also improved the performance of SbF₅, in terms of hygroscopicity and corrosion.