On the Hahn--Mazurkiewicz theorem

The following generalization of the Hahn-Mazurkiewicz theorem is proved: Let (E,e) be a locally compact locally connected metric space. Let M be a continuum in this space and let d,e∈ M. Then there is a continuous mapping f: [0,1]→E such that f(0) = d, f(1)= e and M⊂f([0,1]). Also some corollaries of this theorem are proved.     

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.     

Studies on stereoselective approaches to β-carboline derivatives

Transformation of β-carboline derivatives into optically active entities were studied and the de and ee values of the resulted compounds were detected. Dedicated to Professor Károly Lempert on his 80th birthday.     

Nitrogen bridgehead compounds part 21. Preparation of new quaternary 2,3a,6a-triazaphenalenium salts

The first representatives of a new ring system, the 2,3a,6a-triazaphenalenium quaternary salts are prepared by the cycloaddition of tetrahydro-4H-pyrido[1,2-a] pyrimidin-4-ones containing an α-chloroenamine moiety with azomethines.     

Cyclic sulfonium salts with S ... O interactions 2. Molecular structures with six-membered rings

1-[2-(N-methylcarbamoyl)phenyl]-3H-2,1-naphto-(1,8-d,e)-oxathiin-1-ium chloride (2), 1-[2-(N-methylcarbamoyl)-phenyl]-2-methyl-3-oxo-3H-1, 2-naphto-(1,8-d,e)-thiazin-1-ium chloride (3), 1-[8-(N-methylcarbamoyl)naphtyl]-2-methyl-3-oxo-3H-1, 2-naphto-(1,8-d,e)-thiazin-1-ium chloride (4) and 1-(8-carboxylatonaphtyl)-2-methyl-3-oxo-3H-1,2-naphto-(1,8-d,e)-thiazin-1-ium dipolar ion (5) cyclic sulfonium salts were prepared and their chemical properties investigated (spirosulfurane-formation, hydrolysis). The molecular structures obtained from x-ray diffraction can be described with a considerably distorted trigonal bipyramidal arrangement of the ligands about the sulfonium center, with O/N—S ... O=apical angles of 173.9, 164.9, 156.6, and 159.0°, as well as with S—O/N apical bond lengths of 1.648, 1.671, 1.664, and 1.682 Å. The structures exhibit relatively short S ... O close contacts with interatomic distances of 2.253, 2.448, 2.795, and 2.619 Å.     

Solid-state binding of dimethyl sulphoxide involving carboxylic host molecules. X-ray crystal structures of four inclusion species

The crystal structures of four dimethyl sulphoxide (DMSO) inclusion compounds with different carboxylic acid hosts,1–4, have been studied by single crystal X-ray analysis. Crystals of thetrans-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylic acid inclusion compound (1a), [1 · DMSO (1: 1)] show monoclinic (P2₁/n) symmetry with the unit cell dimensionsa = 11.522(4),b = 18.658(2),c = 8.709(1) Å and = 98.92(2)°. The clathrate of the 9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylic acid (2a), [2 · DMSO (1: 2)] is triclinic (P) with the cell dimensionsa = 15.043(7),b =9.657(4),c = 8.118(7) Å, = 101.81(5), = 96.05(4) and = 100.04(4)°. Triclinic (P) symmetry is shown also by the inclusion compound of 9,10-dihydro-9,10-ethanoanthracene-11-monocarboxylic acid (3a) [3 · DMSO (1:1)] with the cell dimensionsa=6.3132(1),b=7.9846(2),c=17.5314(4) Å, = 96.46(2), = 87.08(2) and = 106.02(2)°. The 9,9-bianthryl-2-monocarboxylic acid clathrate (4a) [4 · DMSO (1:1)] is monoclinic (P2₁/n) and the cell dimensions area = 19.625(18),b = 8.817(1),c = 14.076(8) Å and = 97.92(6)°. In all these structures, the hosts show the same basic recognition pattern for the DMSO guest, involving a strong O-H ... O bond from the COON to the S=O group, and a possible C-H ... O type interaction between the carbonyl O atom of the host and a CH₃ group of the guest. The crystals consist of discrete host-guest aggregates which are mainly held together by weak intermolecular interactions of the Van der Waals' type. The stoichiometries of the aggregates are, however, different.     

Synthesis of 1-aryl-3H-[1,2,5]triazepino[5,4-a]benzimidazol-4(5H)-ones and quantum chemical investigation of the rotamers of the Boc-protected hydrazide key intermediate

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Passive Advection in a Percolation Process: Two-Loop Approximation

Theoretical and Mathematical Physics - We study an instructive model of the directed percolation process near its second-order phase transition between absorbing and active states. We first express...     

Enzyme-catalyzed kinetic resolution of N-Boc-trans-3-hydroxy-4-phenylpyrrolidine

The first enzyme-catalyzed kinetic resolution of tert-butyl-3-hydroxy-4-phenylpyrrolidine-1-carboxylate is presented. Enzyme, solvent and temperature optimization resulted in a new resolution method with E = 40 enantioselectivity. The acetate derivative of the (+)-(3S,4R) enantiomer formed while the (?)-(3R,4S) isomer remained intact. Very good enantioselectivities (E > 200) were achieved in the enzyme-catalyzed alcoholysis of the racemic acetate in i-propanol and t-butanol where the (+)-(3S,4R) enantiomer was prepared in pure form (ee > 99.7%). Absolute configuration of the (?)-(3R,4S)-enantiomer was determined by single crystal X-ray diffraction method.