CAS based approach for discussing subset construction

This paper continues the discussion of teaching nondeterminism (see [6]) where we presented a didactic approach introducing the notion of nondeterministic automata. Although in this paper we use the same methodology we have to face up to new didactic challenges. Namely, teaching the subset construction requires answers to the question how can CAS be used in teaching the different phases of mathematical problem solving so that we can reach higher cognitive efficiency.     

Fejér means of functions on noncommutative Vilenkin groups with respect to the character system

Summary It is known that the Fejér means - with respect to the character system of the Walsh, and bounded Vilenkin groups - of an integrable function converge to the function a.e. In this work we discuss analogous problems on the complete product of finite, not necessarily Abelian groups with respect to the character system for functions that are constant on the conjugacy classes. We find that the nonabelian case differs from the commutative case. We prove the a.e. convergence of the (C,1) means of the Fourier series of square integrable functions. We also prove the existence of a function f∊L^q for some q >1 such that sup |σ_n f | = + ∞ a.e. This is a sharp contrast between the Abelian and the nonabelian cases.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

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.     

Two Stage Solid Phase Extraction with Subsequent HPLC Isolation for Structure Elucidation of Major Metabolites of (+)-(R)-2-{3-(benzo[1,4]dioxan-2-yl-methylamino)-1-propyl}-3(2H)-pyridazinone (GYKI-16084)

GYKI-16084 – (+)-(R)-2-{3-(benzo[1,4]dioxan-2-yl-methylamino)-1-propyl}-3(2H)-pyridazinone hydrochloride – is a new drug candidate for the treatment of benign prostatic hyperplasia. In our study the major metabolites formed in the rat and dog were isolated from dog and rat urine, then their structures were elucidated by means of MS and NMR. A two stage solid phase extraction (SPE) procedure and a semi-preparative HPLC method were developed utilizing various mechanisms of separation. The major metabolites proved to be isomeric glucuronides of the benzodioxane moiety hydroxylated at positions 6 or 7 and {2-(2-carboxyethyl)-3(2H)-pyridazinone}.     

Rh complexes of 1-(2,4,6-triisopropylphenyl-)3-methyl-1H-phosphole: preparation and use as catalysts in the hydroformylation of styrene

In the series of 1-(2,4,6-trialkylphenyl-)3-methyl-1H-phospholes (1a–c) that are to a certain extent of aromaticity, only the isopropyl substituted one (1a) entered into reaction with dimeric (pentamethylcyclopentadienyl)rhodium dichloride to afford Rh(III) complex (2a) in a reversible manner. After a careful workup, (2a) could be prepared and characterized whose stereostructure was elucidated by B3LYP/3–21G*, B3LYP/6–31G* and LANL2DZ calculations. Complex (2a) as a preformed catalyst, as well as the Rh(acac)(CO)₂ + 2(1a) in situ catalytic system were useful in the hydroformylation of styrene and gave the branched aldehyde in regioselectivities of 65–96%.     

Unexpected ring transformation to pyrrolo[3.2-b]pyridine derivatives. Fused azolium salts. 22

2-Arylsulfanyl and 2-benzylsulfanylpyridinium N-arylimides (2) easily prepared from 3-aryltetrazolopyridinium salts (1) with aryl and benzylthiolates, respectively, reacted with various dipolarophiles yielding cycloadducts that underwent transformation to give tetrahydropyrrolo[3,2-b]pyridines (5, 6, and 8) in good yields. A similar rearrangement (formation of 15) was also observed in the case of parent derivatives being unsubstituted in position 2 (12). The abscence of any significant solvent effect, comparison of the sulfur and non-sulfur analogues, as well as the stereoselective nature of the observed ring transformation seem to support a sigmatropic mechanism. Structure elucidation of the products has been carried out by single-crystal X-ray diffraction and (1)H NMR experiments.