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.     

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.     

Nuclear Techniques in the Elucidation of Chemical Structure

The paper offers three applications of nuclear methods in the research of chemical structure. First, progress in positron annihilation spectroscopy is illustrated by a positron beamline study, which obtained results that are not available through conventional experiments. The positron beam was used for the study of Langmuir-Blodgett (LB) films containing 4-58 layers of arachidic acid and its salts. These measurements have shown that this emerging technique is capable of characterizing even such elusive systems. Second, the potential of Mössbauer spectroscopy to answer current challenges of solid state chemistry are shown in a study on perovskites of recent interest. ¹⁵¹Eu Mössbauer spectroscopy was used to study the effect of Pr substitution in EuBa₂Cu₃O_7-. It was shown that the introduction of Pr into the rare earth site as well as into the Ba site results in the appearance of extra electrons both in the copper oxide planes and at the 4f shell of Eu cations. The observed effects were explained by the hole filling effect of Pr. Finally, a survey is presented on the recently developed techniques for nuclear resonant scattering of synchrotron radiation, an exciting and very rapidly developing extension to conventional Mössbauer spectroscopy. An interesting new result is that nuclear inelastic scattering experiments performed on solutions of ⁵⁷Fe complexes show contribution from vibrations rather than from diffusion to the inelastic spectra.     

Determination of myo-inositol in a flow-injection system with co-immobilized enzyme reactors and amperometric detection

A selective and sensitive flow-injection system for the determination of myo-inositol (hexahydroxycyclohexane) is described. Inositol dehydrogenase, IDH, lactate dehydrogenase, LDH, and lactate oxidase, LOD, are co-immobilized on porous glass and used in a packed-bed enzyme reactor. myo-Inositol reacts to produce an equivalent amount of hydrogen peroxide, which oxidizes hexacyanoferrate(II) to hexacyanoferrate(III) in a second reactor containing immobilized peroxidase. The hexacyanoferrate(III) is then detected amperometrically at 0 mV vs. SCE in a flow-through detector. The system responds linearly to injected samples of myo-inositol (25 μl) in the concentration range 1–300 μM. The maximum throughput was 90 samples per hour. The IDH/LDH/LOD reactor was stable for at least 5 weeks.