Scaled-oscillation and regularity

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

     

Studies aimed at the synthesis of morphine V an economic approach to (±)-reticuline from 3,4-dihydropapaverine

Regioselective demethylation of 3,4-dihydropapaveraldine ($\text{2}$a) at 7 and 3' positions affords a properly substituted diphenolic key intermidiate ($\text{2}$d) for the synthesis of reticuline and N-norreticuline.     

Open Problems

Periodica Mathematica Hungarica -     

Rotation about the exocyclic carbon-carbon double bond of amino dienes of the indolo[2,3-a]-and benzo[a]quinolizidine series

Quinolizidines containing an exocyclic double bond at C-2 (1,2) give on mild oxidation the amino dienes (3,4), as mixtures of geometric isomers with respect to the exocyclic double bond. The free enthalpy of activation for the rotation about the double bond has been estimated by NMR.     

N,N'-ethylenebis(pyridoxylideneiminato) and N,N'-ethylenebis(pyridoxylaminato): synthesis, characterization, potentiometric, spectroscopic, and DFT studies of their vanadium(IV) and vanadium(V) complexes

The Schiff base N,N'-ethylenebis(pyridoxylideneiminato) (H(2)pyr(2)en, 1) was synthesized by reaction of pyridoxal with ethylenediamine; reduction of H(2)pyr(2)en with NaBH(4) yielded the reduced Schiff base N,N'-ethylenebis(pyridoxylaminato) (H(2)Rpyr(2)en, 2); their crystal structures were determined by X-ray diffraction. The totally protonated forms of 1 and 2 correspond to H(6)L(4+), and all protonation constants were determined by pH-potentiometric and (1)H NMR titrations. Several vanadium(IV) and vanadium(V) complexes of these and other related ligands were prepared and characterized in solution and in the solid state. The X-ray crystal structure of [V(V)O(2)(HRpyr(2)en)] shows the metal in a distorted octahedral geometry, with the ligand coordinated through the N-amine and O-phenolato moieties, with one of the pyridine-N atoms protonated. Crystals of [(V(V)O(2))(2)(pyren)(2)].2 H(2)O were obtained from solutions containing H(2)pyr(2)en and oxovanadium(IV), where Hpyren is the "half" Schiff base of pyridoxal and ethylenediamine. The complexation of V(IV)O(2+) and V(V)O(2) (+) with H(2)pyr(2)en, H(2)Rpyr(2)en and pyridoxamine in aqueous solution were studied by pH-potentiometry, UV/Vis absorption spectrophotometry, as well as by EPR spectroscopy for the V(IV)O systems and (1)H and (51)V NMR spectroscopy for the V(V)O(2) systems. Very significant differences in the metal-binding abilities of the ligands were found. Both 1 and 2 act as tetradentate ligands. H(2)Rpyr(2)en is stable to hydrolysis and several isomers form in solution, namely cis-trans type complexes with V(IV)O, and alpha-cis- and beta-cis-type complexes with V(V)O(2). The pyridinium-N atoms of the pyridoxal rings do not take part in the coordination but are involved in acid-base reactions that affect the number, type, and relative amount of the isomers of the V(IV)O-H(2)Rpyr(2)en and V(V)O(2)-H(2)Rpyr(2)en complexes present in solution. DFT calculations were carried out and support the formation and identification of the isomers detected by EPR or NMR spectroscopy, and the strong equatorial and axial binding of the O-phenolato in V(IV)O and V(V)O(2) complexes. Moreover, the DFT calculations done for the [V(IV)O(H(2)Rpyr(2)en)] system indicate that for almost all complexes the presence of a sixth equatorial or axial H(2)O ligand leads to much more stable compounds.     

Simple potentiometric method for determination of specific activity of carrier-free125I with the aid of ion-selective membrane electrode

A simple potentiometric method for determination of specific activity of carrier-free¹²⁵I (NaI) has been elaborated. The method is based on the measurement of tracer amounts of iodide present in the¹²⁵I preparate, by using an ion-selective membrane electrode. The method presented is suitable in practice for rapid estimation of specific activity of carrier-free¹²⁵I preparation in cases where the knowledge of its numerical value is necessary.     

Some Periodic and Non-Periodic Recursions

 It is well known that the recurrence relations

The Besicovitch–Federer projection theorem is false in every infinite-dimensional Banach space

The theme of the article is the study of the unipotent part of Arthur’s trace formula for general linear groups. The case of regular (or “regular by blocks”) unipotent orbits has been treated in another paper (cf. [10]). Here we are interested in the contribution of Richardson orbits that are induced by Levi subgroups with two-by-two distinct blocks. In this case, the contribution is remarkably given by a global unipotent weighted orbital integral. As a corollary, we get integral formulas for some of Arthur’s global coefficients. We also present a new construction of Arthur’s local unipotent weighted orbital integral and an explicit computation of some of them.     

Structural variability of endotoxins from R-type isogenic mutants of Shigella sonnei

The structural variations in the rough-type endotoxins [lipopolysaccharides (LPSs)] of Shigella sonnei mutant strains (S. sonnei phase II-4303, R41, 562H and 4350) were investigated by Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and tandem MS. A series of S. sonnei mutants had previously been the subject of analytical studies on the biosynthesis of heptose components in the core oligosaccharide region of LPSs. This study gives a complete overview on the structures of the full core and lipid A of S. sonnei mutant strains by MS. We found that the LPSs of the isogenic rough mutants were formed in a step-like manner containing 0:1:2:3 heptose in the deep core region of 4350, 562H, R41 and 4303, respectively, and the longest LPS from the mutant S. sonnei 4303 contained also five hexoses. The structural variations in the lipid A moiety and in the oligosaccharide part of the intact LPS were followed by MALDI-TOF-MS/MS. For the dissolution and the ionization of the samples, 2,5-dihydroxybenzoic acid in citric acid solution was applied as matrix. The detailed evaluation of the mass spectra indicates heterogeneity in the lipid part due to the differences in the phosphate and fatty acid composition.     

First-return integrals

Properties of first-return integrals of real functions defined on the unit interval are explored. In particular, first-return integrals are shown to be continuous but not absolutely continuous.