Measurability implies continuity for solutions of functional equations - even with few variables

Summary. We prove that - under certain conditions - measurable solutions $f$ of the functional equation $f(x)=h(x,y,f(g_{1}(x,y)),\ldots,f(g_{n}(x,y))),\quad(x,y)\in D \subset \mathbb{R}^{s} \times \mathbb{R}^{l}$ are continuous, even if $1\le l\le s$. As a tool we introduce new classes of functions which - roughly speaking - interpolate between continuous and Lebesgue measurable functions. Connection between these classes are also investigated.     

Assignment of the EPR spectrum of 5,5-dimethyl-1-pyrroline N-oxide (DMPO) superoxide spin adduct

[structure: see text] Spin trapping consists of using a nitrone or a nitroso compound to "trap" an unstable free radical as a long-lived nitroxide that can be characterized by electron paramagnetic resonance (EPR) spectroscopy. The formation of DMPO-OOH, the spin adduct resulting from trapping superoxide (O(2)(*)(-)) with 5,5-dimethyl-1-pyrroline N-oxide (DMPO), has been exploited to detect the generation of superoxide in a wide variety of biological and chemical systems. The 12-line EPR spectrum of DMPO-OOH has been either reported or mentioned in more than a thousand papers. It has been interpreted as resulting from the following couplings: A(N) approximately 1.42 mT, A(H)beta approximately 1.134 mT, and A(H)gamma(1H) approximately 0.125 mT. However, the DMPO-OOH EPR spectrum has an asymmetry that cannot be reproduced when the spectrum is calculated considering a single species. Recently, it was proposed that the 0.125 mT splitting was misassigned and actually results from the superimposition of two individual EPR spectra associated with different conformers of DMPO-OOH. We have prepared 5,5-dimethyl-[3,3-(2)H(2)]-1-pyrroline N-oxide (DMPO-d(2)), and we showed that the EPR spectrum of the corresponding superoxide spin adduct is composed of only six lines, in agreement with the assignment of the 0.125 mT splitting to a gamma-splitting from a hydrogen atom bonded to carbon 3 of DMPO. This result was supported by DFT calculations including water solvation, and the asymmetry of the DMPO-OOH EPR spectrum was nicely reproduced assuming a chemical exchange between two conformers.     

Evaluation of cyclodextrin polymer as a disintegrating agent

Cyclodextrin polymer was compared to other well known disintegrants concerning the swelling properties /water uptake, moisture uptake, hydration capacity, sedimentation volume in water/. Its high disintegrating effect was proved in directly compressed tablets as well as in tablets made by wet granulation. A remarkable improvement in tablet properties was observed. Not only the disintegration of tablets and the dissolution of the drug was accelerated but also the hardness increased when CDP was used as disintegrant.     

Nanosensors based on responsive polymer brushes and gold nanoparticle enhanced transmission surface plasmon resonance spectroscopy

Swelling (and shrinking) of poly(2-vinylpyridine), P2VP, polymer brushes, caused by pH changes, could be readily monitored by transmission surface plasmon resonance, T-SPR, spectroscopy. Gold nanoparticles attached to the P2VP polymer brushes dramatically enhanced the pH-induced shift in the T-SPR absorption spectra. (A 50 nm shift of the absorption maximum of the T-SPR spectrum of the supporting gold nanoislands was observed upon changing the pH from 5.0 to 2.0, corresponding to a swelling of the polymer brushes from 8.1 +/- 0.7 to 24.0 +/- 2.0 nm. Same shift in the opposite direction was observed upon changing the pH from 2.0 to 5.0.)     

Particle-size analysis of latexes by classical and small-angle spectrodissymmetry

The spectral dependence of classical and small-angle dissymmetryZ in polydispersions containing spherical particles with lognormal distribution was theoretically studied. It has been found, for instance, for polystyrene latex that small-angle dissymmetry may be used for determining the distribution parameters in systems with particle medial radius 60–700 nm on the basis of measurements ofZ (10°/5°( at two wavelengths of radiation. For particles outside this interval and by use of working relationships of classical dissymmetry only the application of a wide range of wavelengths comes into consideration by distribution analysis.     

Coordination modes between copper(II) and N-acetylneuraminic (sialic) acid from a 2D-simulation analysis of EPR spectra. Implications for copper mediation of sialoglycoconjugate chemistry relevant to human biology

The equilibrium distribution of species formed between Cu(II) and N-acetylneuraminic (sialic) acid (I, LH) at 298 K has been determined using a two-dimensional (2D) simulation analysis of electron paramagnetic resonance (EPR) spectra. In acidic solutions (pH values < 4), the major species present are Cu(2+), [CuL]+ [logbeta = 1.64(4)], and [CuL2] [logbeta = 2.77(5)]. At intermediate pH values (4.0 < pH < 7.5), [CuL2H-1]- [logbeta = -2.72(7)] and two isomers of [CuLH-1] [logbeta (overall) = -3.37(2)] are present. At alkaline pH values (7.5 < pH < 11), the major species present is [CuL2H-2]2-, modeled as three isomers with unique giso and Aiso values [logbeta (overall) = -8.68(3)]. Two further species ([CuLH-3]2- and [CuL2H-3]3-) appear at pH values > 11. It is proposed that [CuL]+ most likely features I coordinated via the deprotonated carboxylic acid group (O1) and the endocyclic oxygen atom (OR) forming a five-membered chelate ring. Select Cu(II)-I species of the form [CuLH-1] may feature I acting as a dianionic tridentate chelate, via oxygen atoms derived from O1, OR, and one deprotonated hydroxy group (O7 or O8) from the glycerol tail. Alternatively, I may coordinate Cu(II) in a bidentate fashion as the tert-2-hydroxycarboxylato (O1,O2) dianion. Spectra predicted for Cu(II)-I complexes in which I is coordinated in either a O1,OR {I1-} or O1,O2 {I2-} bidentate fashion {e.g., [CuL]+ (O1,O R), [CuL2] (bis-O1,O R), [CuLH-1] (isomer: O1, O2), [CuL2H-1]- (O1, O R; O1, O2), and [CuL2H-2]2- (isomer: bis-O1, O2)} have "irregular" EPR spectra that are ascribed to the existence of Cu(II)-I(monomer) <==> Cu(II)-I(polymer) equilibria. The formation of polymeric Cu(II)-I species will be favored in these complexes because the glycerol-derived hydroxyl groups at the complex periphery (O, 7O, 8O9) are available for further Cu(II) binding. The presence of polymeric Cu(II)-I species is supported by EPR spectral data from solutions of Cu(II) and the homopolymer of I, colominic acid (Ipoly). Conversely, spectra predicted for Cu(II)-I complexes where I is coordinated in a {I2-} tridentate {e.g., [CuLH-1] (isomer: O1, O R, O7, or O8) and [CuL2H-2]2- (isomer: bis-O1,O R,O7, or O8)} or tetradentate fashion {I3-} {e.g., [CuLH-3]2- (O1, O R, O, 8O9)} are typical for mononuclear tetragonally elongated Cu(II) octahedra. In this latter series of complexes, the tendency toward the formation of polymeric Cu(II)-I analogues is small because the polydentate I effectively wraps up the mononuclear Cu(II) center. This work shows that Cu(II) could potentially mediate the chemistry of sialoglycoconjugate-containing proteins in human biology, such as the sialylated amyloid precursor protein of relevance to Alzheimer's disease.     

Encapsulation of magnetite in vesicles

The encapsulation of fine magnetite particles of 10 nm size and marker ANS within asolectin vesicles has been made by sonication of the mixture in water. For the proof of encapsulation of magnetite in vesicles the electron microscope and spectrofluoriphotometer technique were used. The theory for the calculation of the magnetic force acting on the system consisted of non-capsulated magnetic particles dispersed in water and magnetic vesicles was developed.This work was supported by the Slovak Academy of Sciences within the framework of Project GAV No. 1361.     

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Application of complex reaction kinetic models in thermal analysis

The complexity of the phenomena which arise during the heating of the various substances seldom can be described by a single reaction kinetic equation. As a consequence, sophisticated models with several unknown parameters have to be developed. The determination of the unknown parameters and the validation of the models requires the simultaneous evaluation of whole series of experiments. We can accept a model and its parameters if, and only if we get a reasonable fit to several experiments carried out at different experimental conditions. In the field of the thermal analysis the method of least squares alone seldom can select abest model or abest set of parameter values. Nevertheless, the careful evaluation of the experiments may help in the discerning between various chemical or physical assumptions by the quality of the corresponding fit between the experimental and the simulated date. The problem is illustrated by the thermal de-composition of cellulose under various experimental conditions.This research program was funded by the National Science Foundation (grant INT 8914934), the US Hungarian Science and Technology Joint Fund (grants 90b-22 and 93b-375), the Hungarian National Research Fund (OTKA, grant 3077/91) and the Coral Industries Endowment.     

Hybridization of oligonucleotide-modified silver and gold nanoparticles in aqueous dispersions and on gold films

Functionalization of silver and gold nanoparticles by 12mer-thiolated homo-oligonucleotides, SA and ST (containing only adenine or thymine, respectively), and their hybridization and dehybridization in aqueous dispersions have been described. In addition, ST and SA were self-assembled onto gold films and hybridized with their complementary pairs, unlabeled or labeled by gold and silver nanoparticles. The base pairing between DNA strands and the types of oligonucleotides (adenine or thymine) attached to the nanoparticles was detected by Polarization Modulated Fourier Transform Infrared Reflection Absorption Spectroscopy (PM-FTIRRAS).