Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

Use of SPE—TLC for Quality Control of Rhodiola rosea Extracts

SPE and TLC have been used for qualitative and quantitative analysis of salidroside, rosavin, rosarin, and rosin in commercially available dry extracts from Rhodiola rosea roots. The best separation of all the compounds was achieved on silica gel TLC plates with ethyl acetate—methanol—water, 77 + 13 + 10 (v/v), as mobile phase. UV detection was performed at λ = 215 nm for salidroside and at λ= 245 nm for the rosavins (rosavin, rosarin, and rosin). Detection limits for salidroside and the rosavins were 90 ng and 60 ng per spot, respectively. Results from quantitative analysis confirmed the manufacturer’s declaration of the amounts of salidroside and the rosavins in the extracts.

     

The Effect of Cyclodextrins on the Photochemical Stability of 7-Amino-4-methylcoumarin in Aqueous Solution

The effect of -, - and -cyclodextrin onthe photochemical stability of 7-amino-4-methylcoumarin (C120)was studied. Using spectroscopic techniques (UV/Vis absorption spectroscopy, fluorescence, fluorescence anisotropy and circular dichroism) combined with HPLC/MS and MS analysis it was demonstrated that addition of -cyclodextrin to the aqueoussolution of C120 markedly inhibits the photodegradation of that dye. This results from theformation of an inclusion complex between C120 and -cyclodextrin.     

Spectrum analysis of U-doped LaBr3 single crystals. Part 1: crystal-field analysis

Single crystals of U³⁺:LaBr₃ were grown by the Bridgman-Stockbarger technique. High-resolution polarized absorption spectra of the crystals were recorded at 4.2 K in the 4000-50,000 cm⁻¹ range. Sixty-four experimental crystal-field energy levels of the U³⁺ ion were fitted to a semiempirical Hamiltonian employing free-ion, one-electron crystal-field as well as two-particle correlation crystal-field (CCF) operators with an r.m.s. deviation of 28 cm⁻¹. The performed analysis of the spectra enabled the determination of crystal-field parameters and assignment of the observed 5f³→5f³ transitions. The effects of selected CCF operators on the splitting of some specific U³⁺ multiplets have been investigated and the obtained values of Hamiltonian parameters are discussed and compared with those reported in previous analyses.     

Modifying the thermosensitivity of copolymers of sodium styrene sulfonate and<Emphasis Type="Italic"> N</Emphasis>-isopropylacrylamide with dodecyltrimethylammonium chloride

The interactions between copolymers of sodium styrene sulfonate (SSS) and N-isopropylacrylamide (NIPAM), anionic polyelectrolytes, and dodecyltrimethylammonium chloride (DTAC), a cationic surfactant, were studied in aqueous solutions of various ionic strengths. The copolymers were found to be thermoresponsive, showing a lower critical solution temperature (LCST). The influence of the polymer composition, the surfactant concentration, and the ionic strength on the LCST was studied. The surfactant was found to interact strongly with the polymer, forming mixed polymer-surfactant micelles. The critical aggregation concentration (cac) of the polymer-surfactant system was found from fluorescence spectroscopy using pyrene as a fluorescent probe. A strong dependence of the anionic polyelectrolyte-cationic surfactant interactions on the structure of the ionic comonomer was observed.     

Effect of temperature and concentration on the structure of N-methylacetamide-water complexes: Near-infrared spectroscopic study

Generalized two-dimensional (2D) FT-NIR correlation spectroscopy and chemometric methods have been used to study temperature-dependent spectral changes in pure N-methylacetamide (NMA) and NMA-water mixtures. We also examined the effect of varying water content on the structure of the mixture. It has been found that the extent of self-association of NMA in CCl4 is very high; the association occurs even at concentration of 0.001 M. In the pure liquid NMA, the population of the monomers is negligible and the structure is dominated by the linear associates. An increase in temperature reduces the number of hydrogen bonds, but in contrast to alcohols their strength remains nearly the same. This reflects a difference in the mechanism of thermal breaking of the associates of NMA and alcohols. The present results reveal that the interaction between NMA and water in the NMA-rich region (X(H2O) < 0.1) does not have a significant effect on the intrinsic structure of NMA. The structure of NMA is dominant, and the molecules of water do not form separate clusters but are dispersed and incorporated into the structure of NMA. We did not observe the presence of the free OH groups in the mixture. This led to the suggestion that each molecule of water forms two hydrogen bonds to two different molecules of NMA. An analysis of the asynchronous spectra reveals that most of the peaks observed in the asynchronous spectra, constructed from the temperature-dependent data, simply result from the frequency shift. This assumption is supported by the simulation studies.     

Catalytic Oxidative Cyclocondensation of o‐Aminophenols to 2‐Amino‐3H‐phenoxazin‐3‐ones

The catalytic oxidative cyclocondensation of the o‐aminophenols 1a–f was investigated. The oxidants used were air/laccase, H₂O₂/horseradish peroxidase, H₂O₂/ebselen (3), and TBHP/diphenyl diselenide 4. The products obtained were 2‐amino‐3H‐phenoxazin‐3‐one—questiomycin A, its derivative 2b, and cinnabarinic acid and actinocin (2c,d). Substrates with methyl groups at 4 and 5 positions of benzene ring were converted to different dihydrophenoxazinones 2g,h. Compounds having chlorine atoms at the same positions underwent oxidation to planar phenoxa-zinones 2e,f with elimination of one hydrochloride molecule.     

Catalytic Oxidative Domino Degradation of Alkyl Phenols Towards 2- and 3-Substituted Muconolactones

The catalytic oxidative domino degradation of phenols was investigated. Hydrogen peroxide (30% aq.) was used as an oxidant and 2,2′-dinitro-4,4′-ditrifluoromethyldiphenyl diselenide 4e as a catalyst. The products were muconic acid 5, and muconolactones muconolactones—5-carboxymethylfuran-2(5H)-ones 7 and 9. Phenols with alkyl groups at 2 or 4 positions of the benzene ring were converted regioselectively to corresponding muconolactones substituted at alkenylene ring carbon atoms. The reaction mechanism is proposed.     

Chemical Kinetics of Methane Pyrolysis in Microwave Plasma at Atmospheric Pressure

Results of chemical kinetics modeling in methane subjected to the microwave plasma at atmospheric pressure are presented in this paper. The reaction mechanism is based on the methane oxidation model without reactions involving nitrogen and oxygen. For the numerical calculations 0D and 1D models were created. 0D model uses Calorimetric Bomb Reactor whereas 1D model is constructed either as Plug Flow Reactor or as a chain of Plug Flow Reactor and Calorimetric Bomb Reactor. Both models explain experimental results and show the most important reactions responsible for the methane conversion and production of H₂, C₂H₂, C₂H₄ and C₂H₆ detected in the experiment. Main conclusion is that the chemical reactions in our experiment proceed by a thermal process and the products can be defined by considering thermodynamic equilibrium. Temperature characterizing the methane pyrolysis is 1,500–2,000 K, but plasma temperature is in the range of 4,000–5,700 K, which means that methane pyrolysis process is occurring outside the plasma region in the swirl gas flowing around the plasma.     

The process of front-to-side collision of motor vehicles in terms of energy balance

Nonlinear Dynamics - The reconstruction of a road accident can be treated as the resolution of an “inverse problem” in mechanics using analytical or numerical models. In the road...