Immediate extensions of filtered rings

Summary A separated filtered ring has a maximally complete immediate extension. This is an analogue of Krull Theorem from valuation ring theory in the frame of filtered rings.

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Riassunto Un anello separato filtrato ha una immediata estensione massimale completa. Questo risultato è un analogo del teorema di Krull della teoria degli anelli di valutazione nell’ambito degli anelli filtrati.

     

Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.     

N‐{3‐[(2‐Ammonioethyl)amino]propyl}ethane‐1,2‐diaminium tris(trifluoromethanesulfonate): a salt of a folded triply protonated tetramine

The structure of a trifluoromethanesulfonate salt of a nontypical triply protonated linear tetramine, C₇H₂₃N₄³⁺·3CF₃SO₃⁻, with a layered crystal structure is presented. One N atom remains unprotonated. The conformation of the cation is enforced by intra‐ and intermolecular hydrogen bonds. The crystal structure is built of ca 10 Å deep layers, within which cations and anions are hydrogen bonded. Each layer is only weakly bound to its neighbours. This study shows a rare example of an unsymmetrically protonated polyamine and the relation between the lack of protonation, intramolecular hydrogen bonding and the conformation of the cation.     

Metallofullerenes

Summary Endohedral and exohedral metallofullerenes, including metal-doped fullerenes, organometallic fullerenes and fullerene metal complexes, are described in the context of their syntheses and properties.     

Chromatographic competitive binding immunoassays: a comparison of the sequential and simultaneous injection methods

Two approaches for performing competitive binding immunoassays by HPLC and other flow-based systems are the simultaneous and sequential injection methods. Both these techniques make use of a column with a limited amount of antibody, onto which is injected a sample and a fixed amount of a labeled analyte analog. An indirect measure of the unlabeled analyte in the sample is then obtained by looking at the amount of analog in either the nonretained or retained peaks. In the simultaneous injection mode, the sample and labeled analog are applied at the same time to the column, while in the sequential mode the sample is injected first, followed by the analog. This results in a difference in the analytical characteristics of these two approaches. This study used chromatographic theory and previous data obtained for injections of human serum albumin (HSA) onto an anti-HSA antibody column to compare the response, detection limits, range, and sensitivity of these methods. Under equivalent conditions, it was found that the sequential method always provided the best lower limit of detection and sensitivity. However, the simultaneous mode had a broader dynamic range and higher upper limit of detection. From these observations, several guidelines were developed regarding the use and selection of such assays for new applications.     

Spectroscopic and photochemical properties of the lichen compound lobaric acid

Lichens synthesize and accumulate photoprotective compounds against possible damage induced by UV radiation in the photobiont. A biological model has been recently formulated that allows the use of lichens to evaluate changes at different UV radiation levels. The thermodynamics, photophysical and photochemical properties of lobaric acid were studied in acetonitrile, ethanol and Brij 35(3%) micelles at different pH values. Also the sun protector factor (SPF) was determined by in vitro methods. Lobaric acid was extracted from Stereoculon alpinum Laur. and characterized by means of standard procedures. Solutions were irradiated in oxygen and under nitrogen conditions with a UV medium pressure lamp. Lobaric acid absorbs at 287, 303 nm, and no fluorescence emission was observed. The maximum value of the molar extinction coefficient (5479.6 M(-1) cm(-1)) was obtained in Brij 35 at pH 12. Solubility is pH dependant and is highest in Brij 35 at pH 12 (4.45 x 10(-4) M). Photoconsumption quantum yields ranged between 10(-4) and 10(-5) in aerobic and anaerobic experimental conditions. Lobaric acid SPF was very low (0.5) compared with homosalate (4.0), (reference solar filter). Two pKa values, 5.05 (carboxylic acid group deprotonation) and 9.75 (phenolic OH deprotonation), were determined.     

On the Durrmeyer-type modification of some discrete approximation operators

In [10], for continuous functionsf from the domain of certain discrete operatorsL _n the inequalities are proved concerning the modulus of continuity ofL _nf. Here we present analogues of the results obtained for the Durrmeyer-type modification $\tilde L_n $ ofL _n. Moreover, we give the estimates of the rate of convergence of $\tilde L_n f$ in Hölder-type norms     

Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies

The paper is focused on the phenomena of various steady-state oscillations exhibited by the twin-well potential system. Regions of existence of different attractors in the system parameter domain are examined and a picture book of different steady states for fixed damping and forcing is presented: 20 different combinations of single or coexisting, small orbit or large orbit, periodic and chaotic attractors are displayed. Computer simulations are followed by an approximate analytical analysis: A study of various forms of instability of periodic solutions gives close form approximate criteria for occurrence of T-periodic small orbit and large orbit oscillations, and for cross-well chaos.     

Kinetics and mechanism of the phenolysis of asymmetric diaryl carbonates

The reactions 4-methylphenyl 4-nitrophenyl carbonate (MPNPC), 4-chlorophenyl 4-nitrophenyl carbonate (CIPNPC), 4-methylphenyl 2,4-dinitrophenyl carbonate (MPDNPC), and 4-chlorophenyl 2,4-dinitrophenyl carbonate (CIPDNPC) with a homogeneous series of phenoxide anions are subjected to a kinetic investigation in aqueous solution (25.0 degrees C, ionic strength 0.2 M (KCI)). Under an excess of phenoxide with respect to the substrate, all of these reactions obey pseudo-first-order kinetics and are first order in phenoxide. The Br?nsted-type plots for the nucleophilic rate constants (k(N)) are linear, with slopes beta = 0.48 (MPNPC), 0.67 (ClPNPC), 0.41 (MPDNPC), and 0.32 (ClPDNPC). The magnitude of these slopes and the absence of a curvature in the Br?nsted plot at pK(a) = 7.1 for the CIPNPC reactions are consistent with concerted mechanisms (one step). The carbonates MPDNPC and ClPDNPC are more reactive than MPNPC and CIPNPC, respectively, toward phenoxide nucleophiles. This can be explained by the presence of a second nitro group in the nucleofuge of the dinitro derivatives, which (i) leaves their carbonyl carbon more positively charged, making them better electrophiles, and (ii) makes 2,4-dinitrophenoxide a better leaving group than 4-nitrophenoxide. The 4-chloro derivatives are more reactive than the corresponding 4-methyl derivatives. This should be due to the greater electron withdrawal of 4-chloro than 4-methyl, which makes the former carbonyl more electrophilic. Comparison of the concerted phenolysis of MPNPC with the stepwise reactions of secondary alicyclic amines with the same substrate indicates that substitution of a secondary alicyclic amine group in a zwitterionic tetrahedral intermediate by a phenoxy group greatly destabilizes the intermediate. An equation is deduced for log k(N) in terms of the basicity of the nucleophile, the nonleaving moiety, and the leaving group. This equation shows that for these reactions, the sensitivity of log k(N) to the basicity of the nonleaving moiety (beta(nlg) = -0.27) is very similar to that of the nucleofuge (beta(lg) = -0.25).