Banach-Saks operators on spaces of continuous functions

Summary Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Optimization of a New Extraction Technique for Analysis of Verbenone and cis-Verbenol in Pine Seeds

Results from a systematic study of the factors affecting extraction of cis-verbenol and verbenone from pine seeds are presented. Five extraction conditions were investigated: extraction solvent, method of extraction, extraction temperature, volume of solvent, and the ratio of the mass of sample to the amount of extraction solvent. The resulting optimized method uses magnetic-stirring-assisted extraction of pine seeds (5 g) with ethyl acetate (75 mL) for 20 min, at room temperature. RSDs were less than 5% for both compounds. GC–FID was used for quantification of cis-verbenol and verbenone in the extracts.     

In-line pressurized-fluid extraction-solid-phase extraction for determining phenolic compounds in grapes

A procedure to determine 3-alkyl-2-methoxypyrazines in wines is described. It is based on the headspace solid-phase microextraction (HS-SPME) technique after a clean-up of the sample by distillation (previously acidified to pH 0.5) to remove ethanol and other volatile compounds that can interfere in the SPME. Determination is performed by means of capillary gas chromatography using a nitrogen-phosphorus detector. The method allows quantification of 3-isobutyl-2-methoxypyrazine, 3-sec-butyl-2-methoxypyrazine and 3-isopropyl-2-methoxypyrazine at their natural concentration levels and below their sensory thresholds in Cabernet Sauvignon and Merlot wines. The method was successfully applied to experimental red wines and the evolution of their pyrazine contents during the winemaking process was monitored. Pyrazine content increased during the first maceration day but did not change significantly during alcoholic and malolactic fermentation. Final contents in wines were 12-27 ng/l of 3-isobutyl-2-methoxypyrazine and 5-10 ng/l of 3-sec-butyl-2-methoxypyrazine.     

The calculation of equilibrium concentrations in large multimetal/multiligand systems

An algorithm for computing equilibrium concentrations by the “equilibrium constant” method is described. The main features of this algorithm are: (a) a damping procedure in conjunction with the Newton-Raphson technique that avoids divergence in dealing with very complicated (simultaneous presence of simple, mixed, protonated, polynuclear and hydroxypolynuclear species) and/or very large systems; (2) the use of devices to decrease core requirements, calculation time, and ill-conditioned problems; and (3) the calculation of errors in free and species concentrations from the uncertainties in analytical concentrations and in formation constants. Four systems are used for testing computer programs on calculation of equilibrium concentrations.     

Electron-transfer reaction of cinnamic acids and their methyl esters with the DPPH(*) radical in alcoholic solutions

The kinetic behavior of cinnamic acids, their methyl esters, and two catechols 1-10 (ArOH) in the reaction with DPPH(*) in methanol and ethanol is not compatible with a reaction mechanism that involves hydrogen atom abstraction from the hydroxyl group of 1-10 by DPPH(*). The rate of this reaction at 25 degrees C is, in fact, comparatively fast despite that the phenolic OH group of ArOH is hydrogen bonded to solvent molecules. The observed rate constants (k(1)) relative to DPPH(*) + ArOH are 3-5 times larger for the methyl esters than for the corresponding free acids and, for the latter, decrease as their concentration is increased according to the relation k(1) = B/[ArOH](0)(m), where k(1) is given in units of M(-1) s(-1), m is ca. 0.5, and B ranges from 0.02 (p-coumaric acid) to ca. 3.48 (caffeic acid) in methanol and from 0.04 (p-coumaric acid) to ca. 13 (sinapic acid) in ethanol. Apparently, the reaction mechanism of DPPH(*) + ArOH involves a fast electron-transfer process from the phenoxide anion of 1-10 to DPPH(*). Kinetic analysis of the reaction sequence for the free acids leads to an expression for the observed rate constant, k(1), proportional to [ArOH](0)(-1/2) in excellent agreement with the experimental behavior of these phenols. The experimental results are also interpreted in terms of the influence that adventitious acids or bases present in the solvent may have. These impurities dramatically influence the ionization equilibrium of phenols and cause a reduction or an enhancement, respectively, of the measured rate constants.