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.     

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.     

The crystal structure of eudesma-4(15),7(11)-dien-8α, 12-olide: a sesquiterpene lactone fromTrattinickia rhoifolia Willd

The title compound, formula C₁₅H₂₀O₂, is orthorhombic, P2₁2₁2₁ witha=8.747(2),b=12.025(3),c=12.554(3)Å,Z=4, andD _m =1.32(2)g/ml. The structural analysis shows that the compound corresponds to eudesma-4(15),7(11)-dien-8,12-olide, a sesquiterpene lactone previously isolated fromAster umbellatus but whose crystal structure was unknown.     

Detection of soil pollution by hydrocarbons using headspace-mass spectrometry and identification of compounds by headspace-fast gas chromatography-mass spectrometry

The direct coupling of a headspace sampler with a mass spectrometer is proposed as a screening tool for the rapid detection of soil pollution by hydrocarbons from petroleum and derivatives. The samples are subjected to the headspace generation process, with no prior treatment, and the volatiles generated are introduced directly into the mass spectrometer, thereby obtaining a fingerprint of the sample analysed. Suitable treatment of the signal by chemometric techniques allows unequivocal characterisation of the different types of sample. The use of fast gas chromatography with a mass spectrometer detector coupled to the headspace sampler allows identification of the major hydrocarbons present in the mineral and organic polluted samples, interpretation of the results obtained, and demonstrates the analytical potential of headspace-mass spectrometry coupling.     

Optimisation of stir bar sorptive extraction for the analysis of volatile phenols in wines

An easy, fast and reliable analytical method is proposed for the determination of the concentration of volatile phenols (ethyl- and vinylphenols) in wines. The novel stir bar sorptive extraction (SBSE) technique is employed, following a simple and fast procedure that allows 15 samples to be extracted simultaneously using very small sample volume. Extracts are desorbed in a thermodesorption system (TDS) coupled on-line to a gas chromatograph-mass spectrometry system. The SBSE offers better recovery and linear regression coefficient (r2) for the four volatile phenols than solid-phase extraction (SPE). The mass spectrometric detection in selected ion monitoring mode contributes to the lower detection limit and good sensibility obtained with this method.