Glivenko like theorems in natural expansions of BCK‐logic

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK‐logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK‐logic with negation by a family of connectives implicitly defined by equations and compatible with BCK‐congruences. Many of the logics in the current literature are natural expansions of BCK‐logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one‐variable formula in the language of BCK‐logic with negation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray fundamental parameter methods for the determination of some elements in hydrocarbons by WDXRF

Summary X-ray fundamental parameter methods have been applied to the determination of some elements such as Fe, Ca, Zn, Ba and S in solutions of hydrocarbons analysed by means of a wavelength dispersive spectrometer. A comparison is carried out for methods with standards as well as without standards. The influence of different kinds of standards on the results has been investigated. The use of aqueous salt solutions has led to more accurate values than the use of solid standards. The same random errors have been obtained for both kinds of standards. Results obtained without standards are slightly less accurate than those obtained with aqueous standards.     

Indium

Ohne Zusammenfassung     

Meso-[2.2]paracyclophanyltriphenylporphyrin: A simple representative of cyclophanylporphyrins

(R + S)Meso-[2.2]Paracyclophanyltriphenylporphyrin 3 , a member of a novel class of cyclophanylporphyrins, was obtained and characterized by spectroscopic and electrochemical methods. Compared to meso-tetra[2.2]paracyclophanylporphyrin 1, it represents a simplified structure designed for the investigation of electronic interactions between the [2.2]paracyclophane moiety and porphyrin core and for use in metallation reactions.     

All-valence-electron and transition density matrix calculations of the electronic spectra of [2.2]paracyclophanequinones

The combined CNDO/S and transition density matrix methods reproduced well the UV-VIS spectra of the intramolecular charge-transfer complexes of double- and triple-layered [2.2]paracyclophanequinones in which benzene and p-benzoquinone represent the donor and acceptor layers: DA, DDA and DAD. Calculations pointed to the already known experimental bathochromic shifts of the longest wavelength absorption band for the DADDADAD transformations. The electronic transitions corresponding to this band are for DA and DDA the CT transitions of the ^* type; however, for DAD the band represents the n ^* transition localized on the acceptor ring.     

Optimal design of elastic columns subject to the general conservative behaviour of loading

Zusammenfassung Optimale Formen eines gedrückten elastischen Stabes werden bei allgemeinem Verhalten der Druckkraft nach dem Stabilitätsverlust untersucht. Als Zielfunktion wird das minimale Volumen angenommen unter der Nebenbedingung einer konstanten kritischen Belastung. Das konservative Verhalten der Kraft ist mit einer Beziehung verbunden, welche die allgemeine Euler-Lagrangesche Gleichung vereinfacht. Es werden räumlich sowie eben verjüngte Stäbe untersucht und die Resultate bei einigen Beispielen diskutiert.