Weakly Implicative (Fuzzy) Logics I: Basic Properties

This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance.The work was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AVOZ10300504.     

Measurement of gas solutions in small samples of intermetallic alloys

This article describes a measuring system that was proposed so as to enable measurement of the content of dissolved gas in samples, whose shape is determined by the specific requirements of the simultaneous measurements and cannot be modified to satisfy the requirements on solubility measurements. The apparatus — a dynamic UHV vacuum system — consists of a measuring chamber fitted with a heater based on electron bombardment, which permits a change in the sample temperature according to the selected schedule. The design of the heater permits reduction of additional heating in the actual measuring chamber, so that the increase in pressure caused by the action of the heater can be neglected. The measuring part of the system permits recording of changes in the overall pressure and partial pressures of selected gases in the measuring chamber. The lowest detectable amount of dissolved gas is less than 10⁻⁵ Pa m³. The results of measurement of the solubility of hydrogen in Ti and Fe aluminides in samples that are simultaneously used to measure the electrical conductivity are given as an example of the suitability of the apparatus for such measurements. This work is a part of research plan MSM 0021620834 financed by the Ministry of Education, Youth and Sports of the Czech Republic.     

“Self activation”properties of the nanophase photocatalytic titania precursors

Summary Unexpected photocatalytic properties of templated precursors of nanostructured TiO₂(titania) were observed in the development of a generally applicable method for the synthesis of a truly nanocrystalline titania at temperatures compatible with plastic catalytic supports. It specifically comprised the “self-activation”feature of the TiO₂nanostructured precursor (produced within the non-ionic surfactant template) likely induced by the preparation method “imprinted”photoactivity. Such behavior complied with the principal aim to develop the photocatalytic material without recourse to any significant thermal step.     

Multifrequency Two-Dimensional Fourier Transform ESR: An X/Ku–Band Spectrometer

A two-dimensional Fourier Transform ESR (2D FT ESR) spectrometer operating at 9.25 and 17.35 GHz is described. The Ku-band bridge uses an efficient heterodyne technique wherein 9.25 GHz is the intermediate frequency. At Ku-band the sensitivity is increased by almost an order of magnitude. One may routinely collect a full 2D ELDOR spectrum in less than 20 min for a sample containing 0.5–5 nmol of nitroxide spin-probe in the slow-motional regime. Broad spectral coverage at Ku-band is obtained by use of a bridged loop-gap resonator (BLGR) and of a dielectric ring resonator (DR). It is shown that an even more uniform spectral excitation is obtained by using shorter microwave pulses of about 3 ns duration. The dead-time at Ku-band is just 30–40 ns, yielding an improved SNR in 2D ELDOR spectra of nitroxide spin-probes withT₂as short as 20–30 ns. A comparison of 2D ELDOR spectra obtained at 9.25 and 17.35 GHz for spin-labeled phospholipid probes (16PC) in 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) membrane vesicles showed that both spectra could be satisfactorily simulated using the same set of model parameters even though they are markedly different in appearance. The improved sensitivity and shorter dead-time at Ku-band made it possible to obtain orientation-dependent 2D ELDOR spectra of the Cholestane (CSL) spin-probe in macroscopically aligned lipid bilayers of egg yolk PC using samples containing only 1 mg of lipid and just 5 nmol of spin-probe.     

The electronic bandstructure of rhodium and the effects of change of volume

The electronic bandstructures of fcc rhodium have been calculated for the normal value of the lattice constant and one 5% smaller, using the nonrelativistic symmetrized augmented plane wave method. The results of the first calculation are in good agreement with those of other workers. Under pressure the d-bands shift and broaden appreciably, resulting in a slight increase in d-occupation.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

Description of spinning particle in general relativity using commuting spin variables

A general relativistic extension of a recently proposed model of spinning particle using commuting spin variables is given. The results found earlier in an approach using anticommuting (Grassmannian) variables are reproduced and extended to the case with nonzero torsion. The quantization of the model is performed via Feynman path integral and a discretization procedure is proposed leading to a covariant second-order differential equation for the propagator which in the case with zero torsion can be reduced to general relativistic Dirac equation with δ-function source.     

Interference of permeable anions in potassium-sensitive membrane electrodes based on valinomycin and dimethyldibenzo-30-crown-10

Responses of potassium-sensitive electrodes with valinomycin and dimethyldibenzo-30-crown-10 in the poly(vinyl chloride) membrane plasticized with dipentyl phthalate in solutions containing lipophilic anions, i.e., perchlorate and picrate have been measured. Using a general theoretical treatment, the role of possible ion pair formation in the membrane phase in the e.m.f./activity dependences is discussed. The electrode with a crown-compound is characterized by a broader region of cation response with an almost Nernstian slope. The possibility of extending the analytically useful range of these electrodes has been verified by using the membrane phase containing C₁₂—C₁₄ phthalates.     

Statistical evaluation of mobility curves of univalent weak acids

This paper brings a new rigorous and complete statistical approach to the data processing of the mobility curves of univalent weak acids. It is based on a fundamental equation for the mobility curve, on applying the mathematical principle of the best fit, derivation of the related nonlinear equation and finding the mathematical solution of it which gives the best estimates of the mobility curve parameters. The mathematical procedure presented here does not impose any limitations upon the numerical data used, i.e., the experimental values of mobilities and pH may be real numbers (positive, negative, zero). Further, rigorous explicit statistical formulas are derived for SDs of effective mobility, dissociation constant, and ionic mobility of fully ionized anion in question.     

Experimental evidences for some unusual divalent cation complexes of valinomycin

From extraction experiments and γ-activity measurements, the exchange extraction constants corresponding to the general equilibrium M ²⁺ (aq) + 1 · Sr²⁺ (nb) ⇄ 1 · M ²⁺ (nb) + Sr²⁺ (aq) taking place in the two-phase water-nitrobenzene system (M ²⁺ = Cu²⁺, Zn²⁺, Cd²⁺, Pb²⁺, UO₂ ²⁺, Fe²⁺, Co²⁺, and Ni²⁺; 1 = valinomycin; aq = aqueous phase, nb = nitrobenzene phase) were evaluated. Moreover, the stability constants of the 1 · M ²⁺ complexes in water saturated nitrobenzene were calculated; they were found to increase in the order Fe²⁺ < Cd²⁺, Co²⁺ < Ni²⁺ < UO₂ ²⁺, Zn²⁺ < Cu²⁺ < Pb²⁺. Correspondence: Emanuel Makrlík, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic.