There does not exist an enumerable family of context-free grammars that generates the class of single-valued languages

Translated from Matematicheskie Zametki, Vol. 50, No. 1, pp. 34–40, July, 1991.     

Reflection spectroscopy in microstructured light scattering materials

Summary A theoretical model is derived that describes the influence of lateral light diffusion in a scattering medium on the absorptivity of an absorber spot on top of the substrate. The model uses the lateral resolved reflectivity under point irradiation that has been analyzed experimentally with a scanning-micro-laser-reflectometer. The model allows quantification of the absorptivity by one single equation that contains only the mean radial diffusion length of light and the spot area. Experiment and theory are applied to typical substrates for thin layer chromatography (alumina, silica, cellulose). The diffusion lengths in these substrates are given and the absorptivities of the spots are calculated as a function of the spot area.     

Anodic stripping coulometry with collection for absolute trace analysis of lead, using flow-through electrochemical cells with porous working electrodes

Summary Flow-through electrochemical cells with porous working electrodes made of crushed reticulated vitreous carbon and plated with mercury were used for absolute analysis of trace amounts of lead by anodic stripping coulometry with collection (ASCWC) in a flow system. The role of mercury coating, flow rate and pH were investigated. The coulombic content of the collection peak corresponded to the theoretical values calculated by Faraday's law in a concentration range from about 10^–9 to 10^–6 mol/l. The relative error and the relative standard deviation was +0.15% and 0.8%, respectively for 2×10^–6 mol/l analyte concentration. The absolute detection limit (3 s) was 0.1 ng of Pb, the linear response range 7×10⁴. One leave from: Department of Analytical Chemistry, Slovak Technical University, CS-812 37 Bratislava, Czechoslovakia     

REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES

In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the Urysohn-Nachbin lemma is presented which is quite different from the classical one.     

ESTIMATE OF THE UPPER CRITICAL FIELD AND CONCENTRATION FOR SUPERCONDUCTOR

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the upper critical magnetic field Hc3 at which superconductivity can nucleate is estimated. In addition, the authors locate the concentration of the order parameter, which depends on the inhomogeneous term a(x). Unlikely to the homogeneous case, the order parameter may concentrate in the interior of the superconducting material, due to the influence of the inhomogeneous term a(x).     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME

The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.     

ASYMPTOTIC BEHAVIOR OF THE DRIFT-DIFFUSION SEMICONDUCTOR EQUATIONS

This paper is devoted to the long time behavior for the Drift-diffusion semi-conductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) defined by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.