Investigation of the separation efficiency in one-stage and multistage extractions by a numerical method

Theoretical separation efficiencies in one-stage static and multistage dynamic models of liquid-liquid extraction have been studied mathematically. By the use of the iterative numerical method the maximum difference between separation efficiencies in these two models, as well as the absolute values of the respective separation efficiencies were calculated at this maximum. The maximum difference between multistage and one-stage separation efficiencies amounts to 20.36%, when the respective separation efficiencies are about 91.89% and 71.56%.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Effect of degradation of montmorillonite by vibration grinding on the dTA curves in the range 20–1500°C

The effect of vibration grinding on the DTA curves of montmorillonite isolated from the most important locality of bentonite in the Slovak Republic (Jel?ovy potok, Middle Slovakia) was studied in the temperature range 20–1500°C. Interpretation is offered for 6 endothermic and 3 exothermic peaks. vibration grinding modified the course of dehydration of the mineral, suppresses the “dehydroxylation’ peak at 700°C, enables the crystallization of high-temperature quartz, cristobalite and cordierite at lower temperatures in comparison with unground natural montmorillonite. Vibration griding slows down the crystallization of mullite which—unlike quartz, cristobalite and cordierite—does not belong to high-temperature phases of Cheto-montmorillonite. The order in which these high-temperature phases occur is not influenced by vibration grinding.     

Sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ during their transport in undisturbed vertical and horizontal soil cores under dynamic flow conditions

Transport and sorption of ¹²⁵I^?, ¹³⁷Cs⁺, ⁸⁵Sr²⁺ and ^152,154Eu³⁺ in undisturbed soil cores have been studied under dynamic conditions. Radionuclides were dissolved in synthetic groundwater (SGW) of 0.015 mol/dm³ ionic strength, pH 8.4 and redox potential E_h = 145 mV. The soil samples were taken vertically and horizontally from the river bed at 5–100 cm depths, about 120 m southward of the Dukovany Low and Medium Level Radioactive Waste Repository. The respective water-soluble carriers in the 10^?6 mol/dm³ concentration were added into the SGW prior to the experiments. The soil cores of 9 cm height and 3.8 cm in diameter were placed into columns made of 150 cm³ PE injection syringes of suitable dimensions. The SGW was introduced into columns from the Mariotte’s bottle through a glass manifolds to supply the soil columns by gravity flow at a constant flow-rate about 1.2 cm³/h. Into the water stream, radioactive nuclides were added individually in a form of a short pulse in 0.1 cm³ of demineralized water. In the case of ¹²⁵I^? transport, retardation and hydrodynamic dispersion coefficients were determined, using an integral form of a simple advection-dispersion equation. For each radionuclides, sorption and desorption data have been obtained, evaluated and the results were compared mutually. Residual distributions of the sorbed cationic radionuclides along the soil columns were also presented.     

Higher-order Sobolev embeddings and isoperimetric inequalities

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in Rⁿ${\mathbb{R}}^n$, possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces. In particular, our results are applied to any-order Sobolev embeddings in regular (John) domains of the Euclidean space, in Maz'ya classes of (possibly irregular) Euclidean domains described in terms of their isoperimetric function, and in families of product probability spaces, of which the Gauss space is a classical instance.     

Light scattering by longitudinal acoustic modes in supercooled molecular liquids II: microscopic derivation of the phenomenological equations

The constitutive equations for the orientational dynamics of a liquid formed of linear molecules are derived microscopically. The resulting generalised Langevin equations coincide with the phenomenological approach of Dreyfus et al. [1]. Formally exact expressions are given for the phenomenological coefficients and various constraints are shown to be consequences of this microscopic approach. Received 14 August 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: franosch@hmi.de     

An example of a space L on which the Hardy-Littlewood maximal operator is not bounded

We give an example of a function p such that the Hardy-Littlewood maximal operator is not bounded on the generalized Lebesgue space L^p(x).     

Beziehungen zwischen den Verdampfungsw?rmen bin?rer Gemische

Ohne Zusammenfassung