IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Extraction-ability and -selectivity of tetra-aza-crown ethers for transition metal cations

In order to investigate the relative effects of the differences between the structures and lipophilicities of 1, 10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TA-18-crown-6) and the tetrabenzyl derivative of 1,10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TBTA-18-crown-6) on their extraction-abilities and -selectivities for transition metal cations, constants of the overall extraction (logK _ex) of 1:1 (M:L) complexes, the distribution (K _D) for two diluents (CH₂Cl₂ and CHCl₃) with different dielectric constants have been determined at 25 ± 0.1 °C. The magnitude of logK _ex is largely determined by that of K _D. The equilibrium constants of TA-18-crown-6 have been compared with those of TBTA-18-crown-6. It is found that:(i) logK _ex sequences of TA-18-crown-6 and TBTA-18-crown-6 for transition metals in CH₂Cl₂ lie in order: Fe³⁺ > Cu²⁺ > Mn²⁺ > Co²⁺ > Cd²⁺ > Ni²⁺ > Zn²⁺ and Fe³⁺ > Cu²⁺ > Co²⁺ > Mn²⁺ > Ni²⁺ > Cd²⁺ > Zn²⁺ respectively; (ii) the stability sequences of two types of tetra-aza-crown ethers with the transition metal cations in CHCl₃ are the same as follows: Fe³⁺ > Ni²⁺ > Cu²⁺ > Co²⁺ > Zn²⁺ > Cd²⁺ > Mn²⁺, and (iii) unusual selectivities are observed for transition metal-tetra-aza-crowns, e.g. the high Fe³⁺/M ⁿ⁺ selectivity factors (S_f) of TA-18-crown-6, except for the competitive-extractions for the special case in CHCl₃ of TBTA-18-crown-6, it was found that the Mn²⁺/M ⁿ⁺ values were relatively higher according to the other transition metal cations. A systematic sequence in these two types of solvents is not found for a given transition metal cation in terms of the variation of selectivity with the tetra-aza-crown ethers. The results provide alternatives for the rational design of other specific ligands on the transition metal cations.     

Asymptotic Analysis of the Current-Voltage Curve of a pnpn Semiconductor Device

We consider the one-dimensional steady-state semiconductor deviceequations modelling a pnpn device. There are two relevant scalingsof the equations corresponding to small and large applied voltages.In both scalings, the semiconductor equations can be consideredas singularly perturbed. It turns out that the small-voltagescaling breaks down for current values between two saturationcurrents. In that interval, the large-voltage scaling has tobe employed. For both scalings, we derive the first-order termsof an asymptotic expansion and show that the reduced problemhas a solution. An example verifies that the current-voltagecurves obtained have the expected qualitative structure.