Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

q-Sigma-algebra generated by balls

The q--algebra, i.e., the system of sets closed under complementation, countable disjoint unions, and containing the empty set, generated by the system of open balls coincides with the -field of Borel sets inR sun forn=1,2, and 3. A first step to extend the proof forn=4, 5, 6, and 7 is indicated.     

Encapsulation of magnetite in vesicles

The encapsulation of fine magnetite particles of 10 nm size and marker ANS within asolectin vesicles has been made by sonication of the mixture in water. For the proof of encapsulation of magnetite in vesicles the electron microscope and spectrofluoriphotometer technique were used. The theory for the calculation of the magnetic force acting on the system consisted of non-capsulated magnetic particles dispersed in water and magnetic vesicles was developed.This work was supported by the Slovak Academy of Sciences within the framework of Project GAV No. 1361.     

On the critical regimes in the theory of randomly forced magnetohydrodynamic turbulence

In this paper large-scale properties of developed magnetohydrodynamic turbulence have been investigated by using double expansion method in the frame of quantum field renormalization group. It has been shown that universal kinetic scaling regime exists, but the double expansion in general leads to qualitatively different results than those provided by the usual -expansion treatment.This work was supported by Slovak Grant Agency for Science.     

Radionuclide partitioning coefficients in the Sava River ecosystem

The radionuclides⁵⁴Mn,⁶⁰Co,⁹⁰Sr,⁹⁵Nb,⁹⁵Zr,¹⁰³Ru,¹⁰⁶Ru,¹²⁵Sb,¹³¹I,¹³⁴Cs,¹³⁷Cs,¹⁴⁰Ba,¹⁴⁴Ce,²²⁶Ra and²²⁸Ac have been studied in the Sava River environment since the Chernobyl accident in 1986. The measured periphyton concentration ratios (CR) for each radionuclide were correlated with the measured sediment distribution coefficients (K_d) for that radionuclide. The K_d-CR relationships obtained were defined by the equation ln K_d=–0.5 ln CR +7.4. These K_d-CR relationships were assumed to be referable to the Sava River ecosystem and were used to predict the missing soil K_d values and/or the missing CR values for the wide range of radionuclides, respectively. Moreover, the K_d-CR relationship characteristic for the Sava River ecosystem was compared with the K_d-CR relationship proposed by Baes¹ and by Shepard². The characterization of the partition coefficients in the Sava River environment and understanding of the mechanisms affecting radionuclide retardation and bioaccumulation are required for the planning of radioactive waste depositories in the area.     

Electrochemical behaviour of a series of Fe(III) complexes with tetradentate Schiff base ligands

Summary The electrochemical reduction of the Fe(III) complexes with a series of substituted N,N-Ethylenebisacetonimines was investigated by cyclic voltammetry in acetonitrile solution at a platinum electrode. The substituent does not significantly influence the redox properties of the studied complexes. The symmetry of the redox orbital is responsible for the observed behaviour of the complexes.

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Elektrochemisches Verhalten einer Reihe von Fe(III)-Komplexen mit vierzähnigen Schiffschen Basen als Liganden

Zusammenfassung Die elektrochemische Reduktion der Fe(III)-Komplexe einer Reihe von substituierten N,N-Ethylenbisacetoniminen wurde mittels cyclischer Voltammetrie in Acetonitril an einer Platinelektrode untersucht. Der Substituent beeinflußt die Redoxeigenschaften der untersuchten Komplexe nicht signifikant. Das beobachtete Verhalten der Komplexe wird von der Symmetrie des Redoxorbitals bestimmt.

     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

A weak approach to finite elasticity

On the ground of four axioms we define thekinematics of perfectly elastic bodies and in particular the notion ofweak deformations of a perfectly elastic body. Weak deformations turn out to agree withweak diffeomorphisms introduced in [10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining thedynamics of perfectly elastic bodies in terms of twoconstitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, by the European Research Project GADGET, and by Grant n.11957 of the zech Acad. of Sciences.This article was processed by the author using the LaT_EX style filepljour1 from Springer-Verlag.     

Bell-type inequalities in horizontal sums of Boolean algebras

We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.