On the stationary flows of viscous,incompressible and heat-conducting fluids

We consider a boundary-value problem describing the motion of viscous, incompressible and heat-conducting fluids in a bounded domain in ?³. We admit non-homogeneous boundary conditions, the appearance of exterior forces and heat sources. Our aim is to prove the existence of a solution of the problem in Sobolev spaces.     

HPLC determination of PAHs in mineral oils used as dispersing agents for herbicides

Summary The representative refined mineral oil samples, crude petroleum straightrun distillates, potentially used in the manufacture of crop protection products were analysed by isocratic and gradient high performance liquid chromatography (HPLC) to investigate their trace polycyclic aromatic hydrocarbon (PAH) content. Liquid-liquid extraction followed by size-exclusion column chromatography was employed to isolate the fraction containing PAHs with more than two fused rings. The identity of individual PAHs was confirmed by comparing their UV and fluorimetric detector signals with those recorded from reference standards. The level of extracted PAHs in the oil samples are discussed with respect to their physical and chemical properties.     

ON THE ITERATED ω-RULE

Let Γ_n(φ) be a formula of L_PA (PA = Peano Arithmetic) meaning “there is a proof of φ from PA-axioms, in which ω-rule is iterated no more than n times”. We examine relations over pairs of natural numbers of the kind. (n, k) ≦_H (n', k') iff PA + RFN_n' (H_k') ? RFN_n (H_k). Where H denotes one of the hierarchies ∑ or Π and RFN_n(C) is the scheme of the reflection principle for Γ_n restricted to formulas from the class C(Γ_n(φ) implies “φ is true”, for every φ ∈ C). Our main result is that. (n, k) ≦H (n', k') if n ≦ n' and k ≦ max (k', 2n' + 1).     

A facile synthesis of 1,1-bis(silyl)ethenes

Symmetrical 1,1-bis(silyl)ethenes have been easily prepared via ruthenium complex-catalyzed silylative coupling cyclization of 1,2-bis(dimethylvinylsiloxy)ethane to give 2,2,4,4-tetramethyl-3-methylene-1,5-dioxa-2,4-disilacycloheptane with excellent selectivity and good yield, followed by its reaction with Grignard reagents. The cyclic product can also be effectively transformed into cyclic carbosiloxane, 2,2,4,4,6,6,8,8-octamethyl-3,7-dimethylene-1,5-dioxa-2,4,6,8-tetrasilacyclooctane.     

Electrodeposition of ferrocenoyl peptide disulfides

Using electrodeposition of cyclic and acyclic Fc-peptide disulfides tightly-packed Fc-peptide monolayers were conveniently formed, which exhibit significant differences in their electron transfer kinetics.     

Modified Alternating $$\vec{k}$$–generators

This paper deals with a class of pseudorandom bit generators – modified alternating –generators. This class is constructed similarly to the class of alternating step generators. Three subclasses of are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating –generators, designed especially to be more secure, are presented.