Influence of the cathodic polarization on the stability of Ti surface in concentrated KOH solutions

The stability of spontaneous thin layers and thin layers formed upon cathodical polarization of Ti in KOH solutions have been studied by potentiostatic and ellipsometric methods. At open circuit potential (OCP) the strongly adherent films, whose thickness depends on the concentration of the KOH solution, were formed. During the cathodic polarization the transformation of these films to weakly adsorbed precipitated layers on the electrode surface was observed. Comparing the theoretically computed curves with the experimental Ψ vs Δ loci measured ellipsometrically, the complex indices of refraction and the thickness of the generated films, from 3.6 to 60 nm in 1 M KOH and from 36 to 105 nm in 5 M KOH (adherent to the electrode surface), were determined. At OCP the rate of film growth increases with increasing the concentration of KOH solution. Cathodic polarizations change the chemical composition and retard the rate of film growth. Based on the ellipsometric and electrochemical data the chemical compositions of the formed films consisted of TiO₂, Ti₂O₃, TiO₂·H₂O, Ti(OH)₃ and TiOOH·nH₂O.     

Cytochemical differences in bacterial glycocalyx.

To examine new cytochemical aspects of the bacterial adhesion, a strain 41452/01 of the oral commensal Streptococcus sanguis and a wild strain of Staphylococcus aureus were grown with and without sucrose supplementation for 6 days. Osmiumtetraoxyde (OsO4), uranyl acetate (UA), ruthenium red (RR), cupromeronic blue (CB) staining with critical electrolytic concentrations (CECs), and the tannic acid-metal salt technique (TAMST) were applied for electron microscopy. Cytochemically, only RR-positive fimbriae in S. sanguis were visualized. By contrast, some types of fimbriae staining were observed in S. aureus glycocalyx: RR-positive, OsO4-positive, tannophilic and CB-positive with ceasing point at 0.3 M MgCl2. The CB staining with CEC, used for the first time for visualization of glycoproteins of bacterial glycocalyx, also reveals intacellular CB-positive substances-probably the monomeric molecules, that is, subunits forming the fimbriae via extracellular assembly. Thus, glycosylated components of the biofilm matrix can be reliably related to single cells. The visualization of intracellular components by CB with CEC enables clear distinction between S. aureus and other bacteria, which do not produce CB-positive substances. The small quantities of tannophilic substances found in S. aureus makes the use of TAMST for the same purpose difficult. The present work protocol enables, for the first time, a partial cytochemical differentiation of the bacterial glycocalyx.     

Inexpensive d‐dimensional matchings

Suppose that independent U(0, 1) weights are assigned to the ${d\choose 2}n^{2}$ edges of the complete d‐partite graph with n vertices in each of the d maximal independent sets. Then the expected weight of the minimum‐weight perfect d‐dimensional matching is at least $\frac{3}{16}n^{1-(2/d)}$. We describe a randomized algorithm that finds a perfect d‐dimensional matching whose expected weight is at most 5d³n^1?(2/d)+d¹⁵ for all d≥3 and n≥1. © 2002 John Wiley & Sons, Inc. Random Struct. Alg., 20, 50–58, 2002     

Entrapment efficiencies of hydrodynamic boundary layers on rising bubbles

Flotation and separation practice shows that fine hydrophilic solids are often drawn into the froth product. The occurrence of this unwanted event in the classical froth flotation has led to the idea of using it for the separation by size of ground materials. Thus, a method for the extraction of hydrophilic fines by foaming of a suspension was proposed. The aim of the present study is to relate this phenomenon to the residence time of the particles in the vicinities of the rising bubbles. Dynamic interactions of fine solids with rising bubbles cause perturbations in the background flow field. A procedure for the mathematical modeling of these disturbance effects is proposed. The initial idea is that the particles lag behind the background bubble-driven flows. A key point is the possibility of classifying fine entities according to a general criterion, containing only parameters of the outer flow. The basic result is that there exists a range of particle and bubble dimensions for which this entrapment is optimal. The proposed model investigation gives a concise explanation for the observed capture of fine solids in many flotation and separation processes.     

Beitrag zum Problem der quadrierbaren Kreisbogenzweiecke

Ohne Zusammenfassung     

On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings

In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383–429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363–1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

Common fixed point theorems for non-self-mappings in metric spaces of hyperbolic type

In this paper, the concept of a pair of non-linear contraction type mappings in a metric space of hyperbolic type is introduced and the conditions guaranteeing the existence of a common fixed point for such non-linear contractions are established. Presented results generalize and improve some of the known results. An example is constructed to show that our theorems are genuine generalizations of the main theorems of Assad, ?iri?, Khan et al., Rhoades and Imdad and Kumar. One of the possible applications of our results is also presented.     

Contractive type non-self mappings on metric spaces of hyperbolic type

Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of ?iri? [L.B. ?iri?, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. ?iri?, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.