The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

Study of the resistances of organic coatings to filiform corrosion

The filiform corrosion is a special-type atmospheric corrosion, which broadens below the organic coatings and is characterized by its manifestation in the form of fibres or filaments. An important factor for broadening the filiform corrosion involves also the barrier or chemical resistance of the organic coating. The paper deals with the modes of filiform-corrosion initiation and evaluation thereof under nonpigmented organic coatings based on various binder bases. Also the possibility of retardation of the filiform corrosion by means of zinc powder and the effects of lamellar pigment on the filament shapes are studied.     

Natural examples of Valdivia compact spaces

We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L¹ spaces, Banach lattices and noncommutative L¹ spaces.     

Thermal properties and crystallization of BaO–MoO3–P2O5 glasses

Journal of Thermal Analysis and Calorimetry - The thermal behavior and crystallization of barium molybdate-phosphate glasses were studied in two compositional series, namely A:...     

Monotone retractability and retractional skeletons

We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a question of R. Rojas-Hernández and V.V. Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W. Kubi?.     

(I)-envelopes of closed convex sets in Banach spaces

We study the notion of (I)-generating introduced by V. Fonf and J. Lindendstrauss and a related notion of (I)-envelope. As a consequence of our results we get an easy proof of the James characterization of weak* compactness in Banach spaces with weak angelic dual unit ball and an easy proof of the James characterization of reflexivity within a large class of spaces. We also show by an example that the general James theorem cannot be proved by this method. The work is a part of the research project MSM 0021620839 financed by MSMT and partly supported by the research grant GA ČR 201/06/0018.     

On products with the unit interval

We investigate the question which compact convex sets are homeomorphic to their product with the unit interval. We prove it in particular for the space of probability measures on any infinite scattered compact space and for the half-ball of a non-separable Hilbert space equipped with the weak topology. We also show examples of compact spaces for which it is not the case.     

Filling analytic sets by the derivatives of -smooth bumps

If is an infinite-dimensional Banach space, with separable dual, and is an analytic set such that any point can be reached from  by a continuous path contained (except for the point ) in the interior of , then is the range of the derivative of a -smooth function on  with bounded nonempty support.

     

Possibilities for removal of chlorinated dye Mordant Blue 9 from model waste water

This comparative study focused on the different methods used for the treatment of model waste water polluted with the chlorinated acid dye Mordant Blue 9. Low-cost and commercially available ionic liquids — benzalkonium chloride and Aliquat 336 — were applied as liquid ion-exchangers to precipitate the Mordant Blue 9 by way of ion pair formation between the bulky ammonium cations of ionic liquids and anions of the above dye. The decolorisation efficiency of the ionic liquid application and the effect on reduction of the absorbance, adsorbable organic halogens, chemical oxygen demand and biological oxygen demand were compared with the conventional coagulation, sorption and Fenton oxidation techniques.     

A weak Asplund space whose dual is not in Stegall's class

We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund space whose dual, equipped with the weak* topology, is not in Stegall's class. This completes a result by Kenderov, Moors and Sciffer.