A note on pseudocompactifications

There exists a countable spaceV _ω such that:

1. V _ω has a single non-isolated point,
2. V _ω has no pseudocompactificationX witht(X)=ω.

     

Combinatorial geometry of belt bodies

In this paper we consider a new class of convex bodies which was introduced in [11]. This is the class of belt bodies, and it is a natural generalization of the class of zonoids (see the surveys [18, 28, 24]). While the class of zonoids is not dense in the family of all centrally symmetric, convex bodies, the class of belt bodies is dense in the set of all convex bodies. Nevertheless, we shall extend solutions of combinatorial problems for zonoids (cf. [2, 12]) to the class of belt bodies. Therefore, we first introduce the set of belt bodies by using zonoids as starting point. (To make the paper self-contained, a few parts of the approach from [11] are given repeatedly.) Second, complete solutions of three well-known (and generally unsolved) problems from the combinatorial geometry of convex bodies are given for the class of belt bodies. The first of these, connected with the names of I. Gohberg and H. Hadwiger, is the problem of covering a convex body with smaller homothetic copies, or the equivalent illumination problem. The second is the Szökefalvi-Nagy problem, which asks for the determination of the convex bodies whose families of translates have a given Helly dimension. The third problem concerns special fixing systems, a notion which is due to L. Fejes Tóth. These solutions consist of improved and more general approaches to recently solved problems (as in the case of the Helly-dimensional classification of belt bodies) or new results (as those concerning minimal fixing systems, providing also an answer to a problem of B. Grünbaum which is not only restricted to belt bodies).     

A new inorganic-organic polymer for the passivation of thin film capacitors

Inorganic-organic polymers with barrier properties against water vapor, excellent electrical data (3, 2, R _D>10¹⁶ cm, E _D up to 400 V/µm) and good adhesion to various substrate materials have been developed. Tailored modifications of these materials provide an excellent protective coating for thin film capacitors. Several mm thick, expensive, encapsulations could be replaced by thin coatings (up to 10 µm). The polymer coating allows the use of thin film chip capacitors in surface-mount technology. As a measure for the efficiency of the coating, the capacitance decrease under controlled humidity has been used. The influence of the material composition, the type of catalyst during sol-gel processing and the curing conditions have been studied. Adhesion and water vapor permeation properties of the polymers and rheological properties of the coating solutions have been investigated. A protective coating is developed, which increases the withstandness of capacitors against humid conditions (90°C, 100% rel. humidity) by a factor of about 30 (compared to uncoated capacitors) and shows no crack formation during thermal cycling.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

On an eigenvalue problem arising in the study of the stability of ocean currents

We study a singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial -plane. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if is sufficiently small. In this note, we give an analytical proof that the bound of 3/4 is indeed sharp, i.e. there are instabilities for any < 3/4.