<Emphasis Type="Italic">G</Emphasis>-compactness and groups

Lascar described E _KP as a composition of E _L and the topological closure of E _L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G _L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment grant N201 032 32/2231.     

A numerical method to boundary value problems for second order delay differential equations

Summary In the first part of this paper we are dealing with theoretical statements and conditions which lead to existence and uniqueness of the solution of a nonlinear boundary value problem with delay. Next we apply this method successfully to a numerical example. The computations have been carried out at the computer Siemens 4004. The data obtained are presented in two tables.     

Vaught’s conjecture for some meager groups

AssumeG is a superstable group ofM-rank 1 and the division ring of pseudo-endomorphisms ofG is a prime field. We prove a relative Vaught’s conjecture for Th(G). When additionallyU(G) =ω, this yields Vaught’s conjecture for Th(G). Research supported by KBN grant 2 P03A 006 09.     

Preliminary studies on the surface layer of starch

Characterization of the surface layer of starch powder, originated from potato or maize, was carried out applying various experimental techniques: Fourier-transformed infrared internal reflection spectroscopy (FTIR-IRS), inverse gas chromatography (IGC) and scanning electron microscopy (SEM). The main kinds of starch were studied as potential fillers for rubber and results discussed in terms of factors requiring modification to improve starch miscibility and activity towards rubber. Starch of high amylopectine content shows surface enrichment with amylose what makes crystallinity of the surface layer higher than in bulk of the material. Particles of the both kinds of starch have very smooth surface (morphological index, I_m = 0.995), highly resistant to its geometrical development. Dispersive component of the surface energy of starch was found to be similar to that of low energy polymers (γ_s^d = 32.5 mJ/m² at 23°C) and its surface to be of electron-donor character.     

The Effect of Stationary Phase Type and Mobile Phase pH on the Separation of Some Catecholamines

JPC – Journal of Planar Chromatography – Modern TLC - The catecholamines are very important in the control and regulation of a variety of functions acting as neurotransmitters in both...     

On the prime model property

Assume is superstable, is a formula over , is countable and is countable and . We investigate models in assuming has the prime model property. We prove some corollaries on the number of models in . We show an example of an -stable and with having exactly 3 models.

     

Polycondensation Products of Phloroglucine with Difunctional Aliphatic Amines

The known reaction of condensation of a strong amine with phloroglucine under quite mild conditions was the starting point for synthesis of a new series of macromolecular resins not previously dèscribed. Phloroglucine has been condensed with a series of nine aliphatic diamines in aqueous solution under atmospheric pressure. The resins obtained are dark powders, which can be molded under increased pressure in the temperature range of 175–310°C. The thermal, mechanical, chemical, and electrical properties of the new resins have been examined and their structure confirmed. Some properties of resins can be calculated by means of approximate mathematical formulas.     

OPLC Investigation of Formaldehyde Levels in the Hard Tissues of the Teeth in Rare Pathological Cases

JPC – Journal of Planar Chromatography – Modern TLC - Levels of formaldehyde, formed within the cells of plants, animals, and man, are related to the physiological state of an organism....     

Dispersion of components and structure of elastomer system

Elastomer systems as a rule are composed of several ingredients dispersed or dissolved in the matrix. The main components are: crosslinking substances, accelerators, activators, fillers mineral and/or organic, softeners and antioxidants. A random distribution of above mentioned components and also structural elements of a network formed are usually postulated [1]. From the results of investigations performed in our laboratory it follows that this approach in some cases is oversimplified. The problem is illustrated by few examples and some of its aspects are discussed.     

Das Gleichgewicht des Cu2+−Cu+−Cu-systems in konzentrierten Perchloratlösungen

The equilibrium of the reaction Cu²⁺+Cu?2 Cu⁺ has been investigated in cone. solutions of Ca(ClO₄)₂. The apparent equilibrium constants of this reaction and the formal potentials of the Cu²⁺/Cu⁺, Cu²⁺/Cu and Cu⁺/Cu redox systems were determined. From these data the hydration numbers of the Cu²⁺ and Cu⁺ ions were estimated and the scheme of the reaction studied was proposed and discussed. In addition the equilibrium constants of the reaction Cu²⁺+Cu(Hg)?2 Cu⁺ were calculated and discussed.