Invariant measure in hot gauge theories

We investigate properties of the invariant measure for the $A_0$ gauge field in finite temperature gauge theories both on the lattice and in the continuum theory. We have found the cancellation of the naive measure in both cases. The result is quite general and holds at any finite temperature. We demonstrate, however, that there is no cancellation at any temperature for the invariant measure contribution understood as Z(N) symmetrical distribution of gauge field configurations. The spontaneous breakdown of Z(N) global symmetry is entirely due to the potential energy term of the gluonic interaction in the effective potential. The effects of this measure on the effective action, mechanism of confinement and $A_0$ condensation are discussed.Comment: Latex file, 65.5kB, no figure

Phase structure and confinement properties of noncompact gauge theories I

In the context of reviewing noncompact lattice gauge models at zero and finite temperature we study in detail a contribution of the invariant measure and the time-like plaquette configurations to correlation functions, analyze the problem of the compactness of the potentials in respect to the confinement and indicate the essential features to deal with the Wilson gauge theory in the weak coupling region. A method for calculating an effective confining noncompact model is also proposed.Comment: Latex file, 24 pages, no figure

The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa

Ultrasonic Control of Ductile Cast Iron Castings by Phased Array Technique

The goal of this article is non-destructive ultrasonic testing of internal castings defects. Our task was to cast several samples with defects like porosity and cavities (where belongs mostly shrinkages) and then pass these samples under ultrasonic testing. The characteristics of ultrasonic control of castings are presented in the theoretical part of this article. Ultrasonic control is a volume non-destructive method that can detect internal defects in controlled materials without damaging the construction. It is one of the most widely used methods of volume non-destructive testing. For experimental control were made several cylindrical samples from ferritic grey and ductile cast iron. Because of the form and dispersion of graphite of grey cast iron it was not possible to make ultrasonic records on this casting with probe we used, so we worked only with ductile cast iron. Ultrasonic records of casting control are shown and described in the experimental part. The evaluation of the measurement results and the reliability of the ultrasonic method in castings control is listed at the end of this article

Syntéza hvězdicovitých polymerů pro polyurethanové nátery pomocí iontové polymerace

Star polymers were prepared by ionic polymerization. As the star core polyols served e.g.: trimethylol propane (TMP), pentaerythrythol (PETP) and dipentaerythrythol (DPETP) and the star arms were built up from ε-caprolactame, lactide in different ratios of both components. Coatings based on TMP have often anti-slip properties high gloss but lower hardness. On the contrary, coatings based on PETP and DPETP have high hardness, but no anti-slip properties.Hviezdicovité polyméry boli pripravené ionovou polymerizáciou. Ako jadro hviezdy, bol použitý napr. trimetylol propán (TMP), pentaerytritol (PETP), dipentaerytritol (DPETP) a ramená boli syntetizivané z ε-kaprolaktámu a laktidu v roznych pomeroch. Nátery založené na TMP majú proti šmykové vlastnosti, vysoký lesk ale nižšiu tvrdosť. Pre porovnanie, nátery založene na PETP a DPETP majú vysokú tvrdosť, ale žiadne protišmykové vlastnosti