Quark potentials at finite temperatures

We scan the quark-antiquark potential and the meson-meson potential for static quarks in aSU ₃ gluon field from strong coupling to weak coupling. The breakdown of the confinement between quark and antiquark at the phase transition is observed. There is no interaction between pointlike mesons in the whole coupling regime. It is pointed out that the interaction mechanism between two quark clusters can be classified by these two fundamental examples.     

Ein Distributivitätskriterium für Verbände

Those one-place functions on a latticeL with values inL which can be obtained from the identityx and the constant functions by means of the fundamental operations ofL in a finite number of steps are called one-place polynomial functions. —It is shown that a latticeL is distributive iff all its one-place polynomial functions can be represented by words such that in every word the indeterminatex occurs at most once.     

On Bounded Posets Arising from Quantum Mechanical Measurements

Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s ∈ S define a function from S to [0, 1] called a numerical event or, more precisely, an S-probability. If one orders a set P of S-probabilities in respect to the order of functions, further includes the constant functions 0 and 1 and defines p′ = 1 ? p for every p ∈ P, then one obtains a bounded poset of S-probabilities with an antitone involution. We study these posets in respect to various conditions about the existence of the sum of certain functions within the posets and derive properties from these conditions. In particular, questions of relations between different classes of S-probabilities arising this way are settled, algebraic representations are provided and the property that two S-probabilities commute is characterized which is essential for recognizing a classical physical system.     

On algebras of multidimensional probabilities

The probability p(s) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [0, 1]. The function p is called a multidimensional probability or numerical event. Sets of numerical events which are structured either by partially ordering the functions p and considering orthocomplementation or by introducing operations + and · in order to generalize the notion of Boolean rings representing classical event fields are studied with the goal to relate the algebraic operations + and · to the sum and product of real functions and thus to distinguish between classical and quantum mechanical behaviour of the physical system. Necessary and sufficient conditions for this are derived, as well for the case that the functions p can assume any value between 0 and 1 as for the special cases that the values of p are restricted to two or three different outcomes.     

Über die Wortlänge von Polynomfunktionen auf Verbänden

Ohne Zusammenfassung     

The Oxidation of Hexahydrotriazines

Summary. N-Alkyl-2,4-dioxohexahydro-1,3,5-triazines oxidize readily with oxygen to the corresponding cyanuric acid derivates. The oxidation of 1,3,5-trimethyl-2,4-dioxohexahydro-1,3,5-triazine resulted in a stable form of hydroperoxide. During the oxidation of 1,3,5-trimethyl- 6-phenyl-2,4-dioxohexahydro-1,3,5-triazine this hydroperoxide could not be identified, however, the result was the stable reaction product bis-[6-phenyl-1,3,5-trimethyl-2,4-dioxohexahydro-1,3,5-triazin]peroxide.