A model calculation of the value of the electromagnetic coupling constant at q2=mZ2q^2 = m_{Z}^{2}

A QCD model with an infinite number of vector mesons suggested by one of the authors is used to derive the value of the correction $\delta\alpha_{hadr}$ for $\alpha(m_{Z}^{2})$ due to the strong interactions. The result is $\delta\alpha_{hadr} = 0.0275(2)$ ; thus $\alpha(m^{2}_{Z}) = (128.96(3))^{-1}$.Comment: in LaTeX, 6 pages, 0 figures, ITEP Preprint 49-9

Pre-automata as Mathematical Models of Event Flows Recognisers

The new class of recognisers is introduced and studied in the paper. The models are based on the notion of partial action of a free nite generated monoid. Authors called such models by preautomata. Some properties of preautomata were established and proved in the paper. These properties allow to consider the pre-automata as mathematical models of recognizers of event ows in processes of the interaction of software systems

Principal quasi-ideals of cohomological dimension 1

We prove that a principal quasi-ideal of a noncommutative free semigroup has cohomological dimension 1 if and only if it is free

Non-commutative Grillet semigroups

Grillet semigroups are introduced. This class of semigroups contains regular semigroups and complete commutative semigroups (by Grillet’s terminology). Some structural theorems are proved

Decomposition of directed graphs and the Turán problem

We consider vertex decompositions of (di)graphs appearing in the automata theory and establish some properties of these decompositions. These decompositions are applied to the problem of forbidden subgraphs.Розглянуто вершинні декомпозиції (di)графiв, що виникають у теорії автоматів, встановлено деякі їх властивості, а також наведено застосування їх до задачі про заборонені підграфи

Gorenstein Latin squares

We introduce the notion of a Gorenstein Latin square and consider loops and quasigroups related to them. We study some properties of normalized Gorenstein Latin squares and describe all of them with order n≤8

Astrophysical constraints on primordial black holes in Brans-Dicke theory

We consider cosmological evolution in Brans-Dicke theory with a population of primordial black holes. Hawking radiation from the primordial black holes impacts various astrophysical processes during the evolution of the Universe. The accretion of radiation by the black holes in the radiation dominated era may be effective in imparting them a longer lifetime. We present a detailed study of how this affects various standard astrophysical constraints coming from the evaporation of primordial black holes. We analyze constraints from the present density of the Universe, the present photon spectrum, the distortion of the cosmic microwave background spectrum and also from processes affecting light element abundances after nucleosynthesis. We find that the constraints on the initial primordial black hole mass fractions are tightened with increased accretion efficiency.Comment: 15 page

Nonperturbative Effects from the Resummation of Perturbation Theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which usually includes the leading term in the weak coupling expansion, that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with some exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional O(N) nonlinear sigma model. In these models the leading term in weak coupling of the nonperturbative effect can be obtained with good accuracy from the first terms of the perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, we suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear in Phys Rev

Constraints on dark matter particles charged under a hidden gauge group from primordial black holes

In order to accommodate increasingly tighter observational constraints on dark matter, several models have been proposed recently in which dark matter particles are charged under some hidden gauge group. Hidden gauge charges are invisible for the standard model particles, hence such scenarios are very difficult to constrain directly. However black holes are sensitive to all gauge charges, whether they belong to the standard model or not. Here, we examine the constraints on the possible values of the dark matter particle mass and hidden gauge charge from the evolution of primordial black holes. We find that the existence of the primordial black holes with reasonable mass is incompatible with dark matter particles whose charge to mass ratio is of the order of one. For dark matter particles whose charge to mass ratio is much less than one, we are able to exclude only heavy dark matter in the mass range of 10^(11) GeV - 10^(16) GeV. Finally, for dark matter particles whose charge to mass ratio is much greater than one, there are no useful limits coming from primordial black holes.Comment: accepted for publication in JCA