CIPRIAN DARIESCU
Department of Theoretical Physics, "Al. I. Cuza "University, 6600 Iasi, Romania

SHINJI HAMAMOTO
Department of Physics, Toyama University, Gofuku, Toyama 930, Japan
 

Abstract. Basically, in this paper our interest has been focused on the following problem: how did the thermalization of the minimally coupled mass-less scalar field go in the early radiation dominated spatially flat Robertson-Walker Universe and what kind of cosmological consequences did it have by its back-reaction effect? Therefore, we have worked out explicitly the exact frequency modes, quantized the massless field on the (k = 0)-radiation dominated background and, finally, have estimated the many-particle expectation value of the conservative energy-momentum tensor, assuming a Bose-Einstein distribution (at the radiation equilibrium temperature) of the quanta. Unlike the Minkowskian case, when w = 3p for the massless scalar source, this time, we get equal supplementary contributions to the pressure and the energy-density of the thermalized field. They mainly come from the decaying amplitude of the exact frequency modes and principially, strongly influence the evolution of the mixed radiation and thernalized massless scalar field dominated (k = 0)-Robertson-Walker Universe by the back reaction effect. It arises a maximal, Planckian-like, critical tenperature and the mixed matter Universe smoothly goes from the phase of the coherent massless scalar field domination, when a ~t^(1/3) and the deceleration parameter q = 2, to the usual phase of radiation a ~t^(1/2) and q = 1. The exact solution of Einstein equations over the whole of this transition has been concretely estimated in closed form as well as the "luminosity-distance versus cosmological red-shift" relation that fully characterizes the model.

 Key words: spatially flat Robertson-Walker Universe - thermal background radiation - scalar field quantization - thermalization procedure - cosmologies with mixed matter content

CIPRIAN DARIESCU, MARINA-AURA DARIESCU
Department of Theoretical Physics, "Al. I. Cuza" University, 6600 Iasi, Romania
E-mail: marina@uaic.ro

Abstract. Working on a general curved spacetime with Levi-Civita connection, the SO(1,3)-gauge covariant Dirac equation and its dynamical first order solution are derived using a formal algebraic approach in terms of tetrads. The obtained results can be written down for different manifolds of cosmological interest.

Key words: Dirac equation - canonical quantization in curved spacetime

CRISTINA BLAGA
Astronomical Institute of the Romanian Academy
Astronomical Observatory Cluj-Napoca
Str. Ciresilor 19, 3400, Cluj-Napoca, Romania
E-mail: cpblaga@math.ubbcluj.ro

Abstract. In this article we study the equilibrium of polytropes in a poloidal magnetic field. We see that the magnetic field is the solution of a nonhomogeneous Euler equation for which we write the general solution. It depends on the Lane-Emden function. So we determined the exact solution for n = 0,1. To study the relation between the magnetic and the polytropic index we use the first order Padé approximants for the Lane-Emden function.

Key words: stellar structure - magnetic field

EUGENIU GREBENICOV
Institute for Supercomputers of the Russian Academy of Sciences
37,Vavilova St., Moscow 117312, Russia
e-mail: greben @ ext1.ccas.ru

Abstract. One proves that, if n equal masses are initially situated at the vertices of a regular polygon centered in the (n + 1)th mass, and if the initial velocities form a vector field symmetrical with respect to the central mass, then the configuration of regular polygon is kept all along the motion, but with variable sides and variable rotation around the centre. The motion of every mass relative to the centre is provided by the solution of the classical two-body problem.

Key words: celestial mechanics - (n + 1)-body problem

BAZIL PARV
"Babes-Bolyai" University, Faculty of Mathematics and Computer Science,
Str. M. Kogalniceanu 1, 3400 Cluj-Napoca, Romania
E-mail: bparv@cs.ubbcluj.ro

Abstract. This paper deals with the Everhart numerical integration method, a well-known method in astronomical research. This method, a single-step one, is widely used for numerical integration of motion equation of celestial bodies. For an integration step, this method uses unequally-spaced substeps, defined by the roots of the so-called generating polynomial of Everhart's method. For this polynomial, this paper proposes and proves new recurrence formulae. The Maple computer algebra system was used to find and prove these formulae. Again, Maple seems to be well suited and easy to use in mathematical research

Key words: celestial mechanics - Everhart method - computer algebra.

DAN SELARU
Institute for Gravitation and Space Sciences
Laboratory for Gravitation
Str. Mendeleev 21-25, 70168 Bucharest, Romania
E-mail: dselaru@usa.net

Abstract. The extension of applicability domain of Levi-Civita and Kustaanheimo-Stiefel transformation obtained in the previous paper is applied in the Hill case of the three-body problem.

Key words: celestial mechanics - three-body problem (Hill case) - Levi-Civita and Kustaanheimo-Stiefel transformations - action-angle variables

CRISTINA STOICA
Institute for Gravitation and Space Sciences,
Gravitational Research Laboratory
21-25 Mendeleev Str., 70168, Bucharest, Romania
E-mail: cstoica@math.uvic.ca

Abstract. In this paper we continue the study of the motion of a particle under the influence of a generalized Maneff-type potential field. Using previous results, it is established the set of orbital elements for bounded noncollisional motion.

Key words: celestial mechanics - Maneff's generalized law - orbital elements

CRISTINA STOICA
Institute for Gravitation and Space Sciences,
Gravitational Research Laboratory,
Str. Mendeleev 21-25, 70168 Bucharest, Romania
E-mail: cstoica@math.uvic.ca

VASILE MIOC
Astronomical Institute of the Romanian Acadeny,
Astronomical Observatory Cluj-Napoca,
Str. Ciresilor 19, 3400 Cluj-Napoca, Romania
E-mail: vmioc@roastro.astro.ro

Abstract. The Maneff-type problems (these associated to a potential function of the form A/r + B/r?) are tackled again. Starting from the motion equations and first integrals in the space of McGehee's coordinates, one builds the infinity manifold and describes the flow on it.

Key words: celestial mechanics - qualitative analysis - Maneff-type problems

PETRE POPESCU, RADU POPESCU, PETRE PARASCHIV
Astronomical Institute of the Romanian Academy,
Str. Cutitul de Argint 5, 75212 Bucharest 28, Romania
E-mail: petre@roastro.astro.ro, pradu@roastro.astro.ro, paras@roastro.astro.ro

Abstract. In Bucharest was installed a Danjon astrolabe, transferred from the Royal Observatory of Brussels. This paper deals with the improvements brought to this instrument in order to gain stability, observation acccuracy and efficiency. The changing of the transparent prism with a Zerodur reflecting one, the new dual task of this astronomical instrument (self-collimating system and star tracker) and the acquisition of images using a CCD camera are the technical solutions of the modernisation project.

Key words: astrolabe - CCD observations

GHEORGHE BOCSA, MIREL BIRLAN
Astronomical Institute of the Romanian Academy
Str. Cutitul de Argint 5, 75212 Bucharest 28, Romania
E-mail: gbocsa@roastro.astro.ro

Abstract. Precise positions of the comet 1995/01 (Hale-Bopp) observed in Bucharest are presented. These observations were made with a 380/6000 mm astrograph. We used astrophotographic plates and an Ascorecord measuring machine.

Key words: comet - astrometry