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In this paper, we are explaining a decade long investigation of historical, sacral and archaeological sites in the Toplica District (Serbia) as one of the significant cultural heritage sites in Europe with more than 226 objects with different time of origin. The survey was carried out for the purpose of better recognizing the archaeological potential. In science like archaeology, static objects, if not dynamized, remain unrecognizable to the general public, regardless of their historical and archaeological importance. Historical changes during the period of more than 7,000 years, with many sites of cultural heritage in this district, were recognized. Ordinary kriging was employed through Quantum Geographical Information System (QGIS) and System for Automated Geoscientific Analysis (SAGA). The positions of historical objects are registered, from the Neolithic period to modern times. With the help of GIS and geo-statistical methods, archaeological and historical layers can be rediscovered and better recognized. GIS algorithm ordinary kriging was used to complete the cultural heritage potential and archaeological valorization of the objects with geo-spatial dispersion. As a final product, we have obtained maps with historical and archaeological locations. For the first time, we used a scientific name for contour lines (archlines) with an equal number of archaeological units per density. In the end, archaeological and historical objects and their features were shown with the support of geographical and GIS methods.

We applied the theory of regularly varying functions to the analysis of the cosmological parameters for the $\Lambda$CDM model with the matter dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature $k=0, -1$, the expression $H(t)t$\, ($H(t)$ is the Hubble parameter) depends solely on the density parameter $\Omega(t)$. Using this result and the theory of regular variation we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit $\omega= \lim_{t\to\infty} \Omega(t)$ does exist and $\omega \not= 0$ then the cosmological constant $\Lambda$ is equal to $0$. If $\omega=0$ then for the expansion scale factor $a(t)$ we have $a(t)\sim e^{\sqrt{\Lambda/3}}$. On the other hand, if the limit $\lim_{t\to\infty} \Omega(t)$ does not exist then $a(t)$ bounces between two power functions and therefore has infinitely many flexion points. Hence, the deceleration parameter in this case changes the sign infinitely many times., Comment: 20 pages, 4 figures. In revised version: Added new coauthor Viktor Radovi\'c ; Added several new references; Corrected typos; Completely revised section 3.1 and a new result added: if \Omega\ converges to a non-zero value then the Cosmological constant \Lambda\ must be equal 0

Our main aim is to apply the theory of regularly varying functions to the asymptotical analysis at infinity of solutions of Friedmann cosmological equations. A new constant $\Gamma$ is introduced related to the Friedmann cosmological equations. Determining the values of $\Gamma$ we obtain the asymptotical behavior of the solutions, i.e. of the expansion scale factor $a(t)$ of a universe. The instance $\Gamma < 1/4$ is appropriate for both cases, the spatially flat and open universe, and gives a sufficient and necessary condition for the solutions to be regularly varying. This property of Friedmann equations is formulated as the generalized power law principle. From the theory of regular variation it follows that the solutions under usual assumptions include a multiplicative term which is a slowly varying function., Comment: 26 pages, 2 figures

We describe an ongoing project carried out by the Mathematical Institute of Serbian Academy of Sciences and Arts, and the Faculty of Mathematics, Belgrade. The project concerns building of electronic resources and presentations of electronic editions of mathematical works in Serbia, including retro-digitization of old books, articles and the other mathematical works, and development of the corresponding virtual library. The resources built in the project are freely accessible through Internet.

A topological class logic is an infinitary logic formed by combining a first-order logic with the quantifier symbols O and C. The meaning of a formula closed by quantifier O is that the set defined by the formula is open. Similarly, a formula closed by quantifier C means that the set is closed. The corresponding models are a topological class spaces introduced by Ciric and Mijajlovic (Math Bakanica 1990). The completeness theorem is proved.

The aim of this paper is to present an alternative description, based on the non‐standard analysis, of certain processes in dynamical systems. Some examples of applications will be given, including differential equations and geometry. In particular, bifurcations in perturbed systems are studied which may be applied to the study of a body having a complex magnetic field excited by strong microwave fields. A possible application might include modeling of certain facts of magnetic fields of Sun‐like stars. The Karamata notion of a slowly varying function is used for analyzing such processes in infinitesimal neighborhoods (monads). These results, we believe, might give at least new insights into classical problems of dynamical systems.

The classical study of Standard Cosmological Model (SCM) is based on the mathematics over R, the field of real numbers, or C, the field of complex numbers. Both these structures are archimedean, i.e. they do not admit explicitly infinite quantities. Here we discuss two non‐archimedean approaches in the analysis of SCM, p‐adic analysis and non‐standard analysis.

The new astronomical station at the mountain Vidojevica (ASV) nearby the town of Prokuplje will be finished till the end of 2007. A part of the research at the ASV will be dedicated to the stellar spectroscopy. The Astronomical Observatory in Belgrade provided a spectrograph for this purpose. In the town of Belogradchik in Bulgaria, nearby the Bulgarian‐Serbian border, a small astronomical observatory of the size as ASV is situated and equipped similarly as ASV The aim of this paper is to compare the equipment of these observatories and discuss possible cooperation between them, in particular in those areas of astronomy in which the stellar spectroscopy plays an important role.

In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Qx = “there exist uncountably many x” is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Qx can be “syntactically” defined in a first order theory T. That problem was raised by Kosta Dosen when he asked if the quantifier Qx can be eliminated in Peano arithmetic. We answer that question fully in this paper.

On considere des ensembles definissables et des elements dans des modeles non standards de l'arithmetique de Peano

The aim of this article is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of certain known transcendental differential functions, as of $\Gamma(x)$. Furthermore, it also determines differential transcendence of solution of some functional equations.