Nonstandard (Leibnitz) analysis, based on nonstandard real numbers R, introduces a specific mathe... more Nonstandard (Leibnitz) analysis, based on nonstandard real numbers R, introduces a specific mathematical method, as well as a way of thinking. It introduces actual infinitely small quantities and infinitely large quantities. Therefore, it gives good ground in considering physical systems which in idealized form have infinitely many degrees of freedom. Definitions and proofs are more intuitive, and its use is natural and intuitive whenever the considered physical system is composed of infinitely many particles. There are a lot of applications of nonstandard analysis based on this assumption in mathematical physics, in particular in quantum mechanics, fluid mechanics, dynamical systems, etc. Here, we discuss cometary trajectories, in particular the parabolic one, from the standpoint of nonstandard analysis. It appears that in a sense every parabola is an ellipse. Or from the standard point of view, every parabola P is a limit curve of a family F of confocal and coplanar ellipses. In a...
Authors of this paper recently applied the theory of regularly varying functions in asymptotic an... more Authors of this paper recently applied the theory of regularly varying functions in asymptotic analysis of cosmological parameters for the expanding universe. According to this theory, all cosmological parameters depend on a a 0-function ε(t) which is ”hidden” in the integral representation of regularly varying functions. We derived a differential equation for ε(t) and discussed possible solutions.
International Journal of Geometric Methods in Modern Physics, 2019
We applied the theory of regularly varying (RV) functions to the analysis of the cosmological par... more We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the [Formula: see text]CDM model with the matter-dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature [Formula: see text], the expression [Formula: see text] ([Formula: see text] is the Hubble parameter) depends solely on the density parameter [Formula: see text]. Using this result, we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit [Formula: see text] does exist and [Formula: see text], then the cosmological constant [Formula: see text] is equal to [Formula: see text]. If [Formula: see text], then for the expansion scale factor [Formula: see text] of a flat universe, we have [Formula: see text]. On the other hand, if the limit [Formula: see text] does not exist, then [Formula: see text] bounces between two power functions and therefo...
In this paper we present our exploration of geographical and archeological sites in Toplica regio... more In this paper we present our exploration of geographical and archeological sites in Toplica region, a southern district of Serbia. Our survey which lasted a decade, resulted in a detailed digital 3D map having seven layers. In addition to the most important geographical entities there are depicted all known objects in this region related to the national cultural heritage. By use of GPS tracking, the geographical coordinates of these objects are collected and roads which lead to these sites were recorded. As a final product, the multilayer 1:100000 to 1:50000 interactive digital maps are produced, with all layers individually recorded. We also discuss the origin of Toplica valley, the central part of Toplica region.
Professor Vojislav Mišković (1892–1976) was the leading Serbian astronomer in the twentieth Cen-t... more Professor Vojislav Mišković (1892–1976) was the leading Serbian astronomer in the twentieth Cen-tury. He wrote a large number of books and textbooks on astronomy. Eleven of these books, one chart and one scientific work are digitized and they are included into the Virtual Library of the Faculty of mathematics of the University of Belgrade, http://elib.matf.bg.ac.yu:8080/virlib/. In this article we give short reviews of these works and his biography as well.
Publications de l'Institut Math?matique (Belgrade), 2015
We study Hopf algebras over projection functions of the complex vector CX appropriate for computi... more We study Hopf algebras over projection functions of the complex vector CX appropriate for computing inversion formulas from discrete mathematics. Using calculus of projection functions introduced in this way, we derived various inversion formulas, including Gould?s inversion formula and its generalizations.
Some recurrence formulas related to the differential operator δ = θ · D are considered. Some exam... more Some recurrence formulas related to the differential operator δ = θ · D are considered. Some examples, including Kurepa's function, are included.
We discuss cometary orbits from the standpoint of Nonstandard (Leibnitz) analysis, a relatively n... more We discuss cometary orbits from the standpoint of Nonstandard (Leibnitz) analysis, a relatively new branch of mathematics. In particular, we consider parabolic cometary paths. It appears that, in a sense, every parabola is an ellipse.
Publications de l'Institut Math?matique (Belgrade), 2011
We show that certain families of sets and functions related to a countable structure A are analyt... more We show that certain families of sets and functions related to a countable structure A are analytic subsets of a Polish space. Examples include sets of automorphisms, endomorphisms and congruences of A and sets of the combinatorial nature such as coloring of countable plain graphs and domino tiling of the plane. This implies, without any additional set-theoretical assumptions, i.e., in ZFC alone, that cardinality of every such uncountable set is 2?0.
Here are presented the main climate properties and weather conditions of Toplica region. The part... more Here are presented the main climate properties and weather conditions of Toplica region. The particular emphasis is given to astroclimate characteristics in the sur-rounding of the mountain Vidojevica, where should be situated the astronomical station (ASV) of the Astronomical ...
Nonstandard (Leibnitz) analysis, based on nonstandard real numbers R, introduces a specific mathe... more Nonstandard (Leibnitz) analysis, based on nonstandard real numbers R, introduces a specific mathematical method, as well as a way of thinking. It introduces actual infinitely small quantities and infinitely large quantities. Therefore, it gives good ground in considering physical systems which in idealized form have infinitely many degrees of freedom. Definitions and proofs are more intuitive, and its use is natural and intuitive whenever the considered physical system is composed of infinitely many particles. There are a lot of applications of nonstandard analysis based on this assumption in mathematical physics, in particular in quantum mechanics, fluid mechanics, dynamical systems, etc. Here, we discuss cometary trajectories, in particular the parabolic one, from the standpoint of nonstandard analysis. It appears that in a sense every parabola is an ellipse. Or from the standard point of view, every parabola P is a limit curve of a family F of confocal and coplanar ellipses. In a...
Authors of this paper recently applied the theory of regularly varying functions in asymptotic an... more Authors of this paper recently applied the theory of regularly varying functions in asymptotic analysis of cosmological parameters for the expanding universe. According to this theory, all cosmological parameters depend on a a 0-function ε(t) which is ”hidden” in the integral representation of regularly varying functions. We derived a differential equation for ε(t) and discussed possible solutions.
International Journal of Geometric Methods in Modern Physics, 2019
We applied the theory of regularly varying (RV) functions to the analysis of the cosmological par... more We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the [Formula: see text]CDM model with the matter-dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature [Formula: see text], the expression [Formula: see text] ([Formula: see text] is the Hubble parameter) depends solely on the density parameter [Formula: see text]. Using this result, we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit [Formula: see text] does exist and [Formula: see text], then the cosmological constant [Formula: see text] is equal to [Formula: see text]. If [Formula: see text], then for the expansion scale factor [Formula: see text] of a flat universe, we have [Formula: see text]. On the other hand, if the limit [Formula: see text] does not exist, then [Formula: see text] bounces between two power functions and therefo...
In this paper we present our exploration of geographical and archeological sites in Toplica regio... more In this paper we present our exploration of geographical and archeological sites in Toplica region, a southern district of Serbia. Our survey which lasted a decade, resulted in a detailed digital 3D map having seven layers. In addition to the most important geographical entities there are depicted all known objects in this region related to the national cultural heritage. By use of GPS tracking, the geographical coordinates of these objects are collected and roads which lead to these sites were recorded. As a final product, the multilayer 1:100000 to 1:50000 interactive digital maps are produced, with all layers individually recorded. We also discuss the origin of Toplica valley, the central part of Toplica region.
Professor Vojislav Mišković (1892–1976) was the leading Serbian astronomer in the twentieth Cen-t... more Professor Vojislav Mišković (1892–1976) was the leading Serbian astronomer in the twentieth Cen-tury. He wrote a large number of books and textbooks on astronomy. Eleven of these books, one chart and one scientific work are digitized and they are included into the Virtual Library of the Faculty of mathematics of the University of Belgrade, http://elib.matf.bg.ac.yu:8080/virlib/. In this article we give short reviews of these works and his biography as well.
Publications de l'Institut Math?matique (Belgrade), 2015
We study Hopf algebras over projection functions of the complex vector CX appropriate for computi... more We study Hopf algebras over projection functions of the complex vector CX appropriate for computing inversion formulas from discrete mathematics. Using calculus of projection functions introduced in this way, we derived various inversion formulas, including Gould?s inversion formula and its generalizations.
Some recurrence formulas related to the differential operator δ = θ · D are considered. Some exam... more Some recurrence formulas related to the differential operator δ = θ · D are considered. Some examples, including Kurepa's function, are included.
We discuss cometary orbits from the standpoint of Nonstandard (Leibnitz) analysis, a relatively n... more We discuss cometary orbits from the standpoint of Nonstandard (Leibnitz) analysis, a relatively new branch of mathematics. In particular, we consider parabolic cometary paths. It appears that, in a sense, every parabola is an ellipse.
Publications de l'Institut Math?matique (Belgrade), 2011
We show that certain families of sets and functions related to a countable structure A are analyt... more We show that certain families of sets and functions related to a countable structure A are analytic subsets of a Polish space. Examples include sets of automorphisms, endomorphisms and congruences of A and sets of the combinatorial nature such as coloring of countable plain graphs and domino tiling of the plane. This implies, without any additional set-theoretical assumptions, i.e., in ZFC alone, that cardinality of every such uncountable set is 2?0.
Here are presented the main climate properties and weather conditions of Toplica region. The part... more Here are presented the main climate properties and weather conditions of Toplica region. The particular emphasis is given to astroclimate characteristics in the sur-rounding of the mountain Vidojevica, where should be situated the astronomical station (ASV) of the Astronomical ...
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