Papers by Miljan Knezevic
arXiv (Cornell University), Jun 12, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Universe
Deep learning techniques are required for the analysis of synoptic (multi-band and multi-epoch) l... more Deep learning techniques are required for the analysis of synoptic (multi-band and multi-epoch) light curves in massive data of quasars, as expected from the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). In this follow-up study, we introduce an upgraded version of a conditional neural process (CNP) embedded in a multi-step approach for the analysis of large data of quasars in the LSST Active Galactic Nuclei Scientific Collaboration data challenge database. We present a case study of a stratified set of u-band light curves for 283 quasars with very low variability ∼0.03. In this sample, the CNP average mean square error is found to be ∼5% (∼0.5 mag). Interestingly, besides similar levels of variability, there are indications that individual light curves show flare-like features. According to the preliminary structure–function analysis, these occurrences may be associated with microlensing events with larger time scales of 5–10 years.
Some Properties of Harmonic Quasi-Conformal Mappings
Lie Theory and Its Applications in Physics, 2013
We are analyzing the properties of holomorphic functions and the hyperbolic metric to obtain some... more We are analyzing the properties of holomorphic functions and the hyperbolic metric to obtain some geometrically motivated inequalities for quasi-conformal and generalized harmonic mappings. Also, we are interested in which properties of hyperbolic harmonic mappings and the hyperbolic metric are essential for validity of some versions of the Ahlfors–Schwarz lemma.
A note on Infinite Descent Principle
Journal of Mathematical Analysis and Applications, 2007
We prove versions of the Ahlfors-Schwarz lemma for quasiconformal euclidean harmonic functions an... more We prove versions of the Ahlfors-Schwarz lemma for quasiconformal euclidean harmonic functions and harmonic mappings with respect to the Poincaré metric.
Mathematica Moravica
We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Li... more We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the K-quasiconformal, K 1, hyperbolic harmonic mappings of the unit disk D onto itself. Especially, if f is such a mapping and f (0) = 0, we obtained that the following double inequality is valid 2|z|/(K + 1) |f (z)| √ K|z|, whenever z ∈ D.
Filomat
Let A denotes the absolute plane and d a the distance function on it. Using a constructive approa... more Let A denotes the absolute plane and d a the distance function on it. Using a constructive approach which leads to the functional equations, we study which conditions on a "measure" of segments on a given half-line l in the absolute plane are essential to be the restriction of d a on l.
Some Models of Economic Growth and Capital Accumulation
Filomat, 2010
Suppose that h is a harmonic mapping of the unit disc onto a C 1,? domain D. We give sufficient a... more Suppose that h is a harmonic mapping of the unit disc onto a C 1,? domain D. We give sufficient and necessary conditions in terms of boundary function that h is q.c. We announce some new results and also outline application to existence problem of mean distortion minimizers in the Universal Teichm?ller space.
Filomat, 2015
We analyze the properties of harmonic quasiconformal mappings and by comparing some suitably chos... more We analyze the properties of harmonic quasiconformal mappings and by comparing some suitably chosen conformal metrics defined in the unit disc we obtain some geometrically motivated inequalities for those mappings (see for instance ). In particular, we obtain the answers to many questions concerning these classes of functions which are related to the determination of different properties that are of essential importance for validity of the results such as those that generalize famous inequalities of the Schwarz-Pick type. The approach used is geometrical in nature, via analyzing the properties of the Gaussian curvature of the conformal metrics we are dealing with. As a consequence of this approach we give a note to the co-Lipschicity of harmonic quasiconformal self mappings of the unit disc at the origin.
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Papers by Miljan Knezevic