Extended graphical calculus for categorified quantum sl(2)

A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. We obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements. These formulas have integral coefficients and imply that one of the main results of Lauda's paper---identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)---also holds when the 2-category is defined over the ring of integers rather than over a field.Comment: 72 pages, LaTeX2e with xypic and pstricks macro

Constrained Dynamics of Tachyon Field in FRWL Spacetime

In this paper we continue study of tachyon scalar field described by a Dirac-Born-Infeld (DBI) type action with constraints in the cosmological context. The proposed extension of the system introducing an auxiliary field in the minisuperspace framework is discussed. A new equivalent set of constraints is constructed, satisfying the usual regularity conditions.Comment: 10 pages, to be published in the Special Issue of the Facta Universitatis Series: Physics, Chemistry and Technology devoted to the SEENET-MTP Balkan Workshop BSW2019 (3-14 June 2018, Nis, Serbia

The age of the Dinaride Ophiolite Belt: Derived olistostrome melange at the northern slope of Moračka Kapa (Montenegro)

This paper presents the first results of a palynological investigation of the Dinaride Ophiolite Belt - derived olistostrome melange at the northern slope of Moračka Kapa (Montenegro). The analysis of microfloral association provided a reconstruction of the Late Jurassic sedimentation conditions and depositional environment in the Morača Kapa Unit. The samples (8) collected from the different parts of ophiolite matrix yielded palynomorph assemblages (fossil spores, pollen grains and dinoflagellates) of the Upper Jurassic age. The uppermost part of the ophiolite suite on the presented palynomorphs could also indicate the lowermost Lower Cretaceous. These palynological results provide a very interesting framework of these widespread, but poorly stratigraphically understood sediments. The paleoecological results suggest humid and subtropical conditions in the hinterland

Inflationary RSII Model with a Matter in the Bulk and Exponential Potential of Tachyon Field

In this paper we study a tachyon cosmological model based on dynamics of a 3-brane in the second Randall-Sundrum (RSII) model extended to include matter in the bulk. The presence of matter in the bulk changes warp factor which leads to modification of inflationary dynamics. The additional brane behaves effectively as a tachyon. We calculate numerically observation parameters of inflation: the scalar spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) for the exponential potential of tachyon field.Comment: 9 pages, 1 figure, will be published in the Special Issue of Facta Universitatis, Series: Physics, Chemistry and Technology devoted to the SEENET-MTP Balkan Workshop BSW2018 (3-14 June 2018

Numerical Calculation of Hubble Hierarchy Parameters and Observational Parameters of Inflation

We present results obtained by a software we developed for computing observational cosmological inflation parameters: the scalar spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) for a standard single field and tachyon inflation, as well as for a tachyon inflation in the second Randall-Sundrum model with an additional radion field. The calculated numerical values of observational parameters are compared with the latest results of observations obtained by the Planck Collaboration. The program is written in C/C++. The \textit{GNU Scientific Library} is used for some of the numerical computations and R language is used for data analysis and plots.Comment: 8 pages, 5 figures, based on talk presented at The 10th Jubilee Conference of the Balkan Physical Union (BPU10), 26-30 August 2018 (Sofia, Bulgaria