ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**Seminar on Computer Science and Applied Mathematics**

**PROGRAM**

Knez Mihajlova 36

Fakultet organizacionih nauka, Univerzitet u Beogradu,

Jove Ilica 154

IEEE Chapter Computer Science (CO-16) Belgrade, Republic of Serbia

MI SANU, Knez Mihailova 36, sala 301f

Upravni odbor Matematickog instituta SANU je na nedavnoj sednici doneo odluku da se dosadasnji Seminar za primenjenu matematiku, sada nazove Seminar za racunarstvo i primenjenu matematiku, a u cilju potenciranja znacaja racunarstva kao jedne od oblasti delatnosti Instituta. Istovremeno, Upravni odbor doneo je odluku o osnivanju Odeljenja za racunarstvo i primenjenu matematiku i vezao rad novog odeljenja za rad Seminara za racunarstvo i primenjenu matematiku.

**UTORAK, 16.10.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36**

*Katica (Stevanović) Hedrih, Matematički institut SANU, Beograd*

**ROLLING HEAVY BALL OVER THE SPHERE AND ANALYSIS OF DYNAMICS OF VIBRO-IMPACT SYSTEMS WITH ROLLING BALLS OVER THE SPHERE**

(Lecture dedicated to 150 years of birthday of Mihailo Petrovic, founding father of Serbian mathematics)

The ball as a rigid body has six degrees of freedom of motion, but when rolling around the immobile sphere then has three degrees of freedom of movement. The limitations come from the assumption that it rolls around the sphere, so there is a link that the center of the ball is always in the sphere of radius equal to the sum or difference between radius of the sphere and ball, depending whether the ball is rolling inside or outside of the sphere. The other two constraints come from the assumption that rolling without slipping the graze can therefore determine the relation between the angular velocity of rolling about two orthogonal axes tangent to the sphere at the point of contact between the ball and the sphere. Constraints are geometrical and stationary, and system is holonomic and scleronomic.

We propose that system is in gravitational field and that rolling is activated by gravitational force and initial kinetic and potential energy given to ball at initial moment. For mathematical description of the rolling of heavy rigid homogeneous ball over the sphere inside as well as outside of sphere surface, spherical coordinates are used: angle in circular and angle in meridional directions, and angle of ball self rotation about radial direction. Nonlinear differential equations are derived. Angle coordinate in circular direction is cyclic coordinate, and an integral, for circular-cyclic coordinate is derived. Integral constant depends of initial condition and is determined. The main nonlinear differential equation is expressed by angle meridional coordinate and corresponding first integral is derived. The equation of first integral is equation of phase trajectory and by use of this equation and corresponding set of initial conditions phase trajectory portraits are graphically presented. An elliptic integral is derived.

By usage of new Hedrih’s results in theory of collision between two rolling bodies geometry, kinematics and dynamics of successive collisions of two rolling balls over the surface of sphere is analyzed and the methodology for investigate vibro-impact nonlinear dynamics of vibro-impact system with rolling bodies over the sphere surface is presented.

A mathematical analogy between differential equations and phase trajectory portraits of dynamics of rolling heavy ball and material heavy mass particle moving along sphere surface is identified.

References

[1] Hedrih (Stevanović) K., (2018), Non-linear phenomena in vibro-impact dynamics: Central collision and energy jumps between two rolling bodies, Dedicated to memory of Professor and important scientist Ali Nayfeh (December 21, 1933-March 27, 2017). Nonlinear Dynamics, February 2018, Volume 91, Issue 3, pp 1885–1907. DOI: 10.1007/s11071-017-3988-x

[2] Hedrih (Stevanović) K., (2017), Central collision of two rolling balls: theory and examples, Advances in Theoretical and Applied Mechanics, Vol. 10, 2017, no. 1, 33-79. https://doi.org/10.12988/atam.2017.765

[3] Hedrih (Stevanović) K., (2017), Dynamics of Impacts and Collisions of the Rolling Balls, Dynamical Systems: Theoretical and Experimental Analysis, Springer Proceedings in Mathematics & Statistics, Volume Number: 182, Chapter 13, pp. 157-168. Springer, Part of Springer Science+Business, ISBN 978-3-319-42407-1. ISSN 2194-1009 ISSN 2194-1017 (electronic)

[4] Hedrih (Stevanović) R. K., (2016), Vibro-impact dynamics in systems with trigger of coupled three singular points: Collision of two rolling bodies, The 24th International Congress of Theoretical and Applied Mechanics (IUTAM ICTAM 2016), Montreal, Canada, 21 - 26 August, 2016, Book of Papers, pp. 212 -213. IUTAM permanent site. ISBN: NR16-127/2016E-EPUB; Catalogue Number: 978-0-660-05459-9

[5] Hedrih (Stevanović) R. K.,(2017), Generalized rolling pendulum along curvilinear trace: Phase portrait, singular points and total mechanical energy surface, Computer Algebra Systems in Teaching and Research, Edited by Alexander Prokopenya and Agnieszka Gil-Swiderska, Publisher Siedlce University of Natural Sciences and Humanities (Siedlce, Poland), 2017, Vol. VI, pp. 204216. ISSN 2300-7397.

[6] Petrović, M., Elementi matematičke fenomenologije (Elements of mathematical phenomenology), Srpska kraljevska akademija, Beograd, 1911. str. 389.

**UTORAK, 23.10.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36**

*Mirjana Stojanović, Fakultet organizacionih nauka, Univerzitet u Beogradu*

**GENERAL DATA PROTECTION REGULATION: IMPACT AND IMPLICATIONS ON MOBILE OPERATORS**

The EU General Data Protection Regulation significantly expands the rights of the individuals related to the data privacy. At the same time, it defines the new obligations and responsibilities of the companies collecting and processing personal data. The goal of this paper is to provide the analysis of the new regulation in the context of mobile operators’ business. It summarizes the main challenges and identifies the main steps for the practical implementation of the compliance. Finally, it emphasizes the potential for the different business benefits if the compliance to the new regulation is implemented in a correct way.

**UTORAK, 30.10.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36**

*dr Patrik Hrkut, Department of Software Technologies, Faculty of Informatics and Management Science, University of Zilina, Slovakia *

**AN ALGORITHM FOR DETECTING PLAGIARISM IN THE SOURCE CODE**

Informatics and programming are currently among the most popular areas of study in higher education. Variety of resources available on the Internet often encourage students to copy content to their own projects and to commit plagiarism. This research focuses on solving the plagiarism problem in computer science teaching. Available tools to detect plagiarism in the source code will be discussed and compared with the algorithm developed at University of Zilina. Detailed design of the system for plagiarism detection will be described. Further, the accuracy and completeness of the developed approach will be discussed as well.

** RUKOVODIOCI SEMINARA **

** MI SANU Vera Kovačević-Vujčić Milan Dražić FON Zorica Bogdanovic Marijana Despotovic-Zrakic IEEE Bozidar Radenkovic **