## IV Symposium MATHEMATICS AND APPLICATIONS, national conference with international participation, May 24th - 25th, Belgrade

http://alas.matf.bg.ac.rs/~konferencija/home.html

## YU INFO 2013 & ICIST 2013

Conference Information on page:

## MATFdroid - Official Android Application of the Faculty of Mathematics

This application is designed for teachers, students and employees in order to provide them useful information (schedules, contact information, location, etc.).

A list of functions:
- Contact information
- News
- A list of teachers with their contacts
- Current timetable
- Map with all locations where lessons are held and the ability to display the optimal path to the desired location
- The choice of teaching activities
- Prior notification of the selected activities
- Widget that displays next two activities
- Localization (Serbian and English language)
- The ability to move application to the SD card

The application can be installed from the following location:

https://market.android.com/details?id=rs.ac.bg.matf.android

## Mini-Workshop Complex Analysis and applications, Faculty of Mathematics, February 27-28, 2012

Mini-Workshop "Complex Analysis and applications", will be held on Monday and Tuesday, 27-28th of February at Faculty of Mathematics, room BIM (4th floor, Computing lab).

The working language of the Workshop is English.

The schedule is as follows:

MONDAY, 27.2, 12h, room BIM

1. Matti Vuorinen, University of Turku, Finland

"Quasihyperbolic geometry and quasiconformal maps"

Abstract: This talk is a survey of my recent work with my coauthors during the past year. The talk is divided into four parts, each part based on a preprint. X. Zhang and G. Wang are PhD students at the University of Turku.

M. Vuorinen and G. Wang: Bisection of geodesic segments in hyperbolic geometry.
arXiv:1108.2948v2 [math. MG]

2. Miodrag Mateljević, Vladimir Božin, Miljan Knežević, Faculty of Mathematics, University of Belgrade

"Quasiconformality of harmonic mappings between smooth Jordan domains"

Abstract: Suppose that $h$ is a harmonic mapping of the unit disc onto a $\displaystyle C^{1,\,\alpha}$ domain $D$. Then $h$ is q.c. if and only if it is bi-Lipschitz. In particular, we consider sufficient and necessary conditions in terms of boundary function that $h$ is q.c. We give a review of recent related results including the case if domain is the upper half plane. We also consider harmonic mapping with respect to $\rho$ metric on codomain.

3. Discussion

TUESDAY, 28.2, 11h, room BIM

1. Stamatis Pouliasis, Aristotle University, Thessaloniki, Greece

"Versions of Schwarz's lemma for condenser capacity and inner radius"

Abstract: We will consider variants of the classical Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we will examine when a similar monotonicity property holds for the hyperbolic metric. This is joint work with D. Betsakos.

2. Iason Efraimidis, Aristotle University, Thessaloniki, Greece

"Variations of Schwarz lemma"

Abstract: Suppose that f maps the unit disc D holomorphically into D and f(0)=0. A classical inequality due to Littlewood generalizes Schwarz’s lemma and asserts that every w in f(D) has modulus less or equal to the product of the modulus of its pre-images. We present a similar inequality proved by D.Betsakos, in which the assumption of f(D) being a subset of D is replaced by the weaker assumption Diamf(D)=2. The main tools in the proof are Green’s function and Steiner symmetrization.

3. Vesna Manojlović, Faculty of Organization Sciences, University of Belgrade

"Boundary modulus of continuity and quasiconformal mappings"

Abstract :Let $D$ be a bounded domain in $\mathbb R^n$, $n \geq 2$, and
let $f$ be a continuous mapping of $\overline D$ into $\mathbb R^n$ which
is quasiconformal in $D$. Suppose that $|f(x) - f(y)| \leq \omega(|x-y|)$
for all $x$ and $y$ in $\partial D$, where $\omega$ is a non-negative
non-decreasing function satisfying $\omega(2t) \leq 2\omega(t)$ for
$t \geq 0$. We prove, with an additional growth condition on $\omega$, that
$|f(x) - f(y)| \leq C \max \{\omega(|x-y|), |x-y|^\alpha \}$ for all $x, y \in D$, where $\alpha =K_I(f)^{1/(1-n)}$. The talk is based on [AMN].

[AMN] Miloš Arsenović, Vesna Manojlović and Raimo Nakki,
Boundary modulus of continuity and quasiconformal mappings,
to appear in Ann. Acad. Sci. Fenn.

4. Miloš Arsenović, Faculty of Mathematics, University of Belgrade
(title and abstract will be announced)

5. Discussion

## Lecture of dr Frens Stoeckel, director of DAAD Information Center in Serbia, Faculty of Mathematics, March 6th, 2012.

Dr Frens Stoeckel (Herr Dr Frens Stoeckel), director of DAAD Information Center in Serbia (DAAD IC) will give a lecture about the goals of DAAD IC and modern European system of higher education.

Dr Stoeckel will also present possibilities for grants for education, research and institutional cooperation.

We invite you to this lecture that will take place at Faculty of Mathematics, Studentski trg 16/IV, room 706, 4th floor at 14:15.

## Technical challenges that the emerging device spectrum poses, and what it means for software development, 17th Nov 2011.

Technical challenges that the emerging device spectrum poses, and what it means for software development, by Aaron Seigo

17th Nov 2011. 18h, Studentski Trg 16, room 718

## Intensive course 'Optimization' within the Tempus project, 29.8-23.9. 2011.

Intensive course "Optimization" within the curent Tempus project "SEE Doctoral Studies in Mathematical Sciences", will be held at Faculty of Mathematics, Belgrade in the period of 29.8-23.9. The participants of the course are 27 students from faculties-partners in the project. The lecturers are professors from University of Graz and Bulgarian academy of sciences and arts.

More details about the course can be found at:

http://www.matf.bg.ac.rs/tempus/

## 10th CONFERENCE NEW TECHNOLOGIES AND STANDARDS: NATIONAL HERITAGE DIGITIZATION (National conference with international participation)

Conference 'New technologies and standards: digitization of national heritage' is annual meeting which has been organized since 2002. by Faculty of Mathematics University of Belgrade, Mathematical Institute of Serbian Academy of Sciences and Arts (SASA), National Center for Digitization (http://www.ncd.matf.bg.ac.rs, http://www.ncd.org.rs) and subproject 9 of project 44006 of Ministry of Science and Technological Development. Conference is about multidisciplinary aspects of national cultural and scientific heritage digitization.

Themes of the 10th Conference are:

Consideration of elements for national strategy formulation of scientific and cultural heritage digitization

Presentation of current digitization projects, digitization standards, professional processing, preservation and presentation of national heritage, technological aspects of digitization (algorithms, software implementation and new technologies) and other associated topics.

Conference will be held on 22-23rd September 2011, at the Faculty of Mathematics, University of Belgrade, Serbia, Studentski trg 16.

Conference participants, who wish to have presentation on Conference, need to send us paper abstract, in DOC format, until 1st September 2011, to the address ncd@matf.bg.ac.rs (Subject: "NCD conference, abstract submission).

Papers presented on the Conference, which pass reviewing process, will be printed in the journal National Center for Digitization (NCD) Review (http://elib.mi.sanu.ac.rs, http://www.ncd.matf.bg.ac.rs)

Organizing Committee:
Žarko Mijajlović  (Faculty of Mathematics, Belgrade)
Zoran Ognjanović (Mathematical Institute of SASA)
Dragan Blagojević (Mathematical Institute of SASA)
Saša Malkov (Faculty of Mathematics, Belgrade)
Vesna Vučković (Faculty of Mathematics, Belgrade)
Tamara Butigan (National Library of Serbia)
Dragan Dimitrijević (Yugoslav Film Archive)
Neda Jevremović (National Museum of Serbia)
Miomir Korać (Institute of Archaeology, Belgrade)
Ljiljana Blagojević (Serbian Archive)
Siniša Temerinski (Cultural Heritage Preservation Institute of Belgrade)

## Mechanics Seminar, 4th July 2011.

The next meeting of the Seminar will be held on Monday, 4th July at 13:00, at the Mathematical Institute of SASA, room F 307

Lecturer: Prof. Subhash C. Sinha, Alumni Professor and Director of Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849, USA

Title of lecture: ANALYSIS AND CONTROL OF PARAMETRICALLY EXCITED SYSTEMS: A NEW APPROACH

Abstract:

A general framework for the analysis and control of parametrically excited linear/nonlinear dynamical systems is presented. This class of problems appears in the modeling of rotorcraft blades in forward flight, asymmetric rotor-bearing systems, automotive components such as connecting rods, universal joints, asymmetric satellites, fluids under gravity modulations, etc. These dynamical systems are represented by a set of differential equations which contain time-periodic coefficients. First, an efficient computational scheme for the solution of linear problem is discussed through an application of Chebyshev polynomials. The idea is further developed to obtain the Lyapunov-Floquet (L-F) transformation associated with a linearized or a quasilinear time-periodic dynamical system. An application of L-F transformation yields equivalent systems whose linear parts are time-invariant. Therefore, the controls for all time-periodic linear systems can be designed using the standard time-invariant methods such as pole placement or optimal control theory. A symbolic control technique for Floquet multiplier placement is also suggested for linear time-periodic systems. In the case of nonlinear systems, a periodic orbit in the original coordinates has a fixed point representation after the L-F transformation. The local stability and bifurcation analyses are studied via time-dependent 'center manifold reduction' and 'normal form theory'. Results for fold, flip and secondary Hopf bifurcations are discussed. Bifurcation control and feedback linearization techniques for nonlinear time-periodic systems are also developed and applied to some typical problems. Further, the order reduction problem associated with free and forced parametrically excited large-scale nonlinear systems is also addressed using an invariant manifold approach. A methodology for reducedorder controller design is also suggested. The practical significance of these approaches is demonstrated through simulations and experimental investigations of a number of mechanical systems. These include vibration control of a multi-bladed rotor, shafts supported by magnetic bearings, bifurcation analyses of a flexible slider crank mechanism and an autoparametric mechanical system, among others.