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

Seminar for Geometry, education and visualization with applications

 

PROGRAM


MATEMATIČKI INSTITUT SANU
Seminar geometriju, obrazovanje i vizualizaciju sa primenama

PLAN RADA ZA JUN 2011.

ČETVRTAK, 02.06.2011. u 17 sati, sala 301F, MI
Tijana Sukilovic
Naslov: Detekcija krugova koriscenjem diskretne krivine

Apstrakt: Definisemo pojam diskretne krivine vezane za crni piksel crno-belih raster slika. Oblasti primene ukljucuju detekciju proizvoljnih oblika, specijalno onih koji se sastoje od deo po deo glatkih krivih. Koristeci pristup diskretne krivine, opisujemo i implementiramo algoritam za detekciju krugova i lukova i uporedjujemo ga sa postojecim metodama.

ČETVRTAK, 09.06.2011. u 17 sati, sala 301f, MI
Bratislav Ilic
NASLOV: Uvodni deo: Amorfne forme u arhitekturi
Studija slucaja: GEOMETRIJSKA OPTIMIZACIJA SLOBODNIH FORMI NA POLIGONALNOJ OSNOVI

Rezime: Projektovanje amorfnih arhitektonskih oblika pored primene softvera za modelovanje, zahteva intenzivniju primenu matematike. Specificna metodologija projektovanja ukljucuje dva osnovna kriterijuma ekonomske opravdanosti, a to su stabilnost konstrukcije i izvodljivost trodimenzionalnih struktura. Kod jednopojasnih prostornih konstrukcija ostvaruju se povoljni staticki uticaji i deformacije primenom optimalnih geometrijskih oblika zasnovanih na izboru optimalnih krivih (potporne linije luka i lancanice). Nakon toga izborom optimalne geometrijske podele ostvaruje se tipizacija štapova i cvorova u izvodenju. U ovom radu bice prikazani rezultati istraživanja varijantnih rešenja za karakteristican slucaj formiranja prostorne strukture na nepravilnoj poligonalnoj osnovi. Istraživanje ima za cilj unapredenje metodologije projektovanja u arhitekturi kroz multidisciplinarni pristup u rešavanju estetskog, matematickog i tehnickog problema, primenjujuci u varijantnim rešenjima razlicite pristupe. Sa druge strane ce biti iskazan znacaj matematike iz jedne nove vizure - istovremeno kao nezaobilaznog segmenta kreativne industrije dvadeset prvog veka i primenjene nauke u inženjerstvu i arhitekturi.

Kljucne reci: slobodna forma, geometrijska optimizacija,

Geometric Optimization of Freeform Structures Over a Polygonal Base

KEYWORDS: freeform structure, geometric optimization ABSTRACT: Freeform structures are one of the most prominent trends in contemporary architecture. Construction of a complicated geometric shape in architectural design is topic which is not completely covered by available CAD software. The methodology of construction consults three basic criteria: stability of the structure, manufacturing technology and financial aspect. Recent research shows that use of computational and discrete differential geometry has a great potential in achieving these requirements. The first task in construction of single layer freeform structure is the choice of such geometric shape that results in optimal static behavior. The second problem is segmentation of the shape into simpler parts, so called flat panels. In the segmentation process, by using geometric optimization methods, one can achieve standardization of nods and rods, and therefore reduce the cost of the manufacturing. In this paper we apply a geometric approach to obtain a freeform structure over non-regular, polygonal and planar base. We show that there are several possible approaches to this problem, which we compare in the paper. This research has a multidisciplinary character in solving one esthetical, architectural and mathematical problem. We emphasize the importance of contemporary applied mathematics, which is inevitable tool in answering demanding questions of modern architecture.

ČETVRTAK, 16.06.2011. u 17 sati, sala 301f MI SANU
Djordje Kadijevic
Naslov:The use of spreadsheets in the finance industry

Apstrakt:Spreadsheets are major tools in the finance industry. In order to find out how these tools are used, we examined recently published research papers and interviewed seven experienced bankers. This examination showed that spreadsheets may be used insufficiently, uncritically, and erroneously. By focusing on the quality of data and models (to be) exploited, this paper presents main details of this business-risky use of spreadsheets. Implications for vocational education are included.

ČETVRTAK, 23.06.2011. u 17 sati, sala 301f, MI SANU
Jelena Grujic
Naslov: Ajnstajnova jednacina za gravitaciono polje i njena f(R) modifikacija, 1. deo

Sadrzaj: Bice reci o principu najmanjeg dejstva i izvodjenju Ajnstajnovih jednacina iz principa najmanjeg dejstva.

CETVRTAK, 30.06.2011. u 17 sati
Ivan Dimitrijevic
Naslov: Ajnstajnova jednacina za gravitaciono polje i njena f(R) modifikacija, 2. deo

Abstract: Accelerated expansion of the universe still has not satisfactory explanation. This phenomenon is mainly related to the negative pressure of hypothetical dark energy. However, there has been recently increased interest in the modified gravity at large scale distances as a possible alternative mechanism for cosmic acceleration. As a simple approach it is usually considered modification of the Einstein-Hilbert action taking a function $f (R)$ instead of the Ricci scalar $R$. In this talk we will present basic characteristics of $f(R)$ modified gravity and general cosmological properties of some promising approaches. In particular, we will discuss various aspects of $f(R)$ modification, when $f(R)$ contains linear fractional function of $R$.

Sednice seminara odrzavaju se u zgradi Matematickog instituta SANU, Knez-Mihailova 36, na trecem spratu u sali 301f.

Rukovodilac Seminara dr Miroslava Antic