New L2-type exponentiality tests

We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L2 distance between V-empirical Laplace transforms of random variables that appear in the characterization. We derive the asymptotic behaviour under the null hypothesis as well as under fixed alternatives. We compare our tests, in terms of the Bahadur efficiency, to the likelihood ratio test, as well as some recent characterization based goodness-of-fit tests for the exponential distribution. We also compare the power of our tests to the power of some recent and classical exponentiality tests. According to both criteria, our tests are shown to be strong and outperform most of their competitors.Peer Reviewe

Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort

This study presents a continuation of the research on the concave polyhedra of the second sort, adding to this family a new group of related polyhedra. They are formed over a specific type of isotoxal concave polygons that allow geometric arrangement of a double row of equilateral triangles into formations which enclose a deltahedral lateral surface without overlaps and gaps. As in all other representatives of the concave polyhedra of the second sort, we expect to find here the "major" and "minor" type, depending on the way we fold the net. This research has identified both these polyhedra types, which have the same planar net, but are formed over different basic concave polygons. The origination, constructive methods and properties of these solids are elaborated in the paper.http://mongeometrija.com/attachments/article/417/Plan_i_program.pdf Predavanje po pozivu / Invited lecture

Cultural routes and improvement of conservation and presentation of medieval sacral heritage in Serbia

Основна научна област овог рада је историја и теорија архитектуре и проучавање заштите грађевинског наслеђа. С обзиром на научну област, главни проблем проучавања се односи на недостатак јаснијих тумачења одређених питања везаних за моравску архитектуру, а самим тим и неусклађеност постојећих приступа заштите и презентације са новим приступом у сагледавању корпуса домаћег средњовњковног сакралног наслеђа у оквиру ширег тзв. византијског света и путева културе...The main scientific field of the doctoral thesis is History and theory of architecture and the study and protection of architectural heritage. in accordance to the main field of research refers to the lack of clearer interpretation of some questions regarding Morava architecture, and therefore inconsistency of existing approaches to conservation and presentation with the new approach consideration of corpus of Serbiaan domestic medieval religious heritage within the so-called Bysantine word and culture routes..

Zlatni presek i pravilne konkavne bikupole druge vrste

Zlatni presek (racio) predstavlja odnos između strane pravilnog pentagona i njegove dijagonale, a takođe se dovodi u vezu sa susednim članovima Fibonacijevog niza. Istraživaem i upoređivanjem metričkih parametara konkavnih bikupola druge vrste, uočeni su odnosi koji se poklapaju sa proporcijom zlatnog preseka. Dati odnosi svedoče o skladnim proporcijama veličina konkavnih kupola II vrste i doprinose mogućnosti primene ovih tela kao novih geometrijskih formi u arhitektonskoj praksi i dizajnu.The golden section (golden ratio) represents the relationship between the side of a regular pentagon and its diagonal, and is also related to the adjacent members of the Fibonacci sequence. By researching and comparing the metric parameters of concave bicupolae of the second sort, we notice relationships that match the proportion of the golden section. The given relations testify to the harmonious proportions of the measures of concave cupolae of the II sort and contribute to the possibility of application of these solids as new geometric forms in architectural practice and design.http://mongeometrija.com/zbornici/2006/342-obradovi-zlatni-presek-i-pravilne-konkavne-bikupole-druge-vrst

Dimensions reflected - catalog

The 7th International Conference MoNGgeometrija 2020 is organized and supported by Serbian Society for Geometry and Graphics (SUGIG) and the Faculty of Mechanical Engineering, University of Belgrade. Since SUGIG considers geometry and graphics to be the universal languages of science, technics and all visual arts, the conference offers the wide range of topics which found their expression through the special Exhibition of ideas, designs and models under the name “Dimensions Reflected.” The Exhibition discloses and emphasizes the inspiring and fruitful influence of geometry on art, and at the same time the correlation between scientific exactness and poetics of visual arts. This Exhibition assures us that geometry is not only the seed and the core of many different branches of science and techniques, but also the root of aesthetic postulates, clearly recognizable in the works of artists, architects, and designers. Despite the fact that geometry is a primeval knowledge and wisdom, its power does not fade or vanish through the time, but increases its strength and authority through contemporary arts and crafts. Thus, the Exhibition exposes and confirms the importance of geometric comprehension through contributions in various scientific, engineering, and artistic fields, as well as through enhancing this precious base by means of modern digital techniques and technologies.https://mong2020masbg.wordpress.com

Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon

This paper presents a gallery of tessellations created by combining the following equilateral shapes: diamonds and stars, which can be further assembled into a pineapple shape. These three shapes can be decomposed into simpler shapes: an isosceles triangle and a rectangle. The triangle is formed by a subdivision of the regular pentagon into five equal sections, so that each have a base of length �� and legs of length ��. The rectangle is created by having the same �� and �� for its sides. The diamond is formed by two such triangles and one rectangle, while the star is formed by a radial arrangement of five triangles back into the pentagon onto which five more triangles are added (elevated). Using these two shapes, we can tile the Euclidean plane without overlaps and gaps in different ways, including the pentagonal matrix. They can be further assembled into a "pineapple" shape, which can also tile the plane arranged in different ways, using only one shape (tile). We present several examples that include: periodic, non-periodic, rotational, radial and free-form tessellations. These shapes, in addition to their visual attractiveness and decorativeness which can be used in design, also hide the connection with patterns that can be found in nature, similar to Turing patterns.http://mongeometrija.com/zbornici/202