TY  - JOUR
AU  - Malešević, Branko J.
AU  - Petrović, Maja
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1020
AB  - We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.
T2  - Mathematical Inequalities & Applications
T1  - On the extension of the Erdös-Mordell type inequalities
EP  - 281
IS  - 1
SP  - 269
VL  - 17
DO  - 10.7153/mia-17-22
ER  - 

@article{
author = "Malešević, Branko J. and Petrović, Maja and Obradović, Marija and Popkonstantinović, Branislav",
year = "2014",
abstract = "We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.",
journal = "Mathematical Inequalities & Applications",
title = "On the extension of the Erdös-Mordell type inequalities",
pages = "281-269",
number = "1",
volume = "17",
doi = "10.7153/mia-17-22"
}

Malešević, B. J., Petrović, M., Obradović, M.,& Popkonstantinović, B.. (2014). On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications, 17(1), 269-281.
https://doi.org/10.7153/mia-17-22

Malešević BJ, Petrović M, Obradović M, Popkonstantinović B. On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications. 2014;17(1):269-281.
doi:10.7153/mia-17-22 .

Malešević, Branko J., Petrović, Maja, Obradović, Marija, Popkonstantinović, Branislav, "On the extension of the Erdös-Mordell type inequalities" in Mathematical Inequalities & Applications, 17, no. 1 (2014):269-281,
https://doi.org/10.7153/mia-17-22 . .

TY  - JOUR
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
AU  - Petrović, Maja
AU  - Malešević, Branko
AU  - Obradović, Ratko
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1928
AB  - Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.
PB  - Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)
T2  - Technics Technologies Education Management
T1  - Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture
EP  - 1214
IS  - 3
SP  - 1198
VL  - 8
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1928
ER  - 

@article{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav and Petrović, Maja and Malešević, Branko and Obradović, Ratko",
year = "2013",
abstract = "Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.",
publisher = "Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)",
journal = "Technics Technologies Education Management",
title = "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture",
pages = "1214-1198",
number = "3",
volume = "8",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1928"
}

Obradović, M., Mišić, S., Popkonstantinović, B., Petrović, M., Malešević, B.,& Obradović, R.. (2013). Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management
Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)., 8(3), 1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928

Obradović M, Mišić S, Popkonstantinović B, Petrović M, Malešević B, Obradović R. Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management. 2013;8(3):1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, Petrović, Maja, Malešević, Branko, Obradović, Ratko, "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture" in Technics Technologies Education Management, 8, no. 3 (2013):1198-1214,
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
AU  - Đukanović, Gordana
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1983
AB  - The starting constructions is the well known ellipse construction using the concentric circles c1 and c2. By eccentricity of the center C2 for some value w, and for the preserved center of the transformation in the center C1, the degree of the obtained curve rises from two to three, as done by mathematician Fritz Hügelschäffer. If we also displace the center of the transformation from C1, we obtain a variety of higher order curves using the same principle in the constructive procedure.
PB  - Timişoara: Editura Politehnica
C3  - Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS
T1  - Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction
EP  - 114
IS  - 1
SP  - 110
VL  - 58(72)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1983
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja and Đukanović, Gordana",
year = "2013",
abstract = "The starting constructions is the well known ellipse construction using the concentric circles c1 and c2. By eccentricity of the center C2 for some value w, and for the preserved center of the transformation in the center C1, the degree of the obtained curve rises from two to three, as done by mathematician Fritz Hügelschäffer. If we also displace the center of the transformation from C1, we obtain a variety of higher order curves using the same principle in the constructive procedure.",
publisher = "Timişoara: Editura Politehnica",
journal = "Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS",
title = "Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction",
pages = "114-110",
number = "1",
volume = "58(72)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1983"
}

Obradović, M., Malešević, B., Petrović, M.,& Đukanović, G.. (2013). Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction. in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS
Timişoara: Editura Politehnica., 58(72)(1), 110-114.
https://hdl.handle.net/21.15107/rcub_grafar_1983

Obradović M, Malešević B, Petrović M, Đukanović G. Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction. in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS. 2013;58(72)(1):110-114.
https://hdl.handle.net/21.15107/rcub_grafar_1983 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, Đukanović, Gordana, "Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction" in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS, 58(72), no. 1 (2013):110-114,
https://hdl.handle.net/21.15107/rcub_grafar_1983 .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
AU  - Popkonstantinović, Branislav
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2032
AB  - We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - One Application of the  Cone Surfaces on the Erdosh-Mordell inequality
EP  - 351
SP  - 335
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2032
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja and Popkonstantinović, Branislav",
year = "2012",
abstract = "We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality",
pages = "351-335",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2032"
}

Obradović, M., Malešević, B., Petrović, M.,& Popkonstantinović, B.. (2012). One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032

Obradović M, Malešević B, Petrović M, Popkonstantinović B. One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, Popkonstantinović, Branislav, "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):335-351,
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

TY  - JOUR
AU  - Popkonstantinović, Branislav
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Jeli, Zorana
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2028
AB  - Theory of clock, watch and chronometer escapements is important
and interesting part of theory of mechanisms and kinematics. Despite the fact that chronometer escapements are invented in past times, from the viewpoint of kinematics and machine theory, these mechanisms represent the jewel treasuries of knowledge and engineering wisdom. This paper considers and discloses operational principles and constructive geometry of Thomas Earnshaw‟s chronometer detent escapement. Moreover, process of 3D solid modeling, and assembling of all escapement parts, as well as the motion study and simulation of escapement operational cycle are presented and explained. This analysis and considerations enlighten not just the kinematical properties and characteristic of one particular chronometer escapement type, but also clarify and illuminate the process of computer aided mechanism design, construction and motion analysis.
PB  - Iasi: "Gheorghe Asachi" Technical University of Iasi
T2  - Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
T1  - Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism
EP  - 72
IS  - Fasc. 5
SP  - 55
VL  - Tomul LVII (LXI)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2028
ER  - 

@article{
author = "Popkonstantinović, Branislav and Obradović, Marija and Malešević, Branko and Jeli, Zorana",
year = "2011",
abstract = "Theory of clock, watch and chronometer escapements is important
and interesting part of theory of mechanisms and kinematics. Despite the fact that chronometer escapements are invented in past times, from the viewpoint of kinematics and machine theory, these mechanisms represent the jewel treasuries of knowledge and engineering wisdom. This paper considers and discloses operational principles and constructive geometry of Thomas Earnshaw‟s chronometer detent escapement. Moreover, process of 3D solid modeling, and assembling of all escapement parts, as well as the motion study and simulation of escapement operational cycle are presented and explained. This analysis and considerations enlighten not just the kinematical properties and characteristic of one particular chronometer escapement type, but also clarify and illuminate the process of computer aided mechanism design, construction and motion analysis.",
publisher = "Iasi: "Gheorghe Asachi" Technical University of Iasi",
journal = "Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011",
title = "Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism",
pages = "72-55",
number = "Fasc. 5",
volume = "Tomul LVII (LXI)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2028"
}

Popkonstantinović, B., Obradović, M., Malešević, B.,& Jeli, Z.. (2011). Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
Iasi: "Gheorghe Asachi" Technical University of Iasi., Tomul LVII (LXI)(Fasc. 5), 55-72.
https://hdl.handle.net/21.15107/rcub_grafar_2028

Popkonstantinović B, Obradović M, Malešević B, Jeli Z. Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011. 2011;Tomul LVII (LXI)(Fasc. 5):55-72.
https://hdl.handle.net/21.15107/rcub_grafar_2028 .

Popkonstantinović, Branislav, Obradović, Marija, Malešević, Branko, Jeli, Zorana, "Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism" in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011, Tomul LVII (LXI), no. Fasc. 5 (2011):55-72,
https://hdl.handle.net/21.15107/rcub_grafar_2028 .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2052
AB  - A cubic egg curve obtained by Hügelschäffer’s construction,
can be spatially interpreted as a plane section of a type of a conoid
set through a specially chosen 4-th order intersecting curve of two
quadrics: right cylinder and cone. That implies that the apex of a
cone must lay on the axis of a cylinder in order to obtain one sheet
surface. This type of conoid will be of 4-th order, and will exclude
plane sections by conics. We consider a special case of forming an akin conoid that would include also conic sections. If the apex of the cone is set off the cylinder axis, there would appear a double conoid, as a surface set through the intersection curve of the quadrics. Its plane section will be a double egg curve obtained by generalized Hügelschäffer’s construction. In case that cylinder and cone would intersect by a degenerated 4-th degree space curve on two conics (circle and ellipse), there would emerge double egg curve, as a plane section of the double conoid. The curve degenerates onto ellipse and a quartic curve - Granville’s egg. We also gave a mathematical condition of degeneration of the base double egg curve.
PB  - Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)
C3  - PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010
T1  - Conic Section of a Type of Egg Curve Based Conoid
EP  - 466
SP  - 447
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2052
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja",
year = "2010",
abstract = "A cubic egg curve obtained by Hügelschäffer’s construction,
can be spatially interpreted as a plane section of a type of a conoid
set through a specially chosen 4-th order intersecting curve of two
quadrics: right cylinder and cone. That implies that the apex of a
cone must lay on the axis of a cylinder in order to obtain one sheet
surface. This type of conoid will be of 4-th order, and will exclude
plane sections by conics. We consider a special case of forming an akin conoid that would include also conic sections. If the apex of the cone is set off the cylinder axis, there would appear a double conoid, as a surface set through the intersection curve of the quadrics. Its plane section will be a double egg curve obtained by generalized Hügelschäffer’s construction. In case that cylinder and cone would intersect by a degenerated 4-th degree space curve on two conics (circle and ellipse), there would emerge double egg curve, as a plane section of the double conoid. The curve degenerates onto ellipse and a quartic curve - Granville’s egg. We also gave a mathematical condition of degeneration of the base double egg curve.",
publisher = "Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)",
journal = "PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010",
title = "Conic Section of a Type of Egg Curve Based Conoid",
pages = "466-447",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2052"
}

Obradović, M., Malešević, B.,& Petrović, M.. (2010). Conic Section of a Type of Egg Curve Based Conoid. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010
Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)., 447-466.
https://hdl.handle.net/21.15107/rcub_grafar_2052

Obradović M, Malešević B, Petrović M. Conic Section of a Type of Egg Curve Based Conoid. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010. 2010;:447-466.
https://hdl.handle.net/21.15107/rcub_grafar_2052 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, "Conic Section of a Type of Egg Curve Based Conoid" in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 (2010):447-466,
https://hdl.handle.net/21.15107/rcub_grafar_2052 .

TY  - CONF
AU  - Obradović, Marija
AU  - Petrović, Maja
AU  - Malešević, Branko
PY  - 2009
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2026
AB  - Starting from a type of conoid which is based on a cubic egg curve obtained by Hügelschäffer’s construction, it is considered a possible occurrence of related type of conoid, which would include conic curve as a part of its plane section.  The solution is accomplished by constructively – geometrical methods, supported by Rhinoceros software package.
PB  - Novi Sad: Faculty of Sciences, University of Novi Sad - Department of Mathematics and Informatics
C3  - Book of Abstracts / XVIII Conference on Applied Mathematics PRIM 2009, Subotica, 25-27. maj, 2009
T1  - About planar sections of a type of egg curve based conoid
SP  - 14
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2026
ER  - 

@conference{
author = "Obradović, Marija and Petrović, Maja and Malešević, Branko",
year = "2009",
abstract = "Starting from a type of conoid which is based on a cubic egg curve obtained by Hügelschäffer’s construction, it is considered a possible occurrence of related type of conoid, which would include conic curve as a part of its plane section.  The solution is accomplished by constructively – geometrical methods, supported by Rhinoceros software package.",
publisher = "Novi Sad: Faculty of Sciences, University of Novi Sad - Department of Mathematics and Informatics",
journal = "Book of Abstracts / XVIII Conference on Applied Mathematics PRIM 2009, Subotica, 25-27. maj, 2009",
title = "About planar sections of a type of egg curve based conoid",
pages = "14",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2026"
}

Obradović, M., Petrović, M.,& Malešević, B.. (2009). About planar sections of a type of egg curve based conoid. in Book of Abstracts / XVIII Conference on Applied Mathematics PRIM 2009, Subotica, 25-27. maj, 2009
Novi Sad: Faculty of Sciences, University of Novi Sad - Department of Mathematics and Informatics., 14.
https://hdl.handle.net/21.15107/rcub_grafar_2026

Obradović M, Petrović M, Malešević B. About planar sections of a type of egg curve based conoid. in Book of Abstracts / XVIII Conference on Applied Mathematics PRIM 2009, Subotica, 25-27. maj, 2009. 2009;:14.
https://hdl.handle.net/21.15107/rcub_grafar_2026 .

Obradović, Marija, Petrović, Maja, Malešević, Branko, "About planar sections of a type of egg curve based conoid" in Book of Abstracts / XVIII Conference on Applied Mathematics PRIM 2009, Subotica, 25-27. maj, 2009 (2009):14,
https://hdl.handle.net/21.15107/rcub_grafar_2026 .

TY  - JOUR
AU  - Malešević, Branko
AU  - Obradović, Marija
PY  - 2009
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/234
AB  - In this paper we use Groebner bases theory in order to determine planarity of intersections of two algebraic surfaces in R3. We specially considered plane sections of certain type of conoid which has a cubic egg curve as one of the directrices. The paper investigates a possibility of conic plane sections of this type of conoid.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - An application of Groebner bases to planarity of intersection of surfaces
EP  - 55
IS  - 2
SP  - 43
VL  - 23
DO  - 10.2298/FIL0902043M
ER  - 

@article{
author = "Malešević, Branko and Obradović, Marija",
year = "2009",
abstract = "In this paper we use Groebner bases theory in order to determine planarity of intersections of two algebraic surfaces in R3. We specially considered plane sections of certain type of conoid which has a cubic egg curve as one of the directrices. The paper investigates a possibility of conic plane sections of this type of conoid.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "An application of Groebner bases to planarity of intersection of surfaces",
pages = "55-43",
number = "2",
volume = "23",
doi = "10.2298/FIL0902043M"
}

Malešević, B.,& Obradović, M.. (2009). An application of Groebner bases to planarity of intersection of surfaces. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 23(2), 43-55.
https://doi.org/10.2298/FIL0902043M

Malešević B, Obradović M. An application of Groebner bases to planarity of intersection of surfaces. in Filomat. 2009;23(2):43-55.
doi:10.2298/FIL0902043M .

Malešević, Branko, Obradović, Marija, "An application of Groebner bases to planarity of intersection of surfaces" in Filomat, 23, no. 2 (2009):43-55,
https://doi.org/10.2298/FIL0902043M . .