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New York journal of mathematics, ISSN 1076-9803, 2019, Volume 25, pp. 107 - 122
In the present paper we study the Sol geometry, which is one of the eight homogeneous Thurston 3-geometries. We determine the equation of the translation-like... 
Sol geometry | Thurston geometries | Translation-like bisector surface | MATHEMATICS | translation-like bisector surface
Journal Article
Journal of Mathematical Behavior, ISSN 0732-3123, 09/2016, Volume 43, pp. 35 - 52
•We studied conceptions of reflection related to the use of perpendicular bisector.•We found five conceptions of reflection in students’ work on three... 
Geometry | Perpendicular bisector | Problem solving | Geometric transformations | Conceptions | Reflections | Students
Journal Article
Computer Aided Geometric Design, ISSN 0167-8396, 10/2019, Volume 74, p. 101767
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the... 
Offset hypersurface | Reach | Offset curve | Persistent homology | Medial axis | Euclidean Distance Degree | TOPOLOGY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PURITY | BISECTOR
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2016, Volume 439, Issue 2, pp. 651 - 663
It is an elementary fact that if we fix an arbitrary set of d+1 affine independent points {p0,…,pd} in Rd, then the Euclidean distances {|x−pj|}j=0d determine... 
Resolving set | Simplex | Bisector
Journal Article
Computer Aided Geometric Design, ISSN 0167-8396, 10/2016, Volume 47, pp. 189 - 203
In this paper, a general theoretical study, from the perspective of the algebraic geometry, of the untrimmed bisector of two real algebraic plane curves is... 
Parametrization | Bisector | Algebraic curve | Incidence variety | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SURFACES
Journal Article
Foot & Ankle International, ISSN 1071-1007, 9/2011, Volume 32, Issue 9, pp. 867 - 872
Background: Foot deformity associated with diabetes mellitus (DM) and peripheral neuropathy (PN) contributes to joint instability, ulceration and amputation.... 
Calcaneal pitch | Dorsoplantar talocalcaneal bisector | Meary's line | Cuboid height | 2nd metatarsal angle | Dorsoplantar Talocalcaneal Bisector | Calcaneal Pitch | Meary's Line | 2nd Metatarsal Angle | ORTHOPEDICS | Cuboid Height
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2019, Volume 26, Issue 1, pp. 49 - 76
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are... 
Best approximation | Bisector | Generalized minkowski space | Birkhoff orthogonality | Isosceles orthogonality | Gauge | gauge | RECTANGULAR CONSTANT | MATHEMATICS | bisector | BIRKHOFF-JAMES ORTHOGONALITY | OPERATOR NORM ATTAINMENT | isosceles orthogonality | generalized Minkowski space | CURVES
Journal Article
Advances in Geometry, ISSN 1615-715X, 01/2013, Volume 13, Issue 1, pp. 145 - 154
In this note we prove two ellipsoid characterization theorems. The first one is that if K is a convex body in a normed space with unit ball M, and for any... 
Billiard angular bisector | Busemann angular bisector | Normed space | Billiard reflection | Glogovskij angular bisector | Tangent segment | Ellipsoid | MATHEMATICS | billiard reflection | CONVEX-BODIES | billiard angular bisector | tangent segment | ellipsoid | Theorems (Mathematics) | Metric spaces | Research
Journal Article
Computer Aided Geometric Design, ISSN 0167-8396, 08/2017, Volume 56, pp. 52 - 66
In this paper we study situations when non-rational parameterizations of planar or space curves as results of certain geometric operations or constructions are... 
Weierstrass form | Hyperelliptic curves | Rational approximation | Topological graph | Square-root parameterization | OFFSETS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SPACE-CURVES | CANAL SURFACES | BISECTOR | Analysis | Algorithms
Journal Article
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 11/2018, Volume 59, Issue 4, pp. 797 - 804
The article deals with a plane equipped with a convex distance function. We extend the notions of equilateral and acute triangles and consider circumcenters of... 
Geometry | 52A10 | 52A21 | Algebra | Convex distance | Central set | Convex and Discrete Geometry | Acute | Algebraic Geometry | Mathematics | Bisector
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2017, Volume 42, Issue 2, pp. 837 - 845
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix L-pq as the set of equidistant points to p and q. It is known... 
Mediatrix | Bisectors | Equator | MEDIATRICES | MATHEMATICS | CONFLICT SETS | equator | bisectors | EQUIDISTANT SETS
Journal Article
Astrophysical Journal, ISSN 0004-637X, 01/2018, Volume 852, Issue 1, p. 42
The velocity shifts of spectral lines as a function of line strength, so-called the third signature of granulation, are investigated using three published... 
convection | stars: atmospheres | Sun: granulation | line: formation | stars: solar-type | techniques: radial velocities | ROTATION | VELOCITY | ASYMMETRIES | WAVELENGTH SHIFTS | CONVECTION | ASTRONOMY & ASTROPHYSICS | SPECTRAL-LINE BISECTORS | DYNAMICS | PARAMETERS | MODEL | INVERSION | Fluctuations | Granulation | Spectral resolution | Solar flux | Line spectra | Velocity | Atlases
Journal Article
Journal Article
Contributions to Discrete Mathematics, ISSN 1715-0868, 2015, Volume 10, Issue 2, pp. 1 - 9
In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that,... 
Normed plane | Norming functional | Bisector | norming functional | MATHEMATICS | normed plane | SPACES | GEOMETRY
Journal Article
Measurement: Interdisciplinary Research and Perspectives, ISSN 1536-6367, 07/2018, Volume 16, Issue 3, pp. 195 - 202
Equating test scores between different achievement test versions is important to assure comparability between test takers' scores. As many items are modelled... 
IRT observed-score equating | IRT true-score equating | IRT | bisector method | equating coefficients
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 08/2018, Volume 37, Issue 4, pp. 1 - 15
A critical advantage of additive manufacturing is its ability to fabricate complex small-scale structures. These microstructures can be understood as a... 
voronoi diagram | additive manufacturing | 3D printing | Voronoi diagram | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BISECTORS | NUMERICAL SIMULATIONS | GEOMETRY | Computer Aided Engineering | Computer Science | Computational Geometry
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 12/2008, Volume 30, Issue 12, pp. 2204 - 2217
Journal Article
Astronomy and Astrophysics, ISSN 0004-6361, 09/2009, Volume 504, Issue 2, pp. 617 - 623
Context. We found evidence for a sub-stellar companion around the K giant star HD 110014. This cool evolved star, with a spectral type K2III and an estimated... 
Technique: radial velocities | Stars: evolution | Stars: planetary systems | Stars late-type | LINE BISECTOR | stars: evolution | stars: planetary systems | stars late-type | K-GIANTS | COMPANION | ISOCHRONES | RADIAL-VELOCITY VARIATIONS | REDUCTION | ASTRONOMY & ASTROPHYSICS | technique: radial velocities | SYSTEMS | PULSATIONS
Journal Article
IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 08/2014, Volume 26, Issue 8, pp. 2029 - 2044
Journal Article
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