Zobrazeno 1 - 10
of 12
pro vyhledávání: '"Anastasios N. Zachos"'
Autor:
Anastasios N. Zachos
Publikováno v:
Analysis. 41:79-112
We find the equations of the two interior nodes (weighted Fermat–Torricelli points) with respect to the weighted Steiner problem for four points determining a tetrahedron in R 3 \mathbb{R}^{3} . Furthermore, by applying the solution with respect to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e1b87f5300d6a5c16451607e4236a2e3
https://doi.org/10.1515/anly-2020-0042
https://doi.org/10.1515/anly-2020-0042
Autor:
Anastasios N. Zachos
Publikováno v:
Journal of Mathematical Chemistry. 54:1447-1460
We introduce the weighted Fermat–Torricelli–Menger problem for a given sextuple of edge lengths in \({\mathbb {R}}^{3}\) which states that: given a sextuple of edge lengths determining tetrahedra and a positive real number (weight) which correspo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4506bce086eef3823b941f468acb662e
https://doi.org/10.1007/s10910-016-0630-y
https://doi.org/10.1007/s10910-016-0630-y
Autor:
Anastasios N. Zachos
Publikováno v:
Rendiconti del Circolo Matematico di Palermo (1952 -). 64:451-458
We obtain an analytical solution of the weighted Fermat–Torricelli (wFT) problem for a specific equilateral geodesic triangle. This approach is a generalization of Cockayne’s solution given in Cockayne (Math Mag 45:216–219, 1972) for three equa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::add0263cdb53eb7432763a997ba4fdea
https://doi.org/10.1007/s12215-015-0209-7
https://doi.org/10.1007/s12215-015-0209-7
Autor:
Anastasios N. Zachos
Publikováno v:
Analysis. 34:339-352
We introduce a method of differentiation of the length of a variable linear segment with respect to three variable linear segments which generalizes the first variation formula in the three-dimensional Euclidean space. Applying this method, we derive
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::28e94ee903507a1cca0348cdaa68899d
https://doi.org/10.1515/anly-2012-1207
https://doi.org/10.1515/anly-2012-1207
Autor:
Anastasios N. Zachos
Publikováno v:
Mediterranean Journal of Mathematics. 12:1069-1083
We solve a generalized Gauss problem in the Euclidean plane which states that: Given a convex quadrilateral, a positive number (weight) that corresponds to each of its vertices and a length of a linear segment which connects two mobile interior point
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1e5ed24c7db6b6dbe3a9badc8ac0453d
https://doi.org/10.1007/s00009-014-0438-6
https://doi.org/10.1007/s00009-014-0438-6
Autor:
Anastasios N. Zachos
Publikováno v:
Results in Mathematics. 65:167-179
We find the exact location of the weighted Fermat–Torricelli point of a geodesic triangle on flat surfaces of revolution (circular cylinder and circular cone) in the three dimensional Euclidean space by applying a cosine law of three circular helix
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b4ee619fa0e076a79f0c2fe11ef2da10
https://doi.org/10.1007/s00025-013-0338-2
https://doi.org/10.1007/s00025-013-0338-2
Autor:
Anastasios N. Zachos
Publikováno v:
Acta Applicandae Mathematicae. 129:81-134
We derive the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and prove a plasticity principle which states that: Given four shortest arcs which meet at the weighted Fermat-Torricelli point
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b9920cfb13741dec8af9924996e90a4
https://doi.org/10.1007/s10440-013-9831-6
https://doi.org/10.1007/s10440-013-9831-6
Autor:
Anastasios N. Zachos
Publikováno v:
Acta Applicandae Mathematicae. 125:11-26
We prove a plasticity principle of closed hexahedra in the three dimensional Euclidean space which states that: Suppose that the closed hexahedron A 1 A 2?A 5 has an interior weighted Fermat-Torricelli point A 0 with respects to the weights B i and l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8582043199ac697865697724c944ebdc
https://doi.org/10.1007/s10440-012-9778-z
https://doi.org/10.1007/s10440-012-9778-z
Publikováno v:
Journal of Mathematical Analysis and Applications. 373:44-58
We study the weighted Fermat–Torricelli (w.F-T) problem for geodesic triangles on a C 2 complete surface and on an Aleksandrov space of curvature bounded above by a real number K and solve an “inverse” problem on a C 2 complete surface. The sol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb68efdab909abd01add00e750cf0d23
https://doi.org/10.1016/j.jmaa.2010.06.029
https://doi.org/10.1016/j.jmaa.2010.06.029
Autor:
Anastasios N. Zachos
Publikováno v:
Analysis. 34
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d80721fbbdf5e91517abd7556a40fc14
https://doi.org/10.1515/anly-2013-1231
https://doi.org/10.1515/anly-2013-1231