Zobrazeno 1 - 6
of 6
pro vyhledávání: '"Yana Teplitskaya"'
Autor:
Danila Cherkashin, Yana Teplitskaya
Publikováno v:
Fractal and Fractional, Vol 7, Iss 5, p 414 (2023)
We consider a general metric Steiner problem, which involves finding a set S with the minimal length, such that S∪A is connected, where A is a given compact subset of a given complete metric space X; a solution is called the Steiner tree. Paolini,
Externí odkaz:
https://doaj.org/article/970ed791fde94ff896a31cf7887aed6e
Publikováno v:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 60:1-15
We describe the configuration space $$\mathbf {S}$$ of polygons with prescribed edge slopes, and study the perimeter $${\mathcal {P}}$$ as a Morse function on $$\mathbf {S}$$ . We characterize critical points of $${\mathcal {P}}$$ (these are tangenti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::98af53c35687b32bf22bdad8fd64499d
https://doi.org/10.1007/s13366-018-0409-3
https://doi.org/10.1007/s13366-018-0409-3
Autor:
Yana Teplitskaya
Publikováno v:
Journal of Mathematical Sciences. 232:164-169
We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ2 satisfying the inequality max yϵM dist (y, Σ) ≤ r for a given compact set M ⊂ ℝ2 and given r > 0. Such
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::75c02a16552101a41d6107eb01a8e4af
https://doi.org/10.1007/s10958-018-3866-1
https://doi.org/10.1007/s10958-018-3866-1
Autor:
Danila Cherkashin, Yana Teplitskaya
Publikováno v:
ESAIM: Control, Optimisation and Calculus of Variations. 24:1015-1041
We study the properties of sets Σ having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets Σ ⊂ ℝ2 satisfying the inequality maxy∈M dist (y,Σ) ≤ r for a given compact set M ⊂ ℝ2 and some give
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::33514d3a5229934f67f984be438bfad5
https://doi.org/10.1051/cocv/2017025
https://doi.org/10.1051/cocv/2017025
Autor:
Eugene Stepanov, Yana Teplitskaya
Publikováno v:
Journal of the London Mathematical Society. 96:455-481
A curve θ:I→E in a metric space E equipped with the distance d, where I⊂R is a (possibly unbounded) interval, is called self-contracted, if for any triple of instances of time {ti}i=13⊂I with t1⩽t2⩽t3 one has d(θ(t3),θ(t2))⩽d(θ(t3),θ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b8568e2f139d9309c49fc8bde4f2137b
https://doi.org/10.1112/jlms.12068
https://doi.org/10.1112/jlms.12068
We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be the unique solution to a Steiner problem for the given set of points. As a byproduct we get the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f98023a4c2c12cb97d4c86005c21aeec
http://hdl.handle.net/11568/819633
http://hdl.handle.net/11568/819633
