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pro vyhledávání: '"Pittman, Dylanger"'
Autor:
Pittman, Dylanger
We greatly expand upon the results of Kochengin, Oliker and Tempeski [S. Kochengin, V. Oliker, O. von Tempeski, On the design of reflectors with prescribed distribution of virtual sources and intensities, Inverse Problems 14 (1998) 661-678.] to inclu
Externí odkaz:
http://arxiv.org/abs/2301.02106
Autor:
Pittman, Dylanger
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded open set $U$
Externí odkaz:
http://arxiv.org/abs/2301.00845
Autor:
Pittman, Dylanger
The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.
Externí odkaz:
http://arxiv.org/abs/2110.11336
Autor:
Di Giosia, Leonardo, Habib, Jahangir, Hirsch, Jack, Kenigsberg, Lea, Li, Kevin, Pittman, Dylanger, Petty, Jackson, Xue, Christopher, Zhu, Weitao
The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox conjectured that a regular $k$-gonal tile with 120-de
Externí odkaz:
http://arxiv.org/abs/1911.04476
Autor:
Bongiovanni, Eliot, Di Giosia, Leonardo, Diaz, Alejandro, Habib, Jahangir, Kakkar, Arjun, Kenigsberg, Lea, Pittman, Dylanger, Sothanaphan, Nat, Zhu, Weitao
Publikováno v:
Anal. Geom. Metric Spaces 6 (2018) 64-88
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we assume to b
Externí odkaz:
http://arxiv.org/abs/1708.03289
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted area with minimum weighted perimeter. According to Chambers' recent proof of the Log Convex Density Conjecture, for many densities on $\mathbb{R}^n$ the answer
Externí odkaz:
http://arxiv.org/abs/1610.07043
We have discovered a "little" gap in our proof of the sharp conjecture that in $\mathbb{R}^n$ with volume and perimeter densities $r^m$ and $r^k$, balls about the origin are uniquely isoperimetric if $0 < m \leq k - k/(n+k-1)$, that is, if they are s
Externí odkaz:
http://arxiv.org/abs/1610.05830
Autor:
Bongiovanni Eliot, Di Giosia Leonardo, Diaz Alejandro, Habib Jahangir, Kakkar Arjun, Kenigsberg Lea, Pittman Dylanger, Sothanaphan Nat, Zhu Weitao
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 6, Iss 1, Pp 64-88 (2018)
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-conve
Externí odkaz:
https://doaj.org/article/0e22d3c033cb4dfd8a01795b1033afc1
Publikováno v:
In Mathematical Biosciences December 2016 282:181-190
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