Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Fujimura, Masayo"'
We prove an identity which connects the visual angle metric $v_{\mathbb{H}^2}$ and the hyperbolic metric $\rho_{\mathbb{H}^2}$ of the upper half plane $\mathbb{H}^2$. The proof is based on geometric arguments and uses computer algebra methods for for
Externí odkaz:
http://arxiv.org/abs/2404.08942
We prove several new formulas for the visual angle metric of the unit disk in terms of the hyperbolic metric and apply these to prove a sharp Schwarz lemma for the visual angle metric under quasiregular mappings.
Comment: 15 pages, 9 Figures
Comment: 15 pages, 9 Figures
Externí odkaz:
http://arxiv.org/abs/2304.04485
We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic projections of great circles of the Riemann sphere passing through th
Externí odkaz:
http://arxiv.org/abs/2212.09037
Autor:
Fujimura, Masayo, Gotoh, Yasuhiro
Publikováno v:
Computational Methods and Function Theory, 24, 2, (2024) , 389--413
For a circle $ C $ contained in the unit disk, the necessary and sufficient condition for the existence of a triangle inscribed in the unit circle and circumscribed about $ C $ is known as Chapple's formula. The geometric properties of Blaschke produ
Externí odkaz:
http://arxiv.org/abs/2210.01262
Publikováno v:
Complex Variables and Elliptic Equations, 68, 11 (2023) , 1880--1898
We discuss the problem of the reflection of light on spherical and quadric surface mirrors. In the case of spherical mirrors, this problem is known as the Alhazen problem. For the spherical mirror problem, we focus on the reflection property of an el
Externí odkaz:
http://arxiv.org/abs/2111.00709
Publikováno v:
Complex Anal Synerg 7, 6 (2021)
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
Comment: 12 pages, 2 figures. ar
Comment: 12 pages, 2 figures. ar
Externí odkaz:
http://arxiv.org/abs/2005.14035
Publikováno v:
Complex Variables and Elliptic Equations, 66, 8 (2021), 1225--1255
Answering a question about triangle inequality suggested by R. Li, A. Barrlund introduced a distance function which is a metric on a subdomain of ${\mathbb R}^n\,.$ We study this Barrlund metric and give sharp bounds for it in terms of other metrics
Externí odkaz:
http://arxiv.org/abs/1903.12475
Autor:
Fujimura, Masayo
Publikováno v:
Journal of Mathematical Analysis and Applications, 467, no.1 (2018), 711--722
In this paper, for a Blaschke product of degree d, we give some geometrical properties that lie between the interior curve and the exterior curve.
Comment: 10 pages, 11 figures
Comment: 10 pages, 11 figures
Externí odkaz:
http://arxiv.org/abs/1802.08416
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze using a symb
Externí odkaz:
http://arxiv.org/abs/1706.06924
Autor:
Fujimura, Masayo, Gotoh, Yasuhiro
Publikováno v:
Computational Methods & Function Theory; Jun2024, Vol. 24 Issue 2, p389-413, 25p
