Lipschitz constants for a hyperbolic type metric under M\" obius transformations
Y Wu, G Wang, G Jia, X Zhang - arXiv preprint arXiv:2309.03515, 2023 - arxiv.org
Let $ D $ be a nonempty open set in a metric space $(X, d) $ with $\partial D\neq\emptyset $.
Define\begin {equation*} h_ {D, c}(x, y)=\log\left (1+ c\frac {d (x, y)}{\sqrt {d_D (x) d_D …
Define\begin {equation*} h_ {D, c}(x, y)=\log\left (1+ c\frac {d (x, y)}{\sqrt {d_D (x) d_D …
Metrics and quasimetrics induced by point pair function
We study the point pair function in subdomains G of R n. We prove that, for every domain G⊊
R n, this function is a quasi-metric with the constant less than or equal to 5/2. Moreover, we …
R n, this function is a quasi-metric with the constant less than or equal to 5/2. Moreover, we …
The Ptolemy–Alhazen problem and quadric surface mirror reflection
M Fujimura, M Mocanu, M Vuorinen - Complex Variables and …, 2023 - Taylor & Francis
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 …
the case of spherical mirrors, this problem is known as the Alhazen problem. For the …