Zobrazeno 1 - 10
of 459
pro vyhledávání: '"P. Rainio"'
Autor:
Rainio, Oona
We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequalities with the hyperbolic metric and the triangular ratio metric. We al
Externí odkaz:
http://arxiv.org/abs/2406.17387
Objectives: The objectives of this narrative review are to summarize the current state of AI applications in neuroimaging for early Alzheimer's disease (AD) prediction and to highlight the potential of AI techniques in improving early AD diagnosis, p
Externí odkaz:
http://arxiv.org/abs/2406.17822
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
Autor:
Rainio, Oona
We study a hyperbolic type metric $h_{G,c}$ introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant $c>0$, for which this function $h_{G,c}$ is a metric in specific choices of $G$. We give several sharp inequalities between $h_{G,c}$
Externí odkaz:
http://arxiv.org/abs/2404.01017
Autor:
Rainio, Oona, Vuorinen, Matti
Due to the invariance properties of cross-ratio, M\"obius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a problem studied. However, when the points are mapped under a M\"obius tr
Externí odkaz:
http://arxiv.org/abs/2308.10688
Autor:
Rainio, Oona, Kargar, Rahim
We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G\subsetneq\mathbb{R}^n$ by using the arithmetic or the logarithmic mean of the Euclidean distances from the points $x$ and $y$ to the boundary o
Externí odkaz:
http://arxiv.org/abs/2308.06576
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly perfect subset $E$ of $\mathbb{R}^n$ to prove new explicit lower bounds for the Hausdorff dimension of $E.
Externí odkaz:
http://arxiv.org/abs/2305.16723
Autor:
Kargar, Rahim, Rainio, Oona
The modulus metric between two points in a subdomain of $\mathbb{R}^n, n\ge 2,$ is defined in terms of moduli of curve families joining the boundary of the domain with a continuum connecting the two points. This metric is one of the conformally invar
Externí odkaz:
http://arxiv.org/abs/2304.11588
Autor:
Rainio, Oona, Vuorinen, Matti
The Hilbert metric between two points $x,y$ in a bounded convex domain $G$ is defined as the logarithm of the cross-ratio of $x,y$ and the intersection points of the Euclidean line passing through the points $x,y$ and the boundary of the domain. Here
Externí odkaz:
http://arxiv.org/abs/2303.03753
Autor:
Rainio, Oona
We study a new generalized version of the point pair function defined with a constant $\alpha>0$. We prove that this function is a quasi-metric for all values of $\alpha>0$, and compare it to several hyperbolic-type metrics, such as the $j^*$-metric,
Externí odkaz:
http://arxiv.org/abs/2301.03248