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Hilbert Metric in the Unit Ball [PDF]
Studia Scientiarum Mathematicarum Hungarica, 2023 The Hilbert metric between two points š„, š¦ in a bounded convex domain šŗ is defined as the logarithm of the cross-ratio š„, š¦ and the intersection points of the Euclidean line passing through the points š„, š¦ and the boundary of the domain. Here, we study this metric in the case of the unit ball š¹š.
Oona Rainio, Matti Vuorinen
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Triangular ratio metric in the unit disk [PDF]
Complex Variables and Elliptic Equations, 2021 The triangular ratio metric is studied in a domain $G\subsetneq\mathbb{R}^n$, $n\geq2$. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied to study the H lder continuity of quasiconformal mappings.
Oona Rainio, Matti Vuorinen
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Science Education International, 2018 The aim of this study was to examine prospective science teachersā knowledge of and difficulties with the metric unit conversion. The participants of the study were 73 prospective science teachers.
Emrah Oguzhan Dincer +1 more
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Critical review of the levelised cost of energy metric
South African Journal of Industrial Engineering, 2016 The purpose of this paper is to critically review the ālevelised cost of energyā metric used in electricity project development. This metric is widely used, because it is a simple metric to calculate the cost per unit of electricity for a given ...
Sklar-Chik, M. D. +2 more
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Radial balanced metrics on the unit disk
Journal of Geometry and Physics, 2009 Let $ $ be a strictly plurisubharmonic and radial function on the unit disk ${\cal D}\subset {\complex}$ and let $g$ be the \K metric associated to the \K form $ =\frac{i}{2}\partial\bar\partial $. We prove that if $g$ is $g_{eucl}$-balanced of height 3 (where $g_{eucl}$ is the standard Euclidean metric on ${\complex}={\real}^2$), and the function ...
Antonio Greco, Andrea Loi
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Wassersteināmetricābased distributionally robust optimization method for unit commitment considering wind turbine uncertainty [PDF]
Engineering Reports, 2023 The penetration of wind turbines in the power grid is increasing rapidly. Still, the wind turbine output power has uncertainty, leading to poor grid reliability, affecting the grid's dispatching plan, and increasing the total cost.
Gengrui Chen +5 more
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Threshold units: A correct metric for reaction time? [PDF]
Vision Research, 2007 To compare reaction time (RT) to rod incremental and decremental stimuli expressed in physical contrast units or psychophysical threshold units.Rod contrast detection thresholds and suprathreshold RTs were measured for Rapid-On and Rapid-Off ramp stimuli.Threshold sensitivity to Rapid-Off stimuli was higher than to Rapid-On stimuli.
Andrew J. Zele +2 more
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Scalar curvature of a metric with unit volume
Mathematische Annalen, 1987 For a compact n-manifold M equipped with a conformal class C of Riemannian metrics, \(\mu\) (M,C) is defined as the infimum of the Yamabe functional; \(\mu (M,C)=\inf \{\int _{M}R_ gdv_ g;\quad g\in C\quad and\quad Vol(M,g)=1\},\) where \(R_ g\) is the scalar curvature of g. Let \(\mu (M)=\sup _{C}\mu (M,C)\). Then the set \({\mathcal S}(M)=\{R_ g\in C^
Osamu Kobayashi, Osamu Kobayashi
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Unit-cell volume change as a metric of radiation damage in crystals of macromolecules [PDF]
Journal of Synchrotron Radiation, 2002 Raimond B. G. Ravelli +3 more
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MathematicsDefining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis.
Jihnhee Yu, HyunAh Lee, Zohi Sternberg
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