Related papers: 25 years ago: the official farewell to the meter
Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…
The solar eclipse of Good Friday has always been recognized as a problem from the astronomical point of view. The date of Crucifixion has been investigated by many scholars and the most accredited one is friday 3 april 33, when, at sunset…
A finite set of unlabelled points in Euclidean space is the simplest representation of many real objects from mineral rocks to sculptures. Since most solid objects are rigid, their natural equivalence is rigid motion or isometry maintaining…
These are lecture notes prepared for the summer school "Geometric, algebraic and topological methods in quantum field theory", held in Villa de Leyva in July 2017. Our goal is to provide an introduction to a conjecture of Chern that states…
Betelgeuse is the nearest Red Supergiant star and it underwent an unusually deep minimum at optical wavelengths during its most recent pulsation cycle. We present submillimetre observations taken by the James Clerk Maxwell Telescope and…
Accurate positional measurements of planets and satellites are used to improve our knowledge of their dynamics and to infer the accuracy of planet and satellite ephemerides. In the framework of the FP7 ESPaCE project, we provide the…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…
In these notes, based on lectures given as part of the Les Houches summer school on Quantum Optics and Nanophotonics in August, 2013, I have tried to give a brief survey of some important approaches and modern tendencies in quantum…
We investigate the modified trace distance measure of coherence recently introduced in [Phys. Rev. A 94, 060302(R) (2016)]. We show that for any single-qubit state, the modified trace norm of coherence is equal to the $l_{1}$-norm of…
A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is…
The bright supergiant, Betelgeuse (Alpha Orionis, HD 39801), underwent a historic optical dimming during 2020 January 27 $-$ February 13. Many imaging and spectroscopic observations across the electromagnetic spectrum were obtained prior…
Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with…
Knowing the distance of an astrophysical object is key to understanding it. However, at present, comparisons of theory and observations are hampered by precision (or lack thereof) in distance measurements or estimates. Putting the many…
The flat matter dominated Universe that dominated cosmological model building for much of the past 20 years does not correspond to the Universe in which we live. This has profound implications both for our understanding of dark matter, and…
Since the dawn of civilization, humanity has grappled with the big questions of existence and creation. Modern cosmology seeks to answer some of these questions using a combination of mathematics and measurement. The questions people hope…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
The transit of Mercury occurred two times in this century: 2003, May 7 and 2006, November 8. In 2016 there is another opportunity to observe this phenomenon and measure the solar diameter with the method of comparing the ephemerides with…