Virtual knots, defined by Kauffman, provide a natural generalization of classical knots. Most invariants of knots extend in a natural way to give invariants of virtual knots. In this paper we study the fundamental groups of virtual knots and observe several new and unexpected phenomena. In the classical setting, if the longitude of a knot is trivial in the knot group then the group is infinite ...

The distribution of the solar cosmic radiation flux over the earth is not uniform, but the result of complex phenomena involving the interplanetary magnetic field, the geomagnetic field and latitude and longitude of locations on the earth. The latitude effect relates to the geomagnetic shield; the longitude effect relates to local time. For anisotropic solar cosmic ray events the maximum partic...

Working with the mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth, as is considered i...

When releasing data to the public, data stewards are ethically and often legally obligated to protect the confidentiality of data subjects' identities and sensitive attributes. They also strive to release data that are informative for a wide range of secondary analyses. Achieving both objectives is particularly challenging when data stewards seek to release highly resolved geographical informat...

[1] Using densities measured by accelerometers on the CHAMP and GRACE satellites, and taking advantage of the local time precession characteristics of these near-polar orbiting satellites, exosphere temperatures are derived as a function of local time, longitude and latitude. Significant longitude variability (e.g., ±25K maximum to minimum over the equator) in geomagnetically-quiet exosphere te...

Résumé. Nous présentons une étude pour la prédiction des trajectoires de cyclones dans l’océan Atlantique Nord à partir de données issues d’images satellites. On y extrait des mesures de vitesses de vent, de vorticité, d’humidité (base JRA-25) et des mesures de latitude, de longitude et de vitesse de vent instantanée des cyclones toutes les 6 heures (base IBTrACS). Les modèles de référence à ce...

Even before any numerical considerations are confronted, we run into difficulties simply in specifying a coordinate system. It is important to distinguish between true scalarvalued and vector-valued functions. The value of a scalar function, say temperature, is independent of coordinate system. That is, the temperature at some point in space is the same regardless of how we define the position ...

A high-order monotone and conservative Cascade Remapping algorithm between Spherical grids (CaRS) is developed. This algorithm is specifically designed to remap between the cubed-sphere and regular latitude-longitude grids. The remapping approach is based on the conservative cascade method in which a two-dimensional remapping problem is split into two one-dimensional problems. This allows for e...

We present evidence for a substantial overdensity of stars in the direction of the constellations of Hercules and Aquila. The Cloud is centered at a Galactic longitude of l ≈ 40◦ and extends above and below the Galactic plane by at least 50◦. Given its off-centeredness and height, it is unlikely that the Hercules-Aquila Cloud is related to the bulge or thick disk. More likely, this is a new str...

Population counts and longitude and latitude coordinates were estimated for the 50 largest cities in the United States by computational linguistic techniques and by human participants. The mathematical technique Latent Semantic Analysis applied to newspaper texts produced similarity ratings between the 50 cities that allowed for a multidimensional scaling (MDS) of these cities. MDS coordinates ...