Collisions in the asteroid belt frequently lead to catastrophic breakups, where more than half of the target's mass is ejected into space. Several dozen large asteroids have been disrupted by impacts over the past several billion years. These impact events have produced groups of fragments with similar orbits called asteroid families. Here we report the discovery of a very young asteroid family...

The combinatorics of certain tuples of osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. The paths being considered have fixed start and end points on respectively the lower and right boundaries of a rectangle in the square lattice, each path can take only unit steps rightwards or upwards, and two different paths within a tuple are permitted to share...

We consider the problem of computing stereo correspondence for scenes dense in physical structure, such as a bouquet of flowers. Boundaries are then space curves, formally governed by the projective geometry induced by the stereo camera configuration and by the differential structure of the curves in the scene. We propose that the correspondence problem can be solved by relating the differentia...

Both orbital and rotational dynamics employ the method of variation of parameters. We express, in a non-perturbed setting, the coordinates (Cartesian, in the orbital case, or Eulerian in the rotation case) via the time and six adjustable constants called elements (orbital elements or rotational elements). If, under disturbance, we use this expression as ansatz and endow the “constants” with tim...

Both orbital and rotational dynamics employ the method of variation of parameters. We express, in a non-perturbed setting, the coordinates (Cartesian, in the orbital case, or Eulerian in the rotation case) via the time and six adjustable constants called elements (orbital elements or rotational elements). If, under disturbance, we use this expression as ansatz and endow the “constants” with tim...

A curve on a sphere, aane or projective space is called nondegenerate if its osculating frame is nondegenerate at every point. We calculate the number of connected components in the space of all closed nondegenerate curves immersed into S n ; R n or P n. In the cases of S n or R n it is equal to 4 for odd n > 3 and 6 for even n > 4 (for S 2 the answer is also 6). For projective space P n the nu...