15,302 research outputs found
On two conjectures concerning convex curves
We recall two basic conjectures on the developables of convex projective
curves, prove one of them and disprove the other in the firdt nontrivial case
of curves in RP^3. Namely, we show that i) the tangent developable surface of
any convex curve in RP^3 has 'degree' 4 and ii) construct an example of 4
tangent lines to a convex curve in RP^3 such that no real line intersects all
four of them.Comment: AMSTEX, 15 pages, 3 eps pictures. to appear in Int. J. Mat
Region of the anomalous compression under Bondi-Hoyle accretion
We investigate the properties of an axisymmetric non-magnetized gas flow
without angular momentum on a small compact object, in particular, on a
Schwarzschild black hole in the supersonic region near the object; the velocity
of the object itself is assumed to be low compared to the speed of sound at
infinity. First of all, we see that the streamlines intersect (i.e., a caustic
forms) on the symmetry axis at a certain distance from the center on the
front side if the pressure gradient is neglected. The characteristic radial
size of the region, in which the streamlines emerging from the sonic surface at
an angle no larger than to the axis intersect, is To refine the flow structure in this region, we numerically
compute the system in the adiabatic approximation without ignoring the
pressure. We estimate the parameters of the inferred region with anomalously
high matter temperature and density accompanied by anomalously high energy
release.Comment: 10 pages, 2 figure
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