135,326 research outputs found
The Average-Case Area of Heilbronn-Type Triangles
From among triangles with vertices chosen from points in
the unit square, let be the one with the smallest area, and let be the
area of . Heilbronn's triangle problem asks for the maximum value assumed by
over all choices of points. We consider the average-case: If the
points are chosen independently and at random (with a uniform distribution),
then there exist positive constants and such that for all large enough values of , where is the expectation of
. Moreover, , with probability close to one. Our proof
uses the incompressibility method based on Kolmogorov complexity; it actually
determines the area of the smallest triangle for an arrangement in ``general
position.''Comment: 13 pages, LaTeX, 1 figure,Popular treatment in D. Mackenzie, On a
roll, {\em New Scientist}, November 6, 1999, 44--4
Pade-resummed high-order perturbation theory for nuclear structure calculations
We apply high-order many-body perturbation theory for the calculation of
ground-state energies of closed-shell nuclei using realistic nuclear
interactions. Using a simple recursive formulation, we compute the perturbative
energy contributions up to 30th order and compare to exact no-core shell model
calculations for the same model space and Hamiltonian. Generally, finite
partial sums of this perturbation series do not show convergence with
increasing order, but tend to diverge exponentially. Nevertheless, through a
simple resummation via Pade approximants it is possible to extract rapidly
converging and highly accurate results for the ground state energy.Comment: 6 pages, 2 figures, 1 tabl
Follow-up of referrals to the Social Service Department from the Out-Patient Department at the Boston State Hospital during 1950.
Thesis (M.S.)--Boston Universit
Pinching of the First Eigenvalue of the Laplacian and almost-Einstein Hypersurfaces of the Euclidean Space
In this paper, we prove new pinching theorems for the first eigenvalue of the
Laplacian on compact hypersurfaces of the Euclidean space. These pinching
results are associated with the upper bound for the first eigenvalue in terms
of higher order mean curvatures. We show that under a suitable pinching
condition, the hypersurface is diffeomorpic and almost isometric to a standard
sphere. Moreover, as a corollary, we show that a hypersurface of the Euclidean
space which is almost Einstein is diffeomorpic and almost isometric to a
standard sphere.Comment: 18 page
- …