133,868 research outputs found
NASA-ARC 91.5-cm airborne infrared telescope
A 91.5 cm aperture telescope installed aboard NASA-Lockheed C-141A aircraft for the performance of infrared astronomy is described. A unique feature of the telescope is that its entire structure is supported by a 41 cm spherical air bearing which effectively uncouples it from aircraft angular motion, and with inertial stabilization and star tracking, limits tracking errors to less than 1 arc second in most applications. A general description of the system, a summary of its performance, and a detailed description of an offset tracking mechanism is presented
Plane curves in boxes and equal sums of two powers
Given an absolutely irreducible ternary form , the purpose of this paper
is to produce better upper bounds for the number of integer solutions to the
equation F=0, that are restricted to lie in very lopsided boxes. As an
application of the main result, a new paucity estimate is obtained for equal
sums of two like powers.Comment: 15 pages; to appear in Math. Zei
Quadratic polynomials represented by norm forms
The Hasse principle and weak approximation is established for equations of
the shape P(t)=N(x_1,x_2,x_3,x_4), where P is an irreducible quadratic
polynomial in one variable and N is a norm form associated to a quartic
extension of the rationals containing the roots of P. The proof uses analytic
methods.Comment: 55 page
The density of rational points on non-singular hypersurfaces, II
For any integers , let be a non-singular hypersurface of degree that is defined over . The main result in this paper is a proof that the number of -rational points on which have height at most satisfies
for any . The implied constant in this estimate depends at most upon and
A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem
This paper is the second in a series exploring the properties of a functor
which assigns a homotopy double groupoid with connections to a Hausdorff space.
We show that this functor satisfies a version of the van Kampen theorem, and
so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems.
The methods are analogous to those developed by Brown and Higgins for similar
theorems for other higher homotopy groupoids.
An integral part of the proof is a detailed discussion of commutative cubes
in a double category with connections, and a proof of the key result that any
composition of commutative cubes is commutative. These results have recently
been generalised to all dimensions by Philip Higgins.Comment: 19 pages, uses picte
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