Showing papers in "Advances in Applied Mathematics in 1994"

TL;DR: Convolution theorems generalizing well known and useful results from the abelian case are used to develop a sampling theorem on the sphere, which reduces the calculation of Fourier transforms and convolutions of band-limited functions to discrete computations.

TL;DR: In this paper, the authors show that two simplified versions of the problem belong to the class of NP-complete problems, which are conjectured to be computationally intractable.

TL;DR: In this article, a geometrical optics equation for the perturbed vorticity amplitude is derived, and it is shown that under certain conditions this equation can be solved explicitly.

TL;DR: In this article, a sequence of regularized inverses of the Laplace transform is constructed by relating this transform to a convolution operator for functions on the group of the positive real numbers with multiplication.

TL;DR: In this paper, the minimal and maximal operators of an elliptic pseudo-differential operator on Lp(Rn), 1 < p < ∞, were defined and proved to be equal.

TL;DR: In this article, the authors considered the inverse scattering problem for the Schrodinger equation in two dimensions and proposed an approximate solution based on the linearization through the weak scatterer (or Born) approximation.

TL;DR: In this paper, the reliability of a graph G is defined as the probability that G is connected, given that edges are independently operational with probability p, and various sequences associated with this polynomial have been conjectured to be unimodal and indeed, log concave.

TL;DR: In this paper, a strongly nonlinear integral equation of the Hammerstein type is considered, which arises from an important engineering application, and a realistic condition for the linear operator included in the equation is found which gives a precise, constructively built, solution.

TL;DR: In this paper, it was shown that the vector field x = y, y = -(x^3 - x - @l) + @e y(@a + @bx + x^2), @l, @e small, has 0, 1, 2, or 3 limit cycles.

TL;DR: In this article, it was shown that the extreme points of operators [0, A] are the Schur complements of a biharmonic equation in the general infinite dimensional case and necessary and sufficient conditions for an extreme point X"0 to be a short of A were given.

TL;DR: In this article, the authors studied nonlinear systems of ordinary differential equations that arise when considering stationary one-dimensional systems of conservation laws with forcing terms defined in a bounded interval, and they showed the existence of transonic solutions of bounded variation with strong shocks for the equation of stationary gas flow in a duct of variable area as a pointwise limit of artificial viscosity solutions.

TL;DR: In this paper, the authors partition the set of Latin squares of order n in four classes characterized by the values + +, + -, - +, and - - of a bidimensional analog of the sign of a permutation.

TL;DR: In this paper, the authors considered the discretized version of the wave equation, in which a manifold is replaced by a homogeneous tree and the time line was replaced by the natural numbers and gave two methods for finding a closed form of the solution.

TL;DR: In this paper, the authors obtained closed forms for the asymmetry index series?E±(x1, x2,...) and?ALT(x 1, x 2,...) of the species E± and ALT of oriented sets and even permutations.

TL;DR: In this paper, a necessary and sufficient condition for the convergence of non-randomly centered random sums under the hypothesis that sure sums of the same random variables converge is given, and the result contained here subsumes previous results of the authors and others.

TL;DR: In this paper, a constructive existence proof is given for a dumbbell-shaped solution near the two-sphere limit for a model of a steadily rigidly rotating liquid drop held together by surface tension.

TL;DR: In this article, it was shown that the probability distribution of the value of a homogeneous polynomial in two Gaussian variables determines the poynomial up to some explicitly described ambiguity.