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In this note we study the zeros of solutions of differential equations of the form u + pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given. §1. Number of zeros. Consider the linear differential equation u′′(x) + p(x) u(x) = 0 , where p(x) = 1 (1− x) , (1) on the interval −1 < x < 1. Two independent(More)
We study the problem of interpolating all values of a discrete signal f of length N when d &lt;; N values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set J; these comprise the (generalized) bandlimited spaces B<sup>J</sup>. The sampling pattern for f is specified by an index set I, and is(More)
This note is a sequel to our paper [OS] where we generalized the Schwarzian derivative to conformal mappings of Riemannian manifolds. There we found that many of the phenomena familiar from the classical theory have counterparts in the more general setting. Here we advance this another step by giving a generalization of the well known univalence criterion(More)
Any isospectral family of two-dimensional Euclidean domains is shown to be compact in the C(infinity) topology. Previously Melrose, using heat invariants, was able to establish the C(infinity) compactness of the curvature of the boundary curves. The additional ingredient used in this paper to obtain the compactness of the domains is the behavior of the(More)
In this paper we investigate the geometry of the quasihyperbolic metric of domains in R". This metric arises from the conformally flat generalized Riemannian metric d(x, aD)' ldx I. Due to the fact that the density cl(x, aD) -t is not necessarily differentiable, the classical theories of Riemannian geometry do not apply to this metric. The quasihyperbolic(More)
A geometric interpretation of the Schwarzian of a harmonic mapping is given in terms of geodesic curvature on the associated minimal surface, generalizing a classical formula for analytic functions. A formula for curvature of image arcs under harmonic mappings is applied to derive a known result on concavity of the boundary. It is also used to characterize(More)
Because recombinant interleukin 2 (rIL-2) and recombinant alpha-interferon (rIFN-alpha) exhibit synergistic antitumor activity in C3HMT1820 T-cell lymphoma and B16 melanoma tumor systems, we have performed a Phase I study of this combination in 55 patients with advanced malignancies for whom no standard therapy exists. Successive groups of greater than or(More)
All Rights Reserved ii I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of(More)