Algebraic geometry is the mathematical study of geometric objects by means of algebra. Its origins go back to the coordinate geometry introduced by Descartes. A classic example is the circle of radius 1 in the plane, which is

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Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in terms of order, radius and minimum degree. Our result is a strengthening of an old classical theorem of Vizing (1967) if minimum degree is prescribed.

the physical radius is known independently, asteroseismic data can help constrain evolutionary models particularly well, and these are therefore good candidates for observation with MONS. 1. Introduction It is well-known that there is a tendency for all M giants to be variable. The brightness changes can

We study the covering radius of sets of permutations with respect to the Hamming distance. Let f(n, s) be the smallest number m for which there is a set of m permu-tations in Sn with covering radius r ≤ n − s. We study f(n, s) in the general case and also in the case when the set of permutations

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Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum

-homogeneous polynomials such that f(x) = P1 n=0 Pn(x) for all x 2 B, which is called the Taylor series expansion for f about 0. G. Lumer [13] has given a theory of the numerical range for bounded lin-ear operators on a Banach space which is a very successful generalization of the classical theory on a Hilbert space

This paper concerns the coherent states on spheres studied by the authors in [J. Math. Phys. 43 (2002), 1211-1236]. We show that in the odd-dimensional case the coherent states on the sphere approach the classical Gaussian coherent states on Euclidean space as the radius of the sphere tends

Duality under inversion of the cosmological scale factor is discussed both for the classical motion of strings in cosmological backgrounds and for genus zero, low energy effective actions. The string-modified, Einstein-Friedmann equations are then shown to possess physically-inequivalent, duality