We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it.

exponentially fast in the length of the code with arbitrarily small loss in rate.) Conversely, transmitting at rates above this capacity the probability of error is bounded away from zero by a strictly positive constant which is independent of the length of the code and of the number of iterations performed

Abstract. We obtain height estimates for compact embedded surfaces with positive constant mean curvature in a Riemannian product space M 2 × R and boundary on a slice. We prove that these estimates are optimal for the homogeneous spaces R 3 , S 2 × R and H 2 × R and we characterize the surfaces

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 2000 Mathematics Subject Classification: 53C60, 53C25. 1

about the way in which expectancy improves performance. First, when subjects are cued on each trial, they show stronger expectancy effects than when a probable position is held constant for a block, indicating the active nature of the expectancy. Second, while information on spatial position improves

in the form of abstract domains modelling sets of values, projections, or partial equivalence relations. The approach tends to focus more directly on discovering the extensional properties of interest: for constant propagation it might operate on sets of values with constancy corresponding to singletons

perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered

We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts

, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unit-normed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability

. Such an optimum can be realized in a market if perfectly discriminatory pricing is possible. Otherwise we face conflicting problems. A competitive market fulfilling the marginal condition would be unsustainable because total profits would be negative. An element of monopoly would allow positive profits, but would