In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...

Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O( √ n) repetitions of the base algorithms and with high probability finds the index of a 1-bit among these n bits (if there is such an index). This shows that it is not necessary to first significantly reduce the error probability in the ba...

For a graph G, a random n-lift of G has the vertex set V (G) n] and for each edge u; v] 2 E(G), there is a random matching between fug n] and fvg n]. We present bounds on the chromatic number and on the independence number of typical random lifts, with G xed and n ! 1. For the independence number, upper and lower bounds are obtained as solutions to certain optimization problems on the base grap...

A micropaleontological study has been carried out on the samples collected from the Sarv Abad section, the oldest and only known Jurassic sedimentary rocks cropping out in the Moghan area. Studied sequence consists of carbonates bounded at both base and top by clastic deposits. Studied carbonate deposits provide an assemblage of benthic foraminifera as well as calcareous algae. The stratigraphi...

One basic property of the boosting algorithm is its ability to reduce the training error, subject to the critical assumption that the base learners generatèweak' (or more appropriately, `weakly accurate') hypotheses that are better that random guessing. We exploit analogies between regression and classiication to give a characterization on what base learners generate weak hypotheses, by introdu...

A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

For any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consist entirely of bounded elements. It is not too stringent, and is satisfied, for instance, by rings of ...