A universal effective quantum number for centrally symmetric problems

On the number of faces of centrally-symmetric simplicial polytopes

I. Bfirfiny and L. Lovfisz [Acta Math. Acad. Sci. Hung. 40, 323-329 (1982)] showed that a d-dimensional centrally-symmetric simplicial polytope ~ has at least 2 d facets, and conjectured a lower bound for the number f~ of i-dimensional faces o f ~ in terms ofd and the number f0 = 2n of d vertices. Define integers ho . . . . . he by Z f~-1(x 1) d-' = ~ hi xd-'. A. Bj6rner conjectured (uni=O i=O ...

Remarks on axially and centrally symmetric elasticity problems

The solutions to axially and centrally symmetric Lamé problems are derived within the displacement, stress and strain-based approach by the specification of the general boundary conditions which encompass all possible combinations of kinematic and kinetic conditions at the inner and outer boundaries. It is shown that the mathematical structure of the governing differential equations in the stra...

Single-query quantum algorithms for symmetric problems

Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle problems, including the GROUP MULTIPLICATION problem, in which the product of an ordered n-tuple of group elements is to be determined by querying elements of...

UPPER BOUNDS FOR THE COVERING NUMBER OF CENTRALLY SYMMETRIC CONVEX BODIES IN Rn

The covering number c(K) of a convex body K is the least number of smaller homothetic copies of K needed to cover K . We provide new upper bounds for c(K) when K is centrally symmetric by introducing and studying the generalized α -blocking number βα 2 (K) of K . It is shown that when a centrally symmetric convex body K is sufficiently close to a centrally symmetric convex body K′ , then c(K) i...

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