FAVOLASCHIA DYBOWSKYANA (SINGER) SINGER (APHYLLOPHORALES), A NEW ORCHID MYCORRHIZAL FUNGUS FROM TROPICAL AFRICA

LDPC codes from Singer cycles

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...

Wolf Singer

Nilpotent Singer Groups

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

The Kadison-Singer Conjecture

We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...

Kadison–singer from Mathematical Physics: an Introduction

We give an informal overview of the Kadison–Singer extension problem with emphasis on its initial connections to Dirac’s formulation of quantum mechanics. Let H be an infinite dimensional separable Hilbert space, and B (H) the algebra of all bounded operators in H. In the language of operator algebras, the Kadison–Singer problem asks whether or not for a given MASA D in B (H), every pure state ...