5,908 research outputs found
Partitions of the polytope of Doubly Substochastic Matrices
In this paper, we provide three different ways to partition the polytope of
doubly substochastic matrices into subpolytopes via the prescribed row and
column sums, the sum of all elements and the sub-defect respectively. Then we
characterize the extreme points of each type of convex subpolytopes. The
relations of the extreme points of the subpolytopes in the three partitions are
also given
On the maximum of the permanent of (I-A)
Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum
of all elements of A. In this paper we give the upper bound of the permanent of
(I-A) with respect to n and {\sigma}(A)
Unitarity Quadrangles of Four Neutrino Mixing
We present a classification of the unitarity quadrangles in the four-neutrino
mixing scheme. We find that there are totally thirty-six distinct topologies
among twelve different unitarity quadrangles. Concise relations are established
between the areas of those unitarity quadrangles and the rephasing invariants
of CP and violation.Comment: RevTex 10 pages. Minor changes made. Accepted for publication in
Phys. Rev.
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