Decreasing Rearrangements and Doubly Stochastic Operators

Random Rearrangements and Operators

Doubly diastereoselective [3,3]-sigmatropic aza-Claisen rearrangements.

The doubly diastereoselective [3,3]-sigmatropic aza-Claisen rearrangement of silylketene aminals derived from 5-substituted (3S,4E,alphaR)-1-benzyloxy-3-[N-acyl-N-(alpha-methylbenzyl)amino]pent-4-enes furnishes 2,3-disubstituted (R)-N-alpha-methylbenzyl (2S,3R,4E)-7-benzyloxyhept-4-enamides in >90% de under the "matched" control of both stereogenic centres. Rearrangement of the "mismatched" dia...

Parametrizing Doubly Stochastic Measures

Doubly stochastic measures can be identi ed with the trace of a pair of (Lebesgue) measure preserving maps of the unit interval to itself. It has been of traditional interest in probability theory to produce a random vector (or metric space element), which has a given distribution and is de ned on a standard space, such as [0; 1] endowed with Lebesgue measure. In a classic work, L evy [4, secti...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

Doubly stochastic matrices of trees

In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices I...