14,217 research outputs found
A note on a relationship between the inverse eigenvalue problems for nonnegative and doubly stochastic matrices and some applications
In this note, we establish some connection between the nonnegative inverse
eigenvalue problem and that of doubly stochastic one. More precisely, we prove
that if is the spectrum of an
nonnegative matrix A with Perron eigenvalue r, then there exists a least real
number such that is
the spectrum of an nonnegative generalized doubly stochastic matrix
for all As a consequence, any solutions for the nonnegative
inverse eigenvalue problem will yield solutions to the doubly stochastic
inverse eigenvalue problem. In addition, we give a new sufficient condition for
a stochastic matrix A to be cospectral to a doubly stochastic matrix B and in
this case B is shown to be the unique closest doubly stochastic matrix to A
with respect to the Frobenius norm. Some related results are also discussed.Comment: 8 page
Local boundedness property for parabolic BVP's and the gaussian upper bound for their Green functions
In the present note, we give a concise proof for the equivalence between the
local boundedness property for parabolic Dirichlet BVP's and the gaussian upper
bound for their Green functions. The parabolic equations we consider are of
general divergence form and our proof is essentially based on the gaussian
upper bound by Daners \cite{Da} and a Caccioppoli's type inequality. We also
show how the same analysis enables us to get a weaker version of the local
boundedness property for parabolic Neumann BVP's assuming that the
corresponding Green functions satisfy a gaussian upper bound
Investigative powers of the Egyptian Competition Authority: a guide for companies in the Egyptian market
This article explores the investigative powers of the Egyptian Competition Authority vis-Ã -vis companies under scrutiny and discerns whether the documents/correspondences exchanged between these companies, their in-house legal departments and; external consultants are legally privileged under relevant Egyptian laws and regulations
Continuous spin and tensionless strings
A classical action is proposed which upon quantisation yields massless
particles belonging to the continuous spin representation of the Poincar\'e
group. The string generalisation of the action is identical to the tensionless
extrinsic curvature action proposed by Savvidy. We show that the BRST
quantisation of the string action gives a critical dimension of 28. The
constraints result in a number of degrees of freedom which is the same as the
bosonic string.Comment: 13 pages; v2 added references; v3 discussion adde
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