34,300 research outputs found
Surjectivity of maps induced on matrices by polynomials and entire functions
We determine a necessary and sufficient condition for a polynomial over an
algebraically closed field to induce a surjective map on matrix algebras
for . The criterion is given in terms of critical points and
uses simple linear algebra. Following that, we formulate and prove a
corresponding result for entire functions as well.Comment: 5 pages, shortened the document, added an important result in the
end, added reference
Longitudinal momentum densities in transverse plane for nucleons
We present a study of longitudinal momentum densities ()
in the transverse impact parameter space for and quarks in both
unpolarized and transversely polarized nucleons by taking a two dimensional
Fourier transform of the gravitational form factors with respect to the
momentum transfer in the transverse direction. The gravitational form factors
are obtained by the second moments of GPDs. Here we consider the GPDs of two
different soft-wall models in AdS/QCD correspondence.Comment: 12 pages, 9 figures; text modifie
On topological upper-bounds on the number of small cuspidal eigenvalues
Let be a noncompact, finite area hyperbolic surface of type . Let
denote the Laplace operator on . As varies over the {\it
moduli space} of finite area hyperbolic surfaces of type
, we study, adapting methods of Lizhen Ji \cite{Ji} and Scott Wolpert
\cite{Wo}, the behavior of {\it small cuspidal eigenpairs} of . In
Theorem 2 we describe limiting behavior of these eigenpairs on surfaces when converges to a point in
. Then we consider the -th {\it cuspidal
eigenvalue}, , of . Since {\it
non-cuspidal} eigenfunctions ({\it residual eigenfunctions} or {\it generalized
eigenfunctions}) may converge to cuspidal eigenfunctions, it is not known if
is a continuous function. However, applying Theorem 2 we
prove that, for all , the sets are open and contain a neighborhood of
in
. Moreover, using topological properties of
nodal sets of {\it small eigenfunctions} from \cite{O}, we show that
contains a neighborhood of
in
. These results provide evidence in support of a
conjecture of Otal-Rosas \cite{O-R}.Comment: 24 pages, 1 figur
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