30,782 research outputs found
The inertia of weighted unicyclic graphs
Let be a weighted graph. The \textit{inertia} of is the triple
, where
are the number of the positive, negative and zero
eigenvalues of the adjacency matrix of including their
multiplicities, respectively. , is called the
\textit{positive, negative index of inertia} of , respectively. In this
paper we present a lower bound for the positive, negative index of weighted
unicyclic graphs of order with fixed girth and characterize all weighted
unicyclic graphs attaining this lower bound. Moreover, we characterize the
weighted unicyclic graphs of order with two positive, two negative and at
least zero eigenvalues, respectively.Comment: 23 pages, 8figure
Designer Topological Insulators in Superlattices
Gapless Dirac surface states are protected at the interface of topological
and normal band insulators. In a binary superlattice bearing such interfaces,
we establish that valley-dependent dimerization of symmetry-unrelated Dirac
surface states can be exploited to induce topological quantum phase
transitions. This mechanism leads to a rich phase diagram that allows us to
design strong, weak, and crystalline topological insulators. Our ab initio
simulations further demonstrate this mechanism in [111] and [110] superlattices
of calcium and tin tellurides.Comment: 5 pages, 4 figure
The geometric mean is a Bernstein function
In the paper, the authors establish, by using Cauchy integral formula in the
theory of complex functions, an integral representation for the geometric mean
of positive numbers. From this integral representation, the geometric mean
is proved to be a Bernstein function and a new proof of the well known AG
inequality is provided.Comment: 10 page
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