11,762 research outputs found
The dynamical second-order transport coefficients of smeared Dp-brane
The smeared Dp-brane is constructed by having the black Dp-brane uniformly
smeared over several transverse directions. After integrating the spherical
directions and the smeared directions, the smeared Dp-brane turns out to be a
Chamblin-Reall model with one background scalar field. Within the framework of
the fluid/gravity correspondence, we not only prove the equivalence between the
smeared Dp-brane and the compactified Dp-brane by explicitly calculating the 7
dynamical second-order transport coefficients of their dual relativistic
fluids, but also revisit the Correlated Stability Conjecture for the smeared
Dp-brane via the fluid/gravity correspondence.Comment: 25pages, 2 table
Distribution of zeros of matching polynomials of hypergraphs
Let \h be a connected -graph with maximum degree and
let \mu(\h, x) be the matching polynomial of \h. In this paper, we focus on
studying the distribution of zeros of the matching polynomials of -graphs.
We prove that the zeros (with multiplicities) of \mu(\h, x) are invariant
under a rotation of an angle in the complex plane for some
positive integer and is the maximum integer with this property. Let
\lambda(\h) denote the maximum modulus of all zeros of \mu(\h, x). We show
that \lambda(\h) is a simple root of \mu(\h, x) and \Delta^{1\over k}
\leq \lambda(\h)< \frac{k}{k-1}\big((k-1)(\Delta-1)\big)^{1\over k}. To
achieve these, we introduce the path tree \T(\h,u) of \h with respect to a
vertex of \h, which is a -tree, and prove that
\frac{\mu(\h-u,x)}{\mu(\h, x)} = \frac{\mu(\T(\h,u)-u,x)
}{\mu(\T(\h,u),x)}, which generalizes the celebrated Godsil's identity on the
matching polynomial of graphs
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