13,492 research outputs found
Thermodynamic Volume and the Extended Smarr Relation
We continue to explore the scaling transformation in the reduced action
formalism of gravity models. As an extension of our construction, we consider
the extended forms of the Smarr relation for various black holes, adopting the
cosmological constant as the bulk pressure as in some literatures on black
holes. Firstly, by using the quasi-local formalism for charges, we show that,
in a general theory of gravity, the volume in the black hole thermodynamics
could be defined as the thermodynamic conjugate variable to the bulk pressure
in such a way that the first law can be extended consistently. This, so called,
thermodynamic volume can be expressed explicitly in terms of the metric and
field variables. Then, by using the scaling transformation allowed in the
reduced action formulation, we obtain the extended Smarr relation involving the
bulk pressure and the thermodynamic volume. In our approach, we do not resort
to Euler's homogeneous scaling of charges while incorporating the would-be
hairy contribution without any difficulty.Comment: 1+21 pages, plain LaTeX; v2 typo fixed and references adde
New determination of based on recent experimental constraints
The symmetric and traceless part of the matrix element can be
determined from the second moment of the twist-3 parton distribution function
. Recently, novel experimental data on have become available,
which enables us to evaluate the magnitude of the above matrix element with
considerably reduced systematic uncertainties. Based on the new experimental
data, we show that is likely to be at least an order of magnitude smaller
than what previous model-based estimates have so far suggested. We discuss the
consequences of this observation for the analysis of deep inelastic scattering
and QCD sum rules studies at finite density for the vector meson and the
nucleon, in which this matrix element is being used as an input parameter.Comment: 22 pages, 4 figures, 4 tables; published versio
Finding branch-decompositions of matroids, hypergraphs, and more
Given subspaces of a finite-dimensional vector space over a fixed finite
field , we wish to find a "branch-decomposition" of these subspaces
of width at most , that is a subcubic tree with leaves mapped
bijectively to the subspaces such that for every edge of , the sum of
subspaces associated with leaves in one component of and the sum of
subspaces associated with leaves in the other component have the intersection
of dimension at most . This problem includes the problems of computing
branch-width of -represented matroids, rank-width of graphs,
branch-width of hypergraphs, and carving-width of graphs.
We present a fixed-parameter algorithm to construct such a
branch-decomposition of width at most , if it exists, for input subspaces of
a finite-dimensional vector space over . Our algorithm is analogous
to the algorithm of Bodlaender and Kloks (1996) on tree-width of graphs. To
extend their framework to branch-decompositions of vector spaces, we developed
highly generic tools for branch-decompositions on vector spaces. The only known
previous fixed-parameter algorithm for branch-width of -represented
matroids was due to Hlin\v{e}n\'y and Oum (2008) that runs in time
where is the number of elements of the input -represented
matroid. But their method is highly indirect. Their algorithm uses the
non-trivial fact by Geelen et al. (2003) that the number of forbidden minors is
finite and uses the algorithm of Hlin\v{e}n\'y (2005) on checking monadic
second-order formulas on -represented matroids of small
branch-width. Our result does not depend on such a fact and is completely
self-contained, and yet matches their asymptotic running time for each fixed
.Comment: 73 pages, 10 figure
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