1,276 research outputs found
Transitive matrices, strict preference and intensity operators
Let X be a set of alternatives and a_{ij} a positive number expressing how much the alternative x_{i} is preferred to the alternative x_{j}. Under suitable hypothesis of no indifference and transitivity over the pairwise comparison matrix A= (a_{ij}), the alternatives can be ordered as a chain . Then a coherent priority vector is a vector giving a weighted ranking agreeing with the obtained chain and an intensity vector is a coherent priority vector encoding information about the intensities of the preferences. In the paper we look for operators F that, acting on the row vectors translate the matrix A in an intensity vector
Supertubes in Matrix model and DBI action
We show the equivalence between the supertube solutions with an arbitrary
cross section in two different actions, the DBI action for the D2-brane and the
matrix model action for the D0-branes. More precisely, the equivalence between
the supertubes in the D2-brane picture and the D0-brane picture is shown in the
boundary state formalism which is valid for all order in \alpha'. This is an
application of the method using the infinitely many D0-branes and
anti-D0-branes which was used to show other equivalence relations between two
seemingly different D-brane systems, including the D-brane realization of the
ADHM construction of instanton. We also apply this method to the superfunnel
type solutions successfully.Comment: 24 pages, references added, version to appear in JHE
The Non-Abelian Self-Dual String and the (2,0)-Theory
We argue that the relevant higher gauge group for the non-abelian
generalization of the self-dual string equation is the string 2-group. We then
derive the corresponding equations of motion and discuss their properties. The
underlying geometric picture is a string structure, i.e. a categorified
principal bundle with connection whose structure 2-group is the string 2-group.
We readily write down the explicit elementary solution to our equations, which
is the categorified analogue of the 't Hooft-Polyakov monopole. Our solution
passes all the relevant consistency checks; in particular, it is globally
defined on and approaches the abelian self-dual string of charge
one at infinity. We note that our equations also arise as the BPS equations in
a recently proposed six-dimensional superconformal field theory and we show
that with our choice of higher gauge structure, the action of this theory can
be reduced to four-dimensional supersymmetric Yang-Mills theory.Comment: v3: 1+42 pages, presentation improved, typos fixed, published versio
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