61,932 research outputs found
Structural Analysis of Boolean Equation Systems
We analyse the problem of solving Boolean equation systems through the use of
structure graphs. The latter are obtained through an elegant set of
Plotkin-style deduction rules. Our main contribution is that we show that
equation systems with bisimilar structure graphs have the same solution. We
show that our work conservatively extends earlier work, conducted by Keiren and
Willemse, in which dependency graphs were used to analyse a subclass of Boolean
equation systems, viz., equation systems in standard recursive form. We
illustrate our approach by a small example, demonstrating the effect of
simplifying an equation system through minimisation of its structure graph
Relativistic bound-state equations in three dimensions
Firstly, a systematic procedure is derived for obtaining three-dimensional
bound-state equations from four-dimensional ones. Unlike ``quasi-potential
approaches'' this procedure does not involve the use of delta-function
constraints on the relative four-momentum. In the absence of negative-energy
states, the kernels of the three-dimensional equations derived by this
technique may be represented as sums of time-ordered perturbation theory
diagrams. Consequently, such equations have two major advantages over
quasi-potential equations: they may easily be written down in any Lorentz
frame, and they include the meson-retardation effects present in the original
four-dimensional equation. Secondly, a simple four-dimensional equation with
the correct one-body limit is obtained by a reorganization of the generalized
ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving
three-dimensional equations is applied to this four-dimensional equation, thus
yielding a retarded interaction for use in the three-dimensional bound-state
equation of Wallace and Mandelzweig. The resulting three-dimensional equation
has the correct one-body limit and may be systematically improved upon. The
quality of the three-dimensional equation, and our general technique for
deriving such equations, is then tested by calculating bound-state properties
in a scalar field theory using six different bound-state equations. It is found
that equations obtained using the method espoused here approximate the wave
functions obtained from their parent four-dimensional equations significantly
better than the corresponding quasi-potential equations do.Comment: 28 pages, RevTeX, 6 figures attached as postscript files. Accepted
for publication in Phys. Rev. C. Minor changes from original version do not
affect argument or conclusion
Ising spin glass models versus Ising models: an effective mapping at high temperature II. Applications to graphs and networks
By applying a recently proposed mapping, we derive exactly the upper phase
boundary of several Ising spin glass models defined over static graphs and
random graphs, generalizing some known results and providing new ones.Comment: 11 pages, 1 Postscript figur
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