17,371 research outputs found
Cohomology-Developed Matrices -- constructing families of weighing matrices and automorphism actions
The aim of this work is to construct families of weighing matrices via their
automorphism group action. This action is determined from the
-cohomology groups of the underlying abstract group. As a consequence,
some old and new families of weighing matrices are constructed. These include
the Paley Conference, the Projective-Space, the Grassmannian, and the
Flag-Variety weighing matrices. We develop a general theory relying on low
dimensional group-cohomology for constructing automorphism group actions, and
in turn obtain structured matrices that we call \emph{Cohomology-Developed
matrices}. This "Cohomology-Development" generalizes the Cocyclic and Group
Developments. The Algebraic structure of modules of Cohomology-Developed
matrices is discussed, and an orthogonality result is deduced. We also use this
algebraic structure to define the notion of \emph{Quasiproducts}, which is a
generalization of the Kronecker-product
Self-Dual codes from -matrices of skew symmetric type
Previously, self-dual codes have been constructed from weighing matrices, and
in particular from conference matrices (skew and symmetric). In this paper,
codes constructed from matrices of skew symmetric type whose determinants reach
the Ehlich-Wojtas' bound are presented. A necessary and sufficient condition
for these codes to be self-dual is given, and examples are provided for lengths
up to 52
Improved superposition schemes for approximate multi-caloron configurations
Two improved superposition schemes for the construction of approximate
multi-caloron-anticaloron configurations, using exact single (anti)caloron
gauge fields as underlying building blocks, are introduced in this paper. The
first improvement deals with possible monopole-Dirac string interactions
between different calorons with non-trivial holonomy. The second one, based on
the ADHM formalism, improves the (anti-)selfduality in the case of small
caloron separations. It conforms with Shuryak's well-known ratio-ansatz when
applied to instantons. Both superposition techniques provide a higher degree of
(anti-)selfduality than the widely used sum-ansatz, which simply adds the
(anti)caloron vector potentials in an appropriate gauge. Furthermore, the
improved configurations (when discretized onto a lattice) are characterized by
a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly
shortened, changes in the introduction, new results added on the comparison
with exact solution
Time-domain formulation of cold plasma based on mass-lumped finite elements
Recent advances in FDTD simulations of simple dielectrics have opened the possibility of various forms of local refinement [1]. These possibilities are based on writing FDTD as a special case of a finite element technique. We have shown [3] that these techniques can be extended to Body-Of-Revolution (BOR) FDTD which is well-suited for modelling toroidal cavities. Further extending this technique to the time-domain modelling of plasmas presents difficulties: The classical "Whitney" basis-functions (and their analogues in toroidal geometries) are insufficiently smooth to be used as "testing" functions the time-domain constitutive equations of cold plasma [2]. In this paper, we present a set of basis-functions that can be used to write time-domain cold plasma as a mass lumped finite element scheme
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