10,408 research outputs found
On the number of nonequivalent propelinear extended perfect codes
The paper proves that there exist an exponential number of nonequivalent
propelinear extended perfect binary codes of length growing to infinity.
Specifically, it is proved that all transitive extended perfect binary codes
found by Potapov are propelinear. All such codes have small rank, which is one
more than the rank of the extended Hamming code of the same length. We
investigate the properties of these codes and show that any of them has a
normalized propelinear representation
Field sources in a Lorentz symmetry breaking scenario with a single background vector
This paper is devoted to investigating the interactions between stationary
sources of the electromagnetic field, in a model which exhibits explicit
Lorentz-symmetry breaking due to the presence of a single background vector. We
focus on physical phenomena that emerge from this kind of breaking and which
have no counterpart in Maxwell Electrodynamics
Department of Applied Mathematics Academic Program Review, Self Study / June 2010
The Department of Applied Mathematics has a multi-faceted mission to provide an exceptional mathematical education focused on the unique needs of NPS students, to conduct relevant research, and to provide service to the broader community. A strong and vibrant Department of Applied Mathematics is essential to the university's goal of becoming a premiere research university. Because research in mathematics often impacts science and engineering in surprising ways, the department encourages mathematical explorations in a broad range of areas in applied mathematics with specific thrust areas that support the mission of the school
Fast Compensated Algorithms for the Reciprocal Square Root, the Reciprocal Hypotenuse, and Givens Rotations
The reciprocal square root is an important computation for which many very
sophisticated algorithms exist (see for example \cite{863046,863031} and the
references therein). In this paper we develop a simple differential
compensation (much like those developed in \cite{borges}) that can be used to
improve the accuracy of a naive calculation. The approach relies on the use of
the fused multiply-add (FMA) which is widely available in hardware on a variety
of modern computer architectures. We then demonstrate how to combine this
approach with a somewhat inaccurate but fast square root free method for
estimating the reciprocal square root to get a method that is both fast (in
computing environments with a slow square root) and, experimentally, highly
accurate. Finally, we show how this same approach can be extended to the
reciprocal hypotenuse calculation and, most importantly, to the construction of
Givens rotations
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