432 research outputs found
Relativity in Introductory Physics
A century after its formulation by Einstein, it is time to incorporate
special relativity early in the physics curriculum. The approach advocated here
employs a simple algebraic extension of vector formalism that generates
Minkowski spacetime, displays covariant symmetries, and enables calculations of
boosts and spatial rotations without matrices or tensors. The approach is part
of a comprehensive geometric algebra with applications in many areas of
physics, but only an intuitive subset is needed at the introductory level. The
approach and some of its extensions are given here and illustrated with
insights into the geometry of spacetime.Comment: 29 pages, 5 figures, several typos corrected, some discussion
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Flux Compactifications of String Theory on Twisted Tori
Global aspects of Scherk-Schwarz dimensional reduction are discussed and it
is shown that it can usually be viewed as arising from a compactification on
the compact space obtained by identifying a (possibly non-compact) group
manifold G under a discrete subgroup Gamma, followed by a truncation. This
allows a generalisation of Scherk-Schwarz reductions to string theory or
M-theory as compactifications on G/Gamma, but only in those cases in which
there is a suitable discrete subgroup of G. We analyse such compactifications
with flux and investigate the gauge symmetry and its spontaneous breaking. We
discuss the covariance under O(d,d), where d is the dimension of the group G,
and the relation to reductions with duality twists. The compactified theories
promote a subgroup of the O(d,d) that would arise from a toroidal reduction to
a gauge symmetry, and we discuss the interplay between the gauge symmetry and
the O(d,d,Z) T-duality group, suggesting the role that T-duality should play in
such compactifications.Comment: 43 page
Some Results on Generalized Complementary Basic Matrices and Dense Alternating Sign Matrices
The first part of this dissertation answers the questions posed in the article ``A note on permanents and generalized complementary basic matrices , {\it Linear Algebra Appl.} 436 (2012), by M. Fiedler and F. Hall. Further results on permanent compounds of generalized complementary basic matrices are obtained. Most of the results are also valid for the determinant and the usual compound matrix. Determinant and permanent compound products which are intrinsic are also considered, along with extensions to total unimodularity.
The second part explores some connections of dense alternating sign matrices with total unimodularity, combined matrices, and generalized complementary basic matrices.
In the third part of the dissertation, an explicit formula for the ranks of dense alternating sign matrices is obtained. The minimum rank and the maximum rank of the sign pattern of a dense alternating sign matrix are determined. Some related results and examples are also provided
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