93,333 research outputs found
Digital modulator and demodulator Patent
Development of apparatus for generating output signal commensurate with information contained in input signa
A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice
Species doubling is a problem that infects most numerical methods that use a
spatial lattice. An understanding of species doubling can be found in the
Nielsen-Ninomiya theorem which gives a set of conditions that require species
doubling. The transverse lattice approach to solving field theories, which has
at least one spatial lattice, fails one of the conditions of the
Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the
standard Lagrangian formulation of the transverse lattice. We will show that
the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the
transverse lattice does not have species doubling.Comment: 4 pages, v2: a reference and comments added, the version to appear in
Phys. Rev.
Configurations, and parallelograms associated to centers of mass
The purpose of this article is to
\begin{enumerate}
\item define the -fold center of mass arrangement for points
in the plane,
\item give elementary properties of and
\item give consequences concerning the space of distinct points
in the plane, no four of which are the vertices of a parallelogram.
\end{enumerate}
The main result proven in this article is that the classical unordered
configuration of points in the plane is not a retract up to homotopy of the
space of unordered distinct points in the plane, no four of which are the
vertices of a parallelogram. The proof below is homotopy theoretic without an
explicit computation of the homology of these spaces.
In addition, a second, speculative part of this article arises from the
failure of these methods in the case of odd primes . This failure gives rise
to a candidate for the localization at odd primes of the double loop space
of an odd sphere obtained from the -fold center of mass arrangement.
Potential consequences are listed.Comment: 11 page
On injective homomorphisms for pure braid groups, and associated Lie algebras
The question of whether a representation of Artin's pure braid group is
faithful is translated to certain properties of the Lie algebra arising from
the descending central series of the pure braid group, and thus the Vassiliev
invariants of pure braids via work of T. Kohno \cite{kohno1,kohno2}. The main
result is a Lie algebraic condition which guarantees that a homomorphism out of
the classical pure braid group is faithful. However, it is unclear whether the
methods here can be applied to any open cases such as the Gassner
representation.Comment: Change in Contex
The stable braid group and the determinant of the Burau representation
This article gives certain fibre bundles associated to the braid groups which
are obtained from a translation as well as conjugation on the complex plane.
The local coefficient systems on the level of homology for these bundles are
given in terms of the determinant of the Burau representation.
De Concini, Procesi, and Salvetti [Topology 40 (2001) 739--751] considered
the cohomology of the n-th braid group B_n with local coefficients obtained
from the determinant of the Burau representation, H^*(B_n;Q[t^{+/-1}]). They
show that these cohomology groups are given in terms of cyclotomic fields.
This article gives the homology of the stable braid group with local
coefficients obtained from the determinant of the Burau representation. The
main result is an isomorphism
H_*(B_infty; F[t^{+/-1}])-->H_*(Omega^2S^3; F) for any field F where
Omega^2S^3 denotes the double loop space of the 3-connected cover of the
3-sphere. The methods are to translate the structure of H_*(B_n;F[t^{+/-1}]) to
one concerning the structure of the homology of certain function spaces where
the answer is computed.Comment: This is the version published by Geometry & Topology Monographs on 29
January 200
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