9,045 research outputs found
How to determine linear complexity and -error linear complexity in some classes of linear recurring sequences
Several fast algorithms for the determination of the linear complexity of -periodic sequences over a finite
field \F_q, i.e. sequences with characteristic polynomial , have been proposed in the literature.
In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic
polynomial for an arbitrary positive integer , and are presented.
The result is then utilized to establish a fast algorithm for determining the -error linear complexity of
binary sequences with characteristic polynomial
Polynomial super-gl(n) algebras
We introduce a class of finite dimensional nonlinear superalgebras providing gradings of . Odd generators close by anticommutation on polynomials (of
degree ) in the generators. Specifically, we investigate `type I'
super- algebras, having odd generators transforming in a single
irreducible representation of together with its contragredient.
Admissible structure constants are discussed in terms of available
couplings, and various special cases and candidate superalgebras are identified
and exemplified via concrete oscillator constructions. For the case of the
-dimensional defining representation, with odd generators , and even generators , , a three
parameter family of quadratic super- algebras (deformations of
) is defined. In general, additional covariant Serre-type conditions
are imposed, in order that the Jacobi identities be fulfilled. For these
quadratic super- algebras, the construction of Kac modules, and
conditions for atypicality, are briefly considered. Applications in quantum
field theory, including Hamiltonian lattice QCD and space-time supersymmetry,
are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and
reference [60
A Grassmann Path From AdS_3 to Flat Space
We show that interpreting the inverse AdS_3 radius 1/l as a Grassmann
variable results in a formal map from gravity in AdS_3 to gravity in flat
space. The underlying reason for this is the fact that ISO(2,1) is the
Inonu-Wigner contraction of SO(2,2). We show how this works for the
Chern-Simons actions, demonstrate how the general (Banados) solution in AdS_3
maps to the general flat space solution, and how the Killing vectors, charges
and the Virasoro algebra in the Brown-Henneaux case map to the corresponding
quantities in the BMS_3 case. Our results straightforwardly generalize to the
higher spin case: the recently constructed flat space higher spin theories
emerge automatically in this approach from their AdS counterparts. We conclude
with a discussion of singularity resolution in the BMS gauge as an application.Comment: 20 pages, 1 figure; v2: many refs added, minor changes, v3: typos
fixed, one more ref added, JHEP versio
The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra
The family F of all potentials V(x) for which the Hamiltonian H in one space
dimension possesses a high order Lie symmetry is determined. A sub-family F',
which contains a class of potentials allowing a realization of so(2,1) as
spectrum generating algebra of H through differential operators of finite
order, is identified. Furthermore and surprisingly, the families F and F' are
shown to be related to the stationary KdV hierarchy. Hence, the "harmless"
Hamiltonian H connects different mathematical objects, high order Lie symmetry,
realization of so(2,1)-spectrum generating algebra and families of nonlinear
differential equations. We describe in a physical context the interplay between
these objects.Comment: 15 pages, LaTe
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