1,125 research outputs found
Divergence operators and odd Poisson brackets
We define the divergence operators on a graded algebra, and we show that,
given an odd Poisson bracket on the algebra, the operator that maps an element
to the divergence of the hamiltonian derivation that it defines is a generator
of the bracket. This is the "odd laplacian", , of Batalin-Vilkovisky
quantization. We then study the generators of odd Poisson brackets on
supermanifolds, where divergences of graded vector fields can be defined either
in terms of berezinian volumes or of graded connections. Examples include
generators of the Schouten bracket of multivectors on a manifold (the
supermanifold being the cotangent bundle where the coordinates in the fibres
are odd) and generators of the Koszul-Schouten bracket of forms on a Poisson
manifold (the supermanifold being the tangent bundle, with odd coordinates on
the fibres).Comment: 27 pages; new Section 1, introduction and conclusion re-written,
typos correcte
Sedentariness in quantum walks
We present a relaxation of the concept of a sedentary family of graphs
introduced by Godsil [Linear Algebra Appl. 614:356-375, 2021] and provide
sufficient conditions for a given vertex in a graph to exhibit sedentariness.
We show that a vertex with at least two twins (vertices that share the same
neighbours) is sedentary. We also prove that there are infinitely many graphs
containing strongly cospectral vertices that are sedentary, which reveals that,
even though strong cospectrality is a necessary condition for pretty good state
transfer, there are strongly cospectral vertices which resist high probability
state transfer to other vertices. Moreover, we derive results about
sedentariness in products of graphs which allow us to construct new sedentary
families, such as Cartesian powers of complete graphs and stars.Comment: 26 pages, 3 figure
Curves with constant curvature ratios
Curves in Rn for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For n = 3, 4, spherical curves of this kind are also studied and compared with intrinsic helices in the sphere
Simbor, Vicent (2012): Joan Fuster: el projecte de normalització del circuit literari. València: PUV-Cà tedra Joan Fuster, 311 p.
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