36 research outputs found
On Gauss-Bonnet Curvatures
The -th Gauss-Bonnet curvature is a generalization to higher dimensions
of the -dimensional Gauss-Bonnet integrand, it coincides with the usual
scalar curvature for . The Gauss-Bonnet curvatures are used in theoretical
physics to describe gravity in higher dimensional space times where they are
known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos
gravity. In this paper we present various aspects of these curvature invariants
and review their variational properties. In particular, we discuss natural
generalizations of the Yamabe problem, Einstein metrics and minimal
submanifolds.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
On the last nonzero digits of in a given base
In this paper we study the sequence of strings of last nonzero digits of
in a given base . We determine for which this sequence is automatic
and show how to generate it using a uniform morphism. We also compute how often
each possible string of digits appears as the last nonzero digits of
Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3,3^{2h+1})
Using a class of permutation polynomials of obtained from the
Ree-Tits symplectic spreads in , we construct a family of skew
Hadamard difference sets in the additive group of . With the help
of a computer, we show that these skew Hadamard difference sets are new when
and . We conjecture that they are always new when .
Furthermore, we present a variation of the classical construction of the twin
prime power difference sets, and show that inequivalent skew Hadamard
difference sets lead to inequivalent difference sets with twin prime power
parameters.Comment: 18 page
Dynamical error bounds for continuum discretisation via Gauss quadrature rules, -- a Lieb-Robinson bound approach
Instances of discrete quantum systems coupled to a continuum of oscillators
are ubiquitous in physics. Often the continua are approximated by a discrete
set of modes. We derive analytical error bounds on expectation values of system
observables that have been time evolved under such discretised Hamiltonians.
These bounds take on the form of a function of time and the number of discrete
modes, where the discrete modes are chosen according to Gauss quadrature rules.
The derivation makes use of tools from the field of Lieb-Robinson bounds and
the theory of orthonormal polynominals.Comment: 12 pages + 14 pages of proofs and appendices, Journal of Mathematical
Physics, Vol.57, Issue 2 (2016)
http://scitation.aip.org/content/aip/journal/jmp/57/2/10.1063/1.494043