10,917 research outputs found
Smooth Words on a 2-letter alphabets having same parity
International audienceIn this paper, we consider smooth words over 2-letter alphabets {a, b}, where a, b are integers having same parity, with 0 < a < b. We show that all are recurrent and that the closure of the set of factors under reversal holds for odd alphabets only. We provide a linear time algorithm computing the extremal words, w.r.t. lexicographic order. The minimal word is an infinite Lyndon word if and only if either a = 1 and b odd, or a, b are even. A connection is established between generalized Kolakoski words and maximal infinite smooth words over even 2-letter alphabets revealing new properties for some of the generalized Kolakoski words. Finally, the frequency of letters in extremal words is 1/2 for even alphabets, and for a = 1 with b odd, the frequency of b's is 1/(√2b − 1 + 1)
Calibrations and isoperimetric profiles
We equip many non compact non simply connected surfaces with smooth
Riemannian metrics whose isoperimetric profile is smooth, a highly non generic
property. The computation of the profile is based on a calibration argument, a
rearrangement argument, the Bol-Fiala curvature dependent inequality, together
with new results on the profile of surfaces of revolution and some hardware
know-how.Comment: To appear soon in American Journal of Mathematics, a journal
published by The Johns Hopkins University Pres
Classical model of elementary particle with Bertotti-Robinson core and extremal black holes
We discuss the question, whether the Reissner-Nordstr\"{o}m RN) metric can be
glued to another solutions of Einstein-Maxwell equations in such a way that (i)
the singularity at r=0 typical of the RN metric is removed (ii), matching is
smooth. Such a construction could be viewed as a classical model of an
elementary particle balanced by its own forces without support by an external
agent. One choice is the Minkowski interior that goes back to the old Vilenkin
and Fomin's idea who claimed that in this case the bare delta-like stresses at
the horizon vanish if the RN metric is extremal. However, the relevant entity
here is the integral of these stresses over the proper distance which is
infinite in the extremal case. As a result of the competition of these two
factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued
to the Minkowski metric smoothly, so the elementary-particle model as a ball
empty inside fails. We examine the alternative possibility for the extremal RN
metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed
outside the horizon there always exist bare stresses but their amplitude goes
to zero as the radius of the shell approaches that of the horizon. This limit
realizes the Wheeler idea of "mass without mass" and "charge without charge".
We generalize the model to the extremal Kerr-Newman metric glued to the
rotating analog of the BR metric.Comment: 23 pages. Misprints correcte
Toric Kahler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action-Angle Coordinates
In these notes, after an introduction to toric Kahler geometry, we present
Calabi's family of U(n)-invariant extremal Kahler metrics in symplectic
action-angle coordinates and show that it actually contains, as particular
cases, many interesting cohomogeneity one examples of constant scalar
curvature.Comment: 20 pages, 1 figure, for the proceedings of the XI International
Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, June
5--10, 200
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