1,884 research outputs found
Non-positive curvature and the Ptolemy inequality
We provide examples of non-locally compact geodesic Ptolemy metric spaces
which are not uniquely geodesic. On the other hand, we show that locally
compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we
prove that a metric space is CAT(0) if and only if it is Busemann convex and
Ptolemy.Comment: 11 pages, 2 figure
Nonpositive curvature and the Ptolemy inequality
We provide examples of nonlocally, compact, geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally, compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolem
Inertial forces and the foundations of optical geometry
Assuming a general timelike congruence of worldlines as a reference frame, we
derive a covariant general formalism of inertial forces in General Relativity.
Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota,
Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of
spacetime and investigate how these affect the inertial force formalism. While
many ways of describing spatial curvature of a trajectory has been discussed in
papers prior to this, one particular prescription (which differs from the
standard projected curvature when the reference is shearing) appears novel. For
the particular case of a hypersurface-forming congruence, using a suitable
rescaling of spacetime, we show that a geodesic photon is always following a
line that is spatially straight with respect to the new curvature measure. This
fact is intimately connected to Fermat's principle, and allows for a certain
generalization of the optical geometry as will be further pursued in a
companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For
the particular case when the shear-tensor vanishes, we present the inertial
force equation in three-dimensional form (using the bold face vector notation),
and note how similar it is to its Newtonian counterpart. From the spatial
curvature measures that we introduce, we derive corresponding covariant
differentiations of a vector defined along a spacetime trajectory. This allows
us to connect the formalism of this paper to that of Jantzen et. al. (see e.g.
Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure
No evidence of an 11.16 MeV 2+ state in 12C
An experiment using the 11B(3He,d)12C reaction was performed at iThemba LABS
at an incident energy of 44 MeV and analyzed with a high energy-resolution
magnetic spectrometer, to re-investigate states in 12C published in 1971. The
original investigation reported the existence of an 11.16 MeV state in 12C that
displays a 2+ nature. In the present experiment data were acquired at
laboratory angles of 25-, 30- and 35- degrees, to be as close to the c.m.
angles of the original measurements where the clearest signature of such a
state was observed. These new low background measurements revealed no evidence
of the previously reported state at 11.16 MeV in 12C
Hilbert geometry for convex polygonal domains
We prove in this paper that the Hilbert geometry associated with an open
convex polygonal set is Lipschitz equivalent to Euclidean plane
A Scheme to Numerically Evolve Data for the Conformal Einstein Equation
This is the second paper in a series describing a numerical implementation of
the conformal Einstein equation. This paper deals with the technical details of
the numerical code used to perform numerical time evolutions from a "minimal"
set of data.
We outline the numerical construction of a complete set of data for our
equations from a minimal set of data. The second and the fourth order
discretisations, which are used for the construction of the complete data set
and for the numerical integration of the time evolution equations, are
described and their efficiencies are compared. By using the fourth order scheme
we reduce our computer resource requirements --- with respect to memory as well
as computation time --- by at least two orders of magnitude as compared to the
second order scheme.Comment: 20 pages, 12 figure
High-Density Peptide Arrays with Combinatorial Laser Fusing
Combinatorial laser fusing is a new method to produce high-density peptide arrays with feature sizes as small as 10 mu m. It combines the high spot densities achieved by lithographic methods with the cost-efficiency of biofunctional xerography. The method is also adapted for other small molecules compatible with solid phase synthesis
At infinity of finite-dimensional CAT(0) spaces
We show that any filtering family of closed convex subsets of a
finite-dimensional CAT(0) space has a non-empty intersection in the visual
bordification . Using this fact, several results
known for proper CAT(0) spaces may be extended to finite-dimensional spaces,
including the existence of canonical fixed points at infinity for parabolic
isometries, algebraic and geometric restrictions on amenable group actions, and
geometric superrigidity for non-elementary actions of irreducible uniform
lattices in products of locally compact groups.Comment: An erratum filling in a gap in the proof of an application of the
main result has been included to the original pape
Charge separation relative to the reaction plane in Pb-Pb collisions at TeV
Measurements of charge dependent azimuthal correlations with the ALICE
detector at the LHC are reported for Pb-Pb collisions at TeV. Two- and three-particle charge-dependent azimuthal correlations in
the pseudo-rapidity range are presented as a function of the
collision centrality, particle separation in pseudo-rapidity, and transverse
momentum. A clear signal compatible with a charge-dependent separation relative
to the reaction plane is observed, which shows little or no collision energy
dependence when compared to measurements at RHIC energies. This provides a new
insight for understanding the nature of the charge dependent azimuthal
correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published
version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286
A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE
In this small note we are concerned with the solution of Forward-Backward
Stochastic Differential Equations (FBSDE) with drivers that grow quadratically
in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem
is a comparison result that allows comparing componentwise the signs of the
control processes of two different qgFBSDE. As a byproduct one obtains
conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio
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