607 research outputs found
The torsion of a finite quasigroup quandle is annihilated by its order
We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the
torsion of its homology. It is a classical result in reduced homology of finite
groups that the order of a group annihilates its homology. From the very
beginning of the rack homology (between 1990 and 1995) the analogous result was
suspected. The first general results in this direction were obtained
independently about 2001 by R.A.Litherland and S.Nelson, and P.Etingof and
M.Grana. In Litherland-Nelson paper it is proven that if (Q;*) is a finite
homogeneous rack (this includes quasigroup racks) then the torsion of homology
is annihilated by |Q|^n. In Etingof-Grana paper it is proven that if (X;A) is a
finite rack and N=|G^0_Q| is the order of a group of inner automorphisms of Q,
then only primes which can appear in the torsion of homology are those dividing
N (the case of connected Alexander quandles was proven before by T.Mochizuki).
The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki
and in particular, they prove that the torsion part of the homology of the
dihedral quandle R_3 is annihilated by 3. In Niebrzydowski-Przytycki paper it
is conjectured that for a finite quasigroup quandle, torsion of its homology is
annihilated by the order of the quandle. The conjecture is proved by T.Nosaka
for finite Alexander quasigroup quandles. In this paper we prove the conjecture
in full generality. For this version, we rewrote the Section 3 totally and
introduced the concept of the precubic homotopy. In Section 2, the main
addition is Corollary 2.2 which summarizes identities observed in the proof of
the main theorem as we use it later in Section 3.Comment: 13 pages, 1 figure; accepted for publication in Journal of Pure and
Applied Algebr
Measurement of the partial widths of the Z into up- and down-type quarks
Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma
decays were selected by tagging hadronic final states with isolated photon
candidates in the electromagnetic calorimeter. Combining the measured rates of
Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the
simultaneous determination of the widths of the Z into up- and down-type
quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18}
MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with
the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.
Search for R-Parity Violating Decays of Scalar Fermions at LEP
A search for pair-produced scalar fermions under the assumption that R-parity
is not conserved has been performed using data collected with the OPAL detector
at LEP. The data samples analysed correspond to an integrated luminosity of
about 610 pb-1 collected at centre-of-mass energies of sqrt(s) 189-209 GeV. An
important consequence of R-parity violation is that the lightest supersymmetric
particle is expected to be unstable. Searches of R-parity violating decays of
charged sleptons, sneutrinos and squarks have been performed under the
assumptions that the lightest supersymmetric particle decays promptly and that
only one of the R-parity violating couplings is dominant for each of the decay
modes considered. Such processes would yield final states consisting of
leptons, jets, or both with or without missing energy. No significant
single-like excess of events has been observed with respect to the Standard
Model expectations. Limits on the production cross- section of scalar fermions
in R-parity violating scenarios are obtained. Constraints on the supersymmetric
particle masses are also presented in an R-parity violating framework analogous
to the Constrained Minimal Supersymmetric Standard Model.Comment: 51 pages, 24 figures, Submitted to Eur. Phys. J.
Measurement of the Strong Coupling alpha s from Four-Jet Observables in e+e- Annihilation
Data from e+e- annihilation into hadrons at centre-of-mass energies between
91 GeV and 209 GeV collected with the OPAL detector at LEP, are used to study
the four-jet rate as a function of the Durham algorithm resolution parameter
ycut. The four-jet rate is compared to next-to-leading order calculations that
include the resummation of large logarithms. The strong coupling measured from
the four-jet rate is alphas(Mz0)=
0.1182+-0.0003(stat.)+-0.0015(exp.)+-0.0011(had.)+-0.0012(scale)+-0.0013(mass)
in agreement with the world average. Next-to-leading order fits to the
D-parameter and thrust minor event-shape observables are also performed for the
first time. We find consistent results, but with significantly larger
theoretical uncertainties.Comment: 25 pages, 15 figures, Submitted to Euro. Phys. J.
Measurement of the Hadronic Photon Structure Function F_2^gamma at LEP2
The hadronic structure function of the photon F_2^gamma is measured as a
function of Bjorken x and of the factorisation scale Q^2 using data taken by
the OPAL detector at LEP. Previous OPAL measurements of the x dependence of
F_2^gamma are extended to an average Q^2 of 767 GeV^2. The Q^2 evolution of
F_2^gamma is studied for average Q^2 between 11.9 and 1051 GeV^2. As predicted
by QCD, the data show positive scaling violations in F_2^gamma. Several
parameterisations of F_2^gamma are in agreement with the measurements whereas
the quark-parton model prediction fails to describe the data.Comment: 4 pages, 2 figures, to appear in the proceedings of Photon 2001,
Ascona, Switzerlan
The Vega debris disc: A view from Herschel
We present five band imaging of the Vega debris disc obtained using the Herschel Space Observatory. These data span a wavelength range of 70-500 mu m with full-width half-maximum angular resolutions of 5.6-36.9 ''. The disc is well resolved in all bands, with the ring structure visible at 70 and 160 mu m. Radial profiles of the disc surface brightness are produced, and a disc radius of 11 '' (similar to 85AU) is determined. The disc is seen to have a smooth structure thoughout the entire wavelength range, suggesting that the disc is in a steady state, rather than being an ephemeral structure caused by the recent collision of two large planetesimals
A measurement of the tau mass and the first CPT test with tau leptons
We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV
using tau pairs from Z0 decays. To test CPT invariance we compare the masses of
the positively and negatively charged tau leptons. The relative mass difference
is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.
Measurement of Rb in e+e- Collisions at 182 - 209 GeV
Measurements of Rb, the ratio of the bbbar cross-section to the qqbar cross-
section in e+e- collisions, are presented. The data were collected by the OPAL
experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV.
Lepton, lifetime and event shape information is used to tag events containing b
quarks with high efficiency. The data are compatible with the Standard Model
expectation. The mean ratio of the eight measurements reported here to the
Standard Model prediction is 1.055+-0.031+-0.037, where the first error is
statistical and the second systematic.Comment: 21 pages, 5 figures, Submitted to Phys. Letts
Measurement of the B0 Lifetime and Oscillation Frequency using B0->D*+l-v decays
The lifetime and oscillation frequency of the B0 meson has been measured
using B0->D*+l-v decays recorded on the Z0 peak with the OPAL detector at LEP.
The D*+ -> D0pi+ decays were reconstructed using an inclusive technique and the
production flavour of the B0 mesons was determined using a combination of tags
from the rest of the event. The results t_B0 = 1.541 +- 0.028 +- 0.023 ps, Dm_d
= 0.497 +- 0.024 +- 0.025 ps-1 were obtained, where in each case the first
error is statistical and the second systematic.Comment: 17 pages, 4 figures, submitted to Phys. Lett.
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