517 research outputs found
A constructive study of the module structure of rings of partial differential operators
The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media
Anthelmintic activity of Cratyliamollis leaves against gastrointestinal nematodes in goats
Measurement of the branching fraction
The branching fraction is measured in a data sample
corresponding to 0.41 of integrated luminosity collected with the LHCb
detector at the LHC. This channel is sensitive to the penguin contributions
affecting the sin2 measurement from The
time-integrated branching fraction is measured to be . This is the most precise measurement to
date
Model-independent search for CP violation in D0âKâK+ÏâÏ+ and D0âÏâÏ+Ï+Ïâ decays
A search for CP violation in the phase-space structures of D0 and View the MathML source decays to the final states KâK+ÏâÏ+ and ÏâÏ+Ï+Ïâ is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0 fbâ1 collected in 2011 by the LHCb experiment in pp collisions at a centre-of-mass energy of 7 TeV. For the KâK+ÏâÏ+ final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the ÏâÏ+Ï+Ïâ final state is partitioned into 128 bins, each bin with approximately 2500 decays. The p-value under the hypothesis of no CP violation is 41%, and in no bin is a CP asymmetry greater than 5.5% observed. All results are consistent with the hypothesis of no CP violation at the current sensitivity
Measurement of the CP-violating phase \phi s in Bs->J/\psi\pi+\pi- decays
Measurement of the mixing-induced CP-violating phase phi_s in Bs decays is of
prime importance in probing new physics. Here 7421 +/- 105 signal events from
the dominantly CP-odd final state J/\psi pi+ pi- are selected in 1/fb of pp
collision data collected at sqrt{s} = 7 TeV with the LHCb detector. A
time-dependent fit to the data yields a value of
phi_s=-0.019^{+0.173+0.004}_{-0.174-0.003} rad, consistent with the Standard
Model expectation. No evidence of direct CP violation is found.Comment: 15 pages, 10 figures; minor revisions on May 23, 201
Search for the lepton-flavor-violating decays Bs0âe±Όâ and B0âe±Όâ
A search for the lepton-flavor-violating decays Bs0âe±Όâ and B0âe±Όâ is performed with a data sample, corresponding to an integrated luminosity of 1.0ââfb-1 of pp collisions at âs=7ââTeV, collected by the LHCb experiment. The observed number of Bs0âe±Όâ and B0âe±Όâ candidates is consistent with background expectations. Upper limits on the branching fractions of both decays are determined to be B(Bs0âe±Όâ)101ââTeV/c2 and MLQ(B0âe±Όâ)>126ââTeV/c2 at 95% C.L., and are a factor of 2 higher than the previous bounds
Absolute luminosity measurements with the LHCb detector at the LHC
Absolute luminosity measurements are of general interest for colliding-beam
experiments at storage rings. These measurements are necessary to determine the
absolute cross-sections of reaction processes and are valuable to quantify the
performance of the accelerator. Using data taken in 2010, LHCb has applied two
methods to determine the absolute scale of its luminosity measurements for
proton-proton collisions at the LHC with a centre-of-mass energy of 7 TeV. In
addition to the classic "van der Meer scan" method a novel technique has been
developed which makes use of direct imaging of the individual beams using
beam-gas and beam-beam interactions. This beam imaging method is made possible
by the high resolution of the LHCb vertex detector and the close proximity of
the detector to the beams, and allows beam parameters such as positions, angles
and widths to be determined. The results of the two methods have comparable
precision and are in good agreement. Combining the two methods, an overall
precision of 3.5% in the absolute luminosity determination is reached. The
techniques used to transport the absolute luminosity calibration to the full
2010 data-taking period are presented.Comment: 48 pages, 19 figures. Results unchanged, improved clarity of Table 6,
9 and 10 and corresponding explanation in the tex
Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) and the direct CP asymmetry in B0 -> K*0 gamma
The ratio of branching fractions of the radiative B decays B0 -> K*0 gamma
and Bs0 phi gamma has been measured using an integrated luminosity of 1.0 fb-1
of pp collision data collected by the LHCb experiment at a centre-of-mass
energy of sqrt(s)=7 TeV. The value obtained is BR(B0 -> K*0 gamma)/BR(Bs0 ->
phi gamma) = 1.23 +/- 0.06(stat.) +/- 0.04(syst.) +/- 0.10(fs/fd), where the
first uncertainty is statistical, the second is the experimental systematic
uncertainty and the third is associated with the ratio of fragmentation
fractions fs/fd. Using the world average value for BR(B0 -> K*0 gamma), the
branching fraction BR(Bs0 -> phi gamma) is measured to be (3.5 +/- 0.4) x
10^{-5}.
The direct CP asymmetry in B0 -> K*0 gamma decays has also been measured with
the same data and found to be A(CP)(B0 -> K*0 gamma) = (0.8 +/- 1.7(stat.) +/-
0.9(syst.))%.
Both measurements are the most precise to date and are in agreement with the
previous experimental results and theoretical expectations.Comment: 21 pages, 3 figues, 4 table
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