On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling

Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.     

Observation of direct photons in central 158A GeV (208)P(208)b+Pb collisions

A measurement of direct photon production in 208Pb+208Pb collisions at 158A GeV has been carried out in the CERN WA98 experiment. The invariant yield of direct photons in central collisions is extracted as a function of transverse momentum in the interval 0.51.5 GeV/c. The result constitutes the first observation of direct photons in ultrarelativistic heavy-ion collisions. It could be significant for diagnosis of quark-gluon-plasma formation.     

Study of Z Boson Production in PbPb Collisions at √S(NN)=2.76 TeV

A search for Z bosons in the μ(+)μ(-) decay channel has been performed in PbPb collisions at √S(NN)=2.76 TeV with the CMS detector at the LHC, in a 7.2 μb(-1) data sample. The number of opposite-sign muon pairs observed in the 60-120 GeV/c(2) invariant mass range is 39, corresponding to a yield per unit of rapidity (y) and per minimum bias event of [33.8±5.5(stat)±4.4(syst)]×10(-8), in the |y|<2.0 range. Rapidity, transverse momentum, and centrality dependencies are also measured. The results agree with next-to-leading order QCD calculations, scaled by the number of incoherent nucleon-nucleon collisions.     

Search for stopped Gluinos in pp collisions at square root s=7 TeV

The results of the first search for long-lived gluinos produced in 7 TeV pp collisions at the CERN Large Hadron Collider are presented. The search looks for evidence of long-lived particles that stop in the CMS detector and decay in the quiescent periods between beam crossings. In a dataset with a peak instantaneous luminosity of 1×10(32) cm-2 s-1, an integrated luminosity of 10 pb-1, and a search interval corresponding to 62 hours of LHC operation, no significant excess above background was observed. Limits at the 95% confidence level on gluino pair production over 13 orders of magnitude of gluino lifetime are set. For a mass difference mg - mχ1(0) >100 GeV/c2, and assuming BR(g→gχ1(0))=100%, mg < 370 GeV/c2 are excluded for lifetimes from 10 μs to 1000 s.     

Measurement of the t-channel single top quark production cross section in pp collisions at √s=7 TeV

Electroweak production of the top quark is measured for the first time in pp collisions at √=7 TeV, using a data set collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 36 pb?1. With an event selection optimized for t-channel production, two complementary analyses are performed. The first one exploits the special angular properties of the signal, together with background estimates from the data. The second approach uses a multivariate analysis technique to probe the compatibility with signal topology expected from electroweak top-quark production. The combined measurement of the cross section is 83.6±29.8(stat+syst)±3.3(lumi) pb, consistent with the standard model expectation.     

Search for three-jet resonances in pp collisions at square root(s)=7 TeV

A search for three-jet hadronic resonance production in pp collisions at a center-of-mass energy of 7 TeV has been conducted by the CMS Collaboration at the LHC, using a data sample corresponding to an integrated luminosity of 35 pb(-1). Events with high jet multiplicity and a large scalar sum of jet transverse momenta are analyzed using a signature-based approach. The number of expected standard model background events is found to be in good agreement with the observed events. Limits on the cross section times branching ratio are set in a model of gluino pair production with an R-parity-violating decay to three quarks, and the data rule out such particles within the mass range of 200 to 280 GeV/c2.     

Search for supersymmetry at the LHC in events with jets and missing transverse energy

A search for events with jets and missing transverse energy is performed in a data sample of pp collisions collected at √s=7 TeV by the CMS experiment at the LHC. The analyzed data sample corresponds to an integrated luminosity of 1.14 fb(-1). In this search, a kinematic variable α(T) is used as the main discriminator between events with genuine and misreconstructed missing transverse energy. No excess of events over the standard model expectation is found. Exclusion limits in the parameter space of the constrained minimal supersymmetric extension of the standard model are set. In this model, squark masses below 1.1 TeV are excluded at 95% C.L. Gluino masses below 1.1 TeV are also ruled out at 95% C.L. for values of the universal scalar mass parameter below 500 GeV.     

Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma

Expressions for fundamental spectral line parameters are reported for Gaussian and Lorentzian shape profiles for homogeneous plasma at equilibrium in presence of the self-absorption. These expressions for Lorentzian profiles are applied to the determination of the ratios of transition probabilities and the ratios of optical thicknesses by a new method that we propose in this article. The self-absorption is computed by spectral line profiles with a Simplex algorithm program fitting. Applications to some experimental lines illustrate the appropriate corrections.