Ruled surfaces with vanishing second Gaussian curvature

For a surface free of points of vanishing Gaussian curvature in Euclidean space the second Gaussian curvature is defined formally. It is first pointed out that a minimal surface has vanishing second Gaussian curvature but that a surface with vanishing second Gaussian curvature need not be minimal. Ruled surfaces for which a linear combination of the second Gaussian curvature and the mean curvature is constant along the rulings are then studied. In particular the only ruled surface in Euclidean space with vanishing second Gaussian curvature is a piece of a helicoid.     

On Legendre curves in contact 3-manifolds

It is first observed that on a 3-dimensional Sasakian manifold the torsion of a Legendre curve is identically equal to +1. It is then shown that, conversely, if a curve on a Sasakian 3-manifold has constant torsion +1 and satisfies the initial conditions at one point for a Legendre curve, it is a Legendre curve. Furthermore, among contact metric structures, this property is characteristic of Sasakian metrics. For the standard contact structure onR ³ with its standard Sasakian metric the curvature of a Legendre curve is shown to be twice the curvature of its projection to thexy-plane with respect to the Euclidean metric. Thus this metric onR ³ is more natural for the study of Legendre curves than the Euclidean metric.This work was done while the first author was a visiting scholar at Michigan State University.     

Nucleon structure functions from high energy neutrino interactions

Structure functions obtained from high energy neutrino and antineutrino scattering from an iron target are presented. These were extracted from the combined data of Fermilab experiments E616 and E701; these utilized narrow band beam runs between 1979–1982. The structure functions are used to test the validity of quarkparton model (QPM) predictions and to extract the QCD scale parameter Λ from fits to the Altarelli-Parisi equations.     

A measurement of the neutral current electroweak parameters using the fermilab narrow band neutrino beam

We report a measurement of the electroweak parameters sin₂θ ^w and ? based on the ratios of neutral current to charged current events measured in the Fermilab narrow-band neutrino beam at energies of 30–240 GeV. The data are fully corrected for radiative effects, heavy-quark production, and other effects. The best value for sin₂θ ^w obtained, sin₂θ ^w =0.239±0.011, is consistent with the most recent values fromW andZ production, as well as from other neutrino experiments.     

Search for chargino-neutralino production in pp collisions at sq rt[s] = 1.96 TeV

We present a search for associated production of the chargino and neutralino supersymmetric particles using up to 1.1 fb{-1} of integrated luminosity collected by the CDF II experiment at the Tevatron pp collider at sq rt[s]=1.96 TeV. We analyze events with a large transverse momentum imbalance and either three charged leptons or two charged leptons of the same electric charge. The numbers of observed events are consistent with standard model expectations. Upper limits on the production cross section are derived in different theoretical models.     

Measurement of the Lambda b0 lifetime in Lambda b0-->J/psi Lambda 0 in pp collisions at square root s=1.96 TeV

We report a measurement of the Lambda b0 lifetime in the exclusive decay Lambda b0-->J/psi Lambda 0 in pp collisions at square root s=1.96 TeV using an integrated luminosity of 1.0 fb-1 of data collected by the CDF II detector at the Fermilab Tevatron. Using fully reconstructed decays, we measure tau(Lambda b0)=1.593(-0.078)(+0.083)(stat)+/-0.033(syst) ps. This is the single most precise measurement of tau(Lambda b0) and is 3.2sigma higher than the current world average.     

Observation of exclusive electron-positron production in hadron-hadron collisions

We present the first observation of exclusive e(+)e(-) production in hadron-hadron collisions, using pp[over] collision data at (square root) s = 1.96 TeV taken by the run II Collider Detector at Fermilab, and corresponding to an integrated luminosity of 532 pb(-1). We require the absence of any particle signatures in the detector except for an electron and a positron candidate, each with transverse energy E(T) > 5 GeV and pseudorapidity |eta| < 2. With these criteria, 16 events are observed compared to a background expectation of 1.9+/-0.3 events. These events are consistent in cross section and properties with the QED process pp[over] --> p + e(+)e(-) + p[over] through two-photon exchange. The measured cross section is 1.6(-0.3)(+0.5)(stat) +/- 0.3(syst) pb. This agrees with the theoretical prediction of 1.71+/-0.01 pb.     

An extension of Reiner's “Deborah Number” concept to a Wide field of rheological investigations

Summary Reiner defined a numeric, which he called theDeborah Number to represent the ratio of a relaxation time to a natural (observation) time. This implies aMaxwell model but is readily extended to complete relaxation spectra. Similar Numbers are proposed for retardation times and also for some conditions of coagulation thixotropy and for data from certain psychophysical experiments.     

Bochner and conformal flatness on normal complex contact metric manifolds

We will prove that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kähler. If they are also complete and simply connected, they must be isometric to the odd-dimensional complex projective space \({{\mathbb{C}P^{2n+1}}}\)(4) with the Fubini-Study metric. On the other hand, it is not possible for normal complex contact metric manifolds to be conformally flat.