Curves orthogonal to a vector field in Euclidean spaces

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [B.-Y. Chen, Tamkang J. Math. \textbf{48} (2017) 209--214] to any space dimension: we prove that rectifying curves are geodesics on the hypersurface of higher dimensional cones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying and spherical curves in any dimension.Comment: 12 pages; keywords: Rectifying curve, geodesic, cone, spherical curve, plane curve, slant heli

Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. How- ever, most findings were obtained using a case-by-case approach, and it is often unclear what is a consequence of specificities of the ambient manifold and what could be generic. In this work, we propose a theo- retical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a con- stant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices. We prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux field of the directrix. We characterize recti- fying surfaces of constant angle or, equivalently, when their geodesics are slant helices. As a corollary, we show that if every geodesic of a surface of constant angle is a slant helix, the ambient manifold is flat. Finally, we characterize surfaces in the product of a Riemannian surface with the real line making a constant angle with the vertical real direction

Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. How- ever, most findings were obtained using a case-by-case approach, and it is often unclear what is a consequence of specificities of the ambient manifold and what could be generic. In this work, we propose a theo- retical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a con- stant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices. We prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux field of the directrix. We characterize recti- fying surfaces of constant angle or, equivalently, when their geodesics are slant helices. As a corollary, we show that if every geodesic of a surface of constant angle is a slant helix, the ambient manifold is flat. Finally, we characterize surfaces in the product of a Riemannian surface with the real line making a constant angle with the vertical real direction

Morphinofobia: the situation among the general population and health care professionals in North-Eastern Portugal

<p>Abstract</p> <p>Background</p> <p>Morphinofobia among the general population (GP) and among health care professionals (HP) is not without danger for the patients: it may lead to the inappropriate management of debilitating pain. The aim of our study was to explore among GP and HP the representation and attitudes concerning the use of morphine in health care.</p> <p>Methods</p> <p>A cross-sectional study was done among 412 HP (physicians and nurses) of the 4 hospitals and 10 community health centers of Beira Interior (Portugal)and among 193 persons of the GP randomly selected in public places. Opinions were collected through a translated self-administered questionnaire.</p> <p>Results</p> <p>A significant difference of opinion exists among GP and HP about the use of morphine. The word morphine first suggests drug to GP (36,2%) and analgesia to HP (32,9%.). The reasons for not using morphine most frequently cited are: for GP morphine use means advanced disease (56%), risk of addiction (50%), legal requirements (49,7%); for HP it means legal risks (56,3%) and adverse side effects of morphine such as somnolence - sedation (30,5%) The socio-demographic situation was correlated with the opinions about the use of morphine.</p> <p>Conclusions</p> <p>False beliefs about the use of morphine exist among the studied groups. There seems to be a need for developing information campaigns on pain management and the use of morphine targeting. Better training and more information of HP might also be needed.</p

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

Peer reviewe

Measurements of the Electroweak Diboson Production Cross Sections in Proton-Proton Collisions at root s=5.02 TeV Using Leptonic Decays

The first measurements of diboson production cross sections in proton-proton interactions at a center-of-mass energy of 5.02 TeV are reported. They are based on data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 302 pb(-1). Events with two, three, or four charged light leptons (electrons or muons) in the final state are analyzed. The WW, WZ, and ZZ total cross sections are measured as sigma(WW) = 37:0(-5.2)(+5.5) (stat)(-2.6)(+2.7) (syst) pb, sigma(WZ) = 6.4(-2.1)(+2.5) (stat)(-0.3)(+0.5)(syst) pb, and sigma(ZZ) = 5.3(-2.1)(+2.5)(stat)(-0.4)(+0.5) (syst) pb. All measurements are in good agreement with theoretical calculations at combined next-to-next-to-leading order quantum chromodynamics and next-to-leading order electroweak accuracy

Search for lepton-flavor violating decays of the Higgs boson in the mu tau and e tau final states in proton-proton collisions at root s=13 TeV

A search is presented for lepton-flavor violating decays of the Higgs boson to mu t and et. The dataset corresponds to an integrated luminosity of 137 fb(-1) collected at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. No significant excess has been found, and the results are interpreted in terms of upper limits on lepton-flavor violating branching fractions of the Higgs boson. The observed (expected) upper limits on the branching fractions are, respectively, B(H -> mu t) e tau) < 0.22(0.16)% at 95% confidence level.Peer reviewe