Singular Casimir Elements of the Euler Equation and Equilibrium Points

The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Lie-Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of the symplectic operator defining the Poisson bracket. The kernel of the symplectic operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the symplectic operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the symplectic operator (the "dimension" of the center) changes. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket

Development of a versatile laboratory experiment to teach the metabolic transformation of hydrolysis

In this paper we describe an easy, reliable, versatile and inexpensive laboratory experiment to teach the metabolic transformation of hydrolysis to Pharmacy students. The experiment does not require the sacrifice of any experimental animal, or any work with organs or tissues, and so can be implemented in a typical university chemistry laboratory. We used acetylsalicylic acid (ASA), hexyl salicylate (HS) and two enzymes, a lipase and an esterase. Since both ASS and HS liberate salicylic acid (SA) upon hydrolysis, students can evaluate the different enzymatic transformations by monitoring the amount of SA liberated. The learning outcomes are an enhanced student understanding of: (1) the process of hydrolysis; (2) the application of enzymatic transformations of molecules from food to xenobiotics; (3) the differences between the general specificity of substrate of both enzymes; (4) the concepts of the lipophilic pocket; (5) the catalytic triad and its regioselectivity in relation to the ester bond. A questionnaire was administered to participating students at three points in time: at the beginning of the module, after enzymatic hydrolysis was taught in class, and after the laboratory experiment. From an analysis of the questionnaire data we conclude that this practical helped Pharmacy students to understand these concepts

A High-Resolution Map of Synteny Disruptions in Gibbon and Human Genomes

Gibbons are part of the same superfamily (Hominoidea) as humans and great apes, but their karyotype has diverged faster from the common hominoid ancestor. At least 24 major chromosome rearrangements are required to convert the presumed ancestral karyotype of gibbons into that of the hominoid ancestor. Up to 28 additional rearrangements distinguish the various living species from the common gibbon ancestor. Using the northern white-cheeked gibbon (2n = 52) (Nomascus leucogenys leucogenys) as a model, we created a high-resolution map of the homologous regions between the gibbon and human. The positions of 100 synteny breakpoints relative to the assembled human genome were determined at a resolution of about 200 kb. Interestingly, 46% of the gibbon–human synteny breakpoints occur in regions that correspond to segmental duplications in the human lineage, indicating a common source of plasticity leading to a different outcome in the two species. Additionally, the full sequences of 11 gibbon BACs spanning evolutionary breakpoints reveal either segmental duplications or interspersed repeats at the exact breakpoint locations. No specific sequence element appears to be common among independent rearrangements. We speculate that the extraordinarily high level of rearrangements seen in gibbons may be due to factors that increase the incidence of chromosome breakage or fixation of the derivative chromosomes in a homozygous state

Measurement of the cross section for isolated-photon plus jet production in pp collisions at √s=13 TeV using the ATLAS detector

The dynamics of isolated-photon production in association with a jet in proton–proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb−1. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti- algorithm with radius parameter and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon–jet invariant mass and the scattering angle in the photon–jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements

A search for resonances decaying into a Higgs boson and a new particle X in the XH → qqbb final state with the ATLAS detector

A search for heavy resonances decaying into a Higgs boson (H) and a new particle (X) is reported, utilizing 36.1 fb−1 of proton–proton collision data at collected during 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. The particle X is assumed to decay to a pair of light quarks, and the fully hadronic final state is analysed. The search considers the regime of high XH resonance masses, where the X and H bosons are both highly Lorentz-boosted and are each reconstructed using a single jet with large radius parameter. A two-dimensional phase space of XH mass versus X mass is scanned for evidence of a signal, over a range of XH resonance mass values between 1 TeV and 4 TeV, and for X particles with masses from 50 GeV to 1000 GeV. All search results are consistent with the expectations for the background due to Standard Model processes, and 95% CL upper limits are set, as a function of XH and X masses, on the production cross-section of the resonance

Searches for lepton-flavour-violating decays of the Higgs boson in s=13\sqrt{s}=13 TeV pp\mathit{pp} collisions with the ATLAS detector

This Letter presents direct searches for lepton flavour violation in Higgs boson decays, H → eτ and H → μτ , performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton–proton collisions at a centre-of-mass energy √s = 13 TeV, corresponding to an integrated luminosity of 36.1 fb−1. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95% confidence-level upper limits on the leptonflavour-violating branching ratios are 0.47% (0.34+0.13−0.10%) and 0.28% (0.37+0.14−0.10%) for H → eτ and H → μτ , respectively.publishedVersio

Combination of searches for Higgs boson pairs in pp collisions at \sqrts = 13 TeV with the ATLAS detector

This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb(-1) of proton-proton collision data at a centre-of-mass energy root s = 13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the b (b) over barb (b) over bar, b (b) over barW(+)W(-), b (b) over bar tau(+)tau(-), W+W-W+W-, b (b) over bar gamma gamma and W+W-gamma gamma final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio (kappa(lambda)) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to -5.0 &lt; kappa(lambda) &lt; 12.0 (-5.8 &lt; kappa(lambda) &lt; 12.0). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model. For complete list of authors see http://dx.doi.org/10.1016/j.physletb.2019.135103</p