The discriminant and the determinant of a hypersurface of even dimension

For a smooth hypersurface of even dimension, the quadratic character of the absolute Galois group defined by the determinant of the l-adic cohomology of middle dimension is computed via the square root of the discriminant of a defining polynomial of the hypersurface.Comment: 20 pages. In V2, there remains only one author. More details are adde

Influx of nitrogen-rich material from the outer Solar System indicated by iron nitride in Ryugu samples

Large amounts of nitrogen compounds, such as ammonium salts, may be stored in icy bodies and comets, but the transport of these nitrogen-bearing solids into the near-Earth region is not well understood. Here, we report the discovery of iron nitride on magnetite grains from the surface of the near-Earth C-type carbonaceous asteroid Ryugu, suggesting inorganic nitrogen fixation. Micrometeoroid impacts and solar wind irradiation may have caused the selective loss of volatile species from major iron-bearing minerals to form the metallic iron. Iron nitride is a product of nitridation of the iron metal by impacts of micrometeoroids that have higher nitrogen contents than the CI chondrites. The impactors are probably primitive materials with origins in the nitrogen-rich reservoirs in the outer Solar System. Our observation implies that the amount of nitrogen available for planetary formation and prebiotic reactions in the inner Solar System is greater than previously recognized

Four‐dimensional‐STEM analysis of the phyllosilicate‐rich matrix of Ryugu samples

Ryugu asteroid grains brought back to the Earth by the Hayabusa2 space mission are pristine samples containing hydrated minerals and organic compounds. Here, we investigate the mineralogy of their phyllosilicate-rich matrix with four-dimensional scanning transmission electron microscopy (4D-STEM). We have identified and mapped the mineral phases at the nanometer scale (serpentine, smectite, pyrrhotite), observed the presence of Ni-bearing pyrrhotite, and identified the serpentine polymorph as lizardite, in agreement with the reported aqueous alteration history of Ryugu. Furthermore, we have mapped the d-spacings of smectite and observed a broad distribution of values, ranging from 1 to 2 nm, with an average d-spacing of 1.24 nm, indicating significant heterogeneity within the sample. Such d-spacing variability could be the result of either the presence of organic matter trapped in the interlayers or the influence of various geochemical conditions at the submicrometer scale, suggestive of a range of organic compounds and/or changes in smectite crystal chemistry

A dehydrated space-weathered skin cloaking the hydrated interior of Ryugu

Without a protective atmosphere, space-exposed surfaces of airless Solar System bodies gradually experience an alteration in composition, structure and optical properties through a collective process called space weathering. The return of samples from near-Earth asteroid (162173) Ryugu by Hayabusa2 provides the first opportunity for laboratory study of space-weathering signatures on the most abundant type of inner solar system body: a C-type asteroid, composed of materials largely unchanged since the formation of the Solar System. Weathered Ryugu grains show areas of surface amorphization and partial melting of phyllosilicates, in which reduction from Fe3+ to Fe2+ and dehydration developed. Space weathering probably contributed to dehydration by dehydroxylation of Ryugu surface phyllosilicates that had already lost interlayer water molecules and to weakening of the 2.7 µm hydroxyl (–OH) band in reflectance spectra. For C-type asteroids in general, this indicates that a weak 2.7 µm band can signify space-weathering-induced surface dehydration, rather than bulk volatile loss

Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTIC‐HF: baseline characteristics and comparison with contemporary clinical trials

Aims: The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTIC‐HF) trial. Here we describe the baseline characteristics of participants in GALACTIC‐HF and how these compare with other contemporary trials. Methods and Results: Adults with established HFrEF, New York Heart Association functional class (NYHA) ≥ II, EF ≤35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokinetic‐guided dosing: 25, 37.5 or 50 mg bid). 8256 patients [male (79%), non‐white (22%), mean age 65 years] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NT‐proBNP 1971 pg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTIC‐HF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressure < 100 mmHg (n = 1127), estimated glomerular filtration rate < 30 mL/min/1.73 m2 (n = 528), and treated with sacubitril‐valsartan at baseline (n = 1594). Conclusions: GALACTIC‐HF enrolled a well‐treated, high‐risk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation

DFT study of CO oxidation over Au/TiO2(110): The extent of the reactive perimeter zone

O[2] adsorption and CO oxidation on a Au/rutile TiO[2](1 1 0) catalyst have been examined by DFT in order to define the extent of the reactive perimeter zone. O[2] is found to adsorb on the fivefold coordinated Ti sites that are away from the perimeter as well as on those next to the perimeter. Both O[2] show similar reactivity toward a gaseous CO. CO oxidation still occurs predominantly at the perimeter because O[2] adsorption is strongest at the perimeter Ti site and because CO is activated on Au through back donation

DFT study of CO oxidation catalyzed by Au/TiO<inf>2</inf>: Activity of small clusters

Conference -ISSS-7-CO oxidation over a rutile TiO2(110) surface supporting a tetrahedral Au10 cluster has been examined by planewave DFT calculations. O2 adsorbs sideon to the pentacoordinate Ti site of the oxide support with a large energy gain (∼ 2 eV), activated to a peroxide state. O2 adsorption on the cluster is much weaker. The stability and activation state of sideon O2 depends weakly on distance to the cluster. On a Ti site next to the cluster, a sideon O2 reacts with CO adsorbed on the cluster to yield CO2 with a very small energy barrier of 0.13 eV. On a more remote Ti site, a sideon O2 reacts with a gaseous CO to yield CO2 with a barrier of 0.55 eV. Thus, O2 + CO reaction is much faster at the perimeter even for a small cluster such as Au10. Similar results are obtained for a truncated pyramidal Au9, except that a carbonate is formed at the perimeter. The carbonate formation is inhibited if H2O is adsorbed next to O2

Automated Exploration of Free Energy Landscapes Based on Umbrella Integration

We present a new approach for automated exploration of free energy landscapes on the basis of the umbrella integration (UI) method. The method to search points in the landscape relies on the normal distributions and gradients of the potential of mean force (PMF) obtained from UI calculations. We applied this approach to the alanine dipeptide in solution and demonstrated that the equilibrium and the transition states were efficiently found in the ascending order of the PMF values