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We show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas explicitly. This is carried out in detail in the case of the incomplete flag manifold consisting of all (p+1)-planes containing a unit vector.
We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.
We provide a Hopf boundary lemma for the regional fractional Laplacian (−Δ)sΩ, with Ω ⊂ RN a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (−Δ)s u = c(x)u in Ω, we show that the ratio u(x)∕(dist(x, 𝜕Ω))2s−1 is strictly Ω positive as x approaches the boundary 𝜕Ω of Ω. We also prove a strong maximum principle for distributional super-solutions.
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
Wrack burial reduces germination and establishment of the invasive cordgrass Spartina densiflora
(2014)
Germination and emergence of halophytes may decrease significantly by seed burial in dead plant material, or wrack, which is common and abundant in tidal marshes. The effects of plant debris (wrack) burial on seed germination and seedling establishment of Spartina densiflora, an invasive cordgrass, were studied under greenhouse conditions and compared with field observations. Five wrack burial depths were applied: control without wrack, 1 cm (1235 ± 92 g DW wrack m-2), 2 cm (3266 ± 13 g DW m-2), 4 cm (4213 ± 277 g DW m-2), and 8 cm (6138 ± 227 g DW m-2). Sediment pH, electrical conductivity, redox potential and temperature were recorded. Quiescence increased with wrack load up to ~20% at 8 cm deep. Germination decreased with wrack load from 96% to 14%, which could be related with anoxic conditions under the debris since sediment redox potential was as low as -83 ± 7 mV at 8 cm. Germination percentage increased and quiescent and dormant percentages decreased at higher daily sediment temperatures and with higher daily temperature fluctuations, conditions that were recorded without or under low loads of wrack. Spartina densiflora did not show primary dormancy, but its seeds entered into a non-deep physiological dormancy below 1 cm deep in plant debris. The establishment of S. densiflora seedlings was also greatly reduced by wrack burial since only 6 seedlings (11 ± 5 % of germinated seeds) emerged above plant debris from 1 cm and all seedlings died from deeper than 1 cm. S. densiflora seedling development was also reduced by wrack burial. The inverse relationship between germination and emergence of S. densiflora with wrack burial recorded in our study is useful to predict its invasion dynamics and to plan the management of invaded marshes.
The title compound, C20H22O2, crystallizes with two independent molecules in the asymmetric unit. In each molecule, all the non-H atoms lie in a common plane (r.m.s. deviations of 0.098 and 0.079 Å). There is a [pi]-[pi] stacking interaction in the crystal structure. The central aromatic rings of the two molecules, which are stacked head-to-tail one above the other, are separated by centroid-to-centroid distances of 3.872 (13) and 3.999 (10) Å. Key indicators: single-crystal X-ray study; T = 173 K; mean σ(C–C) = 0.003 A° ; R factor = 0.044; wR factor = 0.101; data-to-parameter ratio = 14.6.
The title compound, C14H20O3, is a synthetic analogue with a long aliphatic side chain of the important food additive and flavoring agent, vanillin. There are two independent molecules in the asymmetric unit, each having an essentially planar conformation (r.m.s. deviations of 0.023 and 0.051Å for all non-H atoms of the two molecules in the asymmetric unit). Key indicators: single-crystal X-ray study; T = 173 K; mean σ(C–C) = 0.002 A°; R factor = 0.049; wR factor = 0.144; data-to-parameter ratio = 15.9.
A new species of Liolaemus is described from southwest of the town of Añelo, Neuquén Province, Argentina. Integrative evidence methodology of external morphological characters and molecular phylogenetic analyses of mitochondrial DNA (cyt-b) is used to place the new species to the species group of Liolaemus boulengeri. The new species is phenotypically close to L. mapuche. The new Liolaemus is medium to large in size (males 77.64–83.98 mm, females 72.88–78.58 mm), with evident sexual dichromatism. Genetic distances of the mtDNA (cyt-b) between the new species and its closest relative species are greater than 3% (L. cuyanus 7.48–12.02%; L. josei 7.56–9.60%; L. puelche 8.23–9.93%; L. mapuche 8.51–9.79%). Molecular and morphological phylogenetic results show L. mapuche as the sister species of the new one. The new species is larger than L. mapuche. Dorsal and ventral scales are more numerous in the new species than in L. mapuche, precloacal pores in females are present in L. mapuche and absent in the new species. It has strict psammophilic habits, using sand mounds and sheltering, under Alpataco (Neltuma alpataco) bushes. The L. boulengeri group now contains 75 species distributed in Argentina, Bolivia, Brazil, Chile, Paraguay, Peru and Uruguay.
In high-energy heavy-ion collisions, partonic collectivity is evidenced by the constituent quark number scaling of elliptic flow anisotropy for identified hadrons. A breaking of this scaling and dominance of baryonic interactions is found for identified hadron collective flow measurements in √sNN = 3 GeV Au+Au collisions. In this paper, we report measurements of the first- and second-order azimuthal anisotropic parameters, v1 and v2, of light nuclei (d, t, 3He, 4He) produced in √sNN = 3 GeV Au+Au collisions at the STAR experiment. An atomic mass number scaling is found in the measured v1 slopes of light nuclei at mid-rapidity. For the measured v2 magnitude, a strong rapidity dependence is observed. Unlike v2 at higher collision energies, the v2 values at mid-rapidity for all light nuclei are negative and no scaling is observed with the atomic mass number. Calculations by the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, are in good agreement with our observations, implying baryonic interactions dominate the collective dynamics in 3 GeV Au+Au collisions at RHIC.