On global models for isolated rotating axisymmetric charged bodies; uniqueness of the exterior field

A relatively recent study by Mars and Senovilla provided us with a uniqueness result for the exterior vacuum gravitational field generated by an isolated distribution of matter in axial rotation in equilibrium in General Relativity. The generalisation to exterior electrovacuum gravitational fields, to include charged rotating objects, is presented here.Comment: LaTeX, 21 pages, uses iopart styl

Detection of emission in the Si i 1082.7 nm line core in sunspot umbrae

We analyze spectropolarimetric sunspot umbra observations taken in the near-infrared Si i 1082.7 nm line taking NLTE effects into account. The data were obtained with the GRIS instrument installed at the German GREGOR telescope. A point spread function (PSF) was constructed using prior Mercury observations with GRIS and the information provided by the adaptive optics system of the GREGOR telescope. The data were then deconvolved from the PSF using a principal component analysis deconvolution method and were analyzed via the NICOLE inversion code. The Si i 1082.7 nm line seems to be in emission in the umbra of the observed sunspot after the effects of scattered light are removed. We show how the spectral line shape of umbral profiles changes dramatically with the amount of scattered light. Indeed, the continuum levels range, on average, from 44% of the quiet Sun continuum intensity to about 20%. The inferred levels are in line with current model predictions and empirical umbral models. Current umbral empirical models are not able to reproduce the emission in the deconvolved umbral Stokes profiles. The results of the NLTE inversions suggests that to obtain the emission in the Si i 1082.7 nm line, the temperature stratification should first have a hump located at about log tau -2 and start rising at lower heights when moving into the transition region. This is, to our knowledge, the first time the Si i 1082.7 nm line is seen in emission in sunspot umbrae. The results show that the temperature stratification of current umbral models may be more complex than expected with the transition region located at lower heights above sunspot umbrae. Our finding might provide insights into understanding why the sunspot umbra emission in the millimeter spectral range is less than that predicted by current empirical umbral models

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water, originally proposed by Bell and Lavis. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through orientational order of particles. We have considered the effect of small inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent, by the organization of solvent particles around solute particles, at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum in density (TMD). This coincidence is easily explained for non-interacting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures

Storyline description of Southern Hemisphere midlatitude circulation and precipitation response to greenhouse gas forcing

As evidence of climate change strengthens, knowledge of its regional implications becomes an urgent need for decision making. Current understanding of regional precipitation changes is substantially limited by our understanding of the atmospheric circulation response to climate change, which to a high degree remains uncertain. This uncertainty is reflected in the wide spread in atmospheric circulation changes projected in multimodel ensembles, which cannot be directly interpreted in a probabilistic sense. The uncertainty can instead be represented by studying a discrete set of physically plausible storylines of atmospheric circulation changes. By mining CMIP5 model output, here we take this broader perspective and develop storylines for Southern Hemisphere (SH) midlatitude circulation changes, conditioned on the degree of global-mean warming, based on the climate responses of two remote drivers: the enhanced warming of the tropical upper troposphere and the strengthening of the stratospheric polar vortex. For the three continental domains in the SH, we analyse the precipitation changes under each storyline. To allow comparison with previous studies, we also link both circulation and precipitation changes with those of the Southern Annular Mode. Our results show that the response to tropical warming leads to a strengthening of the midlatitude westerly winds, whilst the response to a delayed breakdown (for DJF) or strengthening (for JJA) of the stratospheric vortex leads to a poleward shift of the westerly winds and the storm tracks. However, the circulation response is not zonally symmetric and the regional precipitation storylines for South America, South Africa, South Australia and New Zealand exhibit quite specific dependencies on the two remote drivers, which are not well represented by changes in the Southern Annular Mode

Largest Digraphs Contained IN All N-tournaments

Let f(n) (resp. g(n)) be the largest m such that there is a digraph (resp. a spanning weakly connected digraph) on n-vertices and m edges which is a subgraph of every tournament on n-vertices. We prove that n log2 n--cxn>=f(n) ~_g(n) ~- n log ~ n--c..n loglog n

Maximum induced trees in graphs

AbstractLet t(G) be the maximum size of a subset of vertices of a graph G that induces a tree. We investigate the relationship of t(G) to other parameters associated with G: the number of vertices and edges, the radius, the independence number, maximum clique size and connectivity. The central result is a set of upper and lower bounds for the function f(n, ϱ), defined to be the minimum of t(G) over all connected graphs with n vertices and n − 1′ + ϱ edges. The bounds obtained yield an asymptotic characterization of the function correct to leading order in almost all ranges. The results show that f(n, ϱ) is surprisingly small; in particular f(n, cn) = 2 loglogn + O(logloglogn) for any constant c > 0, and f(n, n1 + γ) = 2 log(1 + 1γ) ± 4 for 0 < γ < 1 and n sufficiently large. Bounds on t(G) are obtained in terms of the size of the largest clique. These are used to formulate bounds for a Ramsey-type function, N(k, t), the smallest integer so that every connected graph on N(k, t) vertices has either a clique of size k or an induced tree of size t. Tight bounds for t(G) from the independence number α(G) are also proved. It is shown that every connected graph with radius r has an induced path, and hence an induced tree, on 2r − 1 vertices

Surface sensitivity of the spin Seebeck effect

We have investigated the influence of the interface quality on the spin Seebeck effect (SSE) of the bilayer system yttrium iron garnet (YIG) - platinum (Pt). The magnitude and shape of the SSE is strongly influenced by mechanical treatment of the YIG single crystal surface. We observe that the saturation magnetic field H_{sat} for the SSE signal increases from 55.3 mT to 72.8 mT with mechanical treatment. The change in the magnitude of H_{sat} can be attributed to the presence of a perpendicular magnetic anisotropy due to the treatment induced surface strain or shape anisotropy in the Pt/YIG system. Our results show that the SSE is a powerful tool to investigate magnetic anisotropy at the interface.Comment: 5 pages, 4 figure

Good approximation and characterization of subgroups of R/Z

Let α be a real irrational number and A = (x n) be a sequence of positive integers. We call A a characterizing sequence of α or of the group ℤα mod 1 if lim ∥nβ∥ = 0 n∈A n→∞ if and only if β ∈ ℤα mod 1. In the present paper we prove the existence of such characterizing sequences, also for more general subgroups of ℝ/ℤ. In the special case ℤα mod 1 we give explicit construction of a characterizing sequence in terms of the continued fraction expansion of α. Further, we also prove some results concerning the growth and gap properties of such sequences. Finally, we formulate some open problems

Comparison of Post-injection Site Pain Between Technetium Sulfur Colloid and Technetium Tilmanocept in Breast Cancer Patients Undergoing Sentinel Lymph Node Biopsy.

BackgroundNo prior studies have examined injection pain associated with Technetium-99m Tilmanocept (TcTM).MethodsThis was a randomized, double-blinded study comparing postinjection site pain between filtered Technetium Sulfur Colloid (fTcSC) and TcTM in breast cancer lymphoscintigraphy. Pain was evaluated with a visual analogue scale (VAS) (0-100 mm) and the short-form McGill Pain Questionnaire (SF-MPQ). The primary endpoint was mean difference in VAS scores at 1-min postinjection between fTcSC and TcTM. Secondary endpoints included a comparison of SF-MPQ scores between the groups at 5 min postinjection and construction of a linear mixed effects model to evaluate the changes in pain during the 5-min postinjection period.ResultsFifty-two patients underwent injection (27-fTcSC, 25-TcTM). At 1-min postinjection, patients who received fTcSC experienced a mean change in pain of 16.8 mm (standard deviation (SD) 19.5) compared with 0.2 mm (SD 7.3) in TcTM (p = 0.0002). At 5 min postinjection, the mean total score on the SF-MPQ was 2.8 (SD 3.0) for fTcSC versus 2.1 (SD 2.5) for TcTM (p = 0.36). In the mixed effects model, injection agent (p &lt; 0.001), time (p &lt; 0.001) and their interaction (p &lt; 0.001) were associated with change in pain during the 5-min postinjection period. The model found fTcSC resulted in significantly more pain of 15.2 mm (p &lt; 0.001), 11.3 mm (p = 0.001), and 7.5 mm (p = 0.013) at 1, 2, and 3 min postinjection, respectively.ConclusionsInjection with fTcSC causes significantly more pain during the first 3 min postinjection compared with TcTM in women undergoing lymphoscintigraphy for breast cancer