D'atri spaces of type k and related classes of geometries concerning jacobi operators

In this article we continue the study of the geometry of $k$-D'Atri spaces, $$ $\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\geq 1,$ are related to properties of Jacobi operators $R_{v}$ along geodesics, since she has shown that ${\operatorname{tr}}R_{v}$, ${\operatorname{tr}}R_{v}^{2}$ are invariant under the geodesic flow for any unit tangent vector $v$. Here, assuming that the Riemannian manifold is a D'Atri space, we prove in our main result that ${\operatorname{tr}}R_{v}^{3}$ is also invariant under the geodesic flow if $k\geq 3$. In addition, other properties of Jacobi operators related to the Ledger conditions are obtained and they are used to give applications to Iwasawa type spaces. In the class of D'Atri spaces of Iwasawa type, we show two different characterizations of the symmetric spaces of noncompact type: they are exactly the $\frak{C}$-spaces and on the other hand they are $k$ -D'Atri spaces for some $k\geq 3.$ In the last case, they are $k$-D'Atri for all $k=1,...,n-1$ as well. In particular, Damek-Ricci spaces that are $k$-D'Atri for some $k\geq 3$ are symmetric. Finally, we characterize $k$-D'Atri spaces for all $k=1,...,n-1$ as the $\frak{SC}$-spaces (geodesic symmetries preserve the principal curvatures of small geodesic spheres). Moreover, applying this result in the case of 4% -dimensional homogeneous spaces we prove that the properties of being a D'Atri (1-D'Atri) space, or a 3-D'Atri space, are equivalent to the property of being a $k$-D'Atri space for all $k=1,2,3$.Comment: 19 pages. This paper substitute the previous one where one Theorem has been deleted and one section has been adde

High resolution infrared absorption spectra, crystal field, and relaxation processes in CsCdBr_3:Pr^3+

High resolution low-temperature absorption spectra of 0.2% Pr^3+ doped CsCdBr_3 were measured in the spectral region 2000--7000 cm-1. Positions and widths of the crystal field levels within the 3H5, 3H4, 3F2, and 3F3 multiplets of the Pr^3+ main center have been determined. Hyperfine structure of several spectral lines has been found. Crystal field calculations were carried out in the framework of the semiphenomenological exchange charge model (ECM). Parameters of the ECM were determined by fitting to the measured total splittings of the 3H4 and 3H6 multiplets and to the observed in this work hyperfine splittings of the crystal field levels. One- and two-phonon relaxation rates were calculated using the phonon Green's functions of the perfect (CsCdBr_3) and locally perturbed (impurity dimer centers in CsCdBr_3:Pr^3+) crystal lattice. Comparison with the measured linewidths confirmed an essential redistribution of the phonon density of states in CsCdBr_3 crystals doped with rare-earth ions.Comment: 16 pages, 5 tables, 3 figure

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

The Yamato-type (CY) carbonaceous chondrite group: Analogues for the surface of asteroid Ryugu?

We report new mineralogical, petrographic and noble gas analyses of the carbonaceous chondrite meteorites Y-82162 (C1/2ung), Y-980115 (CI1), Y-86029 (CI1), Y-86720 (C2ung), Y-86789 (C2ung), and B-7904 (C2ung). Combining our results with literature data we show that these meteorites experienced varying degrees of aqueous alteration followed by short-lived thermal metamorphism at temperatures of >500 °C. These meteorites have similar mineralogy, textures and chemical characteristics suggesting that they are genetically related, and we strongly support the conclusion of Ikeda (1992) that they form a distinct group, the CYs (“Yamato-type”). The CY chondrites have the heaviest oxygen isotopic compositions (δ17O ˜12‰, δ18O ˜22‰) of any meteorite group, high abundances of Fe-sulphides (˜10 ‒ 30 vol%) and phosphates, and contain large grains of periclase and unusual objects of secondary minerals not reported in other carbonaceous chondrites. These features cannot be attributed to parent body processes alone, and indicate that the CYs had a different starting mineralogy and/or alteration history to other chondrite groups, perhaps because they formed in a different region of the protoplanetary disk. The short cosmic-ray exposure ages (≤1.3 Ma) of the CY chondrites suggest that they are derived from a near-Earth source, with recent observations by the Hayabusa2 spacecraft highlighting a possible link to the rubble-pile asteroid Ryugu

A new class of Roche lobe–filling hot subdwarf binaries

We present the discovery of the second binary with a Roche lobe–filling hot subdwarf transferring mass to a white dwarf (WD) companion. This 56 minute binary was discovered using data from the Zwicky Transient Facility. Spectroscopic observations reveal an He-sdOB star with an effective temperature of T eff = 33,700 ± 1000 K and a surface gravity of log(g) = 5.54 ± 0.11. The GTC+HiPERCAM light curve is dominated by the ellipsoidal deformation of the He-sdOB star and shows an eclipse of the He-sdOB by an accretion disk as well as a weak eclipse of the WD. We infer a He-sdOB mass of M sdOB = 0.41 ± 0.04 M ⊙ and a WD mass of M WD = 0.68 ± 0.05 M ⊙. The weak eclipses imply a WD blackbody temperature of 63,000 ± 10,000 K and a radius R WD = 0.0148 ± 0.0020 R ⊙ as expected for a WD of such high temperature. The He-sdOB star is likely undergoing hydrogen shell burning and will continue transferring mass for ≈1 Myr at a rate of 10−9 M ⊙ yr−1, which is consistent with the high WD temperature. The hot subdwarf will then turn into a WD and the system will merge in ≈30 Myr. We suggest that Galactic reddening could bias discoveries toward preferentially finding Roche lobe–filling systems during the short-lived shell-burning phase. Studies using reddening-corrected samples should reveal a large population of helium core–burning hot subdwarfs with T eff ≈ 25,000 K in binaries of 60–90 minutes with WDs. Though not yet in contact, these binaries would eventually come into contact through gravitational-wave emission and explode as a subluminous thermonuclear supernova or evolve into a massive single WD

Characteristics of aerial dust in finishing buildings

Eleven finishing units were surveyed to study the characteristics of aerial dust and factors that influence dust concentrations. Feed dust was the major portion of the total dust mass and can be minimized with feed additives, less feed wastage, enclosed feed delivery, and periodic cleaning. Ventilation was the primary method for dust removal. Naturally ventilated buildings had higher dust concentrations than mechanically ventilated buildings because of lower average airflow rates, especially during cold weather. Swine workers can minimize respiratory symptoms by wearing face masks