Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sampling statistics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

In-service inspection of radioactive waste tanks at the Savannah River Site - 15410

Liquid radioactive wastes from the Savannah River Site (SRS) separation process are stored in large underground carbon steel tanks. The high level wastes are processed in several of the tanks and then transferred by piping to other site facilities for further processing before they are stabilized in a vitrified or grout waste form. Based on waste removal and processing schedules, many of the tanks, will be required to be in service for times exceeding the initial intended life. Until the waste is removed from storage, transferred, and processed, the materials and structures of the tanks must maintain a confinement function by providing a barrier to the environment and by maintaining acceptable structural stability during design basis events, which include loadings from both normal service and abnormal (e.g., earthquake) conditions. A structural integrity program is in place to maintain the structural and leak integrity functions of these waste tanks throughout their intended service life. In-service inspection (ISI) is an essential element of a comprehensive structural integrity program for the waste tanks at the Savannah River Site (SRS). The ISI program was developed to determine the degree of degradation the waste tanks have experienced due to service conditions. As a result of the inspections, an assessment can be made of the effectiveness of corrosion controls for the waste chemistry, which precludes accelerated localized and general corrosion of the waste tanks. Ultrasonic inspections (UT) are performed to detect and quantify the degree of general wall thinning, pitting and cracking as a measure of tank degradation. The results from these inspections through 2013, for the 27 Type III/IIIA tanks, indicate no reportable in-service corrosion degradation in the primary tank (i.e., general, pitting, or cracking). The average wall thickness for all tanks remains above the manufactured nominal thickness minus 0.25 millimeter and the largest pit identified is approximately 1.70 millimeter deep (i.e., less than 10% through-wall). Improvements to the inspection program were recently instituted to provide additional confidence in the degradation rates. Thickness measurements from a single vertical strip along the accessible height of the primary tank have been used as a baseline to compare historical measurements. Changes in wall thickness and pit depths along this vertical strip are utilized to estimate the rate of corrosion degradation. An independent review of the ISI program methodology, results, and path forward was held in August 2009. The review recommended statistical sampling of the tanks to improve the confidence of the single strip inspection program. The statistical sampling plan required that SRS increase the amount of area scanned per tank. Therefore, in addition to the baseline vertical strip that is obtained for historical comparisons, four additional randomly selected vertical strips are inspected. To date, a total of 104 independent vertical strips along the height of the primary tank have been completed. A statistical analysis of the data indicates that at this coverage level there is a 99.5% confidence level that one of the worst 5% of all the vertical strips was inspected. That is, there is a relatively high likelihood that the SRS inspection program has covered one of the most corroded areas of any of the Type III/IIIA waste tanks. These data further support the conclusion that there are no significant indications of wall thinning or pitting. Random sampling will continue to increase the confidence that one of the worst 5% has been inspected. In order to obtain the additional vertical strips, and minimize budget and schedule impacts, data collection speed for the UT system was optimized. Prior to 2009, the system collected data at a rate of 32 square centimeters per minute. The scan rate was increased to 129 - 160 square centimeters per minute by increasing the scanner step and pixel sizes in the data acquisition set-up. Laboratory testing was utilized to optimize the scan index/pixel size such that the requirements for wall thinning and pit detection were still maintained. SRS continues to evaluate improvements to ultrasonic equipment. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Municipal solid waste composition: Sampling methodology, statistical analyses, and case study evaluation

Highlights: • Tiered approach to waste sorting ensures flexibility and facilitates comparison of solid waste composition data. • Food and miscellaneous wastes are the main fractions contributing to the residual household waste. • Separation of food packaging from food leftovers during sorting is not critical for determination of the solid waste composition. - Abstract: Sound waste management and optimisation of resource recovery require reliable data on solid waste generation and composition. In the absence of standardised and commonly accepted waste characterisation methodologies, various approaches have been reported in literature. This limits both comparability and applicability of the results. In this study, a waste sampling and sorting methodology for efficient and statistically robust characterisation of solid waste was introduced. The methodology was applied to residual waste collected from 1442 households distributed among 10 individual sub-areas in three Danish municipalities (both single and multi-family house areas). In total 17 tonnes of waste were sorted into 10–50 waste fractions, organised according to a three-level (tiered approach) facilitating comparison of the waste data between individual sub-areas with different fractionation (waste from one municipality was sorted at “Level III”, e.g. detailed, while the two others were sorted only at “Level I”). The results showed that residual household waste mainly contained food waste (42 ± 5%, mass per wet basis) and miscellaneous combustibles (18 ± 3%, mass per wet basis). The residual household waste generation rate in the study areas was 3–4 kg per person per week. Statistical analyses revealed that the waste composition was independent of variations in the waste generation rate. Both, waste composition and waste generation rates were statistically similar for each of the three municipalities. While the waste generation rates were similar for each of the two housing types (single-family and multi-family house areas), the individual percentage composition of food waste, paper, and glass was significantly different between the housing types. This indicates that housing type is a critical stratification parameter. Separating food leftovers from food packaging during manual sorting of the sampled waste did not have significant influence on the proportions of food waste and packaging materials, indicating that this step may not be required.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Occurrence of Radio Minihalos in a Mass-limited Sample of Galaxy Clusters

We investigate the occurrence of radio minihalos—diffuse radio sources of unknown origin observed in the cores of some galaxy clusters—in a statistical sample of 58 clusters drawn from the Planck Sunyaev–Zel’dovich cluster catalog using a mass cut ( M {sub 500} > 6 × 10{sup 14} M {sub ⊙}). We supplement our statistical sample with a similarly sized nonstatistical sample mostly consisting of clusters in the ACCEPT X-ray catalog with suitable X-ray and radio data, which includes lower-mass clusters. Where necessary (for nine clusters), we reanalyzed the Very Large Array archival radio data to determine whether a minihalo is present. Our total sample includes all 28 currently known and recently discovered radio minihalos, including six candidates. We classify clusters as cool-core or non-cool-core according to the value of the specific entropy floor in the cluster center, rederived or newly derived from the Chandra X-ray density and temperature profiles where necessary (for 27 clusters). Contrary to the common wisdom that minihalos are rare, we find that almost all cool cores—at least 12 out of 15 (80%)—in our complete sample of massive clusters exhibit minihalos. The supplementary sample shows that the occurrence of minihalos may be lower in lower-mass cool-core clusters. No minihalos are found in non-cool cores or “warm cores.” These findings will help test theories of the origin of minihalos and provide information on the physical processes and energetics of the cluster cores.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2017

Occurrence of Radio Minihalos in a Mass-Limited Sample of Galaxy Clusters

We investigate the occurrence of radio minihalos-diffuse radio sources of unknown origin observed in the cores of some galaxy clusters-in a statistical sample of 58 clusters drawn from the Planck Sunyaev-Zeldovich cluster catalog using a mass cut (M(sub 500) greater than 6 x 10(exp 14) solar mass). We supplement our statistical sample with a similarly sized nonstatistical sample mostly consisting of clusters in the ACCEPT X-ray catalog with suitable X-ray and radio data, which includes lower-mass clusters. Where necessary (for nine clusters), we reanalyzed the Very Large Array archival radio data to determine whether a minihalo is present. Our total sample includes all 28 currently known and recently discovered radio minihalos, including six candidates. We classify clusters as cool-core or non-cool-core according to the value of the specific entropy floor in the cluster center, rederived or newly derived from the Chandra X-ray density and temperature profiles where necessary (for 27 clusters). Contrary to the common wisdom that minihalos are rare, we find that almost all cool cores-at least 12 out of 15 (80%)-in our complete sample of massive clusters exhibit minihalos. The supplementary sample shows that the occurrence of minihalos may be lower in lower-mass cool-core clusters. No minihalos are found in non-cool cores or "warm cores." These findings will help test theories of the origin of minihalos and provide information on the physical processes and energetics of the cluster cores.

catalogs↗
DOE OSTI2015

Low surface brightness galaxies selected from the 40% sky area of the ALFALFA H i Survey. I. Sample and statistical properties

The population of low surface brightness (LSB) galaxies, which are objects with central surface brightnesses at least one magnitude fainter than the night sky, is crucial for understanding the extremes of galactic formation and evolution of the universe. As LSB galaxies are mostly rich in gas (H i), the α.40 Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) sample is one of the best survey combinations to select a sample of them in the local universe. Since the sky backgrounds are systematically overestimated for galactic images by the SDSS photometric pipeline, particularly for luminous galaxies or galaxies with extended LSB outskirts, in this paper, we above all estimated the sky backgrounds of SDSS images accurately in both the g and r bands for each galaxy in the α.40 SDSS DR7 sample, using a precise method of sky subtraction. Once subtracting the sky background, we did surface photometry with the Kron elliptical aperture using the SExtractor software and fitted geometric parameters with an exponential profile model using the Galfit software for each galactic image in the α.40 SDSS DR7 sample. Based on the photometric and geometric results, we further calculated the B-band central surface brightness, μ{sub 0}(B), for each galaxy and ultimately defined a sample of LSB galaxies consisting of 1129 galaxies with μ{sub 0}(B) > 22.5 mag arcsec{sup −2} and the axis ratio b/a > 0.3 from the 12,423 α.40 SDSS DR7 galaxies. This H i-selected sample of LSB galaxies is a relatively unbiased sample of gas-rich and disk-dominated LSB galaxies, which is complete both in H i observation and the optical magnitude within the limit of the SDSS DR7 photometric survey. This LSB galactic sample spans from 22.5 to 28.3 in μ{sub 0}(B) with a fraction of 4% fainter than 25.0 mag arcsec{sup −2} in B-band central surface brightness and distributes from −27.0 to −12.3 mag in absolute magnitude in the B band (M(B)), including the 43 faintest galaxies (M(B) > −17.3 mag). This sample is a blue LSB galactic sample, of which 98% are bluer than 0.75 mag in B–V color. As for 21 cm H i properties, our LSB galactic sample has a median M{sub H i}/L{sub B} = 0.87, and a large portion (95%) has high mass of H i (M(H i) > 10{sup 7.7}M⊙), which supports galaxies in this LSB galactic sample being mostly gas-rich. Additionally, we statistically investigated the environment of our LSB galaxies and found that up to 92% of the total LSB galaxies have less than eight neighboring galaxies, which provides strong evidence that LSB galaxies prefer to reside in the low-density environment.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

An evaluation of grease type ball bearing lubricants operating in various environments

Because many future spacecraft or space stations will require mechanisms to operate for long periods of time in environments which are adverse to most bearing lubricants, a series of tests is continuing to evaluate 38 grease type lubricants in R-4 size bearings in five different environments for a 1 year period. Four repetitions of each test are made to provide statistical samples. These tests were used to select four lubricants for 5 year tests in selected environments with five repetitions of each test for statistical samples. At the present time, 100 test sets are completed and 22 test sets are underway. Three 5 year tests were started in (1) continuous operation and (2) start-stop operation, with both in vacuum at ambient temperatures, and (3) continuous operation at 93.3 C. In the 1 year tests the best results to date in all environments were obtained with a high viscosity index perfluoroalkylpolyether (PFPE) grease.

Mcmurtrey, E. L.↗
DOE OSTI2026

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE↗
NASA NTRS1979

An evaluation of grease type ball bearing lubricants operating in various environments

Grease type lubricants in bearings were evaluated in five different adverse environments for a one year period. Four repetitions of each test were made to provide statistical samples. These tests were then used to select four lubricants for five year tests in selected environments with five repetitions of each test for statistical samples. Three five year tests were started in (1) continuous operation; (2) start-stop operation, with both in vacuum at ambient temperatures; and (3) continuous operation at 93.3 C. To date, in the one year tests, the best results in all environments were obtained with a high viscosity index perfluoroalkylpolyether grease.

Mcmurtrey, E. L.↗
NASA NTRS1984

An evaluation of grease type ball bearing lubricants operating in various environments

Because many future spacecraft or space stations will require mechanisms to operate for long periods of time in environments which are adverse to most bearing lubricants, a series of tests has been completed to evaluate 38 grease type lubricants in R-4 size bearings in five different environments for a 1 year period. Four repetitions of each test were made to provide statistical samples. These tests were also used to select four lubricants for 5 year tests in selected environments with five repetitions of each test for statistical samples. In this completed program, 172 test sets have been completed. The three 5 year tests in: (1) continuous operation and (2) start stop operation, with both in vacuum at ambient temperatures, and (3) continuous vacuum operation at 93.3 C have been completed. In both the 1 year and 5 year tests, the best results in all environments have been obtained with a high viscosity index perfluoroalkylpolyether (PFPE) grease.

Mcmurtrey, E. L.↗
DOE OSTI2016

A Scalable Method for Extracting Soiling Rates from PV Production Data

We present a method for analyzing time series production data from photovoltaic systems to extract the rate at which energy yield is affected by the accumulation of dust, dirt, and other forms of soiling. We describe an approach that is based on prevailing methods which consider the change in energy production during dry periods. The method described here builds upon these methods by considering a statistical sample of soiling intervals from each site under consideration. The method enables straightforward application to a large number of sites with minimal parameterization of data-filtering requirements. Furthermore, it enables statistical confidence intervals and comparisons between sites.

14 SOLAR ENERGY↗
NASA NTRS1978

An evaluation of grease type ball bearing lubricants operating in various environments

Because many future spacecraft or space stations will require mechanisms to operate for long periods of time in environments which are adverse to most bearing lubricants, a series of tests is continuing to evaluate 29 grease type lubricants in R-4 size bearings in five different environments for a 1 year period. Four repetitions of each test are made to provide statistical samples. These tests have also been used to select four lubricants for 5 year tests in selected environments with five repetitions of each test for statistical samples. At the present time, 65 test sets have been completed and 23 test sets are underway. Two (5 year) tests have already been started in (1) continuous operation and (2) start-stop operation, with both in vacuum at ambient temperatures. To date, in the 1 year tests, the best results in all environments have been obtained with a high viscosity index perfluoroalkylpolyether grease.

Mcmurtrey, E. L.↗
NASA NTRS1983

An evaluation of grease-type ball bearing lubricants operation in various environments

Because many future spacecraft or space stations will require mechanisms to operate for long periods of time in environments which are adverse to most bearing lubricants, a series of tests is continuing to evaluate 38 grease type lubricants in R-4 size bearings in five different environments for a 1 year period. Four repetitions of each test are made to provide statistical samples. These tests have also been used to select four lubricants for 5 year tests in selected environments with five repetitions of each test for statistical samples. At the present time, 142 test sets have been completed and 30 test sets are underway. The three 5 year tests in (1) continuous operation and (2) start stop operation, with both in vacuum at ambient temperatures, and (3) continuous vacuum operation at 93.3 C are now completed. To date, in both the 1 year and 5 year tests, the best results in all environments have been obtained with a high viscosity index perfluoroalkylpolyether (PFPE) grease.

Mcmurtrey, E. L.↗
NASA NTRS2018

Realistic Covariance Generation for the GPM Spacecraft

We present several different methods for generating realistic predictive covariance, including Monte-Carlo simulations and more direct linear methods which require the addition of process noise. The Monte-Carlo simulation starts with an epoch uncertainty sample basis and propagates each trial to a time of interest in the future. The variance-covariance of the state elements as well as other higher order sample statistics can be readily computed from the propagated sample. While this method preserves the nonlinear effects on the propagated uncertainty, it is computationally intensive as a statistically significant sample size must be considered in the propagation process. Moreover, if the epoch covariance is optimistic, this can result in an underestimation of the prediction error. Another method is to propagate a state sensitivity matrix simultaneously with the satellite state, which allows the epoch covariances to be propagated forward in a linear fashion. This method does not preserve the non-linearity of the satellite state uncertainty but is much less computationally intensive. The propagated state covariance is the scaled to represent the realistic level of GPM state uncertainty via a "e-tuning process." The tuning process generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Difference tuning strategies are considered and compared via Goodness-of-Fit method testing for the Gaussian properties of the scaled covariance.

prediction error↗
DOE OSTI2012

A MISMATCH IN THE ULTRAVIOLET SPECTRA BETWEEN LOW-REDSHIFT AND INTERMEDIATE-REDSHIFT TYPE Ia SUPERNOVAE AS A POSSIBLE SYSTEMATIC UNCERTAINTY FOR SUPERNOVA COSMOLOGY

We present Keck high-quality rest-frame ultraviolet (UV) through optical spectra of 21 Type Ia supernovae (SNe Ia) in the redshift range 0.11 {<=} z {<=} 0.37 and a mean redshift of 0.22 that were discovered during the Sloan Digital Sky Survey-II (SDSS-II) SN Survey. Using the broadband photometry of the SDSS survey, we are able to reconstruct the SN host-galaxy spectral energy distributions (SEDs), allowing for a correction for the host-galaxy contamination in the SN Ia spectra. Comparison of composite spectra constructed from a subsample of 17 high-quality spectra to those created from a low-redshift sample with otherwise similar properties shows that the Keck/SDSS SNe Ia have, on average, extremely similar rest-frame optical spectra but show a UV flux excess. This observation is confirmed by comparing synthesized broadband colors of the individual spectra, showing a difference in mean colors at the 2.4{sigma}-4.4{sigma} level for various UV colors. We further see a slight difference in the UV spectral shape between SNe with low-mass and high-mass host galaxies. Additionally, we detect a relationship between the flux ratio at 2770 and 2900 A and peak luminosity that differs from that observed at low redshift. We find that changing the UV SED of an SN Ia within the observed dispersion can change the inferred distance moduli by {approx}0.1 mag. This effect only occurs when the data probe the rest-frame UV. We suggest that this discrepancy could be due to differences in the host-galaxy population of the two SN samples or to small-sample statistics.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2006

Debris Flux Comparisons From The Goldstone Radar, Haystack Radar, and Hax Radar Prior, During, and After the Last Solar Maximum

The continual monitoring of low Earth orbit (LEO) debris environment using highly sensitive radars is essential for an accurate characterization of these dynamic populations. Debris populations are continually evolving since there are new debris sources, previously unrecognized debris sources, and debris loss mechanisms that are dependent on the dynamic space environment. Such radar data are used to supplement, update, and validate existing orbital debris models. NASA has been utilizing radar observations of the debris environment for over a decade from three complementary radars: the NASA JPL Goldstone radar, the MIT Lincoln Laboratory (MIT/LL) Long Range Imaging Radar (known as the Haystack radar), and the MIT/LL Haystack Auxiliary radar (HAX). All of these systems are highly sensitive radars that operate in a fixed staring mode to statistically sample orbital debris in the LEO environment. Each of these radars is ideally suited to measure debris within a specific size region. The Goldstone radar generally observes objects with sizes from 2 mm to 1 cm. The Haystack radar generally measures from 5 mm to several meters. The HAX radar generally measures from 2 cm to several meters. These overlapping size regions allow a continuous measurement of cumulative debris flux versus diameter from 2 mm to several meters for a given altitude window. This is demonstrated for all three radars by comparing the debris flux versus diameter over 200 km altitude windows for 3 nonconsecutive years from 1998 through 2003. These years correspond to periods before, during, and after the peak of the last solar cycle. Comparing the year to year flux from Haystack for each of these altitude regions indicate statistically significant changes in subsets of the debris populations. Potential causes of these changes are discussed. These analysis results include error bars that represent statistical sampling errors, and are detailed in this paper.

Stokely, C. L.↗
DOE OSTI2014

THE FIRST HYPERVELOCITY STAR FROM THE LAMOST SURVEY

We report the first hypervelocity star (HVS) discovered from the LAMOST spectroscopic survey. It is a B-type star with a heliocentric radial velocity of about 620 km s{sup –1}, which projects to a Galactocentric radial velocity component of ∼477 km s{sup –1}. With a heliocentric distance of ∼13 kpc and an apparent magnitude of ∼13 mag, it is the closest bright HVS currently known. With a mass of ∼9 M {sub ☉}, it is one of the three most massive HVSs discovered so far. The star is clustered on the sky with many other known HVSs, and its position suggests a possible connection to Galactic center structures. With the current poorly determined proper motion, a Galactic center origin of this HVS remains consistent with the data at the 1σ level, while a disk runaway origin cannot be excluded. We discuss the potential of the LAMOST survey to discover a large statistical sample of HVSs of different types.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The ongoing need for high-resolution regional climate models: Process understanding and stakeholder information

Regional climate modeling addresses our need to understand and simulate climatic processes and phenomena unresolved in global models. High resolution models are generally more skillful in simulating extremes, such as heavy precipitation, strong winds, and severe storms. In addition, research has shown that fine-scale features such as mountains, coastlines, lakes, irrigation, land use, and urban heat islands can substantially influence a region’s climate and its response to changing forcings. Regional climate simulations explicitly simulating convection are now being performed, providing an opportunity to illuminate new physical behavior that previously was represented by parameterizations with large uncertainties. Regional and global models are both advancing toward higher resolution, as computational capacity increases. However, the resolution and ensemble size necessary to produce a sufficient statistical sample of these processes in global models has proven too costly for contemporary supercomputing systems. Regional climate models are thus indispensable tools that complement global models for understanding regional climate variability and change, and are critical for supporting societal responses to changing climate.

Gutowski, William↗
DOE OSTI2015

A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube

Evidence for an extraterrestrial flux of high-energy neutrinos has now been found in multiple searches with the IceCube detector. The first solid evidence was provided by a search for neutrino events with deposited energies ≳30 TeV and interaction vertices inside the instrumented volume. Recent analyses suggest that the extraterrestrial flux extends to lower energies and is also visible with throughgoing, ν{sub μ}-induced tracks from the Northern Hemisphere. Here, we combine the results from six different IceCube searches for astrophysical neutrinos in a maximum-likelihood analysis. The combined event sample features high-statistics samples of shower-like and track-like events. The data are fit in up to three observables: energy, zenith angle, and event topology. Assuming the astrophysical neutrino flux to be isotropic and to consist of equal flavors at Earth, the all-flavor spectrum with neutrino energies between 25 TeV and 2.8 PeV is well described by an unbroken power law with best-fit spectral index −2.50 ± 0.09 and a flux at 100 TeV of (6.7{sub −1.2}{sup +1.1})×10{sup −18} GeV{sup −1} s{sup −1} sr{sup −1} cm{sup −2}. Under the same assumptions, an unbroken power law with index −2 is disfavored with a significance of 3.8σ (p = 0.0066%) with respect to the best fit. This significance is reduced to 2.1σ (p = 1.7%) if instead we compare the best fit to a spectrum with index −2 that has an exponential cut-off at high energies. Allowing the electron-neutrino flux to deviate from the other two flavors, we find a ν{sub e} fraction of 0.18 ± 0.11 at Earth. The sole production of electron neutrinos, which would be characteristic of neutron-decay-dominated sources, is rejected with a significance of 3.6σ (p = 0.014%).

79 ASTRONOMY AND ASTROPHYSICS↗