scholarly journals Biases in the estimation of velocity dispersions and dynamical masses for galaxy clusters

2020 ◽  
Vol 228 ◽  
pp. 00011
Author(s):  
A. Ferragamo ◽  
J.A. Rubiño-Martín ◽  
J. Betancort-Rijo ◽  
E. Munari ◽  
B. Sartoris ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Galaxy Clusters ◽  
Velocity Dispersion ◽  
Mean Velocity ◽  
Dynamical Mass ◽  
Unbiased Estimators ◽  
The Mean ◽  
Velocity Dispersions ◽  
Dynamical Masses

Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime (Ngal ≤ 75), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the σ–M relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that they can retrieve bias-corrected values for both the mean velocity dispersion and the mean mass.

scholarly journals Biases in galaxy cluster velocity dispersion and mass estimates in the small Ngal regime

2020 ◽  
Vol 641 ◽  
pp. A41 ◽  
Author(s):  
A. Ferragamo ◽  
J. A. Rubiño-Martín ◽  
J. Betancort-Rijo ◽  
E. Munari ◽  
B. Sartoris ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Velocity Dispersion ◽  
Galaxy Cluster ◽  
Mean Velocity ◽  
Massive Galaxies ◽  
Unbiased Estimators ◽  
Dispersion Estimate ◽  
Physical Effects ◽  
The Mean ◽  
Selection Of

Aims. We present a study of the statistical properties of three velocity dispersion and mass estimators: biweight, gapper, and standard deviation for a small number of galaxies (Ngal ≤ 75). Methods. Using a set of 73 numerically simulated galaxy clusters, we first characterised the statistical bias and the variance for each one of the three estimators (biweight, gapper, and standard deviation) in the determination of the velocity dispersion and the dynamical mass of the clusters through the σ–M relation. These results were used to define a new set of unbiased estimators that are able to correct for these statistical biases with a minimum increase in associated variance. We also used the same set of numerical simulations to characterise two other physical biases that affect the estimates: the effect of velocity segregation on the selection of cluster members, and the effect of using cluster members within different physical radii from the cluster centre. Results. The standard deviation (and its unbiased counterpart) is the estimator with the lowest variance estimator after the biweight and gapper. The effect of velocity segregation in the selection of galaxies within the sub-sample of the most massive galaxies in the cluster introduces a bias of 2% in the velocity dispersion estimate when it is calculated using a quarter of the most massive cluster members. We also find a dependence of the velocity dispersion estimate on the aperture radius as a fraction of R200. This is consistent with previous results in the literature. Conclusions. The proposed set of unbiased estimators effectively provides a correction of the velocity dispersion and mass estimates from the statistical and physical effects discussed above for small numbers of cluster members. When these new estimators are applied to a subset of simulated observations, they can retrieve bias-corrected values for the mean velocity dispersion and the mean mass; the standard deviation has the lowest variance. Although for a single galaxy cluster the statistical and physical effects discussed here are comparable to or slightly smaller than the bias introduced by interlopers, they are relevant when ensemble properties and scaling relations for large number of clusters are studied.

scholarly journals Velocity dispersions and metallicities of box-shaped galaxies

1993 ◽  
Vol 153 ◽  
pp. 411-412
Author(s):  
R. E. de Souza ◽  
S. dos Anjos ◽  
B. Barbuy
Keyword(s):  
Velocity Dispersion ◽  
Mean Velocity ◽  
The Mean ◽  
Velocity Dispersions ◽  
Disk Component

Velocity dispersions and Mg2 indices were measured from CCD spectra of 13 S0 box-shaped galaxies and 5 ellipticals. Evidence for a different relation between velocity dispersion and metallicity, relative to ellipticals, was found for our S0 sample; we attribute this difference to the S0 disk component, affecting both the mean velocity dispersion and mean metallicity.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

Determination of Maleic Hydrazide Residues in Tobacco and Vegetables

1973 ◽  
Vol 56 (5) ◽  
pp. 1164-1172
Author(s):  
Milan Ihnat ◽  
Robert J Westerby ◽  
Israel Hoffman
Keyword(s):  
Standard Deviation ◽  
Present Method ◽  
Maleic Hydrazide ◽  
Collaborative Study ◽  
Official Method ◽  
Sample Weight ◽  
Relative Standard ◽  
The Mean ◽  
Pipe Tobacco

Abstract The distillation-spectrophotometric method of Hoffman for determining maleic hydrazide has been modified to include a double distillation and was applied to the determination of 1–30 ppm maleic hydrazide residues in tobacco and vegetables. Recoveries of 1–23 μg added maleic hydrazide were independent of weight of maleic hydrazide, but did depend on sample and sample weight. The following recoveries were obtained from 0.5 g sample: pipe tobacco, 84%; commercially dehydrated potato, 83%; cigar tobacco, 81%; dried potato, 76%; fluecured tobacco, 73%; dried carrot, 71%. In the absence of sample, the recovery was 82%. When appropriate standard curves were used, maleic hydrazide levels determined in tobacco samples were essentially independent of sample weight in the range 0.1–3 g. The mean relative standard deviation for a variety of field-treated and fortified tobacco samples containing 1–28 ppm maleic hydrazide was 3%. The precision and sensitivity of this procedure seem to be substantial improvements over official method 29.111–29.117. It is recommended that the present method be subjected to a collaborative study.

Prediction of the Maximum Number of Repetitions and Repetitions in Reserve From Barbell Velocity

2018 ◽  
Vol 13 (3) ◽  
pp. 353-359 ◽  
Author(s):  
Amador García-Ramos ◽  
Alejandro Torrejón ◽  
Belén Feriche ◽  
Antonio J. Morales-Artacho ◽  
Alejandro Pérez-Castilla ◽  
...  
Keyword(s):  
Body Mass ◽  
General Equation ◽  
Bench Press ◽  
Body Height ◽  
Strong Relationship ◽  
Training Set ◽  
Mean Velocity ◽  
The Mean ◽  
Acceptable Reliability

Purpose: To provide 2 general equations to estimate the maximum possible number of repetitions (XRM) from the mean velocity (MV) of the barbell and the MV associated with a given number of repetitions in reserve, as well as to determine the between-sessions reliability of the MV associated with each XRM. Methods: After determination of the bench-press 1-repetition maximum (1RM; 1.15 ± 0.21 kg/kg body mass), 21 men (age 23.0 ± 2.7 y, body mass 72.7 ± 8.3 kg, body height 1.77 ± 0.07 m) completed 4 sets of as many repetitions as possible against relative loads of 60%1RM, 70%1RM, 80%1RM, and 90%1RM over 2 separate sessions. The different loads were tested in a randomized order with 10 min of rest between them. All repetitions were performed at the maximum intended velocity. Results: Both the general equation to predict the XRM from the fastest MV of the set (CV = 15.8–18.5%) and the general equation to predict MV associated with a given number of repetitions in reserve (CV = 14.6–28.8%) failed to provide data with acceptable between-subjects variability. However, a strong relationship (median r2 = .984) and acceptable reliability (CV < 10% and ICC > .85) were observed between the fastest MV of the set and the XRM when considering individual data. Conclusions: These results indicate that generalized group equations are not acceptable methods for estimating the XRM–MV relationship or the number of repetitions in reserve. When attempting to estimate the XRM–MV relationship, one must use individualized relationships to objectively estimate the exact number of repetitions that can be performed in a training set.

Determination of spatial velocity dispersion profile and stream velocity field in galaxy clusters - Application to Coma

1982 ◽  
Vol 252 ◽  
pp. 433 ◽  
Author(s):  
H. V. Capelato ◽  
D. Gerbal ◽  
G. Mathez ◽  
A. Mazure ◽  
E. Salvador-Sole
Keyword(s):  
Velocity Field ◽  
Galaxy Clusters ◽  
Velocity Dispersion ◽  
Stream Velocity ◽  
Dispersion Profile ◽  
Spatial Velocity

Fluorometric Determination of Selenium in Foods

1974 ◽  
Vol 57 (2) ◽  
pp. 368-372 ◽  
Author(s):  
Milan Ihnat
Keyword(s):  
Standard Deviation ◽  
Milk Powder ◽  
Skim Milk ◽  
Skim Milk Powder ◽  
Food Samples ◽  
Fluorometric Method ◽  
Fluorometric Determination ◽  
Relative Standard ◽  
The Mean

Abstract A fluorometric method using 2,3-diaminonaphthalene for estimating selenium has been evaluated with regard to its applicability to food samples. Charring of the sample during digestion appeared to result in losses of native and added selenium from some samples, so a modified wet digestion procedure was introduced. Digestion first in nitric acid followed by a mixture of nitric-perchloric-sulfuric acids substantially reduced the incidence of sample charring for a variety of foods. The mean apparent recovery of selenium added as selenite or selenate at 100 and 500 ng levels to 0.1 and 1.0 g corn cereal, skim milk powder, and meat and 0.1 g fish was 101.0%; the actual recovery of the same levels of selenium from standard solutions was 96.6%. For a variety of samples containing 5—750 ng native or added selenium, the standard deviation as 4.7 + 1.95 X 10-2W ng, where W = ng selenium in the sample taken for analysis. The relative standard deviation (RSD) as a function of selenium weight (ng) was 50% (10), 6.7% (100), 4.3% (200), 3.1% (400), 2.7% (600), and 2.5% (800). The detection limit (weight of selenium at which RSD = 50%) was 10 ng at a mean blank level of 25 ng.

Radioisotope Dilution Technique for Determination of Vitamin B12 in Foods

1982 ◽  
Vol 65 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Patrick J Casey ◽  
Keevin R Speckman ◽  
Frank J Ebert ◽  
William E Hobbs
Keyword(s):  
Standard Deviation ◽  
Vitamin B12 ◽  
Relative Standard Deviation ◽  
Extraction Procedure ◽  
Dilution Technique ◽  
Microbiological Method ◽  
Relative Standard ◽  
Wide Range ◽  
The Mean

Abstract A radioisotope dilution (RID) method for the determination of vitamin B12 is presented. The method combines a standard extraction procedure (AOAC 43.108,12th ed.) with a commercially available RID assay kit. The method was evaluated on a wide range of fortified and unfortified food products. Recovery studies on both groups yielded average recoveries of 98.1 and 95.8%, respectively. Reproducibility data generated from replicate analyses on both groups gave a relative standard deviation of 6.9% for the fortified group and 9.2% for the unfortified group. For the samples studied, the mean vitamin B12 content determined by the RID method was 8.01 μg/100 g vs imean of 7.54 μg/100 g by the AOAC microbiological method; the correlation coefficient was r = 0.983.

A simple spectroturbidimetric method for the determination of the fat content of homogenized ice-cream mixes

1962 ◽  
Vol 29 (1) ◽  
pp. 47-53 ◽  
Author(s):  
J. D. S. Goulden ◽  
P. Sherman
Keyword(s):  
Standard Deviation ◽  
Ice Cream ◽  
Fat Content ◽  
Fat Globule ◽  
The Mean ◽  
Simple Filter

SummaryA rapid spectroturbidimetric method for the determination of the fat content of homogenized ice-cream mixes using a simple filter absorptiometer has been devised. Turbidities are measured at two different wavelengths to allow for changes in the degree of homogenization. The standard deviation of the differences from the values obtained by the Werner-Schmid method was found to be 2·5% of the mean fat content value. The method also enables the mean fat globule diameter to be determined.

Ion Exchange Separations and Atomic Absorption Determination of Trace Metals in Ores after Basic Fusion

1972 ◽  
Vol 26 (2) ◽  
pp. 302-305 ◽  
Author(s):  
T. W. Freudiger ◽  
C. T. Kenner
Keyword(s):  
Standard Deviation ◽  
Ion Exchange ◽  
Metal Ions ◽  
Atomic Absorption ◽  
Strong Acid ◽  
Ion Exchange Resin ◽  
High Concentration ◽  
The Mean ◽  
Trace Constituents

The determination of trace constituents in ores by atomic absorption after basic fusion and solution in strong acid is erratic due to the light scattering and aspirator clogging of the high concentration of sodium salts. The sodium is separated from the trace constituents using a column procedure and an iminodiacetate chelating ion exchange resin which will retain di- and trivalent metal ions at pH values above 6.0 but will not retain alkali metal ions. The trace constituents are determined by atomic absorption after elution with HCl. The precision (standard deviation of the mean) of the atomic absorption method is increased at least fivefold by the resin separation and the method is applicable to concentrations in the low ppm range. The standard deviation of the mean for an NBS sample containing 0.007% Cu is 0.0004%.

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