To review empirical studies that assess saturation in qualitative research in order to identify sample sizes for saturation, strategies used to assess saturation, and guidance we can draw from these ...studies.
We conducted a systematic review of four databases to identify studies empirically assessing sample sizes for saturation in qualitative research, supplemented by searching citing articles and reference lists.
We identified 23 articles that used empirical data (n = 17) or statistical modeling (n = 6) to assess saturation. Studies using empirical data reached saturation within a narrow range of interviews (9–17) or focus group discussions (4–8), particularly those with relatively homogenous study populations and narrowly defined objectives. Most studies had a relatively homogenous study population and assessed code saturation; the few outliers (e.g., multi-country research, meta-themes, “code meaning” saturation) needed larger samples for saturation.
Despite varied research topics and approaches to assessing saturation, studies converged on a relatively consistent sample size for saturation for commonly used qualitative research methods. However, these findings apply to certain types of studies (e.g., those with homogenous study populations). These results provide strong empirical guidance on effective sample sizes for qualitative research, which can be used in conjunction with the characteristics of individual studies to estimate an appropriate sample size prior to data collection. This synthesis also provides an important resource for researchers, academic journals, journal reviewers, ethical review boards, and funding agencies to facilitate greater transparency in justifying and reporting sample sizes in qualitative research. Future empirical research is needed to explore how various parameters affect sample sizes for saturation.
•We reviewed empirically-based studies of sample sizes for saturation in qualitative research.•We confirmed qualitative studies can reach saturation at relatively small sample sizes.•Results show 9–17 interviews or 4–8 focus group discussions reached saturation.•Most studies had a relatively homogenous study population and narrowly defined objectives.
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The third-order particle-hole ring diagrams are evaluated for a NN-contact interaction of the Skyrme type. The pertinent four-loop coefficients in the energy per particle
E
¯
(
k
f
)
∼
k
f
5
+
2
n
...are reduced to double integrals over cubic expressions in Euclidean polarization functions. Dimensional regularization of divergent integrals is performed by subtracting power divergences and the validity of this method is checked against the known analytical results at second order. The complete
𝒪
(
p
2
)
NN-contact interaction is obtained by adding two tensor terms and their third-order ring contributions are also calculated in detail. The third-order ring energy arising from long-range
1
π
-exchange is computed and it is found that direct and exchange contributions are all attractive. The very large size of the three-ring energy due to point-like
1
π
-exchange,
E
¯
(
k
f
0
)
≃
-
92
MeV at saturation density, is however in no way representative for that of realistic chiral NN-potentials. Moreover, the third-order (particle-particle and hole-hole) ladder diagrams are evaluated with the full
𝒪
(
p
2
)
contact interaction, and the simplest three-ring contributions to the isospin-asymmetry energy
A
(
k
f
)
∼
k
f
5
are studied.
Physical Properties of 15 Quasars at z 6.5 Mazzucchelli, C.; Bañados, E.; Venemans, B. P. ...
Astrophysical journal/The Astrophysical journal,
11/2017, Letnik:
849, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Quasars are galaxies hosting accreting supermassive black holes; due to their brightness, they are unique probes of the early universe. To date, only a few quasars have been reported at (<800 Myr ...after the big bang). In this work, we present six additional quasars discovered using the Pan-STARRS1 survey. We use a sample of 15 quasars to perform a homogeneous and comprehensive analysis of this highest-redshift quasar population. We report four main results: (1) the majority of quasars show large blueshifts of the broad C iv λ1549 emission line compared to the systemic redshift of the quasars, with a median value ∼3× higher than a quasar sample at ; (2) we estimate the quasars' black hole masses ( (0.3-5) × 109 M ) via modeling of the Mg ii λ2798 emission line and rest-frame UV continuum and find that quasars at high redshift accrete their material (with ) at a rate comparable to a luminosity-matched sample at lower redshift, albeit with significant scatter (0.4 dex); (3) we recover no evolution of the Fe ii/Mg ii abundance ratio with cosmic time; and (4) we derive near-zone sizes and, together with measurements for quasars from recent work, confirm a shallow evolution of the decreasing quasar near-zone sizes with redshift. Finally, we present new millimeter observations of the C ii 158 m emission line and underlying dust continuum from NOEMA for four quasars and provide new accurate redshifts and C ii/infrared luminosity estimates. The analysis presented here shows the large range of properties of the most distant quasars.
In the majority of agricultural growing regions, crop production is highly dependent on the supply of exogenous nitrogen (N) fertilizers. Traditionally, this dependency and the use of N-fertilizers ...to restore N depleted soils has been rewarded with increased plant health and yields. In recent years, increased competition for non-renewable fossil fuel reserves has directly elevated prices of N-fertilizers and the cost of agricultural production worldwide. Furthermore, N-fertilizer based pollution is becoming a serious issue for many regions where agriculture is highly concentrated. To help minimize the N footprint associated with agricultural production there is significant interest at the plant level to develop technologies which can allow economically viable production while using less applied N. To complement recent reviews examining N utilization efficiency in agricultural plants, this review will explore those strategies operating specifically at the root level, which may directly contribute to improved N use efficiencies in agricultural crops such as cereals, where the majority of N-fertilizers are used and lost to the environment. Root specific phenotypes that will be addressed in the context of improvements to N acquisition and assimilation efficiencies include: root morphology; root to shoot ratios; root vigour, root length density; and root N transport and metabolism.
We study ion transport limitations in composite electrodes for all-solid-state lithium batteries. These electrodes are composed of variable volume fractions of active material particles (Li4Ti5O12) ...and of a sulfide-based solid electrolyte, while the volume fraction of carbon black acting as conductive additive is held constant. The ion transport limitations are characterized by impedance spectroscopic measurements on different types of symmetrical solid-state cells. Ion transport resistances are calculated either based on a transmission line model or from the Li+ ion current under electron-blocking conditions. In addition, we demonstrate a cell setup, for which both types of measurements can be carried out on the same composite electrodes. Effective ion transport tortuosities τeff are then derived from the resistance values and analyzed in dependence on the volume fraction of the solid electrolyte in the composite electrodes, ε . We show that for ε≥0.4, both methods yield very similar tortuosity values, while discrepancies between the results obtained from the two methods are found for ε<0.4. Our results give strong indication that the power density of solid-state batteries with volume fractions ε around 0.4 of the best solid Li+ electrolytes should be at least equal that of commercial liquid electrolyte-based Li-ion batteries.
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•Ion transport limitations in composite electrodes for all-solid-state batteries is studied.•Tortuosities are determined by means of impedance spectroscopy.•Resistances are calculated based on a transmission-line model or from Li + ion current.•Power density of solid-state should at least equal that of liquid-based batteries.
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