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The main insulation structure of the valve‐side winding of converter transformer bears the effect of AC and DC superimposed voltage during operation. The electric field intensity in the pressboard is much higher than that in the pressboard in the AC transformer. This condition increases the probability of failure of insulation structure. Therefore, the design and optimization of the main insulation structure of the valve‐side winding are keys to ensure the stable operation of converter transformer. This study establishes a model of the main insulation structure of the valve‐side winding of the ±1100 kV converter transformer. The influence of the insulating oil–paper configuration on the electric field distribution of the main insulation structure of the valve‐side winding is analysed, and then, an optimization idea is proposed. The oil–paper configuration includes two aspects: oil–paper insulation structural design and combination selection, that is, the influence of typical oil–paper structural design parameters and the aging state of different oil–paper combinations on the electric field distribution. Finally, the optimization idea of the oil–paper configuration for valve‐side winding of converter transformer is obtained, and the established model is optimized.

Heavy metal contaminants in the soil will have a direct effect on human life. The spatial distribution of naturally occurring heavy metals is highly heterogeneous and significantly increased concentrations may be present in the soil at certain locations. Heavy metals in areas of high concentration can be distributed to other areas by surface runoff, groundwater flow, weathering and atmospheric cycles (eg wind, sea salt spray, volcanic eruptions, deposition by rivers). More and more people are now using a combination of geographic information science (GIS) with geostatistical statistical analysis techniques to examine the spatial distribution of heavy metals in soils on a regional scale. The most widely used geostatistical methods are the Inverse Distance Weighted, Kriging, and Spatial Autocorrelation methods as well as other methods. This review paper will explain clearly the source of the presence of heavy metals in soil, geostatistical methods that are often used, as well as case studies on the use of geostatistics for the distribution of heavy metals. The use of geostatistical models allows us to accurately assess the relationship between the spatial distribution of heavy metals and other parameters in a map.

Gheiasvand et al. (2020) use the two larger benthic foraminifera species Simplorbitolina manasi Ciry & Rat and Mesorbitolina parva (Douglass) (Orbitolinidae) as upper Aptian “potential index fossils” for parts of the Taft Formation in Central Iran. This age assignment is accompanied by changes to well-established orbitolinid biozona-tions (e.g. occurrence of Praeorbitolina in the late Aptian) with far-reaching implications. These data were also used in a later “multidisciplinary study” (Gheiasvand et al., 2021) for isotopic correlations (e.g., location of OAE`s), delimitation of palaeobiogeographic faunal provinces and related migration patterns. It is shown herein that the taxa identified as S. manasi and M. parva belong to Iraqia simplex Henson and Palorbitolina lenticularis (Blumenbach) respectively documenting a lower and not an upper Aptian age. This revised age and the different taxononomic inventory do not question all results obtained by Gheiasvand et al. (2020, 2021), but provide a revised basis interpretation.

We analyze the multiauthorship matrix M, defined as the matrix where a cell M (j, @k) denotes the number of times authors with j publications are ranked as the @k^t^h author of an article. We prove that if the distribution of the number of authors per paper follows a power law, then the author rank distribution is approximately equal to this power law (more precisely, equal in Landau's big O sense). We further determine the author rank distribution in the case where authors can be characterized through a seed number; this is the probability of preceding a fixed author in the byline of an article. Such a seed is determined for alphabetical ranking of authors using the standard western alphabet.

Ahmad et al. (2015) consider a Transmuted Kumaraswamy distribution and study certain properties of their distribution. In the title of their paper they mention characterization of this distribution, but no characterization are presented in their paper. In the present short note, we establish certain characterizations of the Transmuted Kumaraswamy distribution in three directions.

Theory is presented for the distribution of the narrowest dimension of voids encountered in a path through a stochastic fibre network from one side of its plane to the other. Using expressions from the literature we show that the mean out-of-plane pore dimension is always less than half the mean in-plane dimension such that out-of-plane pore dimensions have a controlling influence on the measured pore size distribution. An approximate model is derived which predicts that the overall mean pore dimension of a network of fibres with given dimensions is inversely proportional to its areal density and proportional to a simple function of porosity. Good agreement is demonstrated between this model and experimental data. Regression analysis suggests that out-of-plane pore dimensions account for more than 70% of the measured pore size distribution.

In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L ( 1 , X ; y ) : = ∏ p ⩽ y ( 1 − X ( p ) / p ) −1 , where the X ( p ) are independent random variables, taking the values ±1 with equal probability p / 2 ( p + 1 ) and 0 with probability 1 / ( p + 1 ) .

This article is an attempt to throw more light on the problem of choosing plotting positions for the frequencies related to ordered sample values. The problem is particularly pertinent where special-scale graph paper is used such that a straight line indicates conformance of data to type of distribution assumed to apply. Such graph paper is often briefly referred to as “probability paper.” The types of distributions here considered are the normal and the extreme-value distribution of Type I, with the accent on the extreme-value case. Various methods of determining plotting positions have been put forward and there is confusion of thought in judging what plotting convention is optimum. An optimum criterion proposed by Chernoff and Lieberman has received wide attention. Blom in a recent book develops further criteria [2]. To clarify the problem the author has analyzed the purposes to be served in plotting data on probability paper. With a specific concept of the purpose to be served in mind, it bec...

The derivation of the dyadic Green's function for rectangular waveguides and cavities is approached systematically by using the theory of distributions. It is shown that, in order to obtain a complete solution for the field distribution in the entire structure, one must add an additional term to the classical expansion which is valid only outside the source region.

Experiments of the above title are done by middle rotations of the homogenizer, which rotates a little more than 26 r.p.m. and mixes moths twice per rotation by the action of agitation vane inserted at 45 degree to the base of a drum. As the number of an unit group, 600 and 200 moths are adopted in accordance with the ordinary custom of egg producers. Results are as follows.1. After rotation of the homogenizer for only five seconds, the distribution of almost all groups of diseased moths becomes already binomial or normal.2. As the rotation time of the homogenizer becomes longer and longer, the distribution of diseased moths tends more and more to fit the normal formula than the binomial, and in some cases, it takes PEARSON'S II-type distribution curve or in other cases, even if rare, more than halves of the number of experiments centre to the position of population mean value p, though their mode deviate slightly to right or left side of the position p'.3. The effect of homogenizing action of this machine seems to be not seriously influenced by the percentage of diseased moths.4. Interaction-test, comparing p & p' and q & q' or by SNEDECOR'S R×2 method using population variance, pq, shows in all cases the uniformity of variance, after rotated samples for five seconds or more.5. Inspections using confidence interval p±3√pq/nκ and p±2√pq/nκ show equivalence in all former cases and in latter cases, when the time of rotation becomes fifteen seconds or longer. POISSON distribution inspection using x2-test also proves to be equivalent in all cases of experiments.6. Abstraction of the required number of moths to be inspected can be easily done from any part of their unit group by picking out at a sampling and the number of sampling units, fifty, may not necessarily be needed, if the homgenizer is previously used.7. If the high rotatory speed is used, the required time of rotation can be reduced to half, however in order to exclude fine scales of moths, infected with spores of pebrine, by the electric fan, the rotation time for thirty seconds may be desirable.

Background Data on the species diversity and distribution of pteridophytes (lycophytes and ferns) in the Urals and adjacent areas are presented. The dataset includes 13,742 observations of two classes Lycopodiopsida and Polypodiopsida. In total, the dataset contains information on 16 families, 28 generas, 65 species, four subspecies and nine interspecies hybrids. All records are for lycophytes and ferns collected over 170 years between 1853 and 2021. The dataset presented is based on herbarium specimens, published data and field research conducted by the authors. This dataset is the first and important step towards generalising information on the current diversity and geographical distribution of pteridophytes in the Urals and adjacent areas. © Melnikov D et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported in part by the Program for Improving the Competitiveness of the Ural Federal University (the decree no. 211 of the Government of the Russian Federation, contract No. 02.A03.21.0006), the state assignments АААА-А19-119031290052-1 (Komarov Botanical Institute RAS), no. 0111-2019-0001 (Tsitsin Main Botanical Garden of the RAS), no. AAAA-A17-117072810011-1 (Institute Botanical Garden UB RAS) and no. АААА-А19-119031890084-6 (Institute of Plant and Animal Ecology UB RAS). This research was carried out within the project No. 121041600045-8 "Western Siberia in the context of Eurasian ties: man, nature, society". We thank the Ministry of Higher Education and Science of Russian Federation for the supportgiven to the Center of Collective Use “Herbarium MBG RAS” (Agreement No. 075-15-2021-678). The work was carried out as part of the Russia 2021 project.

The standardized mean difference is a well‐known effect size measure for continuous, normally distributed data. In this paper we present a general basis for important other distribution families. As a general concept, usable for every distribution family, we introduce the relative effect, also called Mann–Whitney effect size measure of stochastic superiority. This measure is a truly robust measure, needing no assumptions about a distribution family. It is thus the preferred tool for assumption‐free, confirmatory studies. For normal distribution shift, proportional odds, and proportional hazards, we show how to derive many global values such as risk difference average, risk difference extremum, and odds ratio extremum. We demonstrate that the well‐known benchmark values of Cohen with respect to group differences—small, medium, large—can be translated easily into corresponding Mann–Whitney values. From these, we get benchmarks for parameters of other distribution families. Furthermore, it is shown that local measures based on binary data (2 × 2 tables) can be associated with the Mann–Whitney measure: The concept of stochastic superiority can always be used. It is a general statistical value in every distribution family. It therefore yields a procedure for standardizing the assessment of effect size measures. We look at the aspect of relevance of an effect size and—introducing confidence intervals—present some examples for use in statistical practice.

Background There are limited evidence-based strategies that have been shown to increase the rate at which peer-reviewed articles are cited. In a previously reported randomized controlled trial, we demonstrated that promotion of article links in an online cross-publisher distribution platform (TrendMD) persistently augments citation rates after 12 months, leading to a statistically significant 50% increase in citations relative to the control. Objective This study aims to investigate if the citation advantage of promoted articles upholds after 36 months. Methods A total of 3200 published articles in 64 peer-reviewed journals across 8 subject areas were block randomized at the subject level to either the TrendMD group (n=1600) or the control group (n=1600) of the study. Articles were promoted in the TrendMD Network for 6 months. We compared the citation rates in both groups after 36 months. Results At 36 months, we found the citation advantage endured; articles randomized to TrendMD showed a 28% increase in mean citations relative to the control. The difference in mean citations at 36 months for articles randomized to TrendMD versus the control was 10.52 (95% CI 3.79-17.25) and was statistically significant (P=.001). Conclusions To our knowledge, this is the first randomized controlled trial to demonstrate how a postpublication article promotion intervention can be used to persistently augment citations of peer-reviewed articles. TrendMD is an efficient digital tool for knowledge translation and dissemination to targeted audiences to facilitate the uptake of research.

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In this short paper, we consider certain characterizations of the Exponentiated Marshall-Olkin Discrete Uniform (EMODU) distribution introduced by Gharib et al. (2017) to complete in some manner, the authors' work

IN this paper Haldane points out (p. 142) a difference between his results for the mean and variance of x2 in a 2 x n-fold contingency table when the expectation p is fixed and the results obtained by me in my paper (Annals of Eugenics, Vol. VII, part III, p. 211). The difference is that I have (n 1) throughout where Haldane has n. Haldane writes, "my own results would appear to be slightly more accurate than Cochran's", which might, I think, give the impression that both Haldane's results and mine are only approximations. In fact, both results are mathematically exact, the difference between them being one of definition of x2. My paper is almost entirely concerned with the distribution of x2 when the expectation p is not known. In the results which I gave for the distribution of x2 when p is known, I retained the term S (x -x-)2 in the numerator of x2 instead of S (x np)2, to facilitate comparison between this and my other results. Thus my x2 has (n 1) degrees of freedom, whereas Haldane's x2 has n degrees of freedom. Unfortunately I did not emphasize this point in the passage concerned, and as it may have appeared misleading to others besides Haldane, I welcome this opportunity of drawing attention to it. Haldane's x2 is, of course, the one which is normally appropriate in testing the departure from independence when the expectation is known.

The magnitude of the maximum trapped magnetic field in a bulk, single-grain superconductor is a key performance figure of merit. This is determined, generally, by the magnitude of the critical current density, J c , and the length scale over which it flows. As with all type-II superconductors, J c is related closely to the microstructure of the superconducting material and, in the case of RE–Ba–Cu–O [(RE)BCO, where RE is a rare-earth element or yttrium] single grains, RE2BaCuO5 (RE-211) inclusions in the superconducting REBa2Cu3O7−δ (RE-123) phase matrix are key microstructural features that act effectively as flux pinning centres. Although the distribution of RE-211 in single-grain bulk superconductors has been studied extensively, the variation of J c within a given sample has been much investigated much less thoroughly. A detailed experimental understanding of the variation of J c in these technologically important materials, therefore, is required given the growing popularity and significance of numerical techniques for modelling the behaviour of type-II bulk superconductors. Here we report a systematic investigation of the correlation between Gd-211 particle density and sample porosity, which are microstructural features, and T c and J c in a Gd–Ba–Cu–O bulk, single grain fabricated using a buffer layer and a supply of additional liquid phase. This was performed by cutting the sample into numerous sub-specimens of approximate dimensions 1.8 × 2.8 × 1.5 mm3. We observe that J c decreases with distance from the seed, although more strongly with distance along the c-axis than along the a–b plane. In contrast to what might be expected given the assumed contribution of RE-211 inclusions to flux pinning, we find no evidence of a clear correlation between the local RE-211 precipitate density and local critical current on a length scale of mm. We observe that the porosity of the sample is a more dominant factor in determining the distribution of J c within a single grain.

THERE have been placed in my hands, by Mrs. Bashford Dean, for distribution among students of fishes, certain reprints of Dr. Dean's studies on the archaic fishes, found among his effects after his untimely death.

Knowledge of the uncertainty in model parameters is essential for decision-making in drug development. Contrarily to other aspects of nonlinear mixed effects models (NLMEM), scrutiny towards assumptions around parameter uncertainty is low, and no diagnostic exists to judge whether the estimated uncertainty is appropriate. This work aims at introducing a diagnostic capable of assessing the appropriateness of a given parameter uncertainty distribution. The new diagnostic was applied to case bootstrap examples in order to investigate for which dataset sizes case bootstrap is appropriate for NLMEM. The proposed diagnostic is a plot comparing the distribution of differences in objective function values (dOFV) of the proposed uncertainty distribution to a theoretical Chi square distribution with degrees of freedom equal to the number of estimated model parameters. The uncertainty distribution was deemed appropriate if its dOFV distribution was overlaid with or below the theoretical distribution. The diagnostic was applied to the bootstrap of two real data and two simulated data examples, featuring pharmacokinetic and pharmacodynamic models and datasets of 20–200 individuals with between 2 and 5 observations on average per individual. In the real data examples, the diagnostic indicated that case bootstrap was unsuitable for NLMEM analyses with around 70 individuals. A measure of parameter-specific “effective” sample size was proposed as a potentially better indicator of bootstrap adequacy than overall sample size. In the simulation examples, bootstrap confidence intervals were shown to underestimate inter-individual variability at low sample sizes. The proposed diagnostic proved a relevant tool for assessing the appropriateness of a given parameter uncertainty distribution and as such it should be routinely used.

Sequential batch reactors (SBR) have been successfully developed granular sludge using industrial rubber wastewater on a cylindrical shaped SBR. SBR was introduced to industrial wastewater with varying chemical oxygen demand (COD) loadings from as low as 0.01 to 0.28 kgCOD/m3/d. First phase of experiment utilized 24 hours cycle time whilst second phase of experiment utilized 4 hours cycle time. Granules were successfully developed at the second phase (4 hours) of experiment. Fortunately, the overall performance for both cycles were excellent. COD removal efficiency throughout the experiment was kept at about 78 % to 98 %. Although higher COD removal was observed for both cycle, granulation did not occur in the first phase (24 hours). Decrement of cycling time to 4 hours promotes the growth of dense and structured sludge granules.

The thick ascending limb (TAL) is a major NaCl reabsorbing site in the nephron. Efficient reabsorption along that segment is thought to be a consequence of the establishment of a strong transepithelial potential that drives paracellular Na+uptake. We used a multicell mathematical model of the TAL to estimate the efficiency of Na+transport along the TAL and to examine factors that determine transport efficiency, given the condition that TAL outflow must be adequately dilute. The TAL model consists of a series of epithelial cell models that represent all major solutes and transport pathways. Model equations describe luminal flows, based on mass conservation and electroneutrality constraints. Empirical descriptions of cell volume regulation (CVR) and pH control were implemented, together with the tubuloglomerular feedback (TGF) system. Transport efficiency was calculated as the ratio of total net Na+transport (i.e., paracellular and transcellular transport) to transcellular Na+transport. Model predictions suggest that 1) the transepithelial Na+concentration gradient is a major determinant of transport efficiency; 2) CVR in individual cells influences the distribution of net Na+transport along the TAL; 3) CVR responses in conjunction with TGF maintain luminal Na+concentration well above static head levels in the cortical TAL, thereby preventing large decreases in transport efficiency; and 4) under the condition that the distribution of Na+transport along the TAL is quasi-uniform, the tubular fluid axial Cl−concentration gradient near the macula densa is sufficiently steep to yield a TGF gain consistent with experimental data.

This paper is intended to clarify the use of terminology and notation used in the used in the analysis of aerosol particle sizing on the basis of the log-normal distribution. The connection between log-normal distribution and the normal distribution is shown; the mathematical basis for the various diameters used in the literature is developed, and the reasoning behind the graphical presentation on so-called ``log-normal`` graph paper is presented.