In order to improve our understanding of how the goethite crystal structure is affected by the incorporation of metals (and by variations in the amount of the incorporation), and to review any possible synergistic and antagonistic effects of co-metals, the present investigation focused on the incorporation of multiple (di-, tri-, and tetra-) metals, i.e. Cr, Zn, Cd, and Pb, in the goethite crystallographic structure. A series of single- and multi-metal M-Cr/Zn/Cd/Pb-substituted goethites with M/(M+Fe) molar ratios = 0.10 were prepared. The general sequence of metal entry in single-metal substituted goethites was Zn = Cr > Cd > Pb and in multi-metal-substituted goethites was Zn > Cr ⩾ Cd > Pb. Simultaneous incorporation of Cr, Zn, Cd, and Pb up to 10.5 mole % was achieved in goethite. Synchrotron X-ray diffraction and extended X-ray absorption fine structure (EXAFS) techniques were employed to assess the structural characteristics of the synthesis products. Rietveld refinement of XRD data showed small changes in unit-cell parameters and Fe/M-Fe/M distances due to M substitution(s). A typical goethite-like crystalline structure remained intact, however. The unit-cell parameters were mutually, linearly correlated, though Fe/M-Fe/M distances were not, indicating that complex changes occurred at the local scale. In single-metal substituted goethites, incorporation of Cr reduced the unit-cell volume by 0.13% while that of Zn, Cd, and Pb increased it by 1.09, 3.58, and 0.56%, respectively. The changes in multi-metal-substituted goethites appeared to be the complex combination of that of the individually incorporated metals. The X-ray absorption near edge structure study of Pb-substituted goethites showed that the majority of associated Pb was Pb2+, while Pb4+ was preferred over Pb2+ in the bulk structure. Measurements by EXAFS at the Fe K-edge indicated that the Fe polyhedra contracted in the presence of Cd2+ and Pb2+, providing room for the substitution of larger cations. Measurements by EXAFS at the Cr and Cd K-edges indicated symmetric Cr/Cd polyhedra with single Cr/Cd-O distances and, at Fe and Zn K-edges and the Pb LIII-edge, indicated asymmetric polyhedra with two sets of Fe/Zn/Pb-O distances. The Zn octahedra were possibly Zn(OH)4O2, which enlarged the metal-metal corner-sharing distance to 3.86 Å. This configuration of ligands around the Zn2+ cation might occur to balance local charges. Symmetric polyhedra appeared to reduce steric strains in the structure, compared to the asymmetric polyhedra. The result was that Cr enhanced the incorporation of Zn, Cd, and Pb, while the converse was true for Zn.

We show that there is a measure-preserving system $(X,\mathscr {B}, \mu , T)$ together with functions $F_0, F_1, F_2 \in L^{\infty }(\mu )$ such that the correlation sequence $C_{F_0, F_1, F_2}(n) = \int _X F_0 \cdot T^n F_1 \cdot T^{2n} F_2 \, d\mu $ is not an approximate integral combination of $2$ -step nilsequences.

Over the previous decades, twinning rates worldwide have increased remarkably. This study aimed to describe changes in multiple birth rates and related demographic characteristics, such as maternal age and the level of education of parents in South Korea from 1981 to 2019. This study analyzed birth data obtained from the Korean Statistical Information Service. From 1981 to 2019, the total twinning rate increased from 5 to 22.5 pairs per 1000 births. This rapid increase was due to an increase in dizygotic twin births, which mainly occurred in mothers aged between 30 and 39 years. The average maternal age of multiples increased from 26.06 years in 1981 to 33.98 years in 2019, suggesting that a delay in childbearing contributed to the increase in the twinning rate. The percentage of mothers of multiples who completed a college or higher degree (CHD) increased by 1000% from 1981 to 2019, indicating that a sharp increase in the level of education of females in part explains the delay in childbearing. The percentages of individuals who completed a CHD were higher among parents of multiples than among those of singletons in recent years when public funding arrangements for fertility treatments were available. This result suggested that completion of higher education may be associated with increased use of assisted reproductive technology (ART) independent of the financial status of couples. Taken together, the analysis suggested that increased maternal age, ART and the increased number of females who completed CHD may be responsible for the remarkable increase in the rates of multiple births in South Korea in the last four decades.

Multiple cases of atypical scrapie in the same holding and co-existence with classical scrapie have been reported in Great Britain. A two-stage simulation tool was developed by combining a sampling algorithm and a hierarchical Bayesian model to simulate the number of positive cases of atypical scrapie from: (i) random sampling and (ii) using the actual sampled population in Great Britain, being the output probability of detection of flocks with one and more cases. Cluster analysis was conducted to assess the level of geographical over- and under-sampling over the years. The probability of detecting at least two cases of atypical scrapie in the same holding is much lower in simulated random data than in simulated actual data for all scenarios. Sampling bias in the selection of sheep for testing led to multiple sampling from fewer but larger holdings, Scotland, and areas of Wales were under-sampled and the South-West and East of England oversampled. The pattern of atypical scrapie cases observed is unlikely to be explained by a multi-case event epidemiologically linked. The co-existence of classical and atypical scrapie is a rare event with 19 holdings detected in GB and does not suggest an epidemiological link between the two types of disease.

A 4-month-old boy with Proteus syndrome underwent a successful operation for a left abdominal mass due to hydroureter and hydronephrosis with left ureterovesical stenosis. The operation lasted 4.5 h under general anaesthesia; there were no anaesthetic complications. There is only one previous report on anaesthesia in a patient with Proteus syndrome.