A generalization of the Heine--Stieltjes theorem

We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate interlacing relations between the zeros of different pairs of solutions. This extends recent results of Bourget, McMillen and Vargas for the Heun equation and answers their question on how to generalize their results to higher degrees. Many of the results are new even for the classical case.Comment: 12 pages, typos corrected and refined the interlacing theorem

Localization Properties of the Chalker-Coddington Model

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

Articulation and growth of skeletal elements in balanid barnacles (Balanidae, Balanomorpha, Cirripedia)

The morphology and ultrastructure of the shells of two balanid species have been examined, paying special attention to the three types of boundaries between plates: (i) radii-parietes, (ii) alae-sheaths, and (iii) parietes-basal plate. At the carinal surfaces of the radii and at the rostral surfaces of the alae, there are series of crenulations with dendritic edges. The crenulations of the radius margins interlock with less prominent features of the opposing paries margins, whereas the surfaces of the longitudinal abutments opposing the ala margins are particularly smooth. The primary septa of the parietes also develop dendritic edges, which abut the internal surfaces of the primary tubes of the base plates. In all cases, there are chitino-proteinaceous organic membranes between the abutting structures. Our observations indicate that the very edges of the crenulations and the primary septa are permanently in contact with the organic membranes. We conclude that, when a new growth increment is going to be produced, the edges of both the crenulations and the primary septa pull the viscoelastic organic membranes locally, with the consequent formation of viscous fingers. For the abutting edges to grow, calcium carbonate must diffuse across the organic membranes, but it is not clear how growth of the organic membranes themselves is accomplished, in the absence of any cellular tissue.This research was funded by projects CGL2017-85118-P (A.G.C., C.S. and C.G.) and CGL2015-64683-P (A.B.R.N.) of the Spanish Ministerio de Economía, Industria y Competitividad, the Unidad Científica de Excelencia UCE-PP2016-05 of the University of Granada (A.G.C. and A.B.R.N.) and the Research Group RNM363 of the Junta de Andalucía (A.G.C.). N.A.L. acknowledges support from CONICYT-Chile through grant nos. FONDECYT 1140938, PCI REDES 170106 and PIA ANILLOS ACT172037, for international collaborative research with A.G.C. and A.B.R.N

Pregnancy after liver transplantation under tacrolimus

Background. The maternal and fetal risk of pregnancy after organ transplantation under tacrolimus has not been reported. This was prospectively studied in 27 pregnancies by 21 female liver recipients who were treated with tacrolimus before and throughout gestation. Method. Twenty- seven babies were born between October 1990 and April 1996. In 15 cases, samples were obtained at or after delivery and stored (-40°C) for comparison of tacrolimus concentration in the maternal blood with different combinations of cord and infant venous blood, breast milk, or a section of the placenta. Results. The 21 mothers had surprisingly few serious complications of pregnancy and no mortality. Two infants with 23 and 24 weeks gestation died shortly after birth. The mean birth weight of the other 25 was 2638±781 g after a gestational period of 36.0±3.3 weeks. Mean birth weight percentile for gestational age was 50.2±26.2 (median 40). On the day of delivery, the mean tacrolimus concentrations (ng/ml) were 4.3 in placenta versus 1.5, 0.7, and 0.5 in maternal, cord, and child plasma, and 0.6 in the first breast milk specimens. The infants had a 36% incidence of transient perinatal hyperkalemia (K+>7.0 meq/L) and a mild reversible renal impairment, which were thought to reflect in part maternal homeostasis. One newborn had unilateral polycystic renal disease (the only anomaly). All 25 babies have had satisfactory postnatal growth and development with a current mean weight percentile of 62±37 (median 80). Conclusions. Pregnancy by postliver transplant mothers under tacrolimus was possible with a surprisingly low incidence of the hypertension, preeclampsia, and other maternal complications historically associated with such gestations. As in previous experience with other immunosuppressive regimens, preterm deliveries were common. However, prenatal growth for gestational age and postnatal infant growth for post- partum age were normal

Early Miocene carbonate ramp development in a warm ocean, North West Shelf, Australia

Although carbonate ramps are widely described from the geological record,there is still a debate on the relative influence of water temperature, trophicconditions and type of carbonate factories on their development. Theca2400 km long Australian North West Shelf is among the largest Cenozoic car-bonate provinces worldwide, and records a transition from an early Mioceneramp to a middle Miocene rimmed platform. This change is observable onpublicly available seismic data, giving the opportunity to investigate envi-ronmental influences on platform evolution. This study combines macro-scopic and petrographic descriptions of early Miocene strata cropping out inthe Cape Range Anticline (North West Cape, southern end of the North WestShelf) and of time-equivalent well cuttings from the adjacent, offshoreExmouth Sub-basin. Particular emphasis is placed on the identification oflarger benthic foraminifera at a broad generic level, because differing taxahave a limited range of habitable conditions that serve as environmentalproxies. The results show that early Miocene strata are dominantly com-posed of larger benthic foraminifera with minor coralline algae in the proxi-mal platform, grading to micropackstones in the more distal platform. Aramp margin is inferred from the lithological data on the basis of the lack offramework builders and the presence of open oceanic indicators. Facies shal-low upward through individual outcrops, with a proximal to distal trendtowards the north-west. These trends along outcrops are consistent with theseismic interpretations. Identification of taxa with warm, oligotrophic wateraffinity suggests that the ramp was formed in an oligotrophic and warmocean, despite the absence of coral reefs. Changes of carbonate facies withdepth do not seem to be associated with changes in ramp morphology, andthe latter may have been controlled by physical oceanic parameters, such asoffshore currents and waves.Early Miocene carbonate ramp development in a warm ocean, North West Shelf, AustraliapublishedVersio

Beyond ‘witnessing’: children’s experiences of coercive control in domestic violence and abuse

Children’s experiences and voices are underrepresented in academic literature and professional practice around domestic violence and abuse. The project ‘Understanding Agency and Resistance Strategies’ addresses this absence, through direct engagement with children. We present an analysis from interviews with 21 children in the United Kingdom (12 girls and 9 boys, aged 8-18 years), about their experiences of domestic violence and abuse, and their responses to this violence. These interviews were analysed using interpretive interactionism. Three themes from this analysis are presented: a) ‘Children’s experiences of abusive control’, which explores children’s awareness of controlling behaviour by the adult perpetrator, their experience of that control, and its impact on them; b) ‘Constraint’, which explores how children experience the constraint associated with coercive control in situations of domestic violence, and c) ‘Children as agents’ which explores children’s strategies for managing controlling behaviour in their home and in family relationships. The paper argues that, in situations where violence and abuse occurs between adult intimate partners, children are significantly impacted, and can be reasonably described as victims of abusive control. Recognising children as direct victims of domestic violence and abuse would produce significant changes in the way professionals respond to them, by 1) recognising children’s experience of the impact of domestic violence and abuse; 2) recognising children’s agency, undermining the perception of them as passive ‘witnesses’ or ‘collateral damage’ in adult abusive encounters; and 3) strengthening professional responses to them as direct victims, not as passive witnesses to violence