Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Strong solutions of the thin film equation in spherical geometry

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure

A descriptive analysis of midwifery education, regulation and association in 73 countries: The baseline for a post-2015 pathway

© 2016 The Author(s). Background: Education, regulation and association (ERA) are the supporting pillars of an enabling environment for midwives to provide quality care. This study explores these three pillars in the 73 low- and middle-income countries who participated in the State of the World's Midwifery (SoWMy) 2014 report. It also examines the progress made since the previous report in 2011. Methods: A self-completion questionnaire collected quantitative and qualitative data on ERA characteristics and organisation in the 73 countries. The countries were grouped according to World Health Organization (WHO) regions. A descriptive analysis was conducted. Results: In 82% of the participating countries, the minimum education level requirement to start midwifery training was grade 12 or above. The average length of training was higher for direct-entry programmes at 3.1 years than for post-nursing/healthcare provider programmes at 1.9 years. The median number of supervised births that must be conducted before graduation was 33 (range 0 to 240). Fewer than half of the countries had legislation recognising midwifery as an independent profession. This legislation was particularly lacking in the Western Pacific and South-East Asia regions. In most (90%) of the participating countries, governments were reported to have a regulatory role, but some reported challenges to the role being performed effectively. Professional associations were widely available to midwives in all regions although not all were exclusive to midwives. Conclusions: Compared with the 2011 SoWMy report, there is evidence of increasing effort in low- and middle-income countries to improve midwifery education, to strengthen the profession and to follow international ERA standards and guidelines. However, not all elements are being implemented equally; some variability persists between and within regions. The education pillar showed more systematic improvement in the type of programme and length of training. The reinforcement of regulation through the development of legislation for midwifery, a recognised definition and the strengthening of midwives' associations would benefit the development of other ERA elements and the profession generally

SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results

Timing of singleton births by onset of labour and mode of birth in NHS maternity units in England, 2005-2014: A study of linked birth registration, birth notification, and hospital episode data

BACKGROUND: Maternity care has to be available 24 hours a day, seven days a week. It is known that obstetric intervention can influence the time of birth, but no previous analysis at a national level in England has yet investigated in detail the ways in which the day and time of birth varies by onset of labour and mode of giving birth. METHOD: We linked data from birth registration, birth notification, and Maternity Hospital Episode Statistics and analysed 5,093,615 singleton births in NHS maternity units in England from 2005 to 2014. We used descriptive statistics and negative binomial regression models with harmonic terms to establish how patterns of timing of birth vary by onset of labour, mode of giving birth and gestational age. RESULTS: The timing of birth by time of day and day of the week varies considerably by onset of labour and mode of birth. Spontaneous births after spontaneous onset are more likely to occur between midnight and 6am than at other times of day, and are also slightly more likely on weekdays than at weekends and on public holidays. Elective caesarean births are concentrated onto weekday mornings. Births after induced labours are more likely to occur at hours around midnight on Tuesdays to Saturdays and on days before a public holiday period, than on Sundays, Mondays and during or just after a public holiday. CONCLUSION: The timing of births varies by onset of labour and mode of birth and these patterns have implications for midwifery and medical staffing. Further research is needed to understand the processes behind these findings

Developing capacities of community health workers in sexual and reproductive, maternal, newborn, child, and adolescent health: A mapping and review of training resources

Background: Given country demands for support in the training of community health workers (CHWs) to accelerate progress towards reaching the Millennium Development Goals in sexual and reproductive health and maternal, newborn, child, and adolescent health (SR/MNCAH), the United Nations Health Agencies conducted a synthesis of existing training resource packages for CHWs in different components of SR/MNCAH to identify gaps and opportunities and inform efforts to harmonize approaches to developing the capacity of CHWs. Methods: A mapping of training resource packages for CHWs was undertaken with documents retrieved online and from key informants. Materials were classified by health themes and analysed using agreed parameters. Ways forward were informed by a subsequent expert consultation. Results: We identified 31 relevant packages. They covered different components of the SR/MNCAH continuum in varying breadth (integrated packages) and depth (focused packages), including family planning, antenatal and childbirth care (mainly postpartum haemorrhage), newborn care, and childhood care, and HIV. There is no or limited coverage of interventions related to safe abortion, adolescent health, and gender-based violence. There is no training package addressing the range of evidence-based interventions that can be delivered by CHWs as per World Health Organization guidance. Gaps include weakness in the assessment of competencies of trainees, in supportive supervision, and in impact assessment of packages. Many packages represent individual programme efforts rather than national programme materials, which could reflect weak integration into national health systems. Conclusions: There is a wealth of training packages on SR/MNCAH for CHWs which reflects interest in strengthening the capacity of CHWs. This offers an opportunity for governments and partners to mount a synergistic response to address the gaps and ensure an evidence-based comprehensive package of interventions to be delivered by CHWs. Packages with defined competencies and methods for assessing competencies and supervision are considered best practices but remain a gap. © 2014 Tran et al

Scaling up pro-poor agrobiodiversity interventions as a development option

Pro-poor interventions that use agrobiodiversity for development actions are widely considered relevant only at small scales. Agrobiodiversity interventions are often left out of national-level/large-scale development planning. Scaling-up modalities include adaptation, diffusion, replication, value addition, and temporal scaling up. We undertook a review of 119 interventions that use agrobiodiversity for both the crop and the livestock sector. The interventions ranged from improving the availability of materials and information through management and market-oriented actions to changing norms and enabling policies. The interventions are also organized in accordance with farming-community goals and constraints. The open-access multilingual Diversity Assessment Tool for Agrobiodiversity and Resilience (DATAR) was created as a framework to systemize and structure agrobiodiversity interventions under different scaling-up modalities for the on-the-ground field assessment and scaling-up of agrobiodiversity interventions. The use of the framework enabled the scaling up of small-scale interventions that use agrobiodiversity to have impact on agricultural development at larger spatial and temporal scales

Why Give Birth in Health Facility? Users' and Providers' Accounts of Poor Quality of Birth Care in Tanzania.

In Tanzania, half of all pregnant women access a health facility for delivery. The proportion receiving skilled care at birth is even lower. In order to reduce maternal mortality and morbidity, the government has set out to increase health facility deliveries by skilled care. The aim of this study was to describe the weaknesses in the provision of acceptable and adequate quality care through the accounts of women who have suffered obstetric fistula, nurse-midwives at both BEmOC and CEmOC health facilities and local community members. Semi-structured interviews involving 16 women affected by obstetric fistula and five nurse-midwives at maternity wards at both BEmOC and CEmOC health facilities, and Focus Group Discussions with husbands and community members were conducted between October 2008 and February 2010 at Comprehensive Community Based Rehabilitation in Tanzania and Temeke hospitals in Dar es Salaam, and Mpwapwa district in Dodoma region. Health care users and health providers experienced poor quality caring and working environments in the health facilities. Women in labour lacked support, experienced neglect, as well as physical and verbal abuse. Nurse-midwives lacked supportive supervision, supplies and also seemed to lack motivation. There was a consensus among women who have suffered serious birth injuries and nurse midwives staffing both BEmOC and CEmOC maternity wards that the quality of care offered to women in birth was inadequate. While the birth accounts of women pointed to failure of care, the nurses described a situation of disempowerment. The bad birth care experiences of women undermine the reputation of the health care system, lower community expectations of facility birth, and sustain high rates of home deliveries. The only way to increase the rate of skilled attendance at birth in the current Tanzanian context is to make facility birth a safer alternative than home birth. The findings from this study indicate that there is a long way to go