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)

Little Citizens and their Flags

This delightful coloring book published in 1922 by the F. A. Owen Publishing Company of Dansville, NY features Bess Bruce Cleaveland’s charming illustrations of children from around the world dressed in traditional clothing; colored flags by Genevieve Stump Foster; and short rhyming poems by Maude M. Grant. There are detailed directions for coloring a boy and girl from each of the many countries included (United States, Mexico, Liberia, Argentina, Holland, England, France, Russia, Alaska (Eskimos), the forest (Indians), Switzerland, Denmark, Belgium, Spain, Italy, China, and Japan) so that “they will look prettiest” in the colors selected, plus a blank flag of these countries to color in the “really truly colors shown in the flags.” The book includes a letter from editor Elizabeth P. Bemis “to all little boys and girls who want something to do,” containing instructions for using the illustrations to make patterns for fun craft projects such as a paper doll parade, peace flags, book ends, twine holders, flower holders, garden sticks, and embroidery.https://knightscholar.geneseo.edu/historical-reprints/1033/thumbnail.jp

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

Potential impact of midwives in preventing and reducing maternal and neonatal mortality and stillbirths: a Lives Saved Tool modelling study.

Background Strengthening the capacity of midwives to deliver high-quality maternal and newborn health services has been highlighted as a priority by global health organisations. To support low-income and middle-income countries (LMICs) in their decisions about investments in health, we aimed to estimate the potential impact of midwives on reducing maternal and neonatal deaths and stillbirths under several intervention coverage scenarios. Methods For this modelling study, we used the Lives Saved Tool to estimate the number of deaths that would be averted by 2035, if coverage of health interventions that can be delivered by professional midwives were scaled up in 88 countries that account for the vast majority of the world's maternal and neonatal deaths and stillbirths. We used four scenarios to assess the effects of increasing the coverage of midwife-delivered interventions by a modest amount (10% every 5 years), a substantial amount (25% every 5 years), and the amount needed to reach universal coverage of these interventions (ie, to 95%); and the effects of coverage attrition (a 2% decrease every 5 years). We grouped countries in three equal-sized groups according to their Human Development Index. Group A included the 30 countries with the lowest HDI, group B included 29 low-to-medium HDI countries, and group C included 29 medium-to-high HDI countries. Findings We estimated that, relative to current coverage, a substantial increase in coverage of midwife-delivered interventions could avert 41% of maternal deaths, 39% of neonatal deaths, and 26% of stillbirths, equating to 2·2 million deaths averted per year by 2035. Even a modest increase in coverage of midwife-delivered interventions could avert 22% of maternal deaths, 23% of neonatal deaths, and 14% of stillbirths, equating to 1·3 million deaths averted per year by 2035. Relative to current coverage, universal coverage of midwife-delivered interventions would avert 67% of maternal deaths, 64% of neonatal deaths, and 65% of stillbirths, allowing 4·3 million lives to be saved annually by 2035. These deaths averted would be particularly concentrated in the group B countries, which currently account for a large proportion of the world's population and have high mortality rates compared with group C. Interpretation Midwives can help to substantially reduce maternal and neonatal mortality and stillbirths in LMICs. However, to realise this potential, midwives need to have skills and competencies in line with recommendations from the International Confederation of Midwives, to be part of a team of sufficient size and skill, and to work in an enabling environment. Our study highlights the potential of midwives but there are many challenges to the achievement of this potential. If increased coverage of midwife-delivered interventions can be achieved, health systems will be better able to provide effective coverage of essential sexual, reproductive, maternal, newborn, and adolescent health interventions

The State of the World's Midwifery 2021 report: findings to drive global policy and practice.

The third global State of the World's Midwifery report (SoWMy 2021) provides an updated evidence base on the sexual, reproductive, maternal, newborn and adolescent health (SRMNAH) workforce. For the first time, SoWMy includes high-income countries (HICs) as well as low- and middle-income countries. This paper describes the similarities and differences between regions and income groups, and discusses the policy implications of these variations. SoWMy 2021 estimates a global shortage of 900,000 midwives, which is particularly acute in low-income countries (LICs) and in Africa. The shortage is projected to improve only slightly by 2030 unless additional investments are made. The evidence suggests that these investments would yield important returns, including: more positive birth experiences, improved health outcomes, and inclusive and equitable economic growth. Most HICs have sufficient SRMNAH workers to meet the need for essential interventions, and their education and regulatory environments tend to be strong. Upper-middle-income countries also tend to have strong policy environments. LICs and lower-middle-income countries tend to have a broader scope of practice for midwives, and many also have midwives in leadership positions within national government. Key regional variations include: major midwife shortages in Africa and South-East Asia but more promising signs of growth in South-East Asia than in Africa; a strong focus in Africa on professional midwives (rather than associate professionals: the norm in many South-East Asian countries); heavy reliance on medical doctors rather than midwives in the Americas and Eastern Mediterranean regions and parts of the Western Pacific; and a strong educational and regulatory environment in Europe but a lack of midwife leaders at national level. SoWMy 2021 provides stakeholders with the latest data and information to inform their efforts to build back better and fairer after COVID-19. This paper provides a number of policy responses to SoWMy 2021 that are tailored to different contexts, and suggests a variety of issues to consider in these contexts. These suggestions are supported by the inclusion of all countries in the report, because it is clear which countries have strong SRMNAH workforces and enabling environments and can be viewed as exemplars within regions and income groups

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