Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems

We introduce so called balanced quasi-monotone systems. These are systems $F(x,r,p,X)=(F_1(x,r,p,X),\ldots,F_m(x,r,p,X))$, where $x$ belongs to a domain $\Omega$, $r=u(x)\in\mathbb{R}^m$, $p=Du(x)$ and $X=D^2u(x)$, that can be arranged into two categories that are mutually competitive but internally cooperative. More precisely, for all $i\neq j$ in the set $\{1,2,\ldots,m\}$, $F_j$ is monotone non-decreasing (non-increasing) in $r_i$ if and only if $F_i$ is monotone non-decreasing (non-increasing) in $r_j$ and $F_j$ is a monotone function in $r_i$. We prove the existence and uniqueness of viscosity solutions to systems of this type. For uniqueness we need to require that $F_j$ is monotone increasing in $r_j$, at an at least linear rate. This should be compared to the quasi-monotone systems studied by Ishii and Koike, where they assume that $F(x,r,p,X)\ge F(x,s,p,X)$ if $r\le s$.Comment: 10 page

Synthesis of 1 alpha,25-Dihydroxyvitamin D Analogues Featuring a S-2-symmetric CD-ring Core

Three analogues of 1 alpha,25-dihydroxyvitamin D-3 (calcitriol), featuring a transfused decalin C, D-core with local S-2-symmetry, and possessing identical side-chain and seco-B,A-ring structures, have been synthesized starting from readily available (4aR, 8aS)octahydronaphthalene-1,5-dione(7). The very short sequences involve the simultaneous introduction of the side-chain and seco-B, A-ring fragments via Suzuki and Sonogashira coupling reactions. The analogues are devoid of relevant biological activity

Raising teacher supply: An assessment of three options for increasing wages

A shortage of teachers in primary and secondary schools in the Netherlands is expected in the near future as a large part of the current workforce will retire. Recently, the Dutch government has decided to increase wages of teachers. This paper qualitatively assesses the impact of three options for increasing teaching wages on teacher supply in the medium term: increasing wages at the start of the career, increasing wages at mid career or increasing wages at the end of the career.

A theory evaluation and programme implementer decision analysis for two therapy-driven programmes operating in the disability and rehabilitation sector

This dissertation focused on two therapy-driven programmes operating in the disability and rehabilitation sector in the Western Cape, South Africa. One programme is an inclusive education programme with a classroom component and parenting component to it and the other is a vocational rehabilitation programme. These two programmes, implemented by the Chaeli Campaign (CC), are aligned with the community-based rehabilitation model of service delivery. These programmes are implemented by personnel with a variety of qualifications, including community workers and occupational therapists. Key goals for programmes of this nature are to ensure that all persons with disabilities are active participants of socio-economic life, to ensure that the rights and dignity of all persons are respected and upheld and to reintegrate persons with disabilities into family and community life. Another goal of these programmes is to transfer skills from highly-skilled professionals to workers with less training and lay persons. With respect to the last mentioned goal, the skills required to services persons with disabilities are redistributed, so that professionals such as occupational therapists are no longer solely responsible for serving these persons. Both programmes under evaluation in this document are implemented either exclusively or with help from occupational therapists. Problem Statement: The problem statement is made up of two components. First, the underlying programme theories of the two therapy-driven programmes were not well articulated. According to CC’s director, this poor articulation made it difficult for programme staff to describe their programmes to potential programme donors. Second, the organisation struggles to obtain funding from potential programme donors to finance the use of occupational therapists in their programmes. The difficulty in obtaining funding is assumed to be due to potential donors’ belief that these programmes could be implemented at a reduced cost by community workers. Method: The evaluator decided to conduct two programme evaluations to address the two aspects mentioned in the problem statement. First, programme theory evaluations were done to address the poor articulation of the programmes’ theories. The programme theory evaluation aimed to elicit and articulate the underlying logic of each of the programmes, thus enabling the evaluator to assess their plausibility. Following this, three multi-criteria decision analyses (MCDAs) using the Analytical Hierarchy Process (AHP) were conducted. The MCDAs were intended to establish which implementer (an occupational therapist or a community worker) is most preferred by CC’s current programme stakeholders. The participants of the MCDA included programme beneficiaries, current programme donors, field experts, programme facilitators and programme staff. Results: Programme theories were made explicit and articulated. These were then depicted as logic models. Results indicate that when assessed against social science and evaluation literature, the programme theories elicited in this dissertation are plausible. The MCDA results indicate that programme stakeholders prefer occupational therapists for technical aspects of programme delivery and prefer community workers for psychosocial aspects of rehabilitation, such as relationship-building and providing emotional support. Of note is that stakeholders weighted the perceived benefits of occupational therapists and community workers as more important than the costs associated with each implementer. The results from the MCDA highlight that programme stakeholders perceive the benefits of implementers (occupational therapists and community workers) to be more important than their associated costs. The evaluator assessed these results against social science literature and found that in general, stakeholders value benefits more than costs of implementing personnel. Recommendations: Recommendations are made to the organisation to describe their programmes’ theories more coherently and more clearly express their need for both community workers and occupational therapists Conclusions: Rather than considering cost, potential donors should consider that occupational therapists and community workers serve specific purposes in programme implementation. Their purpose, rather than their cost, should be prioritised in order for programmes to be effective. The field should be made aware of this disjuncture, while costs are important considerations, stakeholders in the field of disability and rehabilitation should not compromise on the quality of services in order to reduce programme costs