An outside-inside view of exclusive practice within an inclusive mainstream school

This article is a reflection on a sabbatical experience in a mainstream school where an inclusive ethos underpinned the curriculum and environmental approaches for all children. The period as Acting Head teacher raised some challenges for me in reconciling inclusion for all children and the exclusive nature of some professional and physical spaces available to the community of adults working in the school. It has highlighted some development opportunities for the senior management of the school and its governing body

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere non-tangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying \textit{a posteriori} a separate work on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has changed nam

Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions

The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied

Intertwining caring science, caring practice and caring education from a lifeworld perspective—two contextual examples

This article describes how caring science can be a helpful foundation for caring practice and what kind of learning support that can enable the transformation of caring science into practice. The lifeworld approach is fundamental for both caring and learning. This will be illustrated in two examples from research that show the potential for promoting health and well-being as well as the learning process. One example is from a caring context and the other is from a learning context. In this article, learning and caring are understood as parallel processes. We emphasize that learning cannot be separated from life and thus caring and education is intertwined with caring science and life. The examples illustrate how an understanding of the intertwining can be fruitful in different contexts. The challenge is to implant a lifeworld-based approach on caring and learning that can lead to strategies that in a more profound way have the potential to strengthen the person's health and learning processes

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

Chord line force versus displacement for thin shallow arc pre-curved bimetallic strip

This is the accepted version of the following article: G D Angel, G Haritos, A Chrysanthou & V Voloshin, “Chord line force versus displacement for thin shallow arc pre-curved bimetallic strip”, Journal of Mechanical Engineering Science, Vol. 229(1): 116-124, first published online April 29, 2014, published by SAGE Publishing. All rights reserved. The version of record is available online at doi: http://dx.doi.org/10.1177/0954406214530873A pre-curved bimetallic strip that is applied with a force in an axial orientation, i.e. along its chord line, exhibits nonlinear force-displacement characteristics. For thin bimetallic strips, whereby the radius of curvature is large compared to the thickness of the strip, the non-linearity tends to be tangent related. The new theoretical formula introduced here was correlated to the results of a set of force-displacement tests, and a good overall fit of the theory to the test data was achieved. The formula put forward in this work enables the evaluation of large chord line displacements but is limited to the permissible stress limits of the material. This work can also be directly applied to thin shallow arc beams of a single material. The application of this work is in the field of bimetallic force-displacement actuators.Peer reviewe

Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the Stokes operator in Lipschitz domain

The mixed problem in L^p for some two-dimensional Lipschitz domains

We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is decomposed into two disjoint sets D and N. We suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary and the Neumann data is in L^p(N). We find conditions on the domain and the sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L^p