2,483 research outputs found
The Hyperplane is the Only Stable, Smooth Solution to the Isoperimetric Problem in Gaussian Space
We study stable smooth solutions to the isoperimetric type problem for a
Gaussian weight on Euclidean Space. That is, we study hypersurfaces that are second order stable critical points of
compact variations that minimize Gaussian weighted area and preserve Gaussian
weighted volume. We show that such satisfy a curvature condition, and
derive the Jacobi operator for the second variation of such .
Our first main result is that for non-planar , bounds on the index of
, acting on volume preserving variations, gives us that splits off
a linear space. A corollary of this result is that hyperplanes are the only
stable smooth complete solutions to this Gaussian isoperimetric type problem,
and that there are no hypersurfaces of index one. Finally, we show that for the
case of , there is a gradient decay estimate
depending on bounds for the curvature condition and an appropriate area growth
bound. This shows that, in the limit as , stable with good area growth
bounds approach hyperplanes.Comment: 20 page
Invisible Market: Energy and Agricultural Technologies for Women's Economic Advancement
This research explores what it takes for technology initiatives, specifically in the energy and agricultural sectors, to reach and economically benefit women in developing countries through market-based strategies that have the potential for achieving scale and financial sustainability. It builds on ICRW's landmark paper, Bridging the Gender Divide: How Technology Can Advance Women Economically, which made the case for how technologies can create pathways for strengthening women's economic opportunities. Through a field-level investigation and interviews with experts, the authors examine how women's use of technology and their involvement in the development and distribution of a technology can not only advance women economically, but also can benefit enterprise-based technology initiatives by expanding their markets and helping them generate greater financial returns
Admiral Nurse Standards: an overview and application of ‘values based practice’
This short presentation will offer an introduction to Values Based Practice through the prism of the Admiral Nurse Standards. It is intended to demonstrate that an understanding of ‘values’ is critical to the delivery of excellent nursing care. In addition, the presentation intends to illustrate that working with values is not a theoretical and ‘airy’ idea, but rather a key practical skill that can be mastered by nurses at various levels.
The presentation seeks to engage participants in a debate on whether working positively with values is a key feature of high level leadership and practice and is worthy of detailed examination
A Transnational History of a Writer in Four Packages
This is the final version. Available on open access from Taylor & Francis via the DOI in this recordArts and Humanities Research Council (AHRC
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