An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

Zoning and Open Spaces, Washington, D.C., 1936 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Base map of the District of Columbia showing public and zoning areas, base prepared in the Office of the Surveyor, D.C., by direction of the Engineer Commissioner, D.C. It was published by Engineer Commissioner in 1936. Scale [ca. 1:19,200]. Base map "complete to June 13, 1933." The image inside the map neatline is georeferenced to the surface of the earth and fit to the Maryland State Plane Coordinate System Meters NAD83 (Fipszone 1900). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as residential areas, open spaces, commercial and industrial areas, alley dwelling areas, roads, block numbers, railroads and stations, drainage, selected public buildings and points of interest, parks, cemeteries, and more. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Autonomy in the global era: Euro-regionalism and new policy spaces in education. ACES Working Papers, August 2010

Framed by a critical discussion of methodological nationalism, this paper explores the intersection of new and evolving regional, central state, and supranational education policy spaces through examples drawn from post-Franco Spain. This work is situated within the broader literature on the development of a European Education Policy Space, which aims to understand changing governance structures in European education (cf. Grek et al., 2009; Lawn & Lingard,2002; N6voa & Lawn, 2002). Using policy documents since 2000 and interview data, the paper first examines Spanish and regional (Catalan) education policy related to devolution, namely Catalonia's recently revised Statute of Autonomy. The paper then places devolution in Spain and Catalonia in a broader context of Euro-regionalism, which has deepened and legitimized regional autonomy. Together these shifts in educational governance and the development of new education policy spaces have promoted a concept of the multi-scalar, European "ideal citizen" (Engel & Ortloff, 2009). The last section presents an overview of the recent influx of immigrants into Catalonia and Spain, exploring whether and to what extent recent education policy promoting the "ideal citizen" has taken non-European immigrants into account.

Homogeneous Spatial Units (HSU) - a Pan-European geographical basis for environmental and socio-economic modelling

The spatial data set delineates areas with similar environmental properties regarding soil, terrain morphology, climate and affiliation to the same administrative unit (NUTS3 or comparable units in size) at a minimum pixel size of 1km2. The scope of developing this data set is to provide a link between spatial environmental information (e.g. soil properties) and statistical data (e.g. crop distribution) available at administrative level. Impact assessment of agricultural management on emissions of pollutants or radiative active gases, or analysis regarding the influence of agricultural management on the supply of ecosystem services, require the proper spatial coincidence of the driving factors. The HSU data set provides e.g. the link between the agro-economic model CAPRI and biophysical assessment of environmental impacts (updating previously spatial units, Leip et al. 2008), for the analysis of policy scenarios. Recently, a statistical model to disaggregate crop information available from regional statistics to the HSU has been developed (Lamboni et al. 2016). The HSU data set consists of the spatial layers provided in vector and raster format as well as attribute tables with information on the properties of the HSU. All input data for the delineation the HSU is publicly available. For some parameters the attribute tables provide the link between the HSU data set and e.g. the soil map(s) rather than the data itself. The HSU data set is closely linked the USCIE data set.

Working in confined spaces.

Mode of access: Internet.

Permit-required confined spaces (permit spaces).

"OSHA 3138."

Singular solutions at boundary intersections in two dimensional quasi-linear homogeneous partial differential equations /

Includes bibliographical references (20).

The pattern articulation unit of ILLIAC III : implementation of the homogeneous instruction "BOOLE" /

Supported by: Contract AT (11-1)-1018 with the U.S. Atomic Energy Commission and the Advanced Research Projects Agency.

A planar geometrical model for representing multidimensional discrete spaces and multiple-valued logic functions /

Bibliography: p. 37-38.

Single-fluid two-region aqueous homogeneous reactor power plant : conceptual design and feasibility study : final report /

"Other issues of this report may bear the number BAW-7."

The motion of turbulent vortex-pairs in homogeneous and density stratified media /

Photocopy of microfilm. Springfield, Va. : National Technical Information Service, [1979]

The electrical admittance of a homogeneous polarized fully electroded circular disc, loss-less and mechanically free : analysis, including Rayleigh correction, data for routine determination of elastic modulus and Piezoelectric coupling, and discussion of limitation of correction, anisotrophy parameters involved, and deductions concerning dimensional standarization /

"ONR Contract No. Nonr-1055(00)."

Flows of homogeneous density in tidal reaches /

Mode of access: Internet.

Proceedings of the Conference on Atmospheric Contamination in Confined Spaces, 30 March-1 April 1965.

Sponsored by the Aerospace Medical Research Laboratories.