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.

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.9 (1866)

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.14 (1871)

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.4 (1861)

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.12 (1869)

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.3 (1860)

Wochenschrift des Vereines zur Beförderung des Gartenbaues in den Königlich Preussischen Staaten für Gärtnerei und Pflanzenkunde.

v.7 (1864)

Aus der Heimath.

1864

Aus der Heimath.

1862

Aus der Heimath.

1865

Aus der Heimath.

1863

Dresden, Germany, 1876 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Plan von Dresden, gezeichnet von Emil Loofs. It was published by Conrad Weiske in 1876. Scale [ca. 1:11,000]. Map in German. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Deutsches Hauptdreiecksnetz (DHDN) 3-degree Gauss-Kruger Zone 5 coordinate system. 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 roads, railroads and stations, drainage, built-up areas and selected buildings, parks, city districts, and more. Includes index. 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.

Nos Rastos da Solidão. Deambulações Sociológicas

Haverá, certamente, muitas maneiras de abordar o fenómeno da solidão. Durkheim, um dos fundadores da Sociologia, aconselhar-nos-ia, provavelmente, a uma definição prévia da solidão no pressuposto de que, como qualquer outro fenómeno social, ela é uma «coisa» com natureza própria. Foi o que fez nos seus célebres estudos sobre o suicídio e a religião. Uma tal definição passaria pela inventariação de um certo número de características «externas» que, mais ou menos perceptíveis, nos permitiriam reconhecer a existência da solidão, impedindo-nos de a confundir com outros fenómenos. Todas as formas de solidão seriam espécies de um mesmo género e, assim sendo, haveria necessariamente elementos comuns a essas diferentes formas de solidão que traduziriam o conteúdo objectivo da ideia que se expressa quando se fala de solidão.

Who reads Tocqueville today?

Esta comunicação irá ser publicada no próximo número da Newsletter do RC16 Sociological Theory da International Sociological Association, em Dezembro de 2016.

The Political Economy of the 2014-2020 Common Agricultural Policy: An Imperfect Storm. CEPS Paperback, 17 August 2015

After five years of debates, consultations and negotiations, the European institutions reached an agreement in 2013 on the Common Agricultural Policy (CAP) for the 2014-2020 period. The outcome has major implications for the EU’s budget and farmers’ incomes but also for Europe’s environment, its contribution to global climate change and to food security in the EU and in the world. It was decided to spend more than €400 billion during the rest of the decade on the CAP.The official claims are that the new CAP will take better account of society's expectations and lead to far-reaching changes by making subsidies fairer and ‘greener’ and making the CAP more efficient. It is also asserted that the CAP will play a key part in achieving the overall objective of promoting smart, sustainable and inclusive growth. However, there is significant scepticism about these claims and disappointment with the outcome of the decision-making, the first in which the European Parliament was involved under the co-decision procedure. In contrast to earlier reforms where more substantive changes were made to the CAP, the factors that induced the policy discussions in 2008-13 and those that influenced the decision-making did not reinforce each other. On the contrary, they sometimes counteracted one another, yielding an ‘imperfect storm’ as it were, resulting in more status quo and fewer changes. This book discusses the outcome of the decision-making and the factors that influenced the policy choices and decisions. It brings together contributions from leading academics from various disciplines and policy-makers, and key participants in the process from the European Commission and the European Parliament.