Dedekind order completion of C(X) by Hausdorff continuous functions

The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined on a topological space X. The main result is that the set of all finite Hausdorff continuous functions on any topological space X is Dedekind order complete. Hence it contains the Dedekind order completion of the set C(X) of all continuous real functions defined on X as well as the Dedekind order completion of the set C_b(X) of all bounded continuous functions on X. Under some general assumptions about the topological space X the Dedekind order completions of both C(X) and C_b(X) are characterised as subsets of the set of all Hausdorff continuous functions. This solves a long outstanding open problem about the Dedekind order completion of C(X). In addition, it has major applications to the regularity of solutions of large classes of nonlinear PDEs

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde

Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory

In Riesz space theory it is good practice to avoid representation theorems which depend on the axiom of choice. Here we present a general methodology to do this using pointfree topology. To illustrate the technique we show that almost f-algebras are commutative. The proof is obtained relatively straightforward from the proof by Buskes and van Rooij by using the pointfree Stone-Yosida representation theorem by Coquand and Spitters

A tale of two capitalisms: preliminary spatial and historical comparisons of homicide rates in Western Europe and the USA

This article examines comparative homicide rates in the United States and Western Europe in an era of increasingly globalized neoliberal economics. The main finding of this preliminary analysis is that historical and spatial correlations between distinct forms of political economy and homicide rates are consistent enough to suggest that social democratic regimes are more successful at fostering the socio-cultural conditions necessary for reduced homicide rates. Thus Western Europe and all continents and nations should approach the importation of American neo-liberal economic policies with extreme caution. The article concludes by suggesting that the indirect but crucial causal connection between political economy and homicide rates, prematurely pushed into the background of criminological thought during the ‘cultural turn’, should be returned to the foreground

Refugee crisis, imperialism and pitiless wars on the poor

According to the UN Refugee Agency, 59.5 million people around the world were forcibly displaced in 2014. The numbers are particularly high in countries which have been subject to a process of ‘redrawing the map’ by imperial powers or their regional allies. The response to the recent developments – a stage which has been dubbed as ‘refugee crisis’ – is as polarising and as problematic as before. On the one hand we have witnessed the heroic acts not only of the refugees themselves who moved collectively and refused to queue ‘orderly’ in the immigration lines, but also the magnificent response of citizens in all over Europe who rushed to feed, clothe, accommodate and welcome them. In contrast the overwhelming institutional response by ‘liberal’ states has been, and remains, depressingly illiberal. The official response to this humanitarian crisis – which is after all the product of ‘humanitarian interventions’ – has nothing to do with whether or not Europe can cope with a ‘swarm of people’ aiming to exploit the ‘host’ countries. It is to do with managing a massive reserve army of labour. Forced migration is not only a product of this staggering inequality but also an important element of how that inequality is produced, maintained and managed

Theories of American Imperialism: A Critical Evaluation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68828/2/10.1177_048661347400600303.pd

The infrastructural power of the military: The geoeconomic role of the US Army Corps of Engineers in the Arabian Peninsula

In analysing the role of the US in the global expansion of capitalist relations, most critical accounts see the US military’s invasion and conquest of various states as paving the way for the arrival of US businesses and capitalist relations. However, beyond this somewhat simplified image, and even in peacetime, the US military has been a major geoeconomic actor that has wielded its infrastructural power via its US Army Corps of Engineers’ overseas activities. The transformation of global economies in the 20th century has depended on the capitalisation of the newly independent states and the consolidation of liberal capitalist relations in the subsequent decades. The US Army Corps of Engineers has not only extended lucrative contracts to private firms (based not only in the US and host country, but also in geopolitically allied states), but also, and perhaps most important, has itself established a grammar of capitalist relations. It has done so by forging both physical infrastructures (roads, ports, utilities and telecommunications infrastructures) and virtual capitalist infrastructures through its practices of contracting, purchasing, design, accounting, regulatory processes and specific regimes of labour and private property ownership