Embedding Properties of sets with finite box-counting dimension

In this paper we study the regularity of embeddings of finite--dimensional subsets of Banach spaces into Euclidean spaces. In 1999, Hunt and Kaloshin [Nonlinearity 12 1263-1275] introduced the thickness exponent and proved an embedding theorem for subsets of Hilbert spaces with finite box--counting dimension. In 2009, Robinson [Nonlinearity 22 711-728] defined the dual thickness and extended the result to subsets of Banach spaces. Here we prove a similar result for subsets of Banach spaces, using the thickness rather than the dual thickness. We also study the relation between the box-counting dimension and these two thickness exponents for some particular subsets of $\ell_{p}$.Comment: Submitted, Referres comments addresse

Meat and Potatoes: Recipes for a Range of Egalitarianism in Three Hunter-Gatherer Societies

Throughout most of human history our ancestors lived by hunting and gathering. Only within the last ten to fifteen thousand years have alternative forms of social organization developed, duly labeled by anthropologists and archaeologists: agricultural, pastoral, and complex state societies, lineal tribes, and a host of other terms which pass in and out of favor in our ongoing (and inescapably human) attempts to categorize our own kind. Classification lies at the heart of science, and anthropology is certainly no exception. However, categorization of any degree (which requires generalization) runs the risk of obscuring important differences between cultural groups. The trick for anthropologists is to strike a balance between grouping to the point of over-generalization, and dealing with cultures on such an individual basis that cross-cultural regularities are not recognized. When we look at the history of anthropological theory, it is clear that this approach is a relatively recent one- and one we continue to struggle with

Illustration of Modern Wind Turbine Ancillary Services

Increasing levels of wind power penetration in modern power systems has set intensively high standards with respect to wind turbine technology during the last years. Security issues have become rather critical and operation of wind farms as conventional power plants is becoming a necessity as wind turbines replace conventional units on the production side. This article includes a review of the basic control issues regarding the capability of the Doubly Fed Induction Generator (DFIG) wind turbine configuration to fulfill the basic technical requirements set by the system operators and contribute to power system security. An overview of ancillary services provided by wind turbine technology nowadays is provided, i.e., fault ride-through capability, reactive power supply and frequency-active power control

Some comments on Laakso graphs and sets of differences

We recall a variation of a construction due to Laakso \cite{LA}, also used by Lang and Plaut \cite{LA} of a doubling metric space $X$ that cannot be embedded into any Hilbert space. We give a more concrete version of this construction and motivated by the results of Olson \& Robinson \cite{OR}, we consider the Kuratowski embedding $\Phi(X)$ of $X$ into $L^{\infty}(X)$ and prove that $\Phi(X)-\Phi(X)$ is not doubling

The 1999 Athens (Greece) Earthquake: Energy and Duration- Related Response Spectral Characteristics of Different Site Conditions

An earthquake of September 7, 1999 (M5.9) has occurred in the Athens (Attika) area and was felt in almost all central Greece. The earthquake caused a lot of damage and extensive loss of life. The most damaged region is located within a distance of 10 km from the epicenter and numerous modem buildings and industrial facilities collapsed. The accelerograms, which have been recorded during the main event, are processed and compared with the empirical predictive relations proposed for Greece. For each record, the bracketed and significant duration as well as various energy-related measures are estimated. The correlation of these measures with the macroseismic intensity of the particular accelerographic site is then examined. Thus, the destructiveness of the individual records, based solely on the analysis of the ground motion process, is established. The influence of duration and frequency content on structural damage is then incorporated into the response spectral values via the adoption of novel site-dependent probabilistic 3Dspectra. Finally all the above characteristics are compared in order to select the strong-motion properties and response spectral parameters that encapsulate the damage potential of the seismic action and therefore are best suited for design purposes