Groups generated by a finite Engel set

A subset $S$ of a group $G$ is called an Engel set if, for all $x,y\in S$, there is a non-negative integer $n=n(x,y)$ such that [x,\,_n y]=1. In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two.Comment: to appear in Journal of Algebr

The Effects of European Integration on Regional Employment - Specialization of Austrian Regions

This paper focuses on employment effects since Austria joined the European Union. The location of economic activity and thus employment has been of interest for the economics profession for a long time. In this respect the question on the employment effects of integration in common markets is of special interest as the hypothesis can be raised that because of increased competition regions will specialize and industries will concentrate. Therefore it is asked how regions have specialized and how industries have concentrated by using various concentration/specialization measures. Moreover, the role of foreign direct investments are observed in explaining concentration/specialization as well as regional employment shifts. It is shown (i) that no general trends in specialization/concentration can be detected, so that on a general level the hypothesis of joining a common market necessarily leads to specialization/concentration must be refused, but for specific industries and regions interesting patterns can be observed and (ii) foreign direct investments have an significant impact on employment in regions.

The Impossibility of Extending Random Dictatorship to Weak Preferences

Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness

Welfare Maximization Entices Participation

We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann-Morgenstern utility functions. We show that every welfare-maximizing mechanism entices participation and that the converse holds under additional assumptions. Two important corollaries of our results are characterizations of an attractive randomized voting rule that satisfies Condorcet-consistency and entices participation. This stands in contrast to a well-known result by Moulin (1988), who proves that no deterministic voting rule can satisfy both properties simultaneously

Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's function returns so-called maximal lotteries, i.e., lotteries that correspond to optimal mixed strategies of the underlying plurality game. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming

SAM 2 measurements of the polar stratospheric aerosol. Volume 3: October 1979 to April 1980

The Stratospheric Aerosol Measurement (SAM) II sensor is aboard the Earth-orbiting Nimbus 7 spacecraft providing extinction measurements of the Antarctic and Arctic stratospheric aerosol with a vertical resolution of 1 km. Representative examples and weekly averages of aerosol data and corresponding temperature profiles for the time and place of each SAM II measurement (Oct. 1979 through Apr. 1980) are presented. Contours of aerosol extinction as a function of altitude and longitude or time are plotted and weekly aerosol optical depths are calculated. Seasonal variations and variations in space (altitude and longitude) for both polar regions are easily seen. Typical values of aerosol extinction at the SAM II wavelength of 1.0 microns for this time period are 2 to 4 times .0001/km in the main stratospheric aerosol layer. Optical depths for the stratosphere are about 0.002 to 0.003, up slightly over normal background levels (due to the eruption of Sierra Negra, Nov. 1979). Polar stratospheric clouds at altitudes of about 22 km were observed during the Arctic winter. A ready-to-use format containing a representative sample of the third 6 months of data to be used in atmospheric and climatic studies is presented