The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Optic variables used to judge future ball arrival position in expert and novice soccer players

Although many studies have looked at the perceptual-cognitive strategies used to make anticipatory judgments in sport, few have examined the informational invariants that our visual system may be attuned to. Using immersive interactive virtual reality to simulate the aerodynamics of the trajectory of a ball with and without sidespin, the present study examined the ability of expert and novice soccer players to make judgments about the ball's future arrival position. An analysis of their judgment responses showed how participants were strongly influenced by the ball's trajectory. The changes in trajectory caused by sidespin led to erroneous predictions about the ball's future arrival position. An analysis of potential informational variables that could explain these results points to the use of a first-order compound variable combining optical expansion and optical displacement.

The influence of video games with apocalyptic content in adolescents

The aim of this study is the dissertation and analysis of the influence (sociological, psychological and cultural) exerted on adolescents by the concept of Apocalypse. Become a key thought of visual culture, the called doomsday theory achieves one of its highest expressions in video games, possibly the favorite entertainment for young people in their leisure time. The results obtained in this research represent a first approach to the subject through the selected samples, two secondary schools from the city of Seville with disparate locations and divergent socioeconomic backgrounds. To reinforce the comparative study, we have included issues related to parental control, principal gaming platforms used by respondents or the number of hours dedicated to this type of entertainment. The conclusions demonstrate an irremediable attraction from our youth towards apocalyptic universes, plotter consciously with leisure and entertainment as escape from their routine of everyday life.

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.

Coalitional Games and Contracts Based on Individual Deviations

We study what coalitions form and how the members of each coalition split the coalition value in coalitional games in which only individual deviations are allowed. In this context we employ three stability notions: individual, contractual, and compensational stability. These notions differ in terms of the underlying contractual assumptions. We characterize the coalitional games in which individually stable outcomes exist by means of the top-partition property. Furthermore, we show that any coalition structure of maximum social worth is both contractually and compensationally stable.

Synthesis of nucleoside analogues in a ball mill: fast, chemoselective and high yielding acylation without undesirable solvents

The chemoselective acylation of primary aliphatic amines has been achieved in under ten minutes (and for aromatic amines under 120 min) using vibration ball-milling, avoiding undesirable solvents which are typically employed for such reactions (e.g. DMF). Under optimised conditions, the synthesis of amides in the presence of both primary and secondary alcohol functions was achieved in high to excellent yields (65-94%). Overall, the methods described have significant practical advantages over conventional approaches based upon bulk solvents including greater yields, higher chemoselectivity and easier product separation.

Labor unions and Nash bargaining using coalition formation games

In this paper we examine the properties of stable coalitions under sequential and simultaneous bargaining by competing labor unions. We do this using the Nash bargaining solution and various notions of stability, namely, Nash, coalitional, contractual and core stability. (C) 2011 Elsevier B.V. All rights reserved,