7,804 research outputs found
Interactive visualization of a thin disc around a Schwarzschild black hole
In the first course of general relativity, the Schwarzschild spacetime is the
most discussed analytic solution to Einstein's field equations. Unfortunately,
there is rarely enough time to study the optical consequences of the bending of
light for some advanced examples. In this paper, we present how the visual
appearance of a thin disc around a Schwarzschild black hole can be determined
interactively by means of an analytic solution to the geodesic equation
processed on current high performance graphical processing units. This approach
can, in principle, be customized for any other thin disc in a spacetime with
geodesics given in closed form. The interactive visualization discussed here
can be used either in a first course of general relativity for demonstration
purposes only or as a thesis for an enthusiastic student in an advanced course
with some basic knowledge of OpenGL and a programming language.Comment: 9 pages, 4 figure
Split strongly abelian p-chief factors and first degree restricted cohomology
In this paper we investigate the relation between the multiplicities of split
strongly abelian p-chief factors of finite-dimensional restricted Lie algebras
and first degree restricted cohomology. As an application we obtain a
characterization of solvable restricted Lie algebras in terms of the
multiplicities of split strongly abelian p-chief factors. Moreover, we derive
some results in the representation theory of restricted Lie algebras related to
the principal block and the projective cover of the trivial irreducible module
of a finite-dimensional restricted Lie algebra. In particular, we obtain a
characterization of finite-dimensional solvable restricted Lie algebras in
terms of the second Loewy layer of the projective cover of the trivial
irreducible module. The analogues of these results are well known in the
modular representation theory of finite groups.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:1206.366
Market leadership through technology – Backward compatibility in the U.S. Handheld Video Game Industry
The introduction of a new product generation forces incumbents in network industries to rebuild their installed base to maintain an advantage over potential entrants. We study if backward compatibility moderates this process of rebuilding an installed base. Using a structural model of the U.S. market for handheld game consoles, we show that backward compatibility lets incumbents transfer network effects from the old generation to the new to some extent but that it also reduces supply of new software. We examine the tradeoff between technological progress and backward compatibility and find that backward compatibility matters less if there is a large technological leap between two generations. We subsequently use our results to assess the role of backward compatibility as a strategy to sustain market leadership
Spatial Smoothing Techniques for the Assessment of Habitat Suitability
Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of the observations is often violated in practice since the points at which the observations are collected are spatially aligned. While several approaches have been developed to analyse and account for spatial correlation in regression models with normally distributed responses, far less work has been done in the context of generalised linear models. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations
Backward Compatibility to Sustain Market Dominance – Evidence from the US Handheld Video Game Industry
The introduction of a new product generation forces incumbents in network industries to rebuild their installed base to maintain an advantage over potential entrants. We study if backward compatibility can help moderate this process of rebuilding an installed base. Using a structural model of the US market for handheld game consoles, we show that backward compatibility lets incumbents transfer network effects from the old generation to the new to some extent but that it also reduces supply of new software. We also find that backward compatibility matters most shortly after the introduction of a new generation. Finally, we examine the tradeoff between technological progress and backward compatibility and find that backward compatibility matters less if there is a large technological leap between two generations. We subsequently use our results to assess the role of backward compatibility as a strategy to sustain a dominant market position
Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings
We study link-diluted Ising spin glass models on the hierarchical
lattice and on a three-dimensional lattice close to the percolation threshold.
We show that previously computed zero temperature fixed points are unstable
with respect to temperature perturbations and do not belong to any critical
line in the dilution-temperature plane. We discuss implications of the presence
of such spurious unstable fixed points on the use of optimization algorithms,
and we show how entropic effects should be taken into account to obtain the
right physical behavior and critical points.Comment: 4 pages, 4 figures. A major typo error in formula (8) has been
correcte
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