3,539 research outputs found
One dimensional description of the gravitational perturbation in a Kerr background
The perturbation equation in a Kerr background is written as a coupled system
of one dimensional equations for the different modes in the time domain.
Numerical simulations show that the dominant mode in the gravitational response
is the one corresponding to the mode of the initial perturbation, allowing us
to conjecture that the coupling among the modes has a weak influence in our
system of equations. We conclude that by neglecting the coupling terms it can
be obtained a one dimensional harmonic equation which indeed describes with
good accuracy the gravitational response from the Kerr black hole with low
spin, while only few couplings are necessary to describe a high spin one. This
result may help to understand the structure of test fields in a Kerr background
and even to generate accurate waveforms for various cases in an efficient
manner.Comment: 14 pages, 3 figure
The Invariant Two-Parameter Function of Algebras ψ
At present, the research on invariant functions for algebras is very extended since Hrivnák
and Novotný defined in 2007 the invariant functions y and j as a tool to study the Inönü–Wigner
contractions (IW-contractions), previously introduced by those authors in 1953. In this paper, we introduce
a new invariant two-parameter function of algebras, which we call ¯y, as a tool which makes easier the
computations and allows researchers to deal with contractions of algebras. Our study of this new function
is mainly focused in Malcev algebras of the type Lie, although it can also be used with any other types of
algebras. The main goal of the paper is to prove, by means of this function, that the five-dimensional
classical-mechanical model built upon certain types of five-dimensional Lie algebras cannot be obtained
as a limit process of a quantum-mechanical model based on a fifth Heisenberg algebra. As an example of
other applications of the new function obtained, its computation in the case of the Lie algebra induced
by the Lorentz group SO(3, 1) is shown and some open physical problems related to contractions are
also formulated.Ministerio de Ciencia e Innovación MTM2013-40455-PMinisterio de Ciencia e Innovación FQM-326 (J.N.-V.)Junta de AndalucÃa FQM-160 (P.P.-F.
Del «utile consiglio» y las «sollazzevoli cose». El Decameron en el marco de la cultura popular.
Sin resume
Did Fátima de Madrid really exist?
In this paper we firstly pose the question of whether Fátima de Madrid, a Spanish mathematician woman allegedly born in Madrid, X-XI centuries, really existed or, on the contrary, she is only a product of the imagination of several authors wellintentioned and secondly, under the premise that she really existed, we show her life and work according to the consulted sources and our own research
Stable cores in information graph games
In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted
Stable cores in information graph games
Stable cores in information graph games Abstract: In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted
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