Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given in the framework of observed (lightlike) simultaneity. Properties and physical interpretations are discussed. Finally, we study relations between them in special relativity, and we give some examples in Schwarzschild and Robertson-Walker spacetimes. arXiv:gr-qc/0506032v5 4 Aug 2011
This paper presents a new numerical approach to the study of non-periodicity
in signals, which can complement the maximal Lyapunov exponent method for
determining chaos transitions of a given dynamical system. The proposed
technique is based on the continuous wavelet transform and the wavelet
multiresolution analysis. A new parameter, the \textit{scale index}, is
introduced and interpreted as a measure of the degree of the signal's
non-periodicity. This methodology is successfully applied to three classical
dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and
the Henon map.Comment: 14 pages, 6 figure
A new method for estimating the contact point in AFM force curves, based on a local regression algorithm, is presented. The main advantage of this method is that can be easily implemented as a computer algorithm and used for a fully automatic detection of the contact points in the approach force curves on living cells. The estimated contact points have been compared to those obtained by other published methods, which were applied either for materials with an elastic response to indentation forces or for experiments at high loading rates. We have found that the differences in the values of the contact points estimated with three different methods were not statistically significant and thus the algorithm is reliable. Also, we test the convenience of the algorithm for batch-processing by computing the contact points of a force curve map of 625 (25×25) curves.
We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that affine distance gives us a new concept of distance in Robertson-Walker space-times, according to Hubble law.
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