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- V. J. Bolós
- 2008

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 reference system. Two of them are given in the framework of spacelike simultaneity and, analogously , the other two are given in the framework of observed… (More)

- V. J. Bolós, V. Liern, J. Olivert
- 2005

We analyze two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity (also known as observed simultaneity), given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that… (More)

- V. J. Bolós
- 2005

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… (More)

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… (More)

- V. J. Bolós, David Klein
- 2011

The expansion of space, and other geometric properties of cosmological models, can be studied using geometrically defined notions of relative velocity. In this paper, we consider test particles undergoing radial motion relative to comoving (geodesic) observers in Robertson-Walker cosmologies, whose scale factors are increasing functions of cosmolog-ical… (More)

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 scale index, is… (More)

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a… (More)

- R. Beńıtez, V. J. Bolós
- 2011

In this paper we use collocation methods for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, first we generalize the results on existence and uniqueness given in a previous paper in order to consider also non locally bounded kernels, which are present in many cases of blow-up problems. Next, we… (More)

- V. J. Bolós
- 2005

We introduce new concepts and properties of lightlike distributions and foliations (of dimension and co-dimension 1) in a space-time manifold of dimension n, from a purely geometric point of view. Given an observer and a lightlike distribution Ω of dimension or co-dimension 1, its lightlike direction is broken down into two vector fields: a timelike vector… (More)

An algorithm, based on the wavelet scalogram energy, for automatically detecting events in force-extension AFM force spectroscopy experiments is introduced. The events to be detected are characterized by a discontinuity in the signal. It is shown how the wavelet scalogram energy has different decay rates at different points depending on the degree of… (More)