The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Resonances of the cusp family

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius--Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.

An empirical study on the preferred size of the participant information sheet in research

Background: Informed consent is a requirement for all research. It is not, however, clear how much information is sufficient to make an informed decision about participation in research. Information on an online questionnaire about childhood development was provided through an unfolding electronic participant sheet in three levels of information. \ud Methods: 552 participants, who completed the web-based survey, accessed and spent time reading the participant information sheet (PIS) between July 2008 and November 2009. The information behaviour of the participants was investigated. The first level contained less information than might be found on a standard PIS, the second level corresponded to a standard PIS, and the third contained more information than on a standard PIS. The actual time spent on reading the information provided in three incremental levels and the participants' evaluation of the information were calculated. \ud Results: 77% of the participants chose to access the first level of information, whereas 12% accessed the first two levels, 6% accessed all three levels of information and 23% participated without accessing information. The most accessed levels of information were those that corresponded to the average reading times. \ud Conclusion: The brief information provided in the first level was sufficient for participants to make informed decisions, while a sizeable minority of the participants chose not to access any information at all. This study adds to the debate about how much information is required to make a decision about participation in research and the results may help inform the future development of information sheets by providing data on participants' actual needs when deciding about questionnaire surveys.\u

A new model for the structure of the DACs and SACs regions in the Oe and Be stellar atmospheres

In this paper we present a new mathematical model for the density regions where a specific spectral line and its SACs/DACs are created in the Oe and Be stellar atmospheres. In the calculations of final spectral line function we consider that the main reasons of the line broadening are the rotation of the density regions creating the spectral line and its DACs/SACs, as well as the random motions of the ions. This line function is able to reproduce the spectral feature and it enables us to calculate some important physical parameters, such as the rotational, the radial and the random velocities, the Full Width at Half Maximum, the Gaussian deviation, the optical depth, the column density and the absorbed or emitted energy. Additionally, we can calculate the percentage of the contribution of the rotational velocity and the ions' random motions of the DACs/SACs regions to the line broadening. Finally, we present two tests and three short applications of the proposed model.Comment: 9 pages, 5 figures, accepted for publication in PAS

Multifractality and nonextensivity at the edge of chaos of unimodal maps

We examine both the dynamical and the multifractal properties at the chaos threshold of logistic maps with general nonlinearity $z>1$. First we determine analytically the sensitivity to initial conditions $\xi_{t}$. Then we consider a renormalization group (RG) operation on the partition function $Z$ of the multifractal attractor that eliminates one half of the multifractal points each time it is applied. Invariance of $Z$ fixes a length-scale transformation factor $2^{-\eta}$ in terms of the generalized dimensions $D_{\beta}$. There exists a gap $\Delta \eta$ in the values of $\eta$ equal to $\lambda _{q}=1/(1-q)=D_{\infty}^{-1}-D_{-\infty}^{-1}$ where $\lambda_{q}$ is the $q$-generalized Lyapunov exponent and $q$ is the nonextensive entropic index. We provide an interpretation for this relationship - previously derived by Lyra and Tsallis - between dynamical and geometrical properties. Key Words: Edge of chaos, multifractal attractor, nonextensivityComment: Contribution to the proceedings of 2nd International Conference on News and Expectations in Thermostatistics (NEXT03), Cagliari, Italy, 21-28/09/2003. Submitted to Physica

Resonances, Unstable Systems and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting, 7-22 July 2004, University of Denver. Accepted for publication in the Internation Journal of Theoretical Physic

One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure

Classical evolution of fractal measures generated by a scalar field on the lattice

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution.Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys.

Editorial: A better tomorrow: towards human-oriented, sustainable transportation systems

In a rapidly changing world, transportation is a big determinant of quality of life, financial growth and progress. New challenges (such as the emergence of the COVID-19 pandemic) and opportunities (such as the three revolutions of shared, electric and automated mobility) are expected to drastically change the future mobility landscape. Researchers, policy makers and practitioners are working hard to prepare for and shape the future of mobility that will maximize benefits. Adopting a human perspective as a guiding principle in this endeavor is expected to help prioritize the “right” needs as requirements. In this special issue, eight research papers outline ways in which transportation research can contribute to a better tomorrow. In this editorial, we position the research within the state-of-the-art, identify the needs for future research, and then outline how the included contributions fit in this puzzle. Naturally, the problem of sustainable future transportation systems is way too complicated to be covered with a single special issue. We thus conclude this editorial with a discussion about open questions and future research topics