A Note on the Shannon Entropy of Short Sequences

For source sequences of length L symbols we proposed to use a more realistic value to the usual benchmark of number of code letters by source letters. Our idea is based on a quantifier of information fluctuation of a source, F(U), which corresponds to the second central moment of the random variable that measures the information content of a source symbol. An alternative interpretation of typical sequences is additionally provided through this approach.Comment: 3 figure

Correction to: Some results on the p(u)-Laplacian problem

Correction to: Mathematische Annalen https://doi.org/10.1007/s00208-019-01803-w In the Original Publication of the article, few errors have been identified in section 5 and acknowledgements section.Agência financiadora Ministry of Education and Science, Russian Federation 117198 Portuguese Foundation for Science and Technology (FCT), Portugal SFRH/BSAB/135242/2017info:eu-repo/semantics/publishedVersio

Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models

We exhibit a resonance mechanism of amplification of density perturbations in inflationary mo-dels, using a minimal set of ingredients (an effective cosmological constant, a scalar field minimally coupled to the gravitational field and matter), common to most models in the literature of inflation. This mechanism is based on the structure of homoclinic cylinders, emanating from an unstable periodic orbit in the neighborhood of a saddle-center critical point, present in the phase space of the model. The cylindrical structure induces oscillatory motions of the scales of the universe whenever the orbit visits the neighborhood of the saddle-center, before the universe enters a period of exponential expansion. The oscillations of the scale functions produce, by a resonance mechanism, the amplification of a selected wave number spectrum of density perturbations, and can explain the hierarchy of scales observed in the actual universe. The transversal crossings of the homoclinic cylinders induce chaos in the dynamics of the model, a fact intimately connected to the resonance mechanism occuring immediately before the exit to inflation.Comment: 4 pages. This essay received an Honorable Mention from the Gravity Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett.

Earthen construction: structural vulnerabilities and retrofit solutions for seismic actions

Earthen structures present very appealing characteristics regarding a more sustainable practice with the preservation of our natural resources. However, when subjected to earthquake ground motions, this type of construction may present a deficient performance, which may cause significant human losses and important structural damage. The seismic response of earthen structures is typically characterized by fragile failures. There are several examples of recent earthquakes that affected earthen buildings in a severe way, evidencing the vulnerability of this type of construction, like the El Salvador earthquake, in 2001, the Bam, Iran earthquake, in 2003, the Pisco, Peru earthquake, in 2007 and the Maule, Chile earthquake, in 2010. The construction of earth structures on earthquake-prone areas must be carefully studied and should include seismic reinforcement solutions in order to improve their seismic performance. In this paper, the performance of earthen structures in recent earthquakes will be examined, analyzing failure modes inherent to these particular construction materials and associated construction techniques. Also, seismic reinforcement approaches and techniques will be presented in a comprehensive manner. Examples of tests conducted for the assessment of retrofitting solutions efficiency will be presented, and the results obtained will be discussed