Gradings on Composition Superalgebras

We classify up to equivalence the gradings on Hurwitz superalgebras and on symmetric composition superalgebras, over any field. Also, classifications up to isomorphism are given in case the field is algebraically closed. By grading, here we mean group grading.     

Tapped granular packings described as complex networks

Abstract

We characterize the structure of simulated two-dimensional granular packings using concepts from complex networks theory. The packings are generated by a simulated tapping protocol, which allows us to obtain states in mechanical equilibrium in a wide range of densities. We show that our characterization method is able to discriminate non-equivalent states that have the same density. We do this by examining differences in the topological structure of the contact network of the packings. In particular, we find that the polygons of the network are specially sensitive probes for the contact structure. Additionally, we compare the network properties obtained in two different scenarios: the tapped and a compressed system.     

Analysis of Minerals and Rocks by Laser-Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy (LIBS) technique was applied for rapid analysis of major and minor elements composing geological samples including minerals, rocks, and a soil sample. The plasma was produced in air at atmospheric pressure by focusing on the targets a pulsed infrared Nd:YAG laser in open-path configuration. The emitted light in the UV-Vis was analyzed by a compact LIBS system to measure spectral emission lines of Si, Al, Fe, Ca, Na, K, Mg, C, Cu, Mn, and Ti. The experimental issues relevant for the analysis of the different samples were investigated by taking into account their peculiar features: drilling through a weathered layer, roughness and grain-size considerations, statistical averaging, and accuracy of the measurements. In this approach, the characterization of the samples was achieved by studying the relative variations of the emission intensities of each element normalized with respect to an internal standard. The present study shows the usefulness of LIBS as a tool for reliable identification of field samples.     

Introduction to Terahertz Raman spectroscopy

This work, intended for advanced undergraduate students, explains the basic concepts and an actual scientific use of Terahertz Raman spectroscopy, displaying some of the benefits of this versatile technique for structural analysis of molecules building up materials since this technique has been increasingly used for molecular characterization in chemistry. A good didactic example of the experimentally applied temperature dependence of molecular vibrations according to the Boltzmann distribution is the ratio of anti-Stokes to Stokes Raman peak intensity used to calculate the temperature of a nylon 6,6 sample. The comparison of the temperature of nylon 6,6 calculated from the experimentally determined anti-Stokes to Stokes peak intensity ratio in the Terahertz region with the temperature set with the help of a heating-freezing stage is discussed. The limitations of Terahertz Raman spectroscopy are also part of this fundamental discussion.     

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent −2$-2$. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape.     

Analytical Instrumental Techniques to Study Archaeological Wood Degradation

Abstract

Historically, a very large variety of everyday artifacts were made of wood, which makes them representative of their historical period or social context and valuable for archaeologists and historians. In order to preserve degraded wood and to develop and apply suitable conservation treatments, chemical and physical characterization of archaeological wood is needed. This review provides the reader with a survey on state-of-the-art of instrumental analytical tools available to understand the morphology and the chemical composition of archaeological wood. The focus is on microscopic and spectroscopic techniques such as scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), Raman, nuclear magnetic resonance (NMR) and analytical techniques based on pyrolysis, such as direct exposure–mass spectrometry (DE-MS), pyrolysis–mass spectrometry (Py-MS), pyrolysis–gas chromtography–mass spectrometry (Py-GC/MS), with emphasis on their respective potentialities and limitations. The advantages of techniques based on synchrotron radiation are also discussed. In addition, the applicability of each examined technique is illustrated and discussed through specific examples from the literature.     

An analog model for quantum lightcone fluctuations in nonlinear optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable.     

The mathematical and geometrical structure of the spacetime and the concept of unification, matter and energy

Geometrical analysis of a new type of Unified Field Theoretical models follow the guidelines of previous works of the authors is presented. These new unified theoretical models are characterized by an underlying hypercomplex structure, zero non-metricity and the geometrical action is determined fundamentally by the curvature provenient of the breaking of symmetry of a group manifold in higher dimensions. This mechanism of Cartan-MacDowell-Mansouri type, permits us to construct geometrical actions of determinantal type leading a non topological physical Lagrangian due the splitting of a reductive geometry. Our goal is to take advantage of the geometrical and topological properties of this theory in order to determine the minimal group structure of the resultant spacetime Manifold able to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined and the existence of an important contribution of the torsion to the giromagnetic factor of the fermions, shown. Also we resume and analyze previous cosmological solutions in this new UFT where, as in our work [Class. Quantum Grav. 22 (2005) 4987–5004] for the non abelian Born-Infeld model, the Hosoya and Ogura ansatz is introduced for the important cases of tratorial, totally antisymmetric and general torsion fields. In the case of spacetimes with torsion the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed.     

Smale’s Fundamental Theorem of Algebra Reconsidered

In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of Newton’s method. In this paper we reconsider his algorithm in the light of work done in the intervening years. Smale’s upper bound estimate was infinite average cost. Ours is polynomial in the Bézout number and the dimension of the input. Hence it is polynomial for any range of dimensions where the Bézout number is polynomial in the input size. In particular it is not just for the case that Smale considered but for a range of dimensions as considered by Bürgisser–Cucker, where the max of the degrees is greater than or equal to n ^1+? for some fixed ?. It is possible that Smale’s algorithm is polynomial cost in all dimensions and our main theorem raises some problems that might lead to a proof of such a theorem.