Cosmology as a search for overall equilibrium

The steps followed by Einstein when he first wrote on cosmology from the point of view of the general theory of relativity are revised. It is argued that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: the constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, a simple and reasonable modification of the cosmological equations of motion is proposed. The solutions of the new cosmological equations give rise to a cosmological model that tries to approach the Einstein static solution. This model exhibits very appealing features in terms of fitting current observations. The text was submitted by the author in English.     

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

Beta decay of 101Sn

The β decay of the very neutron-deficient isotope ¹⁰¹Sn was studied at the GSI on-line mass separator using silicon detectors for recording charged particles and germanium detectors for γ-ray spectroscopy. Based on the β-delayed proton data the production cross-section of ¹⁰¹Sn in the ⁵⁰Cr + ⁵⁸Ni fusion-evaporation reaction was determined to be about 60nb. The half-life of ¹⁰¹Sn was measured to be 1.9(3)s. For the first time β-delayed γ-rays of ¹⁰¹Sn were tentatively identified, yielding weak evidence for a cascade of 352 and 1065keV transitions in ¹⁰¹In. The results for the ¹⁰¹Sn decay as well as those from previous work on the ¹⁰³Sn decay are discussed by comparing them to predictions obtained from shell model calculations employing a new interaction in the ⁸⁸Sr to ¹³²Sn model space.     

Asymptotic singular behaviour of inhomogeneous cosmologies in Einstein-Maxwell-dilaton-axion theory

We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We focus at Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations. Several cases are analyzed and some of them have asymptotically velocity-term dominated (AVTD) singularities.     

Cylindrical magnetization model for glass-coated microwires with circular anisotropy: Statics

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.     

Attenuation of the depolarizing field in a thin film model relaxor

The behavior of the polarization in a microscopic statistical model for a thin film relaxor placed between two metallic electrodes is studied by numerical simulations. Depolarization fields different from zero, due to a non-perfect compensation of surface charges at the metallic electrodes, are taken into account. Different thicknesses and different values of the compositional charge disorder density for the relaxor are considered. Depolarization field is found to be extremely attenuated for large values of the number density of charge carriers in the relaxor. In such a case, field attenuation allows for the existence of a homogeneous ferroelectric ground state.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

Fiber laser intracavity absorption spectroscopy for in situ multicomponent gas analysis in the atmosphere and combustion environments

Intracavity absorption spectroscopy with a broadband Er³⁺-doped fiber laser is applied for the measurements of several molecular species revealing quantitative information about the gas concentration, temperature and chemical reactions in flames. The spectral range of measurements extends from 6200 cm⁻¹ to 6550 cm⁻¹ with the proper choice of the fiber length and by moving an intracavity lens. With a pulsed laser applied in this experiment, the sensitivity to absorption corresponds to an effective absorption path length of 3 km assuming the cavity is completely filled with the sample. For a cw laser, the effective absorption path length is estimated to be 50 km. Absorption spectra of various molecules such as CO₂, CO, H₂O, H₂S, C₂H₂ and OH were recorded separately in the cell and/or in low-pressure methane and propane flames. The presented measurements demonstrate simultaneous in situ detection of three molecular products of chemical reactions at different flame locations. Variation of the relative strengths of OH absorption lines with the temperature enables the estimation of the local flame temperature. The sensitivity of this laser does not depend on the broadband cavity losses and it can be used for in situ measurements of absorption spectra in hostile environments such as contaminated samples, flames or combustion engines. The presented technique can be applied for various diagnostic purposes, such as in environmental, combustion and plasma research, in medicine and in the determination of stable isotope ratios.