Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cerberus styx (Hymenoptera, Vespidae)

In primitively eusocial insect societies, reproductive division of labor is established by dominance-submission interactions which determine a linear dominance hierarchy. As previously observed for other species, in Mischocyttarus cerberus styx (Hymenoptera, Vespidae), the dominant female is the main egg layer. Most of her attacks were to the females directly beneath in the rank establishing a hierarchy. During the pre-emergence stage, the hierarchy was already defined and in the post-emergence stage, pre-male substage, the frequency of dominance interactions were strong but the hierarchy was still maintained by the first-ranked female. In the decline stage there were many neutral individuals which could be the reproductives of a new colony.

Effect of barium titanate seed particles on the sintering and lattice parameters in PbMg1/3Nb2/3O3 ceramics

PbMg1/3Nb2/3O3 (PMN) powder was prepared by citrate organic solution, and barium titanate (BT) seed particles were added to encourage the perovskite phase formation. Sintering was followed using the constant heating rate mode of a dilatometer, and it was observed that the seed concentration affected the PMN shrinkage rate and crystal structure. The study of the lattice parameters of the samples after the sintering process indicates that the diffusion of the titanium and of the barium inside perovskite and pyrochlore PMN phases occurs. Moreover, this substitution provoked a decrease of the lattice parameters as showed by the Rietveld refinement.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Multicharged dyonic integrable models

We introduce and study new integrable models (IMs) of An (1)-nonabelian Toda type which admit U(1) ⊗ U(1) charged topological solitons. They correspond to the symmetry breaking SU(n + 1) → SU(2) ⊗ SU(2) ⊗ U(1)n-2 and are conjectured to describe charged dyonic domain walls of N = 1 SU(n + 1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q = -1 member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q = -1 and q = 2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n + 1) → SU(2)⊗p ⊗ U(1)n-p as well as IM with global SU(2) symmetries are discussed. © 2002 Elsevier Science B.V. All rights reserved.

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of s^l(n) (n = 2, 3) is presented explicitly. © SISSA/ISAS 2003.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae)

Seven colonies of Mischocyttarus cassununga were studied under field conditions at Universidade Federal de Juiz de Fora, MG, in southeastern Brazil: in pre-emergence, post-emergence and decline stages, during 145.8 hours. Dominance interactions among the females were quantified to verify the dynamics of succession in the social hierarchy of the colonies. Early pre-emergence colonies present more intense aggressive interactions than late pre-emergence ones, because the females are engaged in securing the role of main egg layer in the nest. In post-emergence (pre-male) colonies the dominance hierarchy is more defined and the frequency of dominance and subordination behaviors were lower than in pre-emergence stages: most of the agonistic behaviors are restricted to the first ranked females (potentially queens) and the subordinate individuals play the role of workers in the nests. In the post-emergence, post-male, and decline stages the hierarchy is still maintained by the aggressive behaviors of the 1st-ranked female but because the presence of males and future nest foundresses these interactions are not well defined in a linear way.

Nutritional and social hierarchy establishment of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae, Mischocyttarini) and related aspects

The results on the nutritional influence in the social hierarchy establishment among females from six colonies of Mischocyttarus cassununga show that: - there was no caste determination in the pre-imaginal period concerning ingested food quantities, however, in relation to qualification (proteins and carbohydrate) the Mann-Whitney test applied showed variation among colonies: in two colonics (colony 3, p=0.0209; colony 4, p=0.0090) the larvae which ingested a higher quantity of solid food became adults of hierarchically higher position, however in two other colonies, colony 1 (p=0.6744) and colony 2 (p=0.3367) this difference was not statistically significant; in two experimentally manipulated colonies the caste determination was observed in the imaginal phase (it was verified that the larger the food quantity consumed, the higher the assumed hierarchical position by the individuals); - adult individuals of hierarchically higher position in two colonies ingested a greater amount of solid than liquid food (Mann-Whitney; p ≤ 0.05), however in the other three colonies there was no difference. It can be seen that for all colonies (2, 3, 4, 5 and 6) the high tendency to solid food ingestion occurs. In colony 1, this data was not collected because the observation purpose was different); - inside the colony hierarchy, the older individuals were the ones that occupied higher hierarchical positions; - more than one inseminated female per colony was found in the two experimentally manipulated colonies ; - ovarian development is greater in inseminated females; - the average height of the 3rd tergite was greater for inseminated females, indicating an adaptation to accommodate larger ovary development (t-Student test; p ≤ 0.05).

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

The effects of the social hierarchy destabilization on the foraging activity of eusocial wasp Mischocyttarus cerberus styx Richards, 1940 (Hymenoptera: Vespidae: Polistinae)

The genus Mischocyttarus comprises 245 species of neotropical basal eusocial wasps. They form small colonies (rarely more than few tens of individuals); castes are morphologically undifferentiated and determined behaviorally by agonistic interactions. The aim of this study was to verify the effects of the experimental disruption of social hierarchy on foraging activity of Mischocyttarus cerberus styx. We observed six colonies in postemergence phase and recorded data on the foraging activity under two experimental conditions: (1) removal of lower-ranked females and (2) removal of higher ranked females, except the queen. Our results showed that the removal of higher-ranked females had higher effect on the number of foraging trips of M. cerberus styx than the removal of lower-ranked females (the number of foraging trips/hour decreased by 66.4 and 32.7, resp.). Such results are likely due to the social organization of this species and the presence of a distinct class of females, which in this study were regarded as intermediates. Our data also showed that, irrespective of the hierarchical status of the females, the removal of two or three individuals affected significantly the number of foraging trips in this species. Copyright 2011 Vanderlei Conceio Costa Filho et al.

¿Puede funcionar un sistema de jubilación por capitalización generalizado a toda la población?

Incluye Bibliografía

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Division of labor in stable social hierarchy of the independent-founding wasp Mischocyttarus (Monocyttarus) cassununga, von Ihering (Hymenoptera, Vespidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)