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.

Covariant quantization of the superparticle using pure spinors

The ten-dimensional superparticle is covariantly quantized by constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor variable. This same method was recently used for covariantly quantizing the superstring, and it is hoped that the simpler case of the superparticle will be useful for those who want to study this quantization method. It is interesting that quantization of the superparticle action closely resembles quantization of the worldline action for Chern-Simons theory.

Energy and the AdS/CFT correspondence

We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for 'regular' and 'irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformai dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Electromyographic validation of basic exercises for physical conditioning programmes IV. Analysis of the deltoid muscle (anterior portion) and pectoralis major muscle (clavicular portion) in frontal-lateral cross, dumbbells exercises

The electromyographic activity of the shoulder muscles deltoid - anterior portion (DA) and pectoralis major - clavicular portion (PMC) was tested on 24 male volunteers using a 2 channel TEC A TE4 electromyograph and Hewlett Packard surface electrodes during the execution of four different modalities of frontal-lateral cross, dumbbells exercises. The results showed that all of the tested exercises developed high levels of action potential for both muscles. So, we jusfity the indication of all of them for physical fitness programmes for DA and PMC. Some suggestions to the use of the tested exercises are presented.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Covariant quantization of the superstring

After constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor ghost variable, the superstring is covariantly quantized and N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. © 2004 Published by Elsevier B.V.

Nucleation and crystallization of titania nanoparticles in silica titania planar waveguides: A study by low frequency Raman scattering

SiO2 (1-x) - TiO2 (x) waveguides, with the mole fraction x in the range 0.07 - 0.20 and thickness of about 0.4 μm, were deposited on silica substrates by a dip-coating technique. The thermal treatments at 700-900°C, used to fully densify the xerogels, produce nucleation of TiO2 nanocrystals even for the lowest TiO2 content. The nucleation of TiO2 nanocrystals and their growth by thermal annealing up to 1300°C were studied by waveguide Raman spectroscopy, for the SiO2 (0.8) - TiO2 (0.2) composition. By increasing the annealing temperature, the Raman spectrum evolves from that typical of the silica-titania glass to that of anatase, but brookite phase is dominant at intermediate temperatures. In the low. frequency region (5-50 cm-1) of the Raman spectra, acoustic vibrations of the nanocrystals are observed. From the measured line shapes, we can deduce the size distribution of the particles. The results are compared with those obtained from the line widths in the X-ray diffraction patterns. Nanocrystals with a mean size in the range 4-20 nm are obtained, by thermal annealing in a corresponding range of 800-1300°C.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Relating the Green-Schwarz and pure spinor formalisms for the superstring

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring © SISSA/ISAS 2005.

Nonlinear dynamics of short traveling capillary-gravity waves

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1 + 1) traveling-wave solutions for almost all the values of the Bond number θ (the special case θ=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. ©2005 The American Physical Society.

On superfield covariant quantization in general coordinates

We propose a natural extension of the BRST-antiBRST superfield covariant scheme in general coordinates. Thus, the coordinate dependence of the basic tensor fields and scalar density of the formalism is extended from the base supermanifold to the complete set of superfield variables. © Springer-Verlag.

Corn root length density and root diameter as affected by soil compaction and soil water content

Negative effects of soil compaction have been recognized as one of the problems restricting the root system and consequently impairing yields, especially in the Southern Coastal Plain of the USA. Simulations of the root restricting layers in green house studies are necessary for the development of mechanism which alleviates soil compaction problems in these soils. The selection of three distinct bulk densities based on the standard proctor test is also an important factor to determine which bulk density restricts the root layer. The experiment was conducted to assess the root length density and root diameter of the corn (Zea mays L.) crop as a function of bulk density and water stress, characterized by the soil density (1.2; 1.4, and 1.6 g cm -3), and two levels of the water content, approximately (70 and 90% field capacity). The statistical design adopted was completely randomized design, with four replicates in a factorial pattern of (3 × 2). The PVC tubes were superimposed with an internal diameter of 20 cm with a height of 40 cm (the upper tube 20 cm, compacted and inferior tube 10 cm), the hardpan with different levels of soil compaction were located between 20 and 30 cm of the depth of the pot. Results showed that: the main effects of subsoil mechanical impedance were observed on the top layer indicating that the plants had to penetrate beyond the favorable soil conditions before root growth was affected from 3.16; 2.41 to 1.37 cm cm -3 (P<0.005). There was a significant difference at the hardpan layer for the two levels of water and 90% field capacity reduced the root growth from 0.91 to 0.60 cm cm -3 (P<0.005). The root length density and root diameter were affected by increasing soil bulk density from 1.2 to 1.6 g cm -3 which caused penetration resistance to increase to 1.4 MPa. Soil water content of 70% field capacity furnished better root growth in all the layers studied. The increase in root length density resulted in increased root volume. It can also be concluded that the effect of soil compaction impaired the root diameter mostly at the hardpan layer. Soil temperature had detrimental effect on the root growth mostly with higher bulk densities.

α-SiAION: Development and machining test on gray cast iron

The α-SiAlON ceramic cutting tool insert is developed. Silicon nitride and additives powders are pressed and sintered in the form of cutting tool inserts at temperature of 1900 °C. The physics and mechanical properties of the inserts like green density, weight loss, relative density, hardness and fracture toughness are evaluated. Machining studies are conducted on grey cast iron workpiece to evaluate the performance of α-SiAlON ceramic cutting tool. In the paper the cutting tool used in higher speed showed an improvement in the tribological interaction between the cutting tools and the grey cast iron workpiece resulted in a significant reduction of flank wear and roughness, because of better accommodation and the presence of the graphite in gray cast iron. The above results are discussed in terms of their affect at machining parameters on gray cast iron.