Nonlinear Electrodynamics: Alternative Field Theory for Featuring Photon Propagation Over Weak Background Electromagnetic Fields and what Earth Receivers Read off Radio Signals from Interplanetary Spacecraft Transponders

A few observational and/or experimental results have dramatically pushed forward the research program on gravity as those from the radio-metric Doppler tracking received from the Pioneer 10 and 11 spacecrafts when the space vehicles were at heliocentric distances between 20 and 70 Astronomical Units (AU). These data have conclusively demonstrated the presence of an anomalous, tiny and blue-shifted frequency drift that changes smoothly at a rate of $\sim 6 \times 10^{-9}$ Hz s$^{-1}$. Those signals, if interpreted as a gravitational pull of the Sun on each Pioneer vehicle, translates into a deceleration of $a_P = (8.74\pm 1.33) \times 10^{-10}$ m s$^{-2}$. This Sunward acceleration appears to be a violation of Newton's inverse-square law of gravitation, and is referred to as the Pioneer anomaly, the nature of which remains still elusive to unveil. Within the theoretical framework of nonlinear electrodynamics (NLED) in what follows we will address this astrodynamics puzzle, which over the last fifteen years has challenged in a fundamental basis our understanding of gravitational physics. To this goal we will first, and briefly, review the history of the Pioneers 10 and 11 missions. Then a synopsis of currently available Lagrangian formulations of NLED is given. And finally, we present our solution of this enigma by invoking a special class of NLED theories featuring a proper description of electromagnetic phenomena taking place in environments where the strength of the (electro)magnetic fields in the background is decidedly low.Comment: 24, pages, 3 figures. Source of the first publication of this article: InTech Publisher: http://www.intechweb.or

The communication, speech and gesture of a group of hearing-impaired children

The communication skills, speech and gesture of 20 hearing-impaired children were assessed. The children were all being educated in a school using an oral/aural approach. Assessment result comparison indicated the importance of assessing gesture and speech separately for these children and comparing the use of both skills. More informal and formal assessment of gesture and the tools to complete this task effectively are needed to ensure that these children's communication skills are described accurately

Complex Unit Roots and Business Cycles: Are They Real?

In this paper the asymptotic properties of ARMA processes with complex- conjugate unit roots in the AR lag polynomial are studied. These processes behave quite differently from processes with a single root equal to 1. In particular, the asymptotic properties of a standardized version of the periodogram for such processes are analyzed, and a nonparametric test of the complex unit root hypothesis against the stationarity hypothesis is derived. This test is applied to the annual change of the monthly number of unemployed in the US, in order to see whether this time series has complex unit roots in the business cycle frequencies.

Instantons, Twistors, and Emergent Gravity

Motivated by potential applications to holography on space-times of positive curvature, and by the successful twistor description of scattering amplitudes, we propose a new dual matrix formulation of N = 4 gauge theory on S(4). The matrix model is defined by taking the low energy limit of a holomorphic Chern-Simons theory on CP(3|4), in the presence of a large instanton flux. The theory comes with a choice of S(4) radius L and a parameter N controlling the overall size of the matrices. The flat space variant of the 4D effective theory arises by taking the large N scaling limit of the matrix model, with l_pl^2 ~ L^2 / N held fixed. Its massless spectrum contains both spin one and spin two excitations, which we identify with gluons and gravitons. As shown in the companion paper, the matrix model correlation functions of both these excitations correctly reproduce the corresponding MHV scattering amplitudes. We present evidence that the scaling limit defines a gravitational theory with a finite Planck length. In particular we find that in the l_pl -> 0 limit, the matrix model makes contact with the CSW rules for amplitudes of pure gauge theory, which are uncontaminated by conformal supergravity. We also propose a UV completion for the system by embedding the matrix model in the physical superstring.Comment: v2: 64 pages, 3 figures, references added, typos correcte

The hexagonal versus the square lattice

We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in dimensions 2 to 8 the best known lattice sphere packings have `maximal lengths' and goes on to write: "In dimension 2 the conjecture means in particular that the hexagonal lattice is `better' than the square lattice. More precisely, let 0<h_1<h_2<... be the positive integers, listed in ascending order, which can be written as h_i=x^2+3y^2 for integers x and y. Let 0<q_1<q_2<... be the positive integers, listed in ascending order, which can be written as q_i=x^2+y^2 for integers x and y. Then the conjecture is that q_i<=h_i for i=1,2,3,..." Our proof requires computational prime number theory in combination with methods from a preprint of the first author (to appear in Math. Comp.), arXiv:math.NT/0112100.Comment: 24 pages, 6 figures, 2 table