Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

‘ … vayan a San Miguel de Allende, además lleven su visa y su diccionario los que no sepan hablar inglés pues ya se han apropiado de todo los gringos.’ The discursive struggle for interculturality in a gentrified hybrid Mexican city

This paper focuses on interculturality in the discursive construction of the Mexican city of San Miguel de Allende that is culturally hybrid due to Americanisation and gentrification caused by North American migration and tourism. Constructing their own community as ‘expats’, this homogenous group produces and reproduces a dominant discourse that normalises Americanisation and gentrification. There is, however, a resistant discourse from multiple voices, both North American and Mexican, that problematises this hybridity in terms of negative consequences for local Mexicans of rising costs, displacement, and a sense of alienation, particularly felt in how English has become a lingua franca. Este artículo se enfoca en la interculturalidad en la construcción discursiva de la ciudad mexicana de San Miguel de Allende la cual es una ciudad culturalmente híbrida debido a la americanización y gentrificación provocada por la migración y el turismo norteamericano. Construyendo su propia comunidad como ‘expatriados’, este grupo homogéneo produce y reproduce un discurso dominante que normaliza la americanización y la gentrificación. Sin embargo, se observa un discurso resistente de múltiples voces, tanto norteamericanas como mexicanas, que problematizan esta hibridez en términos de consecuencias negativas para los mexicanos locales como los costos crecientes, desplazamiento y una sensación de alienación particularmente en el uso de inglés como una lingua franca

Some Studies on the Use of ACA on Corn

ACA. a N fertilizer additive, is now marketed by United Agri Products of Greeley, Colorado. ACA was developed by Amoco in the mid-1970s. Originally, they developed a soluble form of Zn to market in their anhydrous. The form of Zn was zinc acetate. They noted in some of their tests that at low rates of Zinc acetate they obtained yield increases under conditions where there was no indication from foliar Zn analysis that soil Zn was inadequate. Zinc acetate in strong ammonia solutions exists as 1 molecule of Zn with 2 molecules of acetate, and in the presence of adequate ammonia, 4 molecules of ammonia hold the zinc carboxylate so that it does not ionize. If the complex is diluted with water to the extent that the complex is not held together, a zinc hydroxide precipitate begins to form. Upon further dilution, Zn comes back into solution as the ion. I believe that using ACA in a manner which maintains the zinc acetate ammonia complex is essential for ACA activity

Data compressor Patent

Description of system for recording and reading out data related to distribution of occurrence of plurality of event

Scaling analysis of Kondo screening cloud in a mesoscopic ring with an embedded quantum dot

The Kondo effect is theoretically studied in a quantum dot embedded in a mesoscopic ring. The ring is connected to two external leads, which enables the transport measurement. Using the "poor man's" scaling method, we obtain analytical expressions of the Kondo temperature T_K as a function of the Aharonov-Bohm phase \phi by the magnetic flux penetrating the ring. In this Kondo problem, there are two characteristic lengths. One is the screening length of the charge fluctuation, L_c=\hbar v_F/ |\epsilon_0|, where v_F is the Fermi velocity and \epsilon_0 is the energy level in the quantum dot. The other is the screening length of spin fluctuation, i.e., size of Kondo screening cloud, L_K=\hbar v_F/ T_K. We obtain different expressions of T_K(\phi) for (i) L_c \ll L_K \ll L, (ii) L_c \ll L \ll L_K, and (iii) L \ll L_c \ll L_K, where L is the size of the ring. T_K is markedly modulated by \phi in cases (ii) and (iii), whereas it hardly depends on \phi in case (i). We also derive logarithmic corrections to the conductance at temperature T\gg T_K and an analytical expression of the conductance at T\ll T_K, on the basis of the scaling analysis.Comment: 21pages, 10 figure

Astroglial-axonal interactions during early stages of myelination in mixed cultures using in vitro and ex vivo imaging techniques

<b>Background</b><p></p> Myelination is a very complex process that requires the cross talk between various neural cell types. Previously, using cytosolic or membrane associated GFP tagged neurospheres, we followed the interaction of oligodendrocytes with axons using time-lapse imaging in vitro and ex vivo and demonstrated dynamic changes in cell morphology. In this study we focus on GFP tagged astrocytes differentiated from neurospheres and their interactions with axons.<p></p> <b>Results</b><p></p> We show the close interaction of astrocyte processes with axons and with oligodendrocytes in mixed mouse spinal cord cultures with formation of membrane blebs as previously seen for oligodendrocytes in the same cultures. When GFP-tagged neurospheres were transplanted into the spinal cord of the dysmyelinated shiverer mouse, confirmation of dynamic changes in cell morphology was provided and a prevalence for astrocyte differentiation compared with oligodendroglial differentiation around the injection site. Furthermore, we were able to image GFP tagged neural cells in vivo after transplantation and the cells exhibited similar membrane changes as cells visualised in vitro and ex vivo.<p></p> <b>Conclusion</b><p></p> These data show that astrocytes exhibit dynamic cell process movement and changes in their membrane topography as they interact with axons and oligodendrocytes during the process of myelination, with the first demonstration of bleb formation in astrocytes

Demonstration of a quantile system for compression of data from deep space probes

Quantile system of data compression for space telemetr

Fano effect and Kondo effect in quantum dots formed in strongly coupled quantum wells

We present lateral transport measurements on strongly, vertically coupled quantum dots formed in separate quantum wells in a GaAs/AlGaAs heterostructure. Coulomb oscillations are observed forming a honeycomb lattice consistent with two strongly coupled dots. When the tunnel barriers in the upper well are reduced we observe the Fano effect due to the interfering paths through a resonant state in the lower well and a continuum state in the upper well. In both regimes an in plane magnetic field reduces the coupling between the wells when the magnetic length is comparable to the center to center separation of the wells. We also observe the Kondo effect which allows the spin states of the double dot system to be probed.Comment: 4 pages, 5 figure