The GOAL-to-HAL/S translator specification

The specification sets forth a technical framework within which to deal with the transfer of specific GOAL features to HAL/S. Key technical features of the translator are described which communicate with the data bank, handle repeat statements, and deal with software interrupts. GOAL programs, databank information, and GOAL system subroutines are integrated into one GOAL in HAL/S. This output is fully compatible HAL/S source ready for insertion into the HAL/S compiler. The Translator uses a PASS1 to establish all the global data needed for the HAL/S output program. Individual GOAL statements are translated in PASS2. The specification document makes extensive use of flowcharts to specify exactly how each variation of each GOAL statement is to be translated. The specification also deals with definitions and assumptions, executive support structure and implementation. An appendix, entitled GOAL-to-HAL Mapping, provides examples of translated GOAL statements

The affine preservers of non-singular matrices

When K is an arbitrary field, we study the affine automorphisms of M_n(K) that stabilize GL_n(K). Using a theorem of Dieudonn\'e on maximal affine subspaces of singular matrices, this is easily reduced to the known case of linear preservers when n>2 or #K>2. We include a short new proof of the more general Flanders' theorem for affine subspaces of M_{p,q}(K) with bounded rank. We also find that the group of affine transformations of M_2(F_2) that stabilize GL_2(F_2) does not consist solely of linear maps. Using the theory of quadratic forms over F_2, we construct explicit isomorphisms between it, the symplectic group Sp_4(F_2) and the symmetric group S_6.Comment: 13 pages, very minor corrections from the first versio

Comment on "Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field" [Phys. Plasmas 18, 072505 (2011)]

The geometric analysis of the gyromotion for charged particles in a time-dependent magnetic field by J. Liu and H. Qin [Phys. Plasmas 18, 072505 (2011)] is reformulated in terms of the spatial angles that represent the instantaneous orientation of the magnetic field. This new formulation, which includes the equation of motion for the pitch angle, clarifies the decomposition of the gyroangle-averaged equation of motion for the gyrophase into its dynamic and geometric contributions.Comment: 4 page

On the Theory of Superfluidity in Two Dimensions

The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, the presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for the general vortex gas is shown to be the Kosterlitz---Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz---Thouless ensemble.Comment: 22 pages, one figure, written in plain TeX, published in J. Phys. A24 (1991) 502

Age related diffusion and tractography changes in typically developing pediatric cervical and thoracic spinal cord

Background and objective: Diffusion tensor imaging (DTI) and diffusion tensor tractography (DTT) are two techniques that can measure white matter integrity of the spinal cord. Recently, DTI indices have been shown to change with age. The purpose of this study is (a) to evaluate the maturational states of the entire pediatric spinal cord using DTI and DTT indices including fractional anisotropy (FA), mean diffusivity (MD), mean length of white matter fiber tracts and tract density and (b) to analyze the DTI and DTT parameters along the entire spinal cord as a function of spinal cord levels and age. Method: A total of 23 typically developing (TD) pediatric subjects ranging in age from 6 to 16 years old (11.94 ± 3.26 (mean ± standard deviation), 13 females and 10 males) were recruited, and scanned using 3.0 T MR scanner. Reduced FOV diffusion tensor images were acquired axially in the same anatomical location prescribed for the T2-weighted images to cover the entire spinal cord (C1-mid L1 levels). To mitigate motion induced artifacts, diffusion directional images were aligned with the reference image (b0) using a rigid body registration algorithm performed by in-house software developed in Matlab (MathWorks, Natick, Massachusetts). Diffusion tensor maps (FA and MD) and streamline deterministic tractography were then generated from the motion corrected DTI dataset. DTI and DTT parameters were calculated by using ROIs drawn to encapsulate the whole cord along the entire spinal cord by an independent board certified neuroradiologist. These indices then were compared between two age groups (age group A = 6–11 years (n = 11) and age group B = 12–16 years (n = 12)) based on similar standards and age definitions used for reporting spinal cord injury in the pediatric population. Standard least squared linear regression based on a restricted maximum likelihood (REML) method was used to evaluate the relationship between age and DTI and DTT parameters. Results: An increase in FA (group A = 0.42 ± 0.097, group B = 0.49 ± 0.116), white matter tract density (group A = 368.01 ± 236.88, group B = 440.13 ± 245.24) and mean length of fiber tracts (group A = 48.16 ± 20.48 mm, group B = 60.28 ± 23.87 mm) and a decrease in MD (group A = 1.06 ± 0.23 × 10−3 mm2/s, group B = 0.82 ± 0.24 × 10−3 mm2/s) were observed with age along the entire spinal cord. Statistically significant increases have been shown in FA (p = 0.004, R2 = 0.57), tract density (p = 0.0004, R2 = 0.58), mean length of fiber tracts (p \u3c 0.001, R2 = 0.5) and a significant decrease has been shown in MD (p = 0.002, R2 = 0.59) between group A and group B. Also, it has been shown DTI and DTT parameters vary along the spinal cord as a function of intervertebral disk and mid-vertebral body level. Conclusion: This study provides an initial understanding of age related changes of DTI values as well as DTT metrics of the spinal cord. The results show significant differences in DTI and DTT parameters which may result from decreasing water content, myelination of fiber tracts, and the thickening diameter of fiber tracts during the maturation process. Consequently, when quantitative DTI and DTT of the spinal cord is undertaken in the pediatric population an age and level matched normative dataset should be used to accurately interpret the quantitative results. © 201

On the shopfloor: exploring the impact of teacher trade unions on school-based industrial relations

Teachers are highly unionised workers and their trade unions exert an important influence on the shaping and implementation of educational policy. Despite this importance there is relatively little analysis of the impact of teacher trade unions in educational management literature. Very little empirical research has sought to establish the impact of teacher unions at school level. In an era of devolved management and quasi-markets this omission is significant. New personnel issues continue to emerge at school level and this may well generate increased trade union activity at the workplace. This article explores the extent to which devolved management is drawing school-based union representation into a more prominent role. It argues that whilst there can be significant differences between individual schools, increased school autonomy is raising the profile of trade union activity in the workplace, and this needs to be better reflected in educational management research

Electrodynamics with Lorentz-violating operators of arbitrary dimension

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentz- and CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete characterization of the coefficients for Lorentz violation for all mass dimensions via a decomposition using spin-weighted spherical harmonics. The resulting nine independent sets of spherical coefficients control birefringence, dispersion, and anisotropy. We discuss the restriction of the general theory to various special models, including among others the minimal Standard-Model Extension, the isotropic limit, the case of vacuum propagation, the nonbirefringent limit, and the vacuum-orthogonal model. The transformation of the spherical coefficients for Lorentz violation between the laboratory frame and the standard Sun-centered frame is provided. We apply the results to various astrophysical observations and laboratory experiments. Astrophysical searches of relevance include studies of birefringence and of dispersion. We use polarimetric and dispersive data from gamma-ray bursts to set constraints on coefficients for Lorentz violation involving operators of dimensions four through nine, and we describe the mixing of polarizations induced by Lorentz and CPT violation in the cosmic-microwave background. Laboratory searches of interest include cavity experiments. We present the theory for searches with cavities, derive the experiment-dependent factors for coefficients in the vacuum-orthogonal model, and predict the corresponding frequency shift for a circular-cylindrical cavity.Comment: 58 pages two-column REVTeX, accepted in Physical Review

Height estimates for Killing graphs

The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric analysis on a Killing graph is naturally related to a weighted manifold structure, where the weight is defined in terms of the length of the Killing vector field. According to this viewpoint, we introduce some potential theory on weighted manifolds with boundary and we prove a weighted volume estimate for intrinsic balls on the Killing graph. Finally, using these tools, we provide the desired estimate for the weighted height in the assumption that the Killing graph has constant weighted mean curvature and the weighted geometry of the ambient space is suitably controlled.Comment: 26 pages. Final version. To appear on Journal of Geometric Analysi

Electrostatic boundary value problems in the Schwarzschild background

The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution. Boundary value problems are solved. With a multipole expansion the asymptotic property for the field of any charge distribution is derived. It is shown that one produces a Reissner--Nordstrom black hole if one lowers a test charge distribution slowly toward the horizon. The symmetry of the distribution is not important. All the multipole moments fade away except the monopole. A calculation of the gravitationally induced electrostatic self-force on a pointlike test charge distribution held stationary outside the black hole is presented.Comment: 18 pages, no figures, uses iopart.st

Evaluation of stresses in large diameter, thin walled piping at support locations

The highest stresses in many thin walled piping systems are the local stresses at the pipe supports. These secondary stresses are caused by saddles or other structural discontinuities that restrain pipe ovalization. A static analysis of a thin walled pipe supported on structural steel saddle under dead weight loading is presented. The finite element analysis is performed using a shell model with distributed gravity and hydrostatic pressure loading. Parametric studies on global and local stress are performed to determine the effect of the pipe diameter to thickness ratio. Two aspects of the saddle design are also investigated: the effect of saddle width, and the effect of saddle wrap angle. Additionally, the computed stresses are compared to closed form solutions