Light-cone cuts of I+ for charged-Kerr geometry

By integrating the equations for null geodesics we obtain the light-cone cuts of null infinity for the charged Kerr geometries.Supported by NSF Grant No. PHY800823.     

A general central limit theorem for FKG systems

A central limit theorem is given which is applicable to (not necessarily monotonic) functions of random variables satisfying the FKG inequalities. One consequence is convergence of the block spin scaling limit for the magnetization and energy densities (jointly) to the infinite temperature fixed point of independent Gaussian blocks for a large class of Ising ferromagnets whenever the susceptibility is finite. Another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models.     

Generating sets for rings of algebraic integers

Let R be the ring of integers of some finite algebraic extension of the rationals Q of degree n. A necessary and sufficient condition for s elements of R to be an R-basis is given, in terms of the Hermite normal form of a certain n ×ns integral matrix depending on the elements, and on the structure constants of R.     

Fluorine nuclear magnetic resonance: calibration and system optimization

Fluorine-19 magnetic resonance imaging (MRI) offers advantages for imaging organs and tissues. 19F is readily synthesized into a variety of compounds and offers the potential for in-vivo imaging as a complement to hydrogen MRI. The purpose of this work was to determine the minimum detection sensitivity for a fluorinated compound (CF3-CO2H) as a function of pulse sequence, interpulse times (TE, TI, and TR), gradient values and the number of data averages. CF3-CO2H was chosen because it has a single spectral line and exhibits a minimal frequency shift under the experimental conditions used for this experiment. A resistance MR scanner operating at a resonance frequency of 6.255 MHz was used for imaging both fluorine (.156 T) and hydrogen (.147 T). Critical factors determining the minimum detection sensitivity included system signal-to-noise ratio (S/N), acquisition time, relaxation times (T1, T2), and sample volume. Samples were measured over the range of 0.05 M to 20.0 M and showed a linear relationship between signal strength and concentration. The minimum detection sensitivity was 0.1 M. Use of higher static fields and optimized coils as well as improved system signal-to-noise ratios will improve detection sensitivity. We conclude that imaging of fluorine on low-field system is feasible, although it is necessary to optimize many parameters to maximize detection sensitivity.     

Partial spin depolarization of muonium in ice

Muon spin precession signals arising from both muonium and a diamagnetic muon species have been studied in single crystal of ice over the temperature range 90–263 K. Conversion of initial signal amplitudes to fractions of muon polarization reveals that for temperatures above 200 K part of the original muon polarization is unaccounted for. Such a missing fraction is well known for liquid water. but was not found in earlier work on polycrystalline ice. Muonium signals in Polycrystalline ice were reanalyzed using a non-exponential decay function appropriate to the powder pattern spectrum. Smaller muonium fractions were found. consistent with those determined for single crystall, thus confirming the existence of the missing fraction. The origin of the missing fraction is discussed, and it is proposed that non-reactive spin exchange encounters between muonium and hydrogen atoms may be the cause.     

Slater parameter shifts in substituted lanthanide ions

The usual explanation of the reduction of Slater parameters for lanthanide ions substituted into crystals as being due to covalency is shown to be without foundation. Alternative mechanisms are considered, and the dielectric effect of the host crystal is shown to be important. The dielectric contribution to the crystal field parameters is also discussed.     

The construction of stationary two-dimensional Markoff fields with an application to quantum field theory

It is shown that if φ(f)  ∝_R^dφ(y) f(y) dy is a Markoff random field and X_α are multiplicative functionals of φ (with E(X_α) = 1) which converge locally in L₁, then there exists a locally Markoff random field $\text{φ}{}_1$ such that $\text{E(exp(iφ}{}_1\text{(f))) =}\text{lim}{}_{\mathrm{\alpha }}\text{E(X}{}_{\mathrm{<mtext>\alpha </mtext>}}\text{exp}\text{(iφ(φ)))}$. We choose φ to be the two-dimensional generalization of the Ornstein-Uhlenbeck velocity process and take X_α proportional to exp(?λ∝_R² : P(φ(y)) : g_α(y) dy), where: P(φ(y)) : is a regularized even degree polynomial in φ(y). It is then proved that for an appropriate choice of g_α → 1 and small λ, {X_α} does converge locally in L₁ and that the corresponding $\text{φ}{}_1$ is stationary.     

Tensors,spinors, and functions on the unit sphere

A representation of tensors and spinors at a point of space-time as spin and conformally weighted functions on the unit sphere is derived. Methods for performing algebraic operations on tensors and spinors in this representation are discussed.Supported in part by grants Nos. GP-35773X1 and MPS74-18020 from the National Science Foundation.     

Definite paths and upper bounds on regular regions of velocity phase space

Hamilton's principle states that the path integral of the Langrangian is stationary with respect to variations of a classical path. It does not distinguish between a local minimum, a local maximum or a saddle point in path space. A simple algorithm is devised which provides strict and useful upper bounds on the region of velocity phase space occupied by paths that are either local maxima or local minima. The technique is illustrated graphically for the standard map. It is found that the bounds provide accurate numerical upper estimates for the region of velocity phase space filled by the rotational KAM surfaces at arbitrarily chosen values of the perturbation parameter.