Dielectric properties of beryllia ceramics in the near-millimeter wavelength range

We report the refractive indices and absorption coefficients for four beryllia (BeO) ceramic samples. These dielectric properties have been measured over the range from 4 to 18 cm^–1 by use of a Michelson interferometer. The index n, follows the linear relationship n=0.6517 cm³/g×+0.7130 with density, , over the range 2.8<<3.0 g/cm³.     

Fredholm determinants and inverse scattering problems

The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two different types of Fredholm determinant. As an application of the method, an asymptotic formula of high accuracy is derived for a particular Fredholm determinant that determines the level-spacing distribution-function in the theory of random matrices.Research sponsored by the National Science Foundation, Grant No. GP-40768X.     

MRI of hepatic lymphoma

Thirteen patients with biopsy proven hepatic lymphoma (2 Hodgkin, 11 Non-Hodgkin) and a control group of 15 patients with hepatic metastases were analyzed quantitatively and qualitatively by MRI. Focal hepatic lymphoma was most reliably detected (eight of eight patients) and appeared hypointense relative to liver on T₁ weighted (CNR − 7.4 ± 2.3) and hyperintense on T₂ weighted (CNR + 8.4 ± 2.9) images. The mean T₁ and T₂ relaxation times of focal hepatic lymphoma (T₁ = 832 ± 234 msec, T₂ = 84 ± 16 ms) differed significantly from adjacent non-tumorous liver (T₁ = 420 ± 121 ms, T₂ = 51 ± 9 ms; p < 0.05), however CNR values and relaxation times were similar to those of hepatic metastases. Diffuse hepatic lymphoma (microscopic periportal infiltration) was undetectable by MRI in three patients by either morphologic features or quantitative criteria. A mixed pattern of hepatic lymphoma (focal lesions and diffuse infiltration) showed focal areas of slightly decreased signal intensity on T₁ weighted images (CNR = −1.7 ± 0.4) while T₂ weighted images revealed multiple regions of focal hyperintensity (CNR = +13.3 ± 8.4) superimposed on a diffusely hyperintense liver. Our experience demonstrates that either T₁ or T₂ weighted techniques are useful in detecting focal and that T₂ weighted techniques are useful in detecting mixed hepatic lymphoma. Conventional image derived relaxation time measurements and quantitative parameters were of no additional diagnostic value.     

Some Functions of Points in Projective Spaces

Extending earlier results in the plane, we prove that every n-polygon in sufficiently general position in d-dimensional projective space, n d + 2, gives rise to a derived n-polygon, which preserves a few functions; these functions are the cyclial product of (actually affine) ratios of various points, obtained by proper projections on suitable lines.     

Vibrational control of systems with Arrhenius dynamics

A nonlinear system with S-shape steady state characteristic is referred to as a system with Arrhenius dynamics. The negative slope part of the S-shape curve represents a set of unstable steady states. Using two examples of Arrhenius systems (catalytic reactor and continuous stirred tank reactor), it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new Arrhenius system, the steady state characteristic of which has a smaller negative slope part. Results of analytical investigation as well as numerical simulation are presented. It is shown that vibrational stabilization of Arrhenius systems gives an increase in productivity of the plants.     

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements D^J_MM￠(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ ^J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ ^J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.     

Revisiting non-degenerate parametric down-conversion

The quantum dynamics of a two-mode non-resonant parametric down-conversion process is studied by recasting the time evolution equations for the basic operators in an equivalent spin equation form with simpler exact solutions for a pump field with harmonic time dependence. Expectation values of suitable operators for studying important features such as squeezing and quantum revivals are presented in simple forms.      

Saturation recovery EPR and ELDOR at W-band for spin labels

A reference arm W-band (94 GHz) microwave bridge with two sample-irradiation arms for saturation recovery (SR) EPR and ELDOR experiments is described. Frequencies in each arm are derived from 2 GHz synthesizers that have a common time-base and are translated to 94 GHz in steps of 33 and 59 GHz. Intended applications are to nitroxide radical spin labels and spin probes in the liquid phase. An enabling technology is the use of a W-band loop-gap resonator (LGR) [J.W. Sidabras, R.R. Mett, W. Froncisz, T.G. Camenisch, J.R. Anderson, J.S. Hyde, Multipurpose EPR loop-gap resonator and cylindrical TE₀₁₁ cavity for aqueous samples at 94 GHz, Rev. Sci. Instrum. 78 (2007) 034701]. The high efficiency parameter (8.2 GW^−1/2 with sample) permits the saturating pump pulse level to be just 5 mW or less. Applications of SR EPR and ELDOR to the hydrophilic spin labels 3-carbamoyl-2,2,5,5-tetra-methyl-3-pyrroline-1-yloxyl (CTPO) and 2,2,6,6,-tetramethyl-4-piperidone-1-oxyl (TEMPONE) are described in detail. In the SR ELDOR experiment, nitrogen nuclear relaxation as well as Heisenberg exchange transfer saturation from pumped to observed hyperfine transitions. SR ELDOR was found to be an essential method for measurements of saturation transfer rates for small molecules such as TEMPONE. Free induction decay (FID) signals for small nitroxides at W-band are also reported. Results are compared with multifrequency measurements of T_1e previously reported for these molecules in the range of 2–35 GHz [J.S. Hyde, J.-J. Yin, W.K. Subczynski, T.G. Camenisch, J.J. Ratke, W. Froncisz, Spin label EPR T₁ values using saturation recovery from 2 to 35 GHz. J. Phys. Chem. B 108 (2004) 9524–9529]. The values of T_1e decrease at 94 GHz relative to values at 35 GHz.     

Coherent control of the optical nonlinear and luminescence anisotropies in molecular thin films by multiphoton excitations

Photoinduced orientational distributions are implemented with one- and two-photon absorption interference in polymer films containing chromophores that exhibit luminescent and nonlinear properties. The odd- and even-order parameters of the final distribution are probed by simultaneous measurement of second-harmonic generation (SHG) and two-photon fluorescence (TPF). We show the possibility of engineering local SHG and TPF anisotropies by controlling the polarization states and intensities of the writing optical fields. Complex multipolar orders are modeled with an irreducible spherical tensor-based formalism jointly applied to the molecular polarizabilities and field tensors.     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.