Conformal covariance and the probability interpretation of wave equations

The Dirac and the Schrödinger fields are singled out among all other fields by their conformal dimension $\text{l = ?}\text{3}\text{2}$, a necessary condition for the field to have also a probability interpretation as a wave function. The correct dimension of the Schrödinger field comes about by an intricate contraction of the conformal group to the Schrödinger group.     

Improved analytical prediction of facilitation factors in facilitated transport

An improved analytical solution for the facilitation factor in facilitated transport that covers a wide range from diffusion-limited to reaction-limited mass transport has been developed. This solution is attained after assuming a small non-zero solute concentration at the membrane exit. Based on previous analysis a graph that provides a reasonable downstream solute concentration was extracted. The exit solute concentration was found to be dependent on both the mobility ratio, , and the inverse Damkohler number, ε. The quick and reasonable results in this work can be used for design and scale-up purposes.     

Photochemical reaction detection in HPLC

The versatility of post-column reaction detection in chromatography is greatly enhanced by exploiting the principles of organic photochemistry. Improvements in photochemical reactor design will result in further advantages.     

Supercritical fluid chromatography with redox chemiluminescence detection

Summary The new selective and sensitive redox chemiluminescence detector (RCD), originally developed for gas chromatography, has been successfully interfaced with a capillary column supercritical fluid chromatograph. Interfacing the SFC-RCD was accomplished simply through utilization of the redox reaction chamber presently used for both capillary and packed column GC. The feasibility of this new separation-detection scheme was demonstrated with SFC chromatograms of antioxidant isomers and some compounds of biological relevance. Mobile phase compatibility and signal quenching are also discussed.

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Chromatographie mit überkritischen fluiden phasen unter Verwendung der Redox-Chemiluminescenz-Detektion

     

Airborne radioactivity measurements from the chernobyl plume

Airborne gamma-ray measurements were made aboard the Pacific Northwest Laboratory (PNL) DC-3 and the National Oceanic and Atmospheric Administration (NOAA) King Air research aircraft before and during the first passage of the Chernobyl radioactive cloud over the west coast of the North American continent. Measurements were made from Anchorage, Alaska south to Reno, Nevada. Calculated trajectories were used to estimate the location of the Chernobyl plume. The in-situ gamma-ray analysis systems first detected the cloud on May 8, 1986. Subsequent analysis of concurrently collected air filters indicated that the leading edge of the plume was just reaching the west coast of the United States on May 6, 1986. The ratios of the observed volatile radionuclides (¹³¹I and¹³⁴Cs normalized to¹³⁷Cs) agreed with the reported discharge ratio.Operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

The feasibility pump

In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem of the form min{c^Tx:Ax≥b,x_j integer ∀j ∈ }. Trivially, a feasible solution can be defined as a point x* ∈ P:={x:Ax≥b} that is equal to its rounding , where the rounded point is defined by := x*_j if j ∈ and := x*_j otherwise, and [·] represents scalar rounding to the nearest integer. Replacing “equal” with “as close as possible” relative to a suitable distance function Δ(x*, ), suggests the following Feasibility Pump (FP) heuristic for finding a feasible solution of a given MIP.We start from any x* ∈ P, and define its rounding . At each FP iteration we look for a point x* ∈ P that is as close as possible to the current by solving the problem min {Δ(x, ): x ∈ P}. Assuming Δ(x, ) is chosen appropriately, this is an easily solvable LP problem. If Δ(x*, )=0, then x* is a feasible MIP solution and we are done. Otherwise, we replace by the rounding of x*, and repeat.We report computational results on a set of 83 difficult 0-1 MIPs, using the commercial software ILOG-Cplex 8.1 as a benchmark. The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered. Interestingly, ILOG-Cplex could not find any feasible solution at the root node for 19 problems in our test-bed, whereas FP was unsuccessful in just 3 cases.     

A non-MRA C^r Frame Wavelet with Rapid Decay

A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in . This example has the same multiplicity function as the Journé wavelet, yet has a Fourier transform and can be made to be for any fixed postive integer . L. Baggett and P. Jorgensen were supported by a US–NSF Focused Research Group (FRG) grant.     

Contributions to diophantine approximation in fields of series

The following topics are taken up: (i) the dimension of certain vector spaces defined in terms of denominations of differential polynomials, (ii) examples of series for which a Thue-Siegel-Roth type theorem holds, (iii) approximation of linear forms whose coefficients satisfy algebraic differential equations, and (iv) rational approximations to solutions of algebraic difference-differential equations.Written with partial support from NSF grant NSF-MCS 78-01770.