Explicit integration of the full symmetric Toda hierarchy and the sorting property

We give an explicit formula for the solution to the initial-value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szegö, and is also interpreted as a consequence of the QR factorization method of Symes. The sorting property of the dynamics is also proved for the case of a generic symmetric matrix in the sense described in the text, and generalizations of tridagonal formulae are given for the case of matrices with 2M+1 nonzero diagonals.     

Temperature effects on the carbon-13 NMR shifts of selected compounds

The effects of temperature on the ¹³C NMR shifts of benzene, cyclohexane, pyridine, cyclohexene, neopentane, hexane, and heptane have been determined from +10 to +70°C. In addition, the temperature shift of ²D in D₂O was found to be +10.4 × 10^?3 ppm/°C. All shifts appear to be linear functions of temperature within experimental error.     

Reconstructing supernova-neutrino spectra using low-energy beta beams

Neutrinos are the principal messengers reaching us from the center of a supernova. Terrestrial neutrino telescopes can provide precious information about the processes in the core of the star. But the information that a neutrino detector can supply is restricted by the fact that little experimental data on the neutrino-nucleus cross sections exist and by the uncertainties in theoretical calculations. In this Letter, we propose a novel procedure that determines the response of a target nucleus in a supernova-neutrino detector, by using low-energy beta beams. We show that fitting "synthetic" spectra, constructed by taking linear combinations of beta-beam spectra, to the original supernova-neutrino spectra reproduces the folded differential cross sections very accurately. Comparing the response in a detector to these synthetic responses provides a direct way to determine the main parameters of the supernova-neutrino energy distribution.     

Diamond Electrodes for High Sensitivity Mercury Detection in the Aquatic Environment: Influence of Surface Preparation and Gold Nanoparticle Activity

This work compares polished and unpolished boron doped diamond (BDD) electrodes decorated with two sizes of gold nanoparticles (AuNPs) for use as robust mercury sensors in aquatic environments. The size of the catalytically active AuNPs on the electrode surfaces was demonstrated to have a less significant effect on the sensitivity for mercury detection than the surface preparation of the BDD. The lowest limits of detection were achieved with the polished BDD electrodes, which both detected mercury at a concentration of 1 pM, six orders of magnitude greater sensitivity than the lowest detection limit of 5 μM achieved with an unpolished BDD electrode, and high in comparison with other reported electrode systems.     

Shear wave speed recovery using moving interference patterns obtained in sonoelastography experiments

Two new experiments were created to characterize the elasticity of soft tissue using sonoelastography. In both experiments the spectral variance image displayed on a GE LOGIC 700 ultrasound machine shows a moving interference pattern that travels at a very small fraction of the shear wave speed. The goal of this paper is to devise and test algorithms to calculate the speed of the moving interference pattern using the arrival times of these same patterns. A geometric optics expansion is used to obtain Eikonal equations relating the moving interference pattern arrival times to the moving interference pattern speed and then to the shear wave speed. A cross-correlation procedure is employed to find the arrival times; and an inverse Eikonal solver called the level curve method computes the speed of the interference pattern. The algorithm is tested on data from a phantom experiment performed at the University of Rochester Center for Biomedical Ultrasound.     

Combinatorial Isols and the Arithmetic of Dekker Semirings

In his long and illuminating paper [1] Joe Barback defined and showed to be non‐vacuous a class of infinite regressive isols he has termed “complete y torre” (CT) isols. These particular isols a enjoy a property that Barback has since labelled combinatoriality. In [2], he provides a list of properties characterizing the combinatoria isols. In Section 2 of our paper, we extend this list of characterizations to include the fact that an infinite regressive isol X is combinatorial if and only if its associated Dekker semiring D (X) satisfies all those Π₂ sentences of the anguage L_N for isol theory that are true in the set ω of natural numbers. (Moreover, with X combinatorial, the interpretations in D(X)of the various function and relation symbols of L_N via the “lifting ” to D(X) of their Σ₁ definitions in ω coincide with their interpretations via isolic extension.) We also note in Section 2 that Π₂(L)‐correctness, for semirings D(X), cannot be improved to Π ₃(L)‐correctness, no matter how many additional properties we succeed in attaching to a combinatoria isol; there is a fixed (L) sentence that blocks such extension. (Here L is the usual basic first‐order language for arithmetic.) In Section 3, we provide a proof of the existence of combinatorial isols that does not involve verification of the extremely strong properties that characterize Barback's CT isols.