Long-range tail produced by the CDD ambiguity in a static model

An aspect of a potential-model analogy of the customary CDD ambiguity is studied. Starting from the idea that the known CDD ambiguity in theS-matrix produces an ambiguity in the determination of potentials, the influence of CDD poles upon the long-range behaviour of potentials in the relativistic (Klein-Gordon) static model is demonstrated. Generation of the long-range tail by CDD poles is investigated in terms of a scattering inversion-problem formalism, based on theN/D equations extended off the mass shell.     

Permeability of heterogeneous gels

Gels made by radical copolymerization of monofunctional and difunctional monomer units in the presence of swelling medium will tend to be heterogeneous. A case in point is acrylamide co-polymerized with N,N′-methylene bis-acrylamide in water. Such gels can be assumed to be two-phasic with both phases gels, but of different average concentration and average degree of cross-linking. As Weiss and Silberberg have shown, permeability can be used to characterize the distribution in space. In this paper, their earlier model is expanded and improved by considering specifically the permeability of each of the two phases and taking into account that each of these phases separately must have come into swelling equilibrium with the swelling medium, water. It can be shown that only the length of the Kuhn statistical element remains as a free parameter in this model. Essentially the same value of this parameter, however, accurately accounts for the measured permeability. It is found that at an overall volume fraction of about 0.16, the two-phase structure tends to disappear. For higher degrees of crosslinking, this occurs because the more dilute phase takes over the entire space; for more lightly crosslinked systems, the more concentrated phase takes over. The heterogeneity of the distribution lies in the nanometer range and reasonable agreement between the results obtainable from permeability and from viscoelasticity can be demonstrated. These results are consistent with the model for the polymerization process.     

Über s-reguläre Graphen

Let G be a graph of valency d = 1 + p^rn with p prime and n < p. It is shown that if the automorphism group of G contains a subgroup A which acts as a regular permutation group on the set of s-arcs in G then s ≤ 7 and s ≠ 6; if d = p^r + 1, r = 2^r, v ≥ 1 an integer, p ≠ 2, then s = 1.     

Small momentum transfer measurements of S(k) in 4He at T = 4.27 K as function of density

We report the first measurements of S(k) in ⁴He at a fixed temperature of T = 4.27 K for 126 < p < 164 kg/m³ for the momentum transfer range $\text{0.18 < k < 1.03}\text{A}\text{?}{}^{\mathrm{?1}}$. Our results are consistent with expectations at zero momentum transfer based on thermodynamics.     

A digital integrator for controlled-potential coulometry

Accurate electrolysis current integration is required in controlled-potential coulometry. Analog integrators have been shown to deviate from ideal response by as much as —0.1%. A digital integrator was designed to optimize the linearity of the voltage-to-frequency converter used, minimize the effects of temperature, eliminate integration errors caused by small polarity changes and signal noise, and allow interchangeability with an analog integrator in a state-of-the-art coulometer widely used throughout the nuclear field for controlled-potential coulometry. Evaluation of the digital integrator, calibrated versus the Faraday, showed bias-free determinations of plutonium with a relative standard deviation of approximately 0.02%. The integrator was designed specifically for use in the controlled-potential coulometric determination of plutonium, but many of the features incorporated can be adopted to digital integrators for other uses where accurate integration over long periods of time is required.