Interassociates of the Free Commutative Semigroup on n Generators

The interassociates of the free commutative semigroup on n generators, for n > 1, are identified. For fixed n, let (S, ·) denote this semigroup. We show that every interassociate can be written in the form , depending only on a n-tuple . Next, if and are isomorphic interassociates of (S, ·) such that , for x_ii and x_j in the generating set of S, then . Moreover, if and only if is a permutation of .     

Evaluation of matrix-assisted laser desorption ionization mass spectrometry for polymer characterization

A protocol for the preparation of polymeric samples for time-of-flight matrix-assisted laser desorption ionization mass spectrometry (TOF-MALDI-MS) analysis was developed. Dithranol was identified as a good matrix for polystyrene (PS), and the addition of silver for cationization of molecules was determined to be necessary. Based on this preparative method, low molecular weight samples of other polymers [polyisoprene, polybutadiene, poly(ethylene oxide), poly(methyl methacrylate), and polydimethylsiloxane] were analyzed with molecular weights up to 49 ku. The effects of laser intensity were determined to influence the molecular weight distribution of intact oligomers, most significantly for low molecular weight polymers. Linear and reflectron modes of analysis were evaluated; better signal intensity and resolution were obtained in the reflectron mode. The TOF-MALDI-MS measurements are compared with time-of-flight secondary ion mass spectrometry (TOF-SIMS) and gel permeation chromatography (GPC) for the same polymers. The M _n values calculated by TOF-MALDI-MS consistently are higher than values calculated by TOF-SIMS for all classes of polymers with molecular weights up to 8 ku. The molecular weights of the PS calculated from TOF-MALDI-MS are in good agreement with GPC (±10%). The composition of the terminal group on a polymer chain may affect the ion yields. The ion yields of intact oligomers were evaluated as a function of end group composition for both TOF-MALDI-MS and TOF-SIMS. The slight disparity of results between TOF-SIMS and TOF-MALDI-MS for the perfluoroalkyl-terminated PS suggests that the oligomers are desorbed preferentially from the surface in the TOF-SIMS analysis, rather than having an increased ionization probability.     

Use of CT scans and treatment planning software for validation of the dose component of food irradiation protocols

The challenging problem of estimating the dose delivered to heterogeneous products by radiation modalities of limited penetration can be readily handled by using technologies developed for, and widely used in, radiation therapy applications. In particular, combining CT scanning with radiation treatment planning programs can simulate radiation processing with either photons or electrons, and can provide detailed, high resolution and accurate dose maps for any arbitrary product and package configuration. Such dose maps are an essential part of process validation. Comparison of the simulated dose distributions with measured dose maps verifies the soundness of this approach. The present communication presents results obtained with the simulation technique for a variety of common food items which are likely candidates for radiation processing.     

Optical Zeeman spectroscopy of the (0,0) B(4)Γ - X(4)Φ band systems of titanium monohydride, TiH, and titanium monodeuteride, TiD

The Zeeman effect in the (0,0) bands of the B(4)Γ(5∕2) - X(4)Φ(3∕2) system of titanium monohydride, TiH, and titanium monodeuteride, TiD, has been recorded and analyzed. Magnetic tuning of the spectral features recorded at high resolution (full width at half maximum ? 35 MHz) and at a field strength of 4.5 kG is accurately modeled using an effective Zeeman Hamiltonian. The determined magnetic g-factors for the X(4)Φ(3∕2) (v = 0) state deviate only slightly from those expected for an isolated (4)Φ(3∕2) state whereas those for the B(4)Γ(5∕2)(v = 0) deviate significantly from those of an isolated (4)Γ(5∕2) state. The rotational dependence of the magnetic tuning in the B(4)Γ(5∕2)(v = 0) state is attributed to perturbations from a nearby (4)Φ state.     

Groups and actions in transformation semigroups

Let be a transformation semigroup of degree . To each element we associate a permutation group acting on the image of , and we find a natural generating set for this group. It turns out that the -class of is a disjoint union of certain sets, each having size equal to the size of . As a consequence, we show that two -classes containing elements with equal images have the same size, even if they do not belong to the same -class. By a certain duality process we associate to another permutation group on the image of , and prove analogous results for the -class of . Finally we prove that the Schützenberger group of the -class of is isomorphic to the intersection of and . The results of this paper can also be applied in new algorithms for investigating transformation semigroups, which will be described in a forthcoming paper. Received 16 December 1996; in final form 18 February 1997     

Reproducible tritium generation in electrochemical cells employing palladium cathodes with high deuterium loading

Reproducible tritium generation well above background has been observed in tightly closed D₂SO₄-containing cells in four out of four Pd wire cathodes of one type. Tritium analysis was performed before and after each experiment on the Pd, the electrolyte and the gas in the head space. No tritium generation was observed in four identical Pd cathodes in H₂SO₄ cells operated at the same time under the same conditions. A cyclic loading-unloading regime with low current densities, rather than the usual continuous constant current regime, was employed to attain D/Pd and H/Pd loadings of 1±0.05 reproducibly. D/Pd loadings greater than 0.8±0.05 appear to be necessary to generate tritium. The largest amount of tritium, generated in 7 days of continuous electrolysis, was 2.1 × 10¹¹ tritium atoms, compared with a background of 4 × 10⁹ tritium atoms. The concentration of tritium and its axial distribution in the Pd were determined and concentrations of up to 9 × 10¹⁰ atoms/g Pd were found compared with a maximum background of 5 × 10⁸ atoms g⁻¹. The T/D ratio in the Pd is about 100 times larger than in the electrolyte or gas and indicates that tritium generation occurs in the Pd interior rather than at its surface. No tritium generation was observed in two other types of Pd electrodes in D₂SO₄, despite the attainment of D/Pd ratios near 1:1. Thus high D/Pd ratios appear to be a necessary but not sufficient condition for tritium generation in D₂SO₄ electrolysis.     

Finding groups with a simple genetic algorithm*

A new solution to the old problem of partitioning a matrix of social proximities into groups is proposed. It draws on a heuristic developed in computer science, the simple genetic algorithm. The algorithm is described and its utility is demonstrated with applications to three standard data sets.     

Capillary forces in the acoustics of patchy-saturated porous media

A linearized theory of the acoustics of porous elastic formations, such as rocks, saturated with two different viscous fluids is generalized to take into account a pressure discontinuity across the fluid boundaries. The latter can arise due to the surface tension of the membrane separating the fluids. We show that the frequency-dependent bulk modulus K(omega) for wavelengths longer than the characteristic structural dimensions of the fluid patches has a similar analytic behavior to the case of a vanishing membrane stiffness and depends on the same parameters of the fluid-distribution topology. The effect of the capillary stiffness can be accounted for by renormalizing the coefficients of the leading terms in the low-frequency limit of K(omega).     

Chemiluminescence of Si + N2O flames

Spectra of the chemiluminescent flame produced by the reaction of silicon vapor with N₂O have shown strong emission from the A¹Π-X¹Σ⁺, b³Π-X¹Σ⁺, and a³Σ⁺-X¹Σ⁺ systems of SiO with preferential excitation into the b³Π state. Bandhead measurements of 33 bands of the b-X system yielded the following constants for the b³Π state:

$T_e=33947.0\pm 1.9c{m}^{?1};{\omega }_e=1013.8\pm 1.1c{m}^{?1};{\omega }_e{x}_e=7.57\pm 0.12c{m}^{?1}$

. From partially resolved rotational structure in the a-X bands, an approximate value of B = 0.59 ± 0.01cm^?1 was obtained for the a³Σ⁺ state. The effect of adding active nitrogen and CO to the flame was investigated and the results were shown to be consistent with assigning the a and b states as triplets. The photon yield of the Si + N₂O reaction was measured and found to be small.