A general approach to association using cluster partition functions

A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.     

An auditory basis for the stimulus-length effect in the perception of stops and glides

To investigate possible auditory factors in the perception of stops and glides (e.g., /b/ vs /w/), a two-category labeling performance was compared on several series of /ba/-/wa/ stimuli and on corresponding nonspeech stimulus series that modeled the first-formant trajectories and amplitude rise times of the speech items. In most respects, performance on the speech and nonspeech stimuli was closely parallel. Transition duration proved to be an effective cue for both the stop/glide distinction and the nonspeech distinction between abrupt and gradual onsets, and the category boundaries along the transition-duration dimension did not differ significantly in the two cases. When the stop/glide distinction was signaled by variation in transition duration, there was a reliable stimulus-length effect: A longer vowel shifted the category boundary toward greater transition durations. A similar effect was observed for the corresponding nonspeech stimuli. Variation in rise time had only a small effect in signaling both the stop/glide distinction and the nonspeech distinction between abrupt and gradual onsets. There was, however, one discrepancy between the speech and nonspeech performance. When the stop/glide distinction was cued by rise-time variation, there was a stimulus-length effect, but no such effect occurred for the corresponding nonspeech stimuli. On balance, the results suggest that there are significant auditory commonalities between the perception of stops and glides and the perception of acoustically analogous nonspeech stimuli.     

EPR of cadmium ferric voltaite above the ferrimagnetic transition

A single isotropic EPR line of Fe³⁺ in synthetic cadmium ferric voltaite, (NH₄)₂Cd₅Fe₃Al(SO₄)₁₂ · 18H₂O, was observed in a wide temperature range from 295 to 1.57°K. The ferrimagnetic transition temperature of CdFe voltaite was determined to be ～ 0.7°K using the temperature dependence of the g-factor and the line width. The cubic crystal field parameter, a, for Fe³⁺ in CdFe voltaite is extracted from the EPR line width measurement using the exchange-narrowed line width model of Anderson and Weiss. The parameter a for Fe³⁺ in CdFe voltaite at 4.2°K is 157 × 10^-4cm^-1 which is consistent with the corresponding values for Fe³⁺ in other cubic structures.     

Counting non-isomorphic three-connected planar maps

A counting formula for the number of non-isomorphic planar maps with m edges was obtained by V. A. Liskovets, and non-isomorphic 2-connected planar maps were counted by Liskovets and the author. R. W. Robinson's generalization of Polya's counting theory can be applied to these formulae to count, in polynomial time, non-isomorphic planar maps satisfying various sets of restrictions. Here two sets of planar maps are counted: maps with given 2-connected components, and 3-connected maps.