ON THE DETECTION OF PARALLEL CURVES: MODELS AND REPRESENTATIONS

In this paper, we study three parallel models for curves. Based on their common properties we develop an algorithm for the detection of parallelism among curves. Furthermore, to speed up processing, we developed theorems for fast verification at critical points. False alarm is prevented by an enhancement in tangent representation, thus no postprocessing is required. The new tangent representation is called direction-dependent tangent (DDT). It incorporates concavity information into the tangent representation and prohibits false matching. Based on the theorems and the tangent representation, we show that parallelism detection can be formulated as a correspondence problem. The algorithm handles also partial parallelism, i.e., parallelism in certain ranges along the curves but not lasting throughout the whole curves spans. By "curve" we mean any planar curve with C3 continuity. The technique treats both curves and lines alike and is valid for both open and closed curves.

The OCP, Prosodic Morphology and Sonoran Spanish diminutives: a reply to Crowhurst

Megan Crowhurst's ‘Diminutives and augmentatives in Mexican Spanish: a prosodic analysis’ (1992, henceforth CRO) takes a fresh look at the thorny problem of explicating the distribution of the allomorphs -itV and -(e)citV of the Spanish diminutive suffix. CRO has conspicuous virtues. Among them is the limitation of data to a single dialect, namely Sonoran, of northern Mexico. This narrow focus is insurance against inadvertently mixing incompatible data, a special risk posed by the considerable dialect variability of productive diminutivisation. At the same time, CRO broadens its data base by taking into account the partial parallelism between diminutive -itV/-(e)citV and augmentative -otV/-(e)sotV.

Emission and absorption in the infra-red spectra of mercury, zinc, and cadmium

In a previous paper the writer pointed out that well-marked absorption bands exist in the infra-red region of the spectrum caused by passing white light through non-luminous mercury vapour. These bands occur at λ 1·014, λ 1·129. and λ 1·205, the first and third of these being especially strong. This investigation has since been extended further into the infra-red with mercury vapour, and it has also been repeated with the vapours of zinc and cadmium in place of that of mercury. The results serve to establish at least a partial parallelism in the behaviour of the three metals, the resemblance being most marked in the region of the first line of the series represented by v = (2·5, S)—( m , P), at which wave-length absorption takes place in the case of all three metals with extremely small vapour-pressure. On account of the ease with which the wave-length corresponding to v = (2·5, S)—( m , P) was absorbed, it was suspected that it should be emitted under electronic bombardment. At the suggestion of Prof. McLennan an investigation was undertaken with mercury vapour, in order to determine the speed which electrons must be given in order to stimulate emission of the wave-length λ 1·014. If we apply the quantum relation ve = hv to the frequency of this wave-length, we get V = 1·26 volts. In the experiments which will be described herein, the wave-length λ 1·014 was actually emitted with a voltage as low as 5 volts. There were strong indications that even a lower voltage would suffice to stimulate emission of the wave-length, but under the conditions of the experiment the radiations of this wave-length when emitted were reabsorbed by the intervening layers of mercury vapour.