Imipramine improved the symptoms of patients with chest pain and normal coronary angiograms, possibly through a visceral analgesic effect.

THEODOR WILLIAM MELNYK, OSVALD KNOP, arid WILLIAM ROBERT SMITH. Can. J. Chem. 55, 1745Chem. 55, (1977.We review the formulation and solutions of a number of extremal problems associated with points and unit charges on the surface of a sphere in E3. For one of these problems, namely >?I U(nz,n) = +k C dp,-" = minimum P" 4 where d,, is the Euclidean distance between points P and Q and n1 is the number of points, we discuss the results for m 5 16 and 1 5 n < co. For the cases m = 5, 11, 13-16 we find hitherto undiscovered solutions. Our solutions for in = 5 and 11 correct earlier results in the literature. We also sharpen the existing literature results for m = 7 and 10. The problem, and its equivalents and cognates, of how to arrange nz points (or equivalent particles or discrete unit charges) on the surface of a three-dimensional sphere to satisfy a prescribed extremal condition, is of importance in stereochemistry (VSEPR theory of directed valency, cf. ref. 1) as well as in botany, virology, information theory, and elsewhere (2, 3). However, it is often not appreciated that an 'equilibrium' configuration of the points may in some cases correspond to seceral, quite different, extremal requirements which in general lead to a variety of solutions (cf. ref. 4). Furthermore, the extremal requirements are sometimes inadequately specified and their description is confused; it is in fact not entirely clear which particular set of extremal conditions is the most appropriate to use as a basis of stereochemical theory. In view of this and of the fact that the mathematical literature on extremal configura-'To whom correspondence should be addressed.tions is quite extensive and at times not easily accessible, we set out, in the following, the various equivalent formulations of the extremal conditions of interest and present as concisely as possible the results, exact or conjectured, that have been reported to date. Against this background we then describe the results of our own investigations of problem B below, the extremal problem that has received most attention by chemists.We have investigated problem B for 5 to 16 points by a numerical technique. Rigorous methods (cide infra; refs. 2, 3, 6-8) have so far produced solutions for up to 12 points (in an isolated case, for 24 points), and then only for the so-called 'hard-spheres' case, which is of limited importance in stereochemistry. In yielding solutions for 11 and 24 points the geometric method of proof may be approaching its limit of usefulness. On the other hand, the computational time and effort required to deal with 16 points, and the increasing ease with which competing configuraCan. J. Chem. Downloaded from www.nrcresearchpress.com by 66.108.234.21 on 03/25/19For personal use only.

Thirty-two participants (16 younger adults, mean age of 18, and 16 older adults, mean age of 70) were examined to determine whether older adults adopt mental representations and processes that are less taxing on the cognitive system. Specifically, they were asked to mentally rotate a variety of images with different levels of complexity to examine whether they mentally rotate stimuli holistically or piecemeal; that is, whether they rotate the image as a single undifferentiated unit or as a collection of segments that are connected together to form the image. Using analysis of variance (ANOVA) the authors observed that younger adults found the more complex images harder to rotate, whereas the older adults rotated the complex images with the same effort as the simple images. The data reflected that older adults used holistic representations and processing in visual mental rotation. This information-processing schema reduces the use of cognitive resources as its underpinning because it is less computationally intensive. Furthermore, such a schema is more robust because it is not dependant or affected by the complexity of the image. The younger adults used piecemeal representations and processing. In contrast to the holistic strategy, the piecemeal schema is more volatile because it entails that the demands on the cognitive system vary with different images.

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