Idea Of Symmetry Research Articles

Global symmetry and the conservation of isobaric spin in non-leptonic hyperon decays

The possible existence of a universal V–A interaction and of global symmetry in non-leptonic hyperon decay is discussed. Deviations from the expected symmetry, which occur in actual decays, are explained in terms of the meson structure of the hyperons. A new isobaric spin is defined, equal to 1/2 for all baryons and to 0 or 1 for K-mesons. It is closely connected with the idea of global symmetry, and is conserved in non-leptonic decays.

Symmetrical-Components Analysis of the Four-Phase System

Symmetrical-components concepts are developed for the currents, voltages, and impedances of a four-phase system, and formulas are given for various types of short circuits. The idea of symmetry among the members of each set is based on the angular displacement between the members of the set, rather than that of phase rotation which fits the three-phase case very nicely but is inadequate for the four-phase case. Aside from its possible value for four-phase problems, which are rather rare, the paper is presented here in the expectation of an additional benefit, namely, that the parallelisms and contrasts between the four-phase and the three-phase formulas may throw further light on the general theory and applications of symmetrical components.

SYMMETRY AND REGULATION IN MNEMIOPSIS LEIDYI, AGASSIZ

The ctenophores, a group in which Mnemiopsis is included, are usu ally referred to as biradially symmetrical animals. By some they are believed to have primarily a radial symmetry. There is of course the idea of bilateral symmetry expressed in the term biradial. As one sees this animal swimming freely in water it does seem to possess a radial symmetry. This impression is received because its organs are distrib uted about a central, longitudinal axis. But a close examination of this animal reveals that most of its organs are paired and are located on two opposite sides of the central, single organ, the stomodeum (Figs. 1 and 11). A method other than and including the study of the anatomy of this animal has been used by me in getting information about its sym metry. This information was obtained during a series of experiments which had been planned to show other characters of this animal. The one feature which has been demonstrated repeatedly during experimenta tion on Mnemiopsis is the power to regulate itself. This power to regu late its body following injury either in nature or caused by experiments seems to have some bearing on symmetry. I propose, therefore, to show in this report that Mnemiopsis possesses a particular type of symmetry, bilateral symmetry without dorso-ventrality, as well as the power to regulate itself, and that in this animal symmetry and regulation are asso ciated with each other.

The Asiatic Arcs

Escher’s Definition of bilateral Symmetry All earlier studies of folded mountain ranges ignored the relationship between plan and cross-section or profile. Largely in consequence of this neglect, the forces to which they have been supposed to owe their structure have been assumed to possess a bilateral symmetry. For the classical area of the Alps, the folded region which has been studied for the longest time and in the greatest detail, this idea of bilateral symmetry was expressed in the words of Escher and his pupil Heim as zweiseitigen Druck . Assymmetrical Arrangement of Ranges It was Eduard Suess who as early as 1875, in his Die Entstehung der Alpen, by focusing attention on the plan, rather than the profile, of mountain ranges, showed that an asymmetrical arrangement of the ranges within definite arcs called for an asymmetrical disposition of the forces which had produced them. Very shortly thereafter James Dana, in . . .