Abstract
Bulletin of the American Mathematical Society, November.—On wronskians of functions of a real variable, by Prof. Bôcher, has for its object the settling certain questions connected with the subject so as to clear the way for further investigations—such as whether the roots of wronskians of sets of linearly independent solutions can have an infinite number of roots in a given interval, and also the question to what extent the theory of the adjoint (adjungirte) differential equation remains valid when the coefficients of the differential equation are not assumed to be analytic but merely continuous functions. To do this he considers the slightly more general subject of linear families of which the solutions of a homogeneous linear differential equation form a special case. The paper was communicated at the August meeting of the Society, as also was the following, on the Configurations of the 27 lines on a cubic surface and the 28 bitangents to a quartic curve, by Prof. L. E. Dickson. After determining four systems of simple groups in an arbitrary domain of rationality which include the four systems of simple continuous groups of Lie, the author was led to consider the analogous problem for the five isolated simple continuous groups of 14, 52, 78, 133 and 248 parameters. The groups of 78 and 133 parameters are related to certain interesting forms of the third and fourth degrees respectively (Cartan's thèses), and these suggest certain forms discussed in the paper.—Dr. G. A. Miller gives an account of the mathematical work done at the fiftieth annual general meeting of the American Association for the Advancement of Science. There are given the titles, with abstracts, of twenty-five papers.—Prof. J. S. Ames reviews “Die partiellen Differentialgleichungen der mathematischen Physik” (nach Riemann's Vorlesungen in vierter Auflage neu bearbeitet von Heinrich Weber, erster bd. 1900, zweiter bd. 1901).—Amongst the notes are included the Cambridge mathematical courses for the current academic year.—New publications as usual.
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Scientific Serial . Nature 65, 140 (1901). https://doi.org/10.1038/065140a0
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DOI: https://doi.org/10.1038/065140a0