Rolling simplexes and their commensurability. II: A lemma on the directrix and focus
Although we are told in the summary that ``The law of central-square dynamics \[ (x,y,z)''=-\frac{4\pi^2k}{(\alpha(x-a)+\beta(y-b)+\gamma(z-c)+\delta)^2}(x-a,y-b,z-c), \] expressing the focusing of a plane wave at the point \((a,b,c)\) is discussed and justified'', the paper deals first with the above equation in just \(x\) and \(y\) (so \(\gamma=0\) and no \(z\) above), then moves on to the motion of a harmonic oscillator, to fields of Coulomb type, and to Descartes-Wotton algebras. None of the author's results receives any kind of motivation, nor does the reader find out where the journey leads or what the significance of the intermediate steps are. One has the feeling that one has found a notebook with some entries that the author jotted down for later use, in a context known only to herself. The translator (most likely) introduced on page 305 and 307 a certain author ``O. Whatnot'' in ``The claim of sufficiency of the necessary condition of O. Whatnot directly follows from the lemma on the directrix and focus'' and in the title of a section: ``Extension of O. Whatnot of the Descartes-Wotton Algebra''. For part I, see [the author, J. Math. Sci., New York 186, No. 4, 586--591 (2012); translation from Fundam. Prikl. Mat. 17, No. 2, 87--95 (2011; Zbl 1264.51001)].
scientific article; zbMATH DE number 6533874