Topic
Tschirnhausen cubic
About: Tschirnhausen cubic is a research topic. Over the lifetime, 43 publications have been published within this topic receiving 1035 citations.
Papers
More filters
••
204 citations
••
202 citations
••
TL;DR: In this paper, a review of some conventions and definitions required for the derivation of the irreducible representations of the space groups, and a method to obtain lattice harmonics are given.
Abstract: A review is given of some conventions and definitions required for the derivation of the irreducible representations of the space groups, and of a method to obtain lattice harmonics. These are given for all the irreducible representations of the simple cubic ($\mathrm{Pm}3m$), face-centered cubic ($\mathrm{Fm}3m$) and body-centered cubic ($\mathrm{Im}3m$) space groups for $l\ensuremath{\le}12$. The expansions are given in polar coordinates and care has been taken that different bases corresponding to the same representation span identical, rather than equivalent, representations, which are given in full. Moreover, all the different expansions listed in the tables are fully orthogonal.
184 citations
••
TL;DR: In this article, the Tschirnhausen cubic is used to solve a geometric Hermite interpolation problem, where the Hermite data is obtained from a smooth function.
74 citations
••
TL;DR: The notions of cubic a-ideal and cubic p-ideals are introduced, and several related properties are investigated, and the cubic extension property of a cubicA-Ideal is discussed.
Abstract: The notions of cubic a-ideals and cubic p-ideals are introduced, and several related properties are investigated. Characterizations of a cubic a-ideal are established. Relations between cubic p-ideals, cubic a-ideals and cubic q-ideals are discussed. The cubic extension property of a cubic a-ideal is discussed.
67 citations