English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove that every solution of the Helmholtz equation within an equilateraltriangle, which obeys the Dirichlet conditions on the boundary, is a member ofone of four symmetry classes. We then show how solutions with differentsymmetries, or different energies, can be generated from any given solutionusing symmetry operators or a differential operator derived from symmetryconsiderations. Our method also provides a novel way of generating the groundstate solution (that is, the solution with the lowest energy). Finally, weestablish a correspondence between solutions in the equilateral and (30,60, 90)triangles.

Using symmetry to generate solutions to the Helmholtz equation inside an equilateral triangle