Isospectrality and Heat Content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrodinger operators acting in L-2[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Spirocyclic Acylphloroglucinol Derivatives from Hypericum pyramidatum

Five spirocyclic acylphloroglucinol derivatives (1-5) have been isolated from a hexanes extract of the leaves of Hypericum pyramidatum. Pyramidatones A-D (1-3, 5) are new, and chipericumin C (4) has been previously reported. The acylphloroglucinols were characterized based on spectroscopic (NMR, IR, UV-VIS) and mass spectrometric data.