Shrinking of toroidal decomposition spaces

Shrinking instability of toroidal droplets.

Toroidal droplets are inherently unstable due to surface tension. They can break up, similar to cylindrical jets, but also exhibit a shrinking instability, which is inherent to the toroidal shape. We investigate the evolution of shrinking toroidal droplets using particle image velocimetry. We obtain the flow field inside the droplets and show that as the torus evolves, its cross-section signifi...

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

Tetrachromatic Colour Spaces - Spherical and Toroidal Hue Spaces

From a 4-hypercube colour space, spaces of the type hue-saturation-luminance are derived. The hue component may have the topology of a 2-sphere, a 2-torus or a 3-sphere, in several possibilities we consider.

Metrizability of Decomposition Spaces

Decomposition of Lebesgue Spaces