Proof idea: Roughly, summing an inequality given by Lemma 3.3 over all vertices with clumpy
PFPs bounds a quantity below by the number of vertices with clumpy
PFPs, and summing an inequality given by Lemma 3.2 over all edges incident with a vertex with a clumpy
PFP gives an upper bound of 0 on the same quantity.
The Brian Atwood Zenith shoes are an A-list must-have but they look far too clumpy
on Lily's porcelain legs.
So anything that has dried out or not been used goes, especially the clumpy
mascara you are still trying to pump some life out of!
It can be layered for superthick lashes and is not clumpy
* Bobbi Brown Extreme Party Mascara, pounds 17 THE USP of this mascara is that its formula remains pliable between coats meaning you can re-apply throughout the day for a dramatic look without getting clumpy
The professionals on TV make it look a breeze, literally, whereas I only seem to be able to make it look clumpy
SANITY partially returned to Strictly Come Dancing with the elimination of clueless Kate Garraway on Sunday but once again clumpy
Kenny Logan managed to evade the dance-off thanks to his legion of Scottish voters, writes Jeremy Chapman.
The early universe was smooth and homogenous, quite a contrast from the clumpy
clusters of galaxies observed today.
This composite portrait is providing a closer look at the clumpy
, filamentary nature of the remnant, a more precise measurement of its distance from Earth, and a clearer indication of the type of star that exploded to become Kepler's supernova.
If you have a yeast infection, you might notice a fishy odor and clumpy
I also wanted to make something that challenged my idea of form--of the refinement of form and how that happens." Baked in oil-fired kilns in Cholula, and made with the Texca family of brick makers out of locally available materials, these tiny, clumpy
archetypes formed a collaborative work realized through a collectivity of creators.
Katy Perry Is it the burgundy turtleneck, the pleather-esque ankle grazers or the clumpy
heels that makes us want to scratch our eyes out?