626,698 research outputs found
Comment on "On the importance of the free energy for elasticity under pressure"
Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14
L525) claim that thermodynamic properties of materials under pressure must be
computed using the Gibbs free energy , rather than the internal energy .
Marcus et al. state that ``The minima of , but not of , give the
equilibrium structure; the second derivatives of , but not of , with
respect to strains at the equilibrium structure give the equilibrium elastic
constants.'' Both statements are incorrect.Comment: Commen
Marcus Gunn Jaw Winking Phenomenon - A case of the widening eye
Marcus Gunn jaw winking phenomenon is a congenital synkinetic movement due to synkinesis between the upper eyelid and the pterygoids and it accounts for 8% of patients with congenital ptosis. In rare instances, ptosis may be absent. We present a case of Marcus Gunn Jaw Winking phenomenon without ptosis at presentatio
Hereditary properties of partitions, ordered graphs and ordered hypergraphs
In this paper we use the Klazar-Marcus-Tardos method to prove that if a
hereditary property of partitions P has super-exponential speed, then for every
k-permutation pi, P contains the partition of [2k] with parts {i, pi(i) + k},
where 1 <= i <= k. We also prove a similar jump, from exponential to factorial,
in the possible speeds of monotone properties of ordered graphs, and of
hereditary properties of ordered graphs not containing large complete, or
complete bipartite ordered graphs.
Our results generalize the Stanley-Wilf Conjecture on the number of
n-permutations avoiding a fixed permutation, which was recently proved by the
combined results of Klazar and of Marcus and Tardos. Our main results follow
from a generalization to ordered hypergraphs of the theorem of Marcus and
Tardos.Comment: 25 pgs, no figure
- …