"The Wagner Bubble"

The Mermin-Wagner Theorem

LetA be a C∗ algebra such as the algebra of quasi-local observables of a quantum spin system on Z, and suppose {αt}t∈R is a strongly continuous one-parameter group of automorphisms of A, which we will refer to as the dynamics of the system. The examples we have in mind are the dynamics of a quantum spin system generated by a not-too-long-range interaction Φ, e.g., one that satsifies, for some λ...

Mass murder: the Wagner case.

On the Livingstone-Wagner Theorem

Let G be a permutation group on the set Ω and let S be a collection of subsets of Ω, all of size ≥ m for some integer m . For s ≤ m let ns(G, S) be the number of G-orbits on the subsets of Ω which have a representative y ⊆ x with |y| = s and y ⊆ x for some x ∈ S . We prove that if s < t with s + t ≤ m then ns(G, S) ≤ nt(G, S) . A special case of this theorem is the Livingstone-Wagner Theorem wh...

Numerical Investigation of the Effect of Bubble-Bubble Interaction on the Power of Propagated Pressure Waves

The study of bubble dynamics, especially the interaction of bubbles, has drawn considerable attention due to its various applications in engineering and science. Meanwhile, the study of the oscillation effect of a bubble on the emitted pressure wave of another bubble in an acoustic field which has less been investigated. This issue is investigated in the present study using the coupling of Kell...

Genetics: Doudney and Wagner

2 Neel, J. V., Blood, 6, 389 (1951). rs Valentine, W. N., and Neel, J. V., Arch. Int. Med., 74, 185 (1944). 4Neel, J. V., and Valentine, W. N., Genetics, 32,38 (1947). aPauling, L., Itano, H. A., Singer, S. J., and Wells, I. C., Science, 10, 543 (1948). 6 Liquori, A. M., Nature, 167, 950 (1951). 7 We wish to express our thanks to Dr. Phillip Sturgeon of the Children's Hospital, Los Angeles, Cal...