General deletion lemmas via the Harris inequality

General deletion lemmas via the Harris inequality

We present a new approach to the deletion method that is based on the Harris inequality. We obtain deletion lemmas that are similar in spirit to those of Rödl and Ruciński, but hold for arbitrary decreasing properties. That is, we show that under appropriate conditions, with very high (‘Janson-like’) probability it suffices to delete a small fraction of the edges of a random graph Gn,p to ensur...

Exchange lemmas 2 : General Exchange Lemma ✩

Exchange lemmas are used in geometric singular perturbation theory to track flows near normally hyperbolic invariant manifolds. We prove a General Exchange Lemma, and show that it implies versions of existing exchange lemmas for rectifiable slow flows and loss-of-stability turning points. © 2007 Elsevier Inc. All rights reserved. MSC: 34E15; 34C30

Deletion, Bell's inequality, teleportation

In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell’s inequality. Interestingly we find that for all values of α the state does not violate the Bell’s inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2 3 ).

Two lemmas that changed general equilibrium theory

Regularity in kinetic formulations via averaging lemmas

We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best k...