A manifold obtained by k simultaneous symplectic blow-ups of CP of equal sizes ǫ (where the size of CP ⊂ CP is one) admits an effective two dimensional torus action if k ≤ 3 and admits an effective circle action if (k−1)ǫ < 1. We show that these bounds are sharp if 1/ǫ is an integer. 1. Toric actions and circle actions in dimension four Hamiltonian torus actions. Let a torus T ∼= (S) act on a c...

Let Φ be an irreducible crystallographic root system with Weyl group W , coroot lattice Q̌ and Coxeter number h. Recently the second named author defined a uniform W -isomorphism ζ between the finite torus Q̌/(mh + 1)Q̌ and the set of non-nesting parking functions Park(Φ). If Φ is of type An−1 and m = 1 this map is equivalent to a map defined on labelled Dyck paths that arises in the study of the ...

Physics is introduced as a semantics of a formal set theory. We consider a metatheory of a formal set theory S. We name this metatheory MS, indicating that it is a Meta-theory of S as well as a Meta-Scientific theory as Ronald Swan [1] refers to. The following arguments are all made in MS. We define in MS φ = the class of all well-formed formulae of S. This φ is a countable set in the context o...

Dessy, Chantal, Inkyeom Kim, Carrie L. Sougnez, Regent Laporte, and Kathleen G. Morgan. A role for MAP kinase in differentiated smooth muscle contraction evoked by a-adrenoceptor stimulation. Am. J. Physiol. 275 (Cell Physiol. 44): C1081–C1086, 1998.—The purpose of this study was to investigate the potential role of mitogen-activated protein (MAP) kinase in smooth muscle contraction by monitori...

We describe for any Riemannian manifold M a certain scheme ML, lying in between the first and second neighbourhood of the diagonal of M . Semiconformal maps between Riemannian manifolds are then analyzed as those maps that preserve ML; harmonic maps are analyzed as those that preserve the (LeviCivita-) mirror image formation inside ML. Introduction For any Riemannian manifold M , we describe a ...

Let φ : Mn → B(H) be an injective, completely positive contraction with ‖φ−1 : φ(Mn) → Mn‖cb ≤ 1 + δ(ǫ). We show that if either (i) φ(Mn) is faithful modulo the compact operators or (ii) φ(Mn) approximately contains a rank 1 projection, then there is a complete order embedding ψ : Mn → B(H) with ‖φ − ψ‖cb < ǫ. We also give examples showing that such a perturbation does not exist in general. As ...

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h)−f(x) has the Baire property for every h ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...

Abstract. Fix a strictly increasing right continuous with left limits function W : R → R and a smooth function Φ : [l, r] → R, defined on some interval [l, r] of R, such that 0 < b ≤ Φ ≤ b. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes, with conductances given by W , is described by the weak solutions of the non-linear differential equation...