We prove an index theorem for boundary value problems in Boutet de Monvel’s calculus on a compact manifold X with boundary. The basic tool is the tangent semigroupoid T −X generalizing the tangent groupoid defined by Connes in the boundaryless case, and an associated continuous field C∗ r (T −X) of C∗-algebras over [0, 1]. Its fiber in ~ = 0, C∗ r (T−X), can be identified with the symbol algebr...

Using only the current empirical information on the nucleon electromagnetic form factors we map out the transverse charge density in proton and neutron as viewed from a light front moving towards a transversely polarized nucleon. These charge densities are characterized by a dipole pattern, in addition to the monopole field corresponding with the unpolarized density. Furthermore, we use the lat...

Given a compact Riemannian manifold, we study the regularity of the optimal transport map between two probability measures with cost given by the squared Riemannian distance. Our strategy is to define a new form of the so-called Ma-Trudinger-Wang condition and to show that this condition, together with the strict convexity on the nonfocal domains, implies the continuity of the optimal transport...

A generalization of the Jordan–Schwinger map: classical version and its q–deformation. Abstract For all three–dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan–Schwinger map which is also given for the deformed algebras SL q (2, ...

homotopy groups π∗(Xλ)⊗Q for a family of topological spaces, once we know enough about their additive structure. This allows us to interpret the condition of realizing as an Ak map a multiple of a map f : S1 −→ G between two topological groups in terms of the existence of a rational Whitehead product of order k. Our main example will be when the Xλ are classifying spaces of symplectomorphism gr...

In this work, we consider the challenge of grasping thinwalled deformable objects like plastic bottles and other containers, which are very common in household environments. The deformability of such objects varies considerably along their surface, depending on the local geometry. To consider such phenomenon, we propose a grasp planner, which first uses the Finite Element Method (FEM) for defor...

An approach is presented for addressing the challenge of model rebuilding after molecular replacement in cases where the placed template is very different from the structure to be determined. The approach takes advantage of the observation that a template and target structure may have local structures that can be superimposed much more closely than can their complete structures. A density-guide...