On Domains in Which Harmonic Functions Satisfy Generalized Mean Value Properties

Potential Analysis - Assume that a bounded domain Ω??N (N ≥ 2) has the property that there exists a signed measure µ with compact support in Ω such that, for every...     

How to Build Stable Relationships Between People Who Lie and Cheat

This is a talk delivered at the conference “Mathematics in a Complex World”, on the occasion of the 150th anniversary of the Politecnico di Milano. Asymmetry of information, i.e. the possibility for human beings to hide their information, or not to keep their promises, is a fundamental fact of social life, and must be taken into account. I will show how this creates complexity, even in the very simple situation of a contract between two parties, one of whom commits to work for the other, but cannot be monitored.     

On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.     

Selective Carbanion–Pyridine Coordination of a Reactive P,N Ligand to RhI

Ligands with reactive carbon sites in the periphery of a metal center have emerged as a powerful approach for metal–ligand bond activation. These reactive carbon sites are commonly generated by deprotonation strategies. Carbon–silicon bond cleavage is a potential alternative to access such constructs. Herein, the monodesilylation of bis-silyl-substituted P,N scaffold PN^Si2 in the coordination sphere of [Rh^I(Cl)(CO)( PN^Si2 )] ( 1 ) with sodium azide is disclosed. This affords a unique dinucleating anionic κ²-C,N-κ¹-P ligand with a carbanionic methine carbon atom directly bound to rhodium as part of a four-membered Rh-N-C-C rhodacycle. This dimer undergoes meta-pyridine C−H activation facilitated by weak bases, which leads to a desymmetrization of the system and provides a σ,π-bridging 3-pyridyl fragment bound to Rh^I. The facile Si−C cleavage strategy may pave the way to studying the reactivity and functionalization of a variety of κ²-C,N-coordinated pyridine scaffolds for selective transformations.     

Instability,intermixing and electronic structure at the epitaxial LaAlO3/SrTiO3(001) heterojunction

The question of stability against diffusional mixing at the prototypical LaAlO₃/SrTiO₃(001) interface is explored using a multi-faceted experimental and theoretical approach. We combine analytical methods with a range of sensitivities to elemental concentrations and spatial separations to investigate interfaces grown using on-axis pulsed laser deposition. We also employ computational modeling based on the density function theory as well as classical force fields to explore the energetic stability of a wide variety of intermixed atomic configurations relative to the idealized, atomically abrupt model. Statistical analysis of the calculated energies for the various configurations is used to elucidate the relative thermodynamic stability of intermixed and abrupt configurations. We find that on both experimental and theoretical fronts, the tendency toward intermixing is very strong. We have also measured and calculated key electronic properties such as potential energy gradients and valence band discontinuity at the interface. We find no measurable electric field in either the LaAlO₃ or SrTiO₃, and that the valence band offset is near zero, partitioning the band discontinuity almost entirely to the conduction band edge. Significantly, we find it is not possible to account for these electronic properties theoretically without including extensive intermixing in our physical model of the interface. The atomic configurations which give the greatest electrostatic stability are those that eliminate the interface dipole by intermixing, calling into question the conventional explanation for conductivity at this interface—electronic reconstruction. Rather, evidence is presented for La indiffusion and doping of the SrTiO₃ below the interface as being the cause of the observed conductivity.