Spherical assemblies of the type [PdnL2n]2n+ can be obtained from PdII salts and curved N-donor ligands, L. It is well established that bent angle, α, ligand a decisive factor in self-assembly process, with larger angles leading to complexes higher nuclearity, n. Herein, we report heteroleptic coordination cages [PdnLnL′n]2n+, for which similar correlation between angle nuclearity observed. Tet...

Contents Chapter 1. Introduction 5 Chapter 2. Internal measure-theoretic phenomena 13 1. Amenable groups and nuclearity 13 2. Amenable actions, nuclearity, and exactness 16 3. The type semigroup, invariant measures, and pure infiniteness 21 4. The universal minimal system 29 5. Minimal actions, pure infiniteness, and nuclearity 31 Chapter 3. External measure-theoretic phenomena 33 1. Sofic grou...

A novel coordination nanocage was obtained with in situ-generated tetrazole ligands from the cobalt-thiacalix[4]arene system. Four in situ-generated 1,3-bis(2H-tetrazol-5-yl)benzene ligands bolster eight Co4-calix shuttle-cock-like secondary building units (SBUs) into a hollow tetragonal prism with a high surface area. The unprecedented {Co32} nanocage presents the highest nuclearity example.

A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces.