Matrix representations of truncated Toeplitz operators

In this paper we describe matrix representations of truncated Toeplitz operators on the model space _KB$K_B$, where B is an infinite Blaschke product satisfying some additional conditions. Our results are extensions of that obtained by Cima, Ross and Wogen in 2008.     

How and why nanoparticle's curvature regulates the apparent pKa of the coating ligands

Dissociation of ionizable ligands immobilized on nanopaticles (NPs) depends on and can be regulated by the curvature of these particles as well as the size and the concentration of counterions. The apparent acid dissociation constant (pK(a)) of the NP-immobilized ligands lies between that of free ligands and ligands self-assembled on a flat surface. This phenomenon is explicitly rationalized by a theoretical model that accounts fully for the molecular details (size, shape, conformation, and charge distribution) of both the NPs and the counterions.     

Accelerated Self‐Replication under Non‐Equilibrium,Periodic Energy Delivery

Self‐replication is a remarkable phenomenon in nature that has fascinated scientists for decades. In a self‐replicating system, the original units are attracted to a template, which induce their binding. In equilibrium, the energy required to disassemble the newly assembled copy from the mother template is supplied by thermal energy. The possibility of optimizing self‐replication was explored by controlling the frequency at which energy is supplied to the system. A model system inspired by a class of light‐switchable colloids was considered where light is used to control the interactions. Conditions under which self‐replication can be significantly more effective under non‐equilibrium, cyclic energy delivery than under equilibrium constant energy conditions were identified. Optimal self‐replication does not require constant energy expenditure. Instead, the proper timing at which energy is delivered to the system is an essential controllable parameter to induce high replication rates.     

Mechanically Driven Activation of Polyaniline into Its Conductive Form

Mechanical treatment of polymers produces surface cations and anions which, as demonstrated here for the first time, can drive chemical reactions. In particular, it is shown that such a mechanical treatment transforms nonconductive polyaniline into its conductive form. These results provide a mechanical means of patterning conductive polymers and also coating small polymer objects with conductive polyaniline films preventing accumulation of static electricity.