An Indium‐Seamed Hexameric Metal–Organic Cage as an Example of a Hexameric Pyrogallol[4]arene Capsule Conjoined Exclusively by Trivalent Metal Ions

A hexameric metal–organic nanocapsule is assembled from pyrogallol[4]arene units, which are stitched together with indium ions. This indium‐seamed capsule is the first instance of a M₂₄L₆ type hexameric coordination cage held together exclusively by trivalent metal ions. Explicitly, unlike previously reported pyrogallol[4]arene‐based metal‐seamed capsules, the current In³⁺ seamed capsule is entirely supported by O→In coordinate bonds. This work demonstrates the important proof of concept of the ability of pyrogallol[4]arene to react with metals in higher oxidation states to assemble into atomically‐precise hexameric coordination cages. As such, these results open up exciting avenues toward the assembly of previously unanticipated metal–organic capsules, for example offering inspiration for tackling metals exhibiting high valence states such as in the lanthanide and actinide series.     

Artificial neural system modeling of Monte Carlo simulations of polymers

In this work, a neural network was used to learn features in potential energy surfaces and relate those features to conformational properties of a series of polymers. Specifically, we modeled Monte Carlo simulations of 20 polymers in which we calculated the characteristic ratio and the temperature coefficient of the characteristic ratio for each polymer. We first created 20 rotational potential energy surfaces using MNDO procedures and then used these energy surfaces to produce 10000 chains, each chain 100 bonds long. From these results we calculated the mean-square end-to-end distance, the characteristic ratio and its corresponding temperature coefficient. A neural network was then used to model the results of these Monte Carlo calculations. We found that artificial neural network simulations were highly accurate in predicting the outcome of the Monte Carlo calculations for polymers for which it was not trained. The overall average error for prediction of the characteristic ratio was 4,82%, and the overall average error for prediction of the temperature coefficient was 0,89%.     

A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane

The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies, consideration has been given principally to pure initial-value problems where the wave profile is imagined to be determined everywhere at a given instant of time and the corresponding solution models the further wave motion. The practical, quantitative use of the Korteweg-de Vries equation and its relatives does not always involve the pure initial-value problem. Instead, initial-boundary-value problems often come to the fore. A natural example arises when modeling the effect in a channel of a wave maker mounted at one end, or in modeling near-shore zone motions generated by waves propagating from deep water. Indeed, the initial-boundary-value problem

studied here arises naturally as a model whenever waves determined at an entry point propagate into a patch of a medium for which disturbances are governed approximately by the Korteweg-de Vries equation. The present essay improves upon earlier work on (0.1) by making use of modern methods for the study of nonlinear dispersive wave equations. Speaking technically, local well-posedness is obtained for initial data in the class for \frac34$"> and boundary data in , whereas global well-posedness is shown to hold for when , and for when . In addition, it is shown that the correspondence that associates to initial data and boundary data the unique solution of (0.1) is analytic. This implies, for example, that solutions may be approximated arbitrarily well by solving a finite number of linear problems.

     

Supramolecular stabilization of N(2)H(7)(+)

The cation N(2)H(7)(+) has been stabilized in a largely hydrophobic supramolecular environment and characterized in the solid state. The cation is situated in the bowl-shaped cavity of calix[4]arene. All of the hydrogen atoms are clearly discernible owing to high-quality X-ray data as well as lack of disorder and symmetry-imposed ambiguity. It appears that electrostatic interactions play a critical role in stabilizing the structure.