Asymptotic behavior and uniqueness of blow-up solutions of quasilinear elliptic equations

In this paper, we study the asymptotic behavior of solutions of the problem Δ _p u = f (u) in Ω, u = ∞ on ∂Ω, under general conditions on the function f, where Ω _p is the p-Laplace operator. We show that the technique used by the author for the special case p = 2 works in this more general setting, and that the behavior described by various authors for the case p = 2 is easily derived from this technique for the general case.     

The Cyclical Relationship Between Research and Standards: The Case of Principles and Standards for School Mathematics

The link between standards and research may not be clearcut. However, in this article the authors argue that there is a notable relationship between standards and research, one that is cyclical in nature. Using the standards for school mathematics developed by the National Council of Teachers of Mathematics (NCTM) as a case in point, the authors examine how NCTM's standards have influenced the agenda for mathematics education research and stimulated research on the impact of those standards. In turn, this and other research played a significant role in the development of NCTM's new Principles and Standards for School Mathematics. The authors conclude with a discussion of ways in which the Principles and Standards may continue this cyclical relationship in coming years, potentially promoting investigation of new research areas and systematic research on the impact of standards.     

On the Decomposition of Order-Separable Posets of Countable Width into Chains

Order - A partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable...     

On-Surface Driven Formal Michael Addition Produces m-Polyaniline Oligomers on Pt(111)

On-surface synthesis is emerging as a highly rational bottom-up methodology for the synthesis of molecular structures that are unattainable or complex to obtain by wet chemistry. Here, oligomers of meta-polyaniline, a known ferromagnetic polymer, were synthesized from para-aminophenol building-blocks via an unexpected and highly specific on-surface formal 1,4 Michael-type addition at the meta position, driven by the reduction of the aminophenol molecule. We rationalize this dehydrogenation and coupling reaction mechanism with a combination of in situ scanning tunneling and non-contact atomic force microscopies, high-resolution synchrotron-based X-ray photoemission spectroscopy and first-principles calculations. This study demonstrates the capability of surfaces to selectively modify local molecular conditions to redirect well-established synthetic routes, such as Michael coupling, towards the rational synthesis of new covalent nanostructures.     

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.     

How to write a research article for MRC

This nonscientific tutorial proposes best practice for authors publishing research articles in Magnetic Resonance in Chemistry (MRC). It offers authors essential insights into writing eye-catching article titles, author/co-author names and hierarchy, IMRaD and IRDaM article structures, referencing and the composition of abstracts, introductions, experimental, results and discussion, and conclusions together with the all-important covering letter. This arsenal of insights aims to provide tools for authors to maximize the chance of success for their research articles.