An experiment to discover mathematical talent in a primary school in Kampong Air

It is often said that many pupils have hidden talent in mathematics. This hidden ability is rarely seen in a normal classroom teaching and learning situation if the focus of the teacher is on drilling with routine exercises. To allow pupils to display their mathematical talent and to break from mental set and fixation in mathematics, they must be given opportunity to think by themselves with mininum cue or guidance. The pupils could be left entirely on their own to show their mathematical creativity even on mathematical topics which have not been exposed to them. With this approach, five non-routine questions were administered one at a time to a standard 5 class. One out of the 25 pupils in the class consistently exhibited mathematical creativity and talent is answering the questions. Her responses were shown and discussed in this paper.     

Ab initio calculation of the heptamer (NH3)7 as a reasonable starting point for a description of the ammonia crystal

Quasi-Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH₃)₇, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.     

Specific labeling of cell surface proteins with chemically diverse compounds

The specific and covalent labeling of fusion proteins with synthetic molecules opens up new ways to study protein function in the living cell. Here we present a novel method that allows for the specific and exclusive extracellular labeling of proteins on the surfaces of live cells with a large variety of synthetic molecules including fluorophores, protein ligands, or quantum dots. The approach is based on the specific labeling of fusion proteins of acyl carrier protein with synthetic molecules through post-translational modification catalyzed by phosphopantetheine transferase. The specificity and versatility of the labeling should allow it to become an important tool for studying and manipulating cell surface proteins and for complementing existing approaches in cell surface engineering.     

What is the nature of polyacetylene neutral and anionic chains HC(2n)H and HC(2n)H(-) (n = 6-12) that have recently been observed?

The optimized geometries, adiabatic electron affinities, and IR-active vibrational frequencies have been predicted for the long linear carbon chains HC(2n)H. The B3LYP density functional combined with the DZP basis set was used in this theoretical study. The computed physical properties are discussed. The predicted electron affinities form a remarkably regular sequence: 1.78 (HC(12)H), 2.08 (HC(14)H), 2.32 (HC(16)H), 2.53 (HC(18)H), 2.69 (HC(20)H), 2.83 (HC(22)H), and 2.95 eV (HC(24)H). The predicted structures display an alternating triple and very short single bond pattern, with the degree of bond alternation significantly less for the radical anions.     

Efficient polymer passivation of ligand‐stripped nanocrystal surfaces

Water‐dispersible, polymer‐wrapped nanocrystals are highly sought after for use in biology and chemistry, from nanomedicine to catalysis. The hydrophobicity of their native ligand shell, however, is a significant barrier to their aqueous transfer as single particles. Ligand exchange with hydrophilic small molecules or, alternatively, wrapping over native ligands with amphiphilic polymers is widely employed for aqueous transfer; however, purification can be quite cumbersome. We report here a general two‐step method whereby reactive stripping of native ligands is first carried out using trialkyloxonium salts to reveal a bare nanocrystal surface. This is followed by chemically directed immobilization of a hydrophilic polymer coating. Polyacrylic acids, with side‐chain grafts or functional end groups, were found to be extremely versatile in this regard. The resulting polymer‐wrapped nanocrystal dispersions retained much of the compact size of their bare nanocrystal precursors, highlighting the unique role of monomer side‐chain functionality to serve as effective, conformal ligation motifs. As such, they are well poised for applications where tailored chemical functionality at the nanocrystal's periphery or improved access to their surfaces is desirable. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Higher-order Sobolev embeddings and isoperimetric inequalities

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in Rⁿ${\mathbb{R}}^n$, possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces. In particular, our results are applied to any-order Sobolev embeddings in regular (John) domains of the Euclidean space, in Maz'ya classes of (possibly irregular) Euclidean domains described in terms of their isoperimetric function, and in families of product probability spaces, of which the Gauss space is a classical instance.