Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Sulfur adsorption on Fe(1 1 0): a DFT study

The adsorption of atomic S on the Fe(1 1 0) surface is examined using density functional theory (DFT). Three different adsorption sites are considered, including the atop, hollow and bridge sites and the S is adsorbed at a quarter monolayer coverage in a p(2 × 2) arrangement. The hollow site is found to be the most stable, followed by the bridge and atop sites. At all three sites, S adsorption results in relatively minor surface reconstruction, with the most significant being that for the hollow site, with lateral displacements of 0.09 Å. Comparisons between S-adsorbed and pure Fe surfaces revealed reductions in the magnetic moments of surface-layer Fe atoms in the vicinity of the S. At the hollow site, the presence of S causes an increase in the surface Fe d-orbital density of states between 4 and 5 eV. However, S adsorption has no significant effect on the structure and magnetic properties of the lower substrate layers.     

Accreting neutron stars as probes of dense matter physics

There are over 100 accreting neutron stars in our galaxy, in which matter (typically H/He) is tidally transferred from a secondary companion to the neutron star. Accretion of this matter perturbs the thermal structure of the interior away from that of an isolated cooling neutron star. In this paper. we review how this accretion induces reactions in the crust of the neutron star that keep the interior hot. If the accretion is intermittent, then the heated surface layers are directly observable when accretion stops. This heating also affects the unstable ignition of light elements in the neutron star envelope. Observations of the neutron star cooling following an accretion outburst can in principle constrain the thermal properties of the crust and core.     

Anionic hyperconjugation

Although hyperconjugation involving alkyl groups to a carbocation is a well-established concept, the analogous charge delocalization generated in anions by electronegative substitution has long been a subject of controversy. We have investigated this phenomenon for the β-hydroxyethyl and β-trifluoroethyl anions using ab initio electronic structure calculations. Split valence basis sets augmented by diffuse functions were used with fully optimized geometries. Three dimensional molecular orbital plots clearly show an in-plane HOMO-LUMO mixing of a C-X σ antibonding orbital with the carbon lone pair which yields hyperconjugative π bonding in the anti conformation. Deformation density maps further demonstrate that this delocalization leads to the development of a π component as well as a previously unrecognized sigma enhancement. These results support and extend the work of Apeloig and that of Schleyer and Kos, but are in opposition to the induction hypothesis of Streitwieser and Holtz. The recent experimental determination of the acidity of (CF₃)₃CH by Tatlow $\text{et al}$ and their interpretation in terms of fluorine hyperconjugation are also in accord with this work.     

Phase separation of p53 precedes aggregation and is affected by oncogenic mutations and ligands

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF). The mechanism of the formation of the aggregates in the nucleus remains uncertain. The present study demonstrated that the DNA-binding domain of p53 (p53C) underwent phase separation (PS) on the pathway to aggregation under various conditions. p53C phase separated in the presence of the crowding agent polyethylene glycol (PEG). Similarly, mutant p53C (M237I and R249S) underwent PS; however, the process evolved to a solid-like phase transition faster than that in the case of wild-type p53C. The data obtained by microscopy of live cells indicated that transfection of mutant full-length p53 into the cells tended to result in PS and phase transition (PT) in the nuclear compartments, which are likely the cause of the GoF effects. Fluorescence recovery after photobleaching (FRAP) experiments revealed liquid characteristics of the condensates in the nucleus. Mutant p53 tended to undergo gel- and solid-like phase transitions in the nucleus and in nuclear bodies demonstrated by slow and incomplete recovery of fluorescence after photobleaching. Polyanions, such as heparin and RNA, were able to modulate PS and PT in vitro. Heparin apparently stabilized the condensates in a gel-like state, and RNA apparently induced a solid-like state of the protein even in the absence of PEG. Conditions that destabilize p53C into a molten globule conformation also produced liquid droplets in the absence of crowding. The disordered transactivation domain (TAD) modulated both phase separation and amyloid aggregation. In summary, our data provide mechanistic insight into the formation of p53 condensates and conditions that may result in the formation of aggregated structures, such as mutant amyloid oligomers, in cancer. The pathway of mutant p53 from liquid droplets to gel-like and solid-like (amyloid) species may be a suitable target for anticancer therapy.

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF).     

Matrix polyelectrolyte microcapsules: new system for macromolecule encapsulation

A new approach to fabricate polyelectrolyte microcapsules is based on exploiting porous inorganic microparticles of calcium carbonate. Porous CaCO3 microparticles (4.5-5.0 microns) were synthesized and characterized by scanning electron microscopy and the Brunauer-Emmett-Teller method of nitrogen adsorption/desorption to get a surface area of 8.8 m2/g and an average pore size of 35 nm. These particles were used as templates for polyelectrolyte layer-by-layer assembly of two oppositely charged polyelectrolytes, poly(styrene sulfonate) and poly(allylamine hydrochloride). Calcium carbonate core dissolution resulted in formation ofpolyelectrolyte microcapsules with an internal matrix consisting of a polyelectrolyte complex. Microcapsules with an internal matrix were analyzed by confocal Raman spectroscopy, scanning electron microscopy, force microscopy, and confocal laser-scanning fluorescence microscopy. The structure was found to be dependent on a number of polyelectrolyte adsorption treatments. Capsules have a very high loading capacity for macromolecules, which can be incorporated into the capsules by capturing them from the surrounding medium into the capsules. In this paper, we investigated the loading by dextran and bovine serum albumin as macromolecules. The amount of entrapped macromolecules was determined by two independent methods and found to be up to 15 pg per microcapsule.     

Selective separations by reactive ion exchange: Part 4. Preconcentration of cadmium and zinc by in situ precipitation as hexacyanoferrate(II) salts on gel and macroporous ion-exchange resins

The in situ precipitation of traces of cadmium(II) and zinc(II) ions as hexacyanoferrates from aqueous matrices was studied on conventional polystyrene gel and macroporous cation- and anion-exchange resins. Coprecipitation with each other or with copper(II) ions present in binary cation resins or in solution, and the influence of added nonprecipitating ions of the same charge type such as magnesium(II) were investigated. Microporous (gel) cation exchangers gave reasonable recoveries and macroporous cation exchangers gave very good recoveries; but macroporous anion exchangers performed best, suggesting macroporous hexacyanoferrate(II) resin as an ideal phase for collection/preconcentration of traces of Cu²⁺, Cd²⁺, Zn²⁺, and possibly Co²⁺, Ni²⁺, and Pb²⁺ from waters. As expected, very low yields were obtained with conventional anion exchange resin in the hexacyanoferrate form. Uniform distribution of Cu²⁺, Zn²⁺, and Cd²⁺ over macroporous anion-exchange resin phases were established by means of electron probe scans and taken as evidence for the formation of a uniform, well-developed precipitate layer covering the entire resin particle surface.     

Electrophilic acetylation and bromination reactions of benzo[b]naphtho[2,3-e][1,4]dioxin

The reactivity of benzo[b]naphtho[2,3-e][1,4]dioxin in the electrophilic aromatic substitution reactions has been studied. Friedel-Crafts acetylation resulted in the formation of three out of the possible five monoacetylated products, with the acetyl group located in positions 8 (major), 7 and 6 (minor) of the heterocycle. In the bromination reaction a higher selectivity was observed with the 6-bromo derivative found as the only monobrominated product and the 6,11-dibromo derivative found as the only polybrominated product. A ratio of unreacted heterocycle:6-bromo:6,11-dibromo derivatives in the bromination reaction has been found to depend strongly on the reaction conditions and on the heterocycle:bromine ratio.     

Polymer-supported nitroxyl radical catalyst for selective aerobic oxidation of primary alcohols to aldehydes

PS-TEMPO, a polymer-supported 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO), was successfully applied as a recyclable, active and selective catalyst for the oxidation of primary aliphatic and benzylic alcohols to aldehydes by molecular oxygen in the presence of Co(NO3)2 and Mn(NO3)2 as co-catalysts.     

Two-Photon Excitation of 4'-Hydroxymethyl-4,5',8-Trimethylpsoralen

Abstract— Psoralens are a class of pharmaceutical agents commonly used to treat several cutaneous disorders. When irradiated with a mode-locked titanium: sapphire (Ti: sapphire) laser tuned to 730 nm, an aqueous solution of 4'-hydroxymethyl-4,5',8-trimethylpsoralen (HMT) emits blue light. The emission spectrum is centered at 452 nm and is identical to that obtained by one-photon excitation with UVA excitation, and its magnitude depends quad-ratically on the intensity of laser excitation. These results suggest that two-photon excitation occurs to a potentially photochemically active state. To estimate the two-photon absorption cross section, it was first necessary to measure the emission quantum yield of HMT using 365 nm excitation at room temperature that resulted in a value of 0.045 ± 0.007. The two-photon absorption cross section of HMT at 730 nm is therefore estimated to be 20 ± 10⁻⁵⁰ cm⁴ s (20 Göppert-Mayer). The excited-state photophysics and photochemistry of psoralens suggest potential applications to cutaneous phototherapy in diseases such as psoriasis and dystrophic epidermolysis bullosa.