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.     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

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.     

The renaissance of palladium(II)-catalyzed oxidation chemistry

Palladium(II)-catalyzed oxidations constitute a paramount reaction class but have remained immature over the past few decades. Recently, this field has reappeared at the forefront of organometallic catalysis. This emerging area article outlines recent developments in palladium(II)-catalyzed oxidation chemistry with discussion of potential future growth.     

Molecular structure of 4,4′-sulfandiyl-bis-thiophenol from electron diffraction

The molecular structure of 4,4′-sulfanidyl-bis-thiophenol (C₁₂H₁₀S₃) has been determined by gas electron diffraction. Assuming identical geometry and D_2h local symmetry for ---SC₆H₄S--- moieties, the following bond lengths (r_g) and bond angles were obtained: C---H = 1.101 ± 0.005, S---H = 1.388 ± 0.019, (C---C)_mean = 1.400 ± 0.003, (S---C)_mean = 1.778 ± 0.004 Å, C_ar---S---C_ar = 103.5 ± 1.3, C---C(S)---C = 120.4 ± 0.3, C(H)---C(H)---H = 119.1 ± 0.9 and C---S---H = 94.6 ± 3.1°. Two ratational forms were found to reproduce the experimental data, characterized by dihedral angles of the benzene rings with respect to the C_arSC_ar plane; ₁ = 67.8 ± 2.0°, ₂ = 4.5 ± 7.2°, and ₁ = 69.4 ± 2.0δ, ₂ = −26.6 ± 7.1°. Identical signs of ₁ and ₂ indicate that the two benzene rings are rotated in the same direction about the respective S_central---C axes.