Supernumerary teeth: a review of the literature and four case reports

The document attached has been archived with permission from the Australian Dental Association. An external link to the publisher’s copy is included.A review of the literature relating to supernumerary teeth is presented along with four case reports to illustrate some possible presentations, diagnostic features, and treatment options.Mark A. Scheiner and Wayne J. Sampso

Studies of dispersion energy in hydrogen‐bonded systems. H2O–HOH, H2O–HF, H3N–HF, HF–HF

Dispersion energy is calculated in the systems H2O–HOH, H2O–HF, H3N–HF, and HF–HF as a function of the intermolecular separation using a variety of methods. M≂ller–Plesset perturbation theory to second and third orders is applied in conjunction with polarized basis sets of 6‐311G∗∗ type and with an extended basis set including a second set of polarization functions (DZ+2P). These results are compared to a multipole expansion of the dispersion energy, based on the Unsöld approximation, carried out to the inverse tenth power of the intermolecular distance. Pairwise evaluation is also carried out using both atom–atom and bond–bond formulations. The MP3/6‐311G∗∗ results are in generally excellent accord with the leading R−6 term of the multipole expansion. This expansion, if carried out to the R−10 term, reproduces extremely well previously reported dispersion energies calculated via variation‐perturbation theory. Little damping of the expansion is required for intermolecular distances equal to or greater than the equilibrium separation. Although the asymptotic behavior of the MP2 dispersion energy is somewhat different than that of the other methods, augmentation of the basis set by a second diffuse set of d functions leads to quite good agreement in the vicinity of the minima. Both the atom–atom and bond–bond parametrization schemes are in good qualitative agreement with the other methods tested. All approaches produce similar dependence of the dispersion energy upon the angular orientation between the two molecules involved in the H bond

Correction of the basis set superposition error in SCF and MP2 interaction energies. The water dimer

There has been some discussion concerning whether basis set superposition error is more correctly evaluated using the full set of ghost orbitals of the partner molecule or some subset thereof. A formal treatment is presented, arguing that the full set is required at the Møller–Plesset level. Numerical support for this position is provided by calculation of the interaction energy between a pair of water molecules, using a series of moderate sized basis sets ranging from 6‐31G∗∗ to the [432/21] contraction suggested by Clementi and Habitz. These energies, at both the SCF and MP2 levels, behave erratically with respect to changes in details of the basis set, e.g., H p‐function exponent. On the other hand, after counterpoise correction using the full set of partner ghost orbitals, the interaction energies are rather insensitive to basis set and behave in a manner consistent with calculated monomer properties. For long intersystem separations, the contribution of correlation to the interaction is repulsive despite the attractive influence of dispersion. This effect is attributed to partial account of intrasystem correlation and can be approximated at long distances via electrostatic terms linear in MP2‐induced changes in the monomer moments

Electronic structure and bonding in unligated and ligated FeII porphyrins

The electronic structure and bonding in a series of unligated and ligated FeII porphyrins (FeP) are investigated by density functional theory (DFT). All the unligated four-coordinate iron porphyrins have a 3A2g ground state that arises from the (dxy)2(dz2)2(dπ)2 configuration. The calculations confirm experimental results on Fe tetraphenylporphine but do not support the resonance Raman assignment of Fe octaethylporphine as 3Eg, nor the early assignment of Fe octamethyltetrabenzporphine as 5B2g. For the six-coordinate Fe–P(L)2 (L = HCN, pyridine, CO), the strong-field axial ligands raise the energy of the Fe dz2 orbital, thereby making the iron porphyrin diamagnetic. The calculated redox properties of Fe–P(L)2 are in agreement with experiment. As models for deoxyheme, the energetics of all possible low-lying states of FeP(pyridine) and FeP(2-methylimidazole) have been studied in detail. The groundstate configuration of FeP(2-methylimidazole) was confirmed to be high-spin (dxy)2(dz2)1(dπ)2(dx2−y2)1; FeP (pyridine) is shown to be a poor model for high-spin deoxyheme. © 2002 American Institute of Physics

Complexes Containing CO2 and SO2. Mixed Dimers, Trimers and Tetramers

Mixed dimers, trimers and tetramers composed of SO2 and CO2 molecules are examined by ab initio calculations to identify all minimum energy structures. While AIM formalism leads to the idea of a pair of C···O bonds in the most stable heterodimer, bound by some 2 kcal mol(-1), NBO analysis describes the bonding in terms of charge transfer from O lone pairs of SO2 to the CO π* antibonding orbitals. The second minimum on the surface, just slightly less stable, is described by AIM as containing a single O···O chalcogen bond. The NBO picture is that of two transfers in opposite directions: one from a SO2 O lone pair to a π* antibond of CO2, supplemented by CO2 Olp → π*(SO). Decomposition of the interaction energies points to electrostatic attraction and dispersion as the dominant attractive components, in roughly equal measure. The various heterotrimers and tetramers generally retain the dimer structure as a starting point. Cyclic oligomers are favored over linear geometries, with a preference for complexes containing larger numbers of SO2 molecules

Cognitive processes underlying mathematical concept construction: The missing process of structural abstraction

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This classification provides the identification of an often overlooked fundamental cognitive process, namely structural abstraction. On the other hand, this work shows a theory-driven and research-based approach illuminating the hidden architecture of cognitive processes involved in structural abstraction that gives new insights into an integrated framework on abstraction in learning mathematics. Based on our findings in empirical investigations, the paper outlines a theoretical framework on the cognitive processes taking place on mental (rather than physical) objects

Emerging insights from the evolving framework of structural abstraction

Only recently ‘abstraction from objects’ has attracted attention in the literature as a form of abstraction that has the potential to take account of the complexity of students’ knowing and learning processes compatible with their strategy of giving meaning. This paper draws attention to several emerging insights from the evolving framework of structural abstraction in students’ knowing and learning of the limit concept of a sequence. Particular ideas are accentuated that we need to understand from a theoretical point of view since they reveal a new way of understanding knowing and learning advanced mathematical concepts

Images of abstraction in mathematics education: Contradictions, controversies, and convergences

In this paper we offer a critical reflection of the mathematics education literature on abstraction. We explore several explicit or implicit basic orientations, or what we call images, about abstraction in knowing and learning mathematics. Our reflection is intended to provide readers with an organized way to discern the contradictions, controversies, and convergences concerning the many images of abstraction. Given the complexity and multidimensionality of the notion of abstraction, we argue that seemingly conflicting views become alternatives to be explored rather than competitors to be eliminated. We suggest considering abstraction as a constructive process that characterizes the development of mathematical thinking and learning and accounts for the contextuality of students’ ideas by acknowledging knowledge as a complex system