Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self‐identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.     

Reporting of quantitative oxygen mapping in EPR imaging

Oxygen maps derived from electron paramagnetic resonance spectral-spatial imaging (EPRI) are based upon the relaxivity of molecular oxygen with paramagnetic spin probes. This technique can be combined with MRI to facilitate mapping of pO(2) values in specific anatomic locations with high precision. The co-registration procedure, which matches the physical and digital dimensions of EPR and MR images, may present the pO(2) map at the higher MRI resolution, exaggerating the spatial resolution of oxygen, making it difficult to precisely distinguish hypoxic regions from normoxic regions. The latter distinction is critical in monitoring the treatment of cancer by radiation and chemotherapy, since it is well-established that hypoxic regions are three or four times more resistant to treatment compared to normoxic regions. The aim of this article is to describe pO(2) maps based on the intrinsic resolution of EPRI. A spectral parameter that affects the intrinsic spatial resolution of EPRI is the full width at half maximum (FWHM) height of the gradient-free EPR absorption line in frequency-encoded imaging. In single point imaging too, the transverse relaxation times (T(2)(?)) limit the resolution since the signal decays by exp(-t(p)/T(2)(?)) where the delay time after excitation pulse, t(p), is related to the resolution. Although the spin densities of two point objects may be resolved at this separation, it is inadequate to evaluate quantitative changes of pO(2) levels since the linewidths are proportionately affected by pO(2). A spatial separation of at least twice this resolution is necessary to correctly identify a change in pO(2) level. In addition, the pO(2) values are blurred by uncertainties arising from spectral dimensions. Blurring due to noise and low resolution modulates the pO(2) levels at the boundaries of hypoxic and normoxic regions resulting in higher apparent pO(2) levels in hypoxic regions. Therefore, specification of intrinsic resolution and pO(2) uncertainties are necessary to interpret digitally processed pO(2) illustrations.     

cis‐Di­chloro­(di­methyl­aminomethyl­ene)­(tri­phenyl­phosphine)palladium(II) acetone solvate

The synthesis and X‐ray structural analysis of the title compound, [PdCl₂(C₃H₇N)(C₁₈H₁₅P)]·C₃H₆O, are described. The crystal structure contains discrete monomeric mol­ecules of the carbene complex and solvent mol­ecules separated by normal van der Waals distances. The Pd atom is four‐coordinate in an essentially square‐planar environment, with the chlorine ligands mutually cis; Pd—P = 2.2495 (7), Pd—Cl = 2.3508 (7) and 2.3600 (7), Pd—C 1.948 (2) and N—C(carbene) 1.274 (3) Å.     

An LX-10 kinetic model calibrated using simulations of multiple small-scale thermal safety tests

A new chemical kinetic model for the beta-delta transition and decomposition of LX-10 (95% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, 5% Viton A binder) is presented here. This model implements aspects of previous kinetic models but calibrates the model parameters to data sets of three experiments: differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and one-dimensional time to explosion (ODTX). The calibration procedure contains three stages: one stage uses open-pan DSC and TGA to develop a base reaction for formation of heavy gases, a second stage features closed-pan DSC to ascertain the autocatalytic behavior of reactant gases attacking the solid explosive, and a final stage adjusts the rate for the breakdown of heavy reactant gases using ODTX experimental data. The resultant model presents a large improvement in the agreement between simulated DSC and TGA results and their respective experiments while maintaining the same level of agreement with ODTX, scaled thermal explosion, and laser heating explosion times when compared to previous models.     

Microwave-assisted preparations of amidrazones and amidoximes

In an operationally straightforward and efficient method, amidrazones and amidoximes are prepared in yields of 65-87% from imidoylbenzotriazoles by microwave heating for 5-20 min with the appropriate hydrazine or hydroxylamine.     

Experimental and theoretical electron density study of estrone

The electron density and the electrostatic potential (ESP) distributions of estrone have been determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer at 20 K. The electron density in the estrone crystal has been described with the multipole model, which allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution was obtained via a single-point calculation with a large basis set at the experimental geometry and subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be well correlated to the experimental electron density at the bond critical points through an exponential relationship. The aromaticity of ring A, chemical bonding, the O(1)...O(2) distance necessary for estrogenic activity, and the electrostatic potential features are also discussed.     

A hydrogen-bonded adduct containing seven-component supramolecular aggregates

The title compound is a salt, 3,6,9,16,19,22-hexaaza­tri­cyclo­[22.2.2.2^11,14]­triaconta-1(26),11(29),12,14(30),24,27-hexa­ene–3,5-di­nitro­benzoic acid–methanol (1/4/2), C₂₄H₄₂N₆⁴⁺·4C₇H₃N₂O₆⁻·2CH₄O, in which the cation lies across a centre of inversion and one of the two independent anions is positionally disordered over two sets of atom sites having equal occupancy. The components are linked by four types of N—H⃛O hydrogen bond [N⃛O 2.674 (2)–2.815 (2) Å; N—H⃛O 149–163°] and one type of O—H⃛O hydrogen bond in which the acceptor is disordered over two closely adjacent sites [O⃛O 2.67 (4) and 2.75 (4) Å; O—H⃛O 172 and 173°], forming centrosymmetric seven-component aggregates.     

Vanadium(V) tartrato complexes: speciation in the H3O+(OH-)/H2VO4-/(2R,3R)-tartrate system and X-ray crystal structures of Na4[V4O8(rac-tart)2].12H2O and (NEt4)4[V4O8((R,R)-tart)2].6H2O (tart = C4H2O6(4-))

A study of the aqueous H3O+(OH-)/H2VO4-/(2R,3R)-tartrate system has been performed at 273 K in a 1.0 mol/L Na+(Cl-) ionic medium using 51V NMR spectroscopy. In this relatively complicated system, more than 12 different species were observed. Ligand concentration, vanadate concentration, and pH variation studies were carried out, particularly for the range of pH 5.8-8.0 and for pH 2.4. Chemical shifts, vanadium-ligand stoichiometry, and also composition and formation constants for some, but not all, species are given. Despite some reduction of vanadium(V) to vanadium(IV) in an acidic medium at pH approximately 2.4, the stoichiometries of the principal species in solution at this pH were determined. Electrospray ionization mass spectra for some solutions were obtained and were in accordance with the conclusions drawn from the speciation studies. A series of crystalline vanadium(V) tartrato complexes M4[V4O8(tart)2].aq were also prepared and characterized. X-ray diffraction studies of Na4[V4O8(rac-tart)2].12H2O (1) and (NEt4)4[V4O8((R,R)-tart)2].6H2O (2) revealed unique tetranuclear [V4O8(tart)2]4- ions for which the {V4O4} rings have boat conformations.     

Interaction of the antimicrobial peptide dicynthaurin with membrane phospholipids at the air-liquid interface

This paper reports the first study on the interaction of the antimicrobial peptide dicynthaurin with 1,2-dipalmitoyl-glycerophosphatidyl-glycerol investigated in monolayers at the air-liquid interface. The influence of the peptide on the two-dimensional phase behavior of the negatively charged lipid was elucidated by means of pressure-area isotherm measurements, fluorescence microscopy, and grazing incidence X-ray diffraction measurements. The pure peptide forms a stable monolayer at the air-liquid interface up to 30 mN/m as shown for both the monomeric and the dimeric cynthaurins. The peptide lipid interaction was monitored in isotherm measurements showing a strong adsorption of the peptide and stabilization at the interface promoted by the lipid monolayer. The X-ray diffraction measurements in agreement with fluorescence microscopy studies showed that the peptide destabilizes the condensed chain lattice, leading to a complete fluidization of the condensed lipid phase on physiological buffer. The adsorption of the peptide to the negatively charged lipid monolayer and the fluidization of the condensed chain lattice suggest a direct link to the peptides' ability to expand the bacterial membrane that would be relevant for the in vivo mode of action.