High School Precalculus Students' Understanding of Slope as Measure

Twenty-two high school precalculus students were interviewed to examine their understanding of slope as measure. The students examined and discussed real-world situations involving slope: physical situations involving slope as a measure of steepness and functional situations involving slope as a measure of rate of change. For the various physical situations, students measured steepness with angles instead of ratios. Overall, they demonstrated a better understanding of slope in functional situations, but many students had trouble interpreting slope as a measure of rate of change. Instruction should focus on helping students form connections and providing opportunities for students to communicate their understanding.     

From realizability to induction via dependent intersection

In this paper, it is shown that induction is derivable in a type-assignment formulation of the second-order dependent type theory $\lambda P2$, extended with the implicit product type of Miquel, dependent intersection type of Kopylov, and a built-in equality type. The crucial idea is to use dependent intersections to internalize a result of Leivant's showing that Church-encoded data may be seen as realizing their own type correctness statements, under the Curry–Howard isomorphism.     

The Effect of Temperature and Excitation on the Single- and Two-Photon Excited Emission Spectrum of Curium in a Glass Matrix

Single and two-photon excited emission has been observed from a curiumdoped borosilicate glass matrix at both room and liquid nitrogen temperatures. The emission spectrum was measured using several different excitation energies and intensities. In addition to the expected line narrowing, variations in the ratios of emission intensities between states, and between crystal field levels within the each state were observed with cooling. Slight variations in the emission spectrum also arose as a function of the excitation intensity. These variations in the Cm ion's emission spectrum as a function of experimental parameters are presented and discussed.     

Polyimide structure–property relationships. II. Polymers from isomeric diamines

An extensive study of the effects of stereoisomeric variations in aromatic polyimide structures on polyimide properties was conducted. The structural variations were incorporated into the polyimides through the use of two complete series of isomeric aromatic diamine monomers, the diaminodiphenylmethanes and the diaminobenzophenones, as well as several pairs of diamine isomers. The ability of the diamines to polymerize was related to the basicities, and thus reactivities, of the amino groups. Diamines with an amino group located ortho to the group connecting the two aromatic rings were successfully polymerized with dianhydrides for the first time to high molecular weight poly(amic acids). The stereoisomeric polyimides were characterized by determining the glass transition temperatures T_g, mechanical properties, and thermooxidative stabilities of thin films of the polymers. The polymers prepared from p-diamines were shown to have the highest softening points and thus, the most rigid molecular structures. Those synthesized from m-diamines had the lowest T_g values, inferring the most flexible molecular backbone. With limited exceptions, the use of diamines with ortho-oriented amine groups failed to improve the flexibility of the polyimides since their T_g values were usually as high as those of polymers made from p-diamines. Only slight differences in mechanical properties of the isomeric polyimide films were attributable to the variations in isomeric structure, except for those properties dependent upon T_g changes, such as elevated temperature mechanical properties. A study of the thermooxidative stability of the polyimides showed little difference between the polymers prepared from the diaminobenzophenones, but marked differences were observed between the individual members of the diaminodiphenylmethane-derived polyimides.     

Bending Boundary Layers in a Moving Strip

The high-speed transport of thin-sheet materials occurs in avariety of industrial processes. In this paper the method of matchedasymptotic expansions is used to solve the low tension, large-deflectionshape of a convected strip hanging under gravity. To leading order theequations for the deflection in the boundary layer and in the centre ofthe span are nonlinear. Previous treatments of this problem have notaccurately solved the leading-order equation within the boundary layer.The composite analytic solution of the full nonlinear equation isobtained and compares well with numerical solutions.     

Optical waveguides structured with photoaligning polymers

We present a novel fast fabrication method for making optical waveguides by using a photoaligning and a liquid-crystal polymer. A difference in the refractive indices in the core and cladding regions is achieved by use of polarized UV light to align the polymer chains differently. A refractive-index difference of Deltan = 0.07 was achieved. The propagation loss in a channel waveguide is 4 dB/cm at a wavelength of 1.55 microm. The fabrication method has only a few processing steps and yields short fabrication times. The waveguide structures offer possibilities for generating devices with new applications related to the polarization of the guided light.     

A New Class of Inhibitors for the Metalloprotease Neprilysin Based on a Central Imidazole Scaffold

Neprilysin (NEP; neutral endopeptidase EC 3.4.24.11) is a Zn^II‐dependent, membrane‐bound endopeptidase. NEP is widely distributed in the organs, particularly in the kidneys and lungs, and it is involved in the metabolism of a number of smaller regulatory peptides. Inhibition of NEP has been proposed as a potential target for analgesic and antihypertensive therapies. In this study, new nonpeptidic inhibitors of neprilysin ((±)‐ 1 , (±)‐ 43 , (±)‐ 45 , and (±)‐ 46 ; Table) were designed, based on the X‐ray crystal structure of NEP complexed to phosphoramidon (Fig. 1). They feature an imidazole ring as the central scaffold, acting as a peptide bond isoster to undergo H‐bonding with the side chains of Asn542 and Arg717 (Fig. 2). The scaffold is decorated with a thiol group to ligate to the Zn^II ion and two aromatic residues to bind into the hydrophobic S1′ and S2′ pockets. The synthesis of the new inhibitors was approached by two routes (Schemes 1–4 and 5–8), with the second one involving a double directed ortho‐metallation of the imidazole platform and a Stille cross‐coupling, providing the desired target molecules as hydrochloride salts. In a fluorescence assay, inhibitors (±)‐ 1 , (±)‐ 43 , (±)‐ 45 , and (±)‐ 46 all exhibit IC₅₀ values in the single‐digit micromolar activity range (2–4 μM , Table), which validates the binding mode postulated by modeling. Useful guidelines for a next lead optimization cycle were obtained in several control runs.     

Production and decay of F+(2030) observed in νμ interactions in emulsion

An event representing the production and decay of the charmed F⁺ meson has been identified by means of a 3-constraint fit to decay hypothesis F⁺ → π⁺π⁺π^?π⁰, in which both γ-rays from the π⁰ converted. The event was produced by a charged current ν_μ interaction in an emulsion stack located inside the Fermilab 15-foot bubble chamber. The F⁺ traveled 50 μm, corresponding to a proper time of 1.4 × 10^?13 seconds, before decaying in flight. Its mass was determined to be 2017 ± 25MeV.     

Anisotropy in the Compton profiles of Nb and NbH0.76

The Compton profiles of Nb and NbH_0.76 single crystals have been measured along [100] and [110] using 412 keV gamma-radiation from a¹⁹⁸Au source. The changes in the band electron profile of the metal following the introduction of hydrogen are interpreted in terms of the protonic model of the hydride. Qualitative changes in the directional profiles can be understood within the rigid band approximation.     

Small angle critical scattering of neutrons by nickel

The critical magnetic scattering of neutrons by nickel was studied as a function of temperature and of the scattering vector κ in the range 0.008?0.04 Å^?1 for various specimens ranging from a single crystal to heavily deformed polycrystals. The shift of the temperature where the maximum of the scattered intensity is found as a function of scattering vector κ depends on the degree of crystalline imperfection. For the single crystal the observed shift is ΔT/T? 5 · 10^?3. On the basis of the Ornstein-Zernike theory the observed scattering by the single crystal yields the critical index \(\gamma = 2v = 1.32 \pm _{0.14}^{0.20} \) as predicted by most of the theories.