Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Computational design of a β-peptide that targets transmembrane helices

The design of β-peptide foldamers targeting the transmembrane (TM) domains of complex natural membrane proteins has been a formidable challenge. A series of β-peptides was designed to stably insert in TM orientations in phospholipid bilayers. Their secondary structures and orientation in the phospholipid bilayer was characterized using biophysical methods. Computational methods were then devised to design a β-peptide that targeted a TM helix of the integrin α(IIb)β(3). The designed peptide (β-CHAMP) interacts with the isolated target TM domain of the protein and activates the intact integrin in vitro.     

C-glycosylation reactions of sulfur-substituted glycosyl donors: evidence against the role of neighboring-group participation

Nucleophilic substitution reactions of C-4 sulfur-substituted tetrahydropyran acetals revealed that neighboring-group participation does not control product formation. Spectroscopic evidence for the formation of an intermediate sulfonium ion is provided, as are data from nucleophilic substitution reactions demonstrating that products are formed from oxocarbenium ion intermediates. The selectivity was not sensitive to solvent or to which Lewis acid was employed. The identity of the heteroatom at the C-4 position also did not significantly impact diastereoselectivity. Consequently, neighboring-group participation was not responsible for the formation of either the major or the minor products. These studies implicate a Curtin-Hammett kinetic scenario in which the formation of a low-energy intermediate does not necessitate its involvement in the product-forming pathway.     

The use of Volterra series in the analysis of the nonlinear Schrödinger equation

A Volterra series analysis is used to analyse the dispersive behaviour in the frequency domain for the non-linear Schrödinger equation (NLS). It is shown that the solution of the initial value problem for the nonlinear Schrödinger equation admits a local multi-input Volterra series representation. Higher order spatial frequency responses of the nonlinear Schrödinger equation can therefore be defined in a similar manner as for lumped parameter non-linear systems. A systematic procedure is presented to calculate these higher order spatial frequency response functions analytically. The frequency domain behaviour of the equation, subject to Gaussian initial waves, is then investigated to reveal a variety of non-linear phenomena such as self-phase modulation (SPM), cross-phase modulation (CPM), and Raman effects modelled using the NLS.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.