Preparation of Designer Resins via Living Free Radical Polymerization of Functional Monomers on Solid Support

Merrifield resin is converted to a solid-supported free radical initiator by reacting with the TEMPO-Na. Heating TEMPO-methyl resin with a variety of functionalized styrene and acrylate monomers gives larger resin beads via living free radical polymerization. We have coined the term Rasta resin to describe resin beads prepared in this fashion. The process can be described as a solvent-free suspension polymerization. It is particularly well suited for preparation of resin beads from monomers which contain electrophilic groups that would be destroyed upon suspension polymerization in water. Rasta resins have a novel macromolecular architecture wherein long straight chain polymers bearing reactive functional groups emanate from the phenyl groups of a cross-linked polystyrene core. With judicious choice of co-monomers and polymerization strategy, the solvent affinity, loading capacity, and distance of functionality from the cross-linked core may be controlled giving beads with properties that are tailored to specific uses as synthesis supports and scavenging resins.     

The contribution of high frequencies to human brain activity underlying horizontal localization of natural spatial sounds

Background  

In the field of auditory neuroscience, much research has focused on the neural processes underlying human sound localization. A recent magnetoencephalography (MEG) study investigated localization-related brain activity by measuring the N1m event-related response originating in the auditory cortex. It was found that the dynamic range of the right-hemispheric N1m response, defined as the mean difference in response magnitude between contralateral and ipsilateral stimulation, reflects cortical activity related to the discrimination of horizontal sound direction. Interestingly, the results also suggested that the presence of realistic spectral information within horizontally located spatial sounds resulted in a larger right-hemispheric N1m dynamic range. Spectral cues being predominant at high frequencies, the present study further investigated the issue by removing frequencies from the spatial stimuli with low-pass filtering. This resulted in a stepwise elimination of direction-specific spectral information. Interaural time and level differences were kept constant. The original, unfiltered stimuli were broadband noise signals presented from five frontal horizontal directions and binaurally recorded for eight human subjects with miniature microphones placed in each subject's ear canals. Stimuli were presented to the subjects during MEG registration and in a behavioral listening experiment.     

On the extensional vibrations of rotating bars

The extensional equations of motion for a cantilever bar rotating about an axis fixed in space are derived. It is shown that the form of the non-linear strain-displacement relation is important in determining the nature of the relationship between the frequency of extensional oscillations and the rotational speed. In particular, the frequency may or may not increase monotonically with rotational speed, depending on the degree of hardening in the effective extensional spring. The determination whether an instability occurs as the rotational speed increases is beyond the limits of engineering beam theory.     

Local probe (170Yb3+) measurements of magnetic fields in YBa2Cu3Ox

We introduce the technique of studying the field dependence of the electro-nuclear energy levels of a rare earth to measure the magnetic field present at the rare earth/yttrium site in YBa₂Cu₃O_x. Measurements were made by¹⁷⁰Yb Mössbauer spectroscopy. The hyperfine spectrum of the ground state Kramers doublet for Yb³⁺ ions diluted into this matrix is sensitive to fields in the range 100 to 2000G. Flux penetration and trapping at the local site level have been measured in superconducting samples. A molecular field exists on the rare earth site in non superconducting samples suggesting that the ordered Cu2 magnetic moments are intrinsically non colinear.     

Axial instability of rotating rods revisited

For strain sufficiently small such that Hooke's Law is valid, it is shown that only a linear model for axial deformation of rotating rods can be derived. As discussed in the literature, this linear model exhibits an instability when the angular speed reaches a certain critical value. However, unless this linear model is valid for large strain, it is impossible to determine whether this instability really exists; because, as the angular speed is increased, the strain becomes large well short of the critical speed. Next, axial deformation of rotating rods is analyzed using two strain energy functions to model non-linear elastic behavior. The first of these functions is the usual quadratic strain energy function augmented with a cubic term. With this model it is shown that no instability exists if the non-linearity is stiffening (i.e. if the coefficient of the cubic term is positive), although the strain can become large. If the non-linearity is of the softening variety, then the critical angular speed drops as the degree of softening increases. Still, the strains are large enough that, except for rubber-like materials, a non-linear elastic model is not likely to be appropriate. The second strain energy function is based on the square of the logarithmic strain and yields a softening model. It quite accurately models the behavior of certain rubber rods which exhibit the instability within the validated range of elongation.     

A Comparison of Textbooks' Presentation of Fractions

In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that teaching and learning of fractions is a complex process, and that fraction understanding is the foundation for later topics such as proportionality, algebra, and probability, makes it important to examine the variation in presentation of fraction concepts in U.S. textbooks, especially the difference between traditional and standards‐based curricula. The purpose of this study is to determine if differences exist in the presentation of fractions in conventional and standards‐based textbooks and how these differences align with the recommendations of National Council of Teachers of Mathematics, Common Core State Standards, and the research on the teaching and learning of fractions.     

Frequency-stabilized cavity ring-down spectrometer for high-sensitivity measurements of water vapor concentration

We present a portable spectrometer that uses the frequency-stabilized cavity ring-down spectroscopy technique capable of high-precision measurements of trace water vapor concentration. Measuring one of the strongest rovibrational transitions in the ν₁+ν₃ water vapor combination band near ˜ν=7181.156 cm^-1, we compare spectroscopic and thermodynamic determinations of trace water vapor in N₂, and find systematic differences attributable to water vapor background effects and/or uncertainties in line intensities. We also compare the frequency-stabilized ring-down method with other cavity ring-down approaches that are based on unstabilized probe lasers and unstabilized ring-down cavities. We show that for the determination of water vapor concentration, the frequency-stabilized cavity ring-down method has the minimum measurement uncertainty of these techniques. The minimum noise-equivalent absorption coefficient of the spectrometer was 1.2×10^-10 cm^-1 Hz^-1/2, which further corresponds to a minimum detectable water vapor mole fraction equal to 0.7×10^-9 for an absorption spectrum of 10 minutes duration. PACS 33.20.-t; 33.70.Jg; 33.70.Fd; 42.62.Fi     

Sample shape dependent EPR and the measurement of Van Vleck paramagnetism

The dependence of the EPR resonance field on sample shape has been measured for Fe³⁺ and Yb³⁺ ions substituted into thullium gallium garnet. The results enable the second order paramagnetism of the lowest singlet Tm³⁺ energy level to be found.     

Enumeration of matrices of given rank with submatrices of given rank

The authors determine the number of (n+m)×t matrices A¹ of rank r+v, over a finite field GF(q), whose last m rows are those of a given matrix A of rank r+v over GF(q) and whose first n rows have a given rank u.