Semiclassical <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> Estimates of Quasimodes on Curved Hypersurfaces

Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L ² normalized family of functions such that P(h)u(h) is O(h) in L ²(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L ^p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch ^−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator.     

A comparative investigation of the presence of psychological conditions in high achieving eighth graders from TIMSS 2007 Mathematics

This study is a second analysis of Trends in International Mathematics and Science Study (TIMSS) 2007 background questionnaires to investigate high achieving eighth-grade students’ possession of three elements of Krutetskii’s (The Psychology of Mathematical Abilities in Schoolchildren, The University of Chicago, 1976) psychological conditions. Analyses were made between high achieving eighth graders and their lower achieving counterparts, and between Korean high achievers and their high achieving peers across ten high performing TIMSS participating countries. After reviewing 44,643 students across selected countries, we conclude that a larger percentage of students with mathematical talent demonstrate positive attitudes toward mathematics, value mathematics, and have self-confidence in their ability to learn mathematics than their peers without high achievement in mathematics. However, a larger portion of high achieving Korean students displayed low self-confidence and valued mathematics less than their peers from other high performing countries. Findings from this study will provide insight into some educational issues in science, technology, engineering and mathematics education.     

Evidence of a Uranium-Paddlewheel Node in a Catecholate-Based Metal–Organic Framework

The interactions between uranium and non-innocent organic species are an essential component of fundamental uranium redox chemistry. However, they have seldom been explored in the context of multidimensional, porous materials. Uranium-based metal–organic frameworks (MOFs) offer a new angle to study these interactions, as these self-assembled species stabilize uranium species through immobilization by organic linkers within a crystalline framework, while potentially providing a method for adjusting metal oxidation state through coordination of non-innocent linkers. We report the synthesis of the MOF NU-1700 , assembled from U⁴⁺-paddlewheel nodes and catecholate-based linkers. We propose this highly unusual structure, which contains two U⁴⁺ ions in a paddlewheel built from four linkers—a first among uranium materials—as a result of extensive characterization via powder X-ray diffraction (PXRD), sorption, transmission electron microscopy (TEM), and thermogravimetric analysis (TGA), in addition to density functional theory (DFT) calculations.     

Toward a Holistic Understanding and Models of Nonphotochemical Quenching Effects on In Vivo Fluorometry of Chlorophyll a in Coastal Waters

Nonphotochemical quenching (NPQ) is known to depress in vivo fluorescence (IVF) of chlorophyll a (Chla) in aquatic environments, which makes it difficult to interpret the hour-to-hour variations in Chla measured by in situ fluorometers. We hypothesized that ratios between quenched and unquenched IVF are a function of both NPQ and photochemical quenching. In this study, two diatom model species Thalassiosira pseudonana (CCMP1335) and Thalassiosira weissflogii (CCMP1047) incubated under a sinusoidal light:dark cycle were studied; IVF was recorded continuously, and Chla and photo-physiological variables were measured seven times a day. The maximal decline in Chla-specific IVF (IVF^B) attributable to quenching was 50% under the experimental settings. An NPQ and photochemical quenching-based modeling equation exhibited a better match to the measured IVF^B than equations representing the sole NPQ effect. Photochemical quenching induced by measuring light beam varied substantially during the day, and the part of the model for this process is excitation intensity-dependent (which is differed between models of in situ fluorometers, implying no straightforward method to correct Chla for all instrument models, instrument-specific parameterization is required). The forms of the IVF^B-light relationship are discussed as well. The findings foster a holistic understanding of NPQ effects on in vivo Chla fluorometry.     

Functionalized latexes as substrates for atom transfer radical polymerization

The application of atom transfer radical polymerization (ATRP) to the homopolymerization of 2‐hydroxyethyl acrylate and 2‐(methacryloyloxy) ethyl trimethylammonium chloride at the surface of a crosslinked polystyrene latex functionalized with alkyl bromide groups is reported. Polymerization was carried out using the surface groups of the dialyzed latex as initiators. The resulting hydrophobic core, hydrophilic shell latexes, were analyzed by FTIR, ¹³C‐NMR spectroscopy, and dynamic light scattering.     

Polymer electrostatics: detection and speciation of trapped electric charges by electric probe and analytical electron microscopy

This work reviews new probe and electron microscopy approaches for the detection of charged domains in insulating polymers, as well as for the identification of the charge-bearing species: scanning electric potential microscopy (SEPM), electric force microscopy (EFM) and energy-loss spectroscopy imaging in the transmission electron microscope (ESI-TEM). The SEPM and EFM micrographs show patterned domains bearing excess electric charges and extending for tens of nanometers, in polymer latex particles and films. The charged species are identified by ESI-TEM as emulsion polymerization initiator and surfactant residues, as well as the associated counter-ions. Charged domains are also observed in common thermoplastic polymers, producing unexpectedly large electric potential gradients.