Integral Modular Categories of Frobenius-Perron Dimension <Emphasis Type="Italic">pq</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Integral modular categories of Frobenius-Perron dimension pq ⁿ , where p and q are primes, are considered. It is already known that such categories are group-theoretical in the cases of 0 ≤ n ≤ 4. In the general case we determine that these categories are either group-theoretical or contain a Tannakian subcategory of dimension q ⁱ for i > 1. We then show that all integral modular categories \(\mathcal {C}\) with \(\text {FPdim}(\mathcal {C})=pq^{5}\) are group-theoretical, and, if in addition p < q, all with \(\text {FPdim}(\mathcal {C})=pq^{6}\) or pq ⁷ are group-theoretical. In the process we generalize an existing criterion for an integral modular category to be group-theoretical.     

1H and 13C NMR assignments for the sesquiterpene aldehydes, lepidozenal and isobicyclogermacrenal, from Eucalyptus dawsonii

Lepidozenal and isobicyclogermacrenal were isolated from the leaves of Eucalyptus dawsonii and a complete assignment of their 1H and 13C NMR spectra was carried out using 2D NMR methods.     

Structural and initial biological analysis of synthetic arylomycin A2

The growing threat of untreatable bacterial infections has refocused efforts to identify new antibiotics, especially those acting by novel mechanisms. While the inhibition of pathogen proteases has proven to be a successful strategy for drug development, such inhibitors are often limited by toxicity due to their promiscuous inhibition of homologous and mechanistically related human enzymes. Unlike many protease inhibitors, inhibitors of the essential type I bacterial signal peptidase (SPase) may be more specific and thus less toxic due to the enzyme's unique structure and catalytic mechanism. Recently, the arylomycins and related lipoglycopeptide natural products were isolated and shown to inhibit SPase. The core structure of the arylomycins and lipoglycopeptides consists of a biaryl-linked, N-methylated peptide macrocycle attached to a lipopeptide tail, and in the case of the lipoglycopeptides, a deoxymannose moiety. Herein, we report the first total synthesis of a member of this group of antibiotics, arylomycin A2. The synthesis relies on Suzuki-Miyaura-mediated biaryl coupling, which model studies suggested would be more efficient than a lactamization-based route. Biological studies demonstrate that these compounds are promising antibiotics, especially against Gram-positive pathogens, with activity against S. epidermidis that equals that of the currently prescribed antibiotics. Structural and biological studies suggest that both N-methylation and lipidation may contribute to antibiotic activity, whereas glycosylation appears to be generally less critical. Thus, these studies help identify the determinants of the biological activity of arylomycin A2 and should aid in the design of analogs to further explore and develop this novel class of antibiotic.     

Size and shape separation of gold nanoparticles with preparative gel electrophoresis

We employed agarose gel preparative electrophoresis to separate gold nanoparticles based on size, shape, and charge. The separating technique was first demonstrated by size separation of 5 nm, 15 nm, and 20 nm spherical gold nanoclusters; and further evidenced through the purification of crude 15 +/- 2.7 nm nanoclusters to nanoclusters that were 15 +/- 0.4 nm. The ability to separate gold nanoparticles by shape was also shown by the purification of a mixture of gold spheres, plates, and long rods.     

The impact of electrolyte on the adsorption of sodium dodecyl sulfate/polyethyleneimine complexes at the air-solution interface

The addition of electrolyte (0.1 M NaCl) is shown to have a significant impact upon the surfactant concentration and solution pH dependence of the adsorption of sodium dodecyl sulfate (SDS)/polyethyleneimine (PEI) complexes at the air-solution interface. Substantial adsorption is observed over a wide surfactant concentration range (from 10(-6) to 10(-)2 M), and over much of that range of concentrations the adsorption is characterized by the formation of surface multilayers. The surface multilayer formation is most pronounced at high pH and for PEI with a lower molecular weight of 2K, compared to the higher molecular weight of 25K. These results, obtained from a combination of neutron reflectivity and surface tension, highlight the substantial enhancement in surfactant adsorption achieved by the addition of a combination of the polyelectrolyte, PEI, and a simple electrolyte. Furthermore the effect of electrolyte on the pH dependence of the adsorption further highlights the importance of the hydrophobic interaction in surface surfactant/polyelectrolyte complex formation.     

Modeling the enzymatic hydrolysis of dilute-acid pretreated Douglas Fir

Glucose yield from the enzymatic hydrolysis of cellulose was investigated as a function of cellulase enzyme loading (7–36 filter paper units [FPU]/g cellulose) and solids concentration (7–18% total solids) for up to 72 h on dilute sulfuric-acid pretreated Douglas Fir. The saccharification was performed on whole hydrolysate with no separation or washing of the solids. Enzyme loading had a significant effect on glucose yield; solids concentration had a much smaller effect even at higher glucose concentrations. The data were used to generate an empirical model for glucose yield, and to fit parameters of a cellulose hydrolysis kinetic model. Both models could be used for economic evaluation of a separate hydrolysis and fermentation process.     

Large eddy simulation of serration effects on an ultra-high-bypass-ratio engine exhaust jet

Serrated jet nozzles are considered to be an efficient and practical passive control approach for jet noise. However, some fundamental mechanisms of serration effects on jet noise are not fully understood, especially in terms of the sound source. In this paper, a high-fidelity simulation framework using large-eddy simulation (LES) is demonstrated to predict near-field turbulence and far-field acoustics from an ultra-high-bypass-ratio engine with round and serrated nozzles. Far-field sound is predicted using Ffowcs Willams–Hawkings (FWH) integration. The results show that the serrated nozzle increases mixing near the nozzle and hence the turbulence decay rate, reducing the turbulence level downstream. The serrations shift the energy from the low frequencies to the high frequencies and decrease overall sound pressure levels by about 3 dB over the low-frequency range. Sound sources are analysed based on fourth-order space–time correlations. There are six major source components ($R_{1111}$, $R_{2222}$, $R_{3333}$, $R_{1313}$, $R_{1212}$, and $R_{2323}$) inside the jet shear layers. The serrations are able to reduce the amplitude of these source terms, causing them to decay rapidly to a level below the round nozzle jet within 2D downstream of the nozzle.     

Capillary electrophoresis using core‐based hyperbranched polyethyleneimine (CHPEI) static‐coated capillaries

With unique 3‐D architecture, the application of core‐based hyperbranched polyethyleneimine (CHPEI), as a capillary coating in capillary electrophoresis, is demonstrated by manipulation of the electroosmotic mobility (EOF). CHPEI coatings (CHPEI5, M_w ≈? 5000 and CHPEI25, M_w ≈? 25 000) were physically adsorbed onto the inner surface of bare fused‐silica capillary (BFS) via electrostatic interaction of the oppositely charged molecules by rinsing the capillaries with different CHPEI aqueous solutions. The EOF values of the coated capillaries were measured over the pH range of 4.0–9.0. At higher pH (pH >6) the coated capillary surface possesses excess negative charges, which causes the reversal of the EOF. The magnitudes of the EOF obtained from the coated capillaries were three‐fold lower than that of BFS capillary. Desirable reproducibility of the EOF with % RSD (n = 5) ? 2 was obtained. Effect of ionic strength, stability of the coating (% RSD = 0.3) and the dependence of the EOF on pH (% RSD = 0.5) were also investigated. The CHPEI‐coated capillaries were successfully utilized to separate phenolic compounds, B vitamins, as well as basic drugs and related compounds with reasonable analysis time (<20 min) and acceptable migration‐time repeatability (<0.7% RSD for intra‐capillary and <2% RSD for inter‐capillary).     

Using neural networks to represent potential surfaces as sums of products

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.