Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Extreme red shifted SERS nanotags

Surfaced enhanced Raman scattering (SERS) nanotags operating with 1280 nm excitation were constructed from reporter molecules selected from a library of 14 chalcogenopyrylium dyes containing phenyl, 2-thienyl, and 2-selenophenyl substituents and a surface of hollow gold nanoshells (HGNs). These 1280 SERS nanotags are unique as they have multiple chalcogen atoms available which allow them to adsorb strongly onto the gold surface of the HGN thus producing exceptional SERS signals at this long excitation wavelength. Picomolar limits of detection (LOD) were observed and individual reporters of the library were identified by principal component analysis and classified according to their unique structure and SERS spectra.     

Antimicrobial Metabolites against Methicillin-Resistant Staphylococcus aureus from the Endophytic Fungus Neofusicoccum australe

Antimicrobial bioassay-guided fractionation of the endophytic fungi Neofusicoccum australe led to the isolation of a new unsymmetrical naphthoquinone dimer, neofusnaphthoquinone B (1), along with four known natural products (2–5). Structure elucidation was conducted by nuclear magnetic resonance (NMR) spectroscopic methods, and the antimicrobial activity of all the natural products was investigated, revealing 1 to be moderately active towards methicillin-resistant Staphylococcus aureus (MRSA) with a minimum inhibitory concentration (MIC) of 16 µg/mL.     

Isolation of Elusive HAsAsH in a Crystalline Diuranium(IV) Complex

The HAsAsH molecule has hitherto only been proposed tentatively as a short‐lived species generated in electrochemical or microwave‐plasma experiments. After two centuries of inconclusive or disproven claims of HAsAsH formation in the condensed phase, we report the isolation and structural authentication of HAsAsH in the diuranium(IV) complex [{U(Tren^TIPS)}₂(μ‐η²:η²‐As₂H₂)] ( 3 , Tren^TIPS=N(CH₂CH₂NSiPrⁱ₃)₃; Prⁱ=CH(CH₃)₂). Complex 3 was prepared by deprotonation and oxidative homocoupling of an arsenide precursor. Characterization and computational data are consistent with back‐bonding‐type interactions from uranium to the HAsAsH π*‐orbital. This experimentally confirms the theoretically predicted excellent π‐acceptor character of HAsAsH, and is tantamount to full reduction to the diarsane‐1,2‐diide form.     

Concerning time and length scale estimates made from burst-mode LDA autocorrelation measurements

 An investigation was performed in grid-generated turbulence to highlight the difficulties in estimating integral and microscales from discrete autocorrelation measurements made using a burst-mode laser Doppler anemometer (LDA). Comparison was made to hot-wire results and the theoretical growth laws determined by the decay of turbulent energy. The chief concern was the presence of a spike in the measured autocorrelation coefficient functions at t=0. It was found that renormalizing the autocorrelation to a value at t=0 determined by “backfitting” a quadratic equation to the slots near t=0 led to microscale estimates that showed the same trend as the decay law and were in agreement with those determined using a hot-wire. Additionally, practical guidelines are presented for making accurate autocorrelation measurements by LDA. Received: 12 January 1995/Accepted: 9 June 1997     

Neurofibrillary tangles and plaques are not accompanied by white matter pathology in aged triple transgenic-Alzheimer disease mice

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that is the most common cause of dementia in aging populations. Although senile plaques and neurofibrillary tangles are well-established hallmarks of AD, changes in cerebral white matter correlate with cognitive decline and may increase the risk of the development of dementia. We used the triple transgenic (3xTg)-AD mouse model of AD, previously used to show that white matter changes precede plaque formation, to test the hypothesis that MRI detectable changes occur in the corpus callosum, external capsule and the fornix. T₂-weighted and diffusion tensor magnetic resonance imaging and histological stains were employed to assess white matter in older (11–17 months) 3xTg-AD mice and controls. We found no statistically significant changes in white matter between 3xTg-AD mice and controls, despite well-developed neurofibrillary tangles and beta amyloid immunoreactive plaques. Myelin staining was normal in affected mice. These data suggest that the 3xTg-AD mouse model does not develop MRI detectable white matter changes at the ages we examined.     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of a Defined Cellulolytic and Xylanolytic Bacterial Consortium for Bioprocessing of Cellulose and Hemicelluloses

Diminishing fossil fuel reserve and increasing cost of fossil hydrocarbon products have rekindled worldwide effort on conversion of lignocellloloses (plant biomass) to renewable fuel. Inedible plant materials such as grass, agricultural, and logging residues are abundant renewable natural resources that can be converted to biofuel. In an effort to mimic natural cellulolytic–xylanolytic microbial community in bioprocessing of lignocelluloses, we enriched cellulolytic–xylanolytic microorganisms, purified 19 monocultures and evaluated their cellulolytic–xylanolytic potential. Five selected isolates (DB1, DB2, DB7, DB8, and DB13) were used to compose a defined consortium and characterized by 16S ribosomal RNA gene sequence analysis. Nucleotide sequence blast analysis revealed that DB1, DB2, DB7, DB8, and DB13 were respectively similar to Pseudoxanthomonas byssovorax (99%), Microbacterium oxydans (99%), Bacillus sp. (99%), Ochrobactrum anthropi (98%), and Klebsiella trevisanii (99%). The isolates produced an array of cellulolytic–xylanolytic enzymes (filter paper cellulase, β-glucosidase, xylanase, and β-xylosidase), and significant activities were recorded in 30 min. Isolates DB1 and DB2 displayed the highest filter paper cellulase: 27.83 and 31.22 U mg⁻¹, respectively. The highest β-glucosidase activity (18.07 U mg⁻¹) was detected in the culture of isolate DB1. Isolate DB2 produced the highest xylanase activity (103.05 U mg⁻¹), while the highest β-xylosidase activity (7.72 U mg⁻¹) was observed with DB13. Use of microbial consortium in bioprocessing of lignocelluloses could reduce problems such as incomplete synergistic enzymes, end-product inhibition, adsorption, and requirement for high amounts of enzymes in direct use of enzymes.     

Cyclotomic factors of Coxeter polynomials

In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of nmod360, and come exclusively from spherical subdiagrams.