A short proof of a conjecture of Aougab–Huang

Geometriae Dedicata - In response to Sanki–Vadnere, we present a short proof of the following theorem: a pair of simple curves on a hyperbolic surface whose complementary regions are disks...     

Trace elemental analysis of Nigerian crude oils by INAA using miniature neutron source reactor

Copper foils of 10 and 20 mm thickness were exposed to deuteron beams of 2.0 and 2.5 MeV. To avoid structural damage of the targets by high beam intensities, during extended irradiation periods of at least ten hours, liquid nitrogen was used as a refrigerant. Under these conditions equilibrium temperatures of less than 100 °C were achieved. This revised version was published online in August 2006 with corrections to the Cover Date.     

Haglund’s conjecture on 3-column Macdonald polynomials

We prove a positive combinatorial formula for the Schur expansion of LLT polynomials indexed by a 3-tuple of skew shapes. This verifies a conjecture of Haglund (Proc Natl Acad Sci USA 101(46):16127–16131, 2004). The proof requires expressing a noncommutative Schur function as a positive sum of monomials in Lam’s (Eur J Combin 29(1):343–359, 2008) algebra of ribbon Schur operators. Combining this result with the expression of Haglund et al. (J Am Math Soc 18(3):735–761, 2005) for transformed Macdonald polynomials in terms of LLT polynomials then yields a positive combinatorial rule for transformed Macdonald polynomials indexed by a shape with 3 columns.     

Regioselective synthesis of asymmetrically substituted 2-quinoxalinol salen ligands

Diamino-2-quinoxalinols are reacted with salicylaldehyde derivatives to produce 2-quinoxalinol imines regioselectively as one isomer in good yield. Regioselectivity has been determined through the use of isotopic 15N labeling experiments. The 2-quinoxalinol imines may then be reacted without further purification with additional salicylaldehyde derivatives to yield asymmetrically substituted 2-quinoxalinol salens.     

Hydroxyl radical self-recombination reaction and absorption spectrum in water up to 350 degrees C

The rate constant for the self-recombination of hydroxyl radicals (*OH) in aqueous solution giving H2O2 product has been measured from 150 to 350 degrees C by direct measurement of the *OH radical transient optical absorption at 250 nm. The values of the rate constant are smaller than previously predicted by extrapolation to the 200-350 degrees C range and show virtually no change in this range. In combining these measurements with previous results, the non-Arrhenius behavior can be well described in terms of the Noyes equation kobs-1 = kact-1+ kdiff-1, using the diffusion-limited rate constant kdiff estimated from the Smoluchowski equation and an activated barrier rate kact nearly equal to the gas-phase high-pressure limiting rate constant for this reaction. The aqueous *OH radical spectrum between 230 and 320 nm is reported up to 350 degrees C. A weak band at 310 nm grows in at higher temperature, while the stronger band at 230 nm decreases. An isosbestic point appears near 305 nm. We assign the 230 nm band to hydrogen-bonded *OH radical, and the 310 nm band is assigned to "free" *OH. On the basis of the spectrum change relative to room temperature, over half of the *OH radicals are in the latter form at 350 degrees C.     

Reaction of O2 with the hydrogen atom in water up to 350 degrees C

The reaction of the H* atom with O2, giving the hydroperoxyl HO2* radical, has been investigated in pressurized water up to 350 degrees C using pulse radiolysis and deep-UV transient absorption spectroscopy. The reaction rate behavior is highly non-Arrhenius, with near diffusion-limited behavior at room temperature, increasing to a near constant limiting value of approximately 5 x 10(10) M(-1) s(-1) above 250 degrees C. The high-temperature rate constant is in near-perfect agreement with experimental extrapolations and ab initio calculations of the gas-phase high-pressure limiting rate. As part of the study, reaction of the OH* radical with H2 has been reevaluated at 350 degrees C, giving a rate constant of (6.0 +/- 0.5) x 10(8) M(-1) s(-1). The mechanism of the H* atom reaction with the HO2* radical is also investigated and discussed.     

Multi elemental analysis of indigenous food spices in Southern Ethiopia using INAA technique

The objective of this study is a quantitative and qualitative analysis of essential and trace elements of four indigenous Ethiopian spices and herbs using instrumental neutron activation analysis technique. Results obtained for 16 elements: Major elements; Mg, Cl, and K; Minor elements; Na, Fe, and Mn, Zn, Br. While Al, V, Sm, Sc, La, Ba, Eu, Rb were found in traces. The spices, Affromumom korarima and Lippa Adonesis var. Koseret sebsebe were found to be very good sources of essential trace elements like Fe, Zn and Mn. The highest concentration of Mg was found in Ajowan whereas K and Fe were measured in Coriander seeds. The average daily dietary intake of some essential elements from the use of these spices were found to be below the recommended upper limit by WHO.

     

Sensitivity analysis,calibration and validation of a snow indentation model

Quantification of the mechanical behavior of snow in response to loading is of importance in vehicle-terrain interaction studies. Snow, like other engineering materials, may be studied using indentation tests. However, unlike engineered materials with targeted and repeatable material properties, snow is a naturally-occurring, heterogeneous material whose mechanical properties display a statistical distribution. This study accounts for the statistical nature of snow behavior that is calculated from the pressure-sinkage curves from indentation tests. Recent developments in the field of statistics were used in conjunction with experimental results to calibrate, validate, and study the sensitivity of the plasticity-based snow indentation model. It was found that for material properties, in the semi-infinite zone of indentation, the cohesion has the largest influence on indentation pressure, followed by one of the the hardening coefficients. In the finite depth zone, the friction angle has the largest influence on the indentation pressure. A Bayesian metamodel was developed, and model parameters were calibrated by maximizing a Gaussian likelihood function. The calibrated model was validated using three local and global confidence-interval based metrics with good results.