Affine Arithmetic: Concepts and Applications

Affine arithmetic is a model for self-validated numerical computation that keeps track of first-order correlations between computed and input quantities. We explain the main concepts in affine arithmetic and how it handles the dependency problem in standard interval arithmetic. We also describe some of its applications.     

Identifying several biased coins encountered by a hidden random walk

Suppose that attached to each site z ∈ ? is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}_z∈?, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of ?. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Mössbauer study of spin-glass Fe x Zn1−x F2 system

⁵⁷Fe Mössbauer effect measurements in the diluted Ising antiferromagnet Fe _x Zn_1?x F₂ withx=0.25 andx=0.57 at temperatures between 4.2 and 55 K, are reported. DC suceptibility measurements show a spin-glass (SG) phase at low temperatures forx≤0.31. Our Mössbauer spectra show a phase transition to a SG state with antiferromagnetic order (AFSG) forx=0.25 and only antiferromagnetic order forx=0.57.     

The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

High-performance liquid chromatography and thin-layer chromatography assays for Devil's Club (Oplopanax horridus)

Devil's root, Oplopanax horridus, is a widely used folk medicine in Alaska and British Columbia. The inner bark of the root and stem has been used to treat colds, cough, fever, and diabetes. The present study involves the development of high-pressure liquid chromatography (HPLC) and thin-layer chromatography (TLC) methods to detect the presence of trans-nerolidol and sterols in the root bark. The HPLC and TLC analytical methods presented are suitable for the characterization and identification of Oplopanax horridus.     

Lipase from a Brazilian StrainPenicillium citrinum Cultured in a Simple and Inexpensive Medium st]Heat-Denaturation, Kinetics, and pH Stability

This work is a study of lipase production by a Brazilian strain ofPenicillium citrinum using an inexpensive and simple medium without organic nitrogen sources and of some important industrial properties, including thermostability in relation to ionic strength. The maximal lipase activity (1585 U/L) was obtained whenPenicillium citrinum was cultured on 0.75% ammonium sulfate complemented with minerals salts instead of yeast extract. Although this activity was about 55% lower than that produced in medium with yeast extract (2850 U/L), the specific activity (7.8 U/mg proteins) was higher than that obtained with the yeast extract (4.9 U/mg proteins). The morphology of fungus changed totally, with yeast extract there are smooth, solid, and spherical pellets whereas on ammonium sulfate there are small “hairy” pellets uniformly suspended in the medium. The effect of ferrous (Fe⁺⁺) ions was carried out using medium MA with and without Fe⁺⁺ ions. Lipase production byPenicillium citrinum in medium MA requires Fe⁺⁺ ions, the absence of which caused a decreased of about 50% in the specific activity (3.5 U/mg proteins). The utilization of commercial, locally available oils as carbon sources, such as soybean oil (236 U/L) and corn oil (74 U/L) resulted in lower activity compared to olive oil, showing that lipase production byPenicillium citrinum is specifically induced by olive oil. Potassium concentration in the medium can effects the production of lipase (1 mM (1585 U/L), 10 mM (1290 U/L), and 30 mM (1238 U/L), 50 mM (195 U/L), and 100 mM (2 U/L). The crude culture filtered was susceptable to thermal deactivation. It was stable at pH 6.0, but was not stable at the optimum pH (8.0-8.5) at 50 mM. At the low ionic concentration (1-25 mM) this lipase was stable at low pH (3.5-4.0). The activation energy was 22.4 ±2.2 Kcal. mol 1.     

Electrospray mass and tandem mass spectrometry of homologous and isomeric singly, doubly, triply and quadruply charged cationic ruthenated meso-(phenyl)m-(meta- and para-pyridyl)n (m + n = 4) macrocyclic porphyrin complexes

Ten homologous or isomeric singly, doubly, triply and quadruply charged cationic macrocyclic complexes I-Va, bn+ (n = 1-4) formed by the coordination of [Ru(bipy)2Cl]+ to the pyridyl N-atoms of a series of meso-(phenyl)m-(meta or para-pyridyl)n-porphyrins (m + n = 4) were transferred to the gas phase and structurally characterized by electrospray ionization (ESI) mass (MS) and tandem mass (MS/MS) spectrometry. Previously known to be stable in solution and in the solid state, I-Va, bn+ are found to constitute also a new class of stable, long-lived multiply charged gas-phase ions with spatially separated charge sites. Increasing intramolecular electrostatic repulsion from Ia, b+ to IVa, b3+ facilitates in-source and tandem collision-induced dissociation (CID). However, for the quadruply charged ions Va, b4+, electrostatic repulsion is alleviated mainly by ion pairing with the CF3SO3- counterion forming the salt clusters [Va,b/CF3SO3]3+ and [Va,b/(CF3SO3)2]2+ with reduced charge states. Ion-pairing that yields [IVa,b/CF3SO3]2+ is also observed as a minor ESI process for the triply charged ions IVa, b3+. The gaseous ions I-Va, bn+ (n = 2, 3 or 4) dissociate by sequential 'charge partitioning' with the formation of two cationic fragments by the release of [Ru(bipy)2Cl]+. The meta (a) and para (b) isomers and the positional isomers II2+ and III2+ display nearly identical ESI-MS and ESI-MS/MS spectra. ESI-MS/MS of I-Va, bn+ shows that the Ru-py(P) is, intrinsically, the weakest bond since this bond breaks preferentially upon CID.