Linearly recurring solution sequences for equations over finite fields

Methods based on character sums are used to study conditions under which the sequence {N_t} of numbers of solutions to sequences of equations, parametrized by their number t of variables, over a finite field satisfies a linear recurrence.     

Differential activation of nerve fibers with magnetic stimulation in humans

Background  

Earlier observations in our lab had indicated that large, time-varying magnetic fields could elicit action potentials that travel in only one direction in at least some of the myelinated axons in peripheral nerves. The objective of this study was to collect quantitative evidence for magnetically induced unidirectional action potentials in peripheral nerves of human subjects. A magnetic coil was maneuvered to a location on the upper arm where physical effects consistent with the creation of unidirectional action potentials were observed.     

Temperature effects on supercritical carbon dioxide extractions of hydrocarbons from geological samples

The extraction of aliphatic and aromatic hydrocarbons from New Albany Shale by supercritical carbon dioxide at different extraction temperatures is described. The main goal of this work was to determine the effect of the temperature on the extraction process (i.e. relative extraction rate and efficiency). The data suggest that temperature changes of 20 and 40 degrees for the relatively moderate extraction temperatures tested (55, 75, and 95°C), can have significant effects on both relative extraction rates and yields. While lower molecular weight aromatics presented exponential extraction profiles, similar to those of the aliphatic hydrocarbons, higher molecular weight aromatics, such as the phenanthrenes, showed a linear extraction profile. This behavior cannot be explained by solubility differences in the supercritical fluid alone, and are, therefore, most likely based on differences in the speciation of the hydrocarbons within the sample matrix. Extractions at elevated temperatures (300°C) resulted in significant increments in the relative recoveries of all compounds, but particularly for the aromatic hydrocarbons. This may be caused by structural rearrangement of the sample matrix with subsequent release of trapped hydrocarbons and possibly by C-S and S-S bond breakage.     

Kinetics and mechanism of the iodine oxidation of hydroxylamine

Studies of the stoichiometry and kinetics of the reaction between hydroxylamine and iodine, previously studied in media below pH 3, have been extended to pH 5.5. The stoichiometry over the pH range 3.4–5.5 is 2NH₂OH + 2I₂ = N₂O + 4I^? + H₂O + 4H⁺. Since the reaction is first-order in [I₂] + [I₃^?], the specific rate law, k₀, is k₀ = (k₁ + k₂/[H⁺]) {[NH₃OH⁺]₀/(1 + K_p[H⁺])} {1/(1 + K_I[I^?])}, where [NH₃OH⁺]₀ is total initial hydroxylamine concentration, and k₁, k₂, K_p, and K_I are (6.5 ± 0.6) × 10⁵ M^?1 s^?1, (5.0 ± 0.5) s^?1, 1 × 10⁶ M^?1, and 725 M^?1, respectively. A mechanism taking into account unprotonated hydroxylamine (NH₂OH) and molecular iodine (I₂) as reactive species, with intermediates NH₂OI₂^?, HNO, NH₂O, and I₂^?, is proposed.     

Methylated antimony(V) compounds: Synthesis,hydride generation properties and implications for aquatic speciation

Reports in the literature that the compounds MeSb(O)(OH)₂ and Me₂Sb(O)(OH) are present in marine and fresh-waters need to be re-examined. The results of several synthetic strategies suggest that these methylantimony(V) compounds are either environmentally inaccessible or polymeric in nature. Pure samples of various di- and tri- methylated antimony(V) species were prepared and found to undergo molecular rearrangement reactions when subjected to hydride generation procedures typically used for aquatic speciation.