Finite element approximations of a nonlinear diffusion model with memory

The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results.     

The endocannabinoid anandamide is a precursor for the signaling lipid N-arachidonoyl glycine by two distinct pathways

Background  

N-arachidonoyl glycine (NAGly) is an endogenous signaling lipid with a wide variety of biological activity whose biosynthesis is poorly understood. Two primary biosynthetic pathways have been proposed. One suggests that NAGly is formed via an enzymatically regulated conjugation of arachidonic acid (AA) and glycine. The other suggests that NAGly is an oxidative metabolite of the endogenous cannabinoid, anandamide (AEA), through an alcohol dehydrogenase. Here using both in vitro and in vivo assays measuring metabolites with LC/MS/MS we test the hypothesis that both pathways are present in mammalian cells.     

On the new family of optimal eighth order methods developed by Lotfi et al.

Recently Lotfi et al. (Numer. Algor. 68, 261–288, 5) have developed a new family of optimal order eight for the solution of nonlinear equations. They have experimented with 3 members of the family and compared them to other eighth order methods. One of the best known eight order method was not included. They also did not mention the best choice of parameters in the methods used and why. The basins of attraction were given for several examples without a quantitative comparison. It will be shown how to choose the best parameters in all these methods, and to quantitatively compare the methods.     

Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

A reduced shallow water model under constant, non-zero advection in the infinite channel is considered. High-order (Givoli-Neta) non-reflecting boundary conditions are introduced in various configurations to create a finite computational space and solved using a spectral element formulation with high-order time integration. Numerical examples are used to demonstrate the synergy of using high-order spatial, time, and boundary discretization. We show that by balancing all numerical errors involved, high-order accuracy can be achieved for unbounded domain problems.     

Temperature dependence of the rate constants for reactions of the carbonate radical with organic and inorganic reductants

Rate constants have been measured by pulse radiolysis for the reactions of the carbonate radical, CO₃^·?, with a number of organic and inorganic reactants as a function of temperature, generally over the range 5 to 80°C. The reactants include the substitution-inert cyano complexes of Fe^II, Mo^IV, and W^IV, the simple inorganic anions SO₃^2?, ClO₂^?, NO₂^?, I^?, and SCN^?, several phenolates, ascorbate, tryptophan, cysteine, cystine, methionine, triethylamine, and allyl alcohol. The measured rate constants ranged from less than 10⁵ to 3 × 10⁹ M^?1 s^?1, the activation energies ranged from ?11.4 to 18.8 kJ mol^?1, and the pre-exponential factors ranged from log A = 6.4 to 10.7. The activation energies for the metal complexes and inorganic anions generally decrease with increasing driving force for the reaction, as expected for an outer sphere electron transfer. For highly exothermic reactions, however, the activation energy appears to increase, probably reflecting the temperature dependence of diffusion. For many of the organic reactants, the activation energies were low and independent of driving force, suggesting that the oxidation is via an inner sphere mechanism.     

General, fast, and high yield oxidation of thiols and disulfides to sulfonic and sulfinic acids using HOF·CH3CN

Thiols and disulfides are oxidized to the corresponding sulfonic and sulfinic acids using HOF·CH₃CN. This oxidation is suitable for a variety of thiols and disulfides and proceeds under mild conditions, in short reaction times and with high yields.     

Rate constants for reactions of iodine atoms in solution

Laser flash photolysis (at 248 or 308 nm) or aryl iodides in water or water/methanol solutions produces iodine atoms and phenyl radicals. Iodine atoms react rapidly with added I^? to form I₂^? but do not react rapidly with O₂ (k ? 10⁷ L mol^?1 s^?1). Iodine atoms oxidize phenols to phenoxyl radicals, with rate constants that vary from 1.6 × 10⁷ L mol^?1 s^?1 for phenol to about 6 × 10⁹ L mol^?1 s^?1 for 4-methoxyphenol and hydroquinone. Ascorbate and a Vitamin E analogue are also oxidized very rapidly. N-Methylindole is oxidized by I atoms to its radical cation with a diffusion-controlled rate constant, 1.9 × 10¹⁰ L mol^?1 s^?1. Iodine atoms also oxidize sulfite and ferrocyanide ions rapidly but do not add to double bonds. The phenyl radicals, produced along with the I atoms, react with O₂ to give phenylperoxyl radicals, which react with phenols much more slowly than I atoms. © 1995 John Wiley & Sons, Inc.     

Families of methods for ordinary differential equations based on trigonometric polynomials

We consider the construction of methods based on trigonometric polynomials for the initial value problems whose solutions are known to be periodic. It is assumed that the frequency w can be estimated in advance. The resulting methods depend on a parameter ν = hw, where h is the step size, and reduce to classical multistep methods if ν → 0. Gautschi [4] developed Adams and Störmer type methods. In our paper we construct Nyström's and Milne-Simpson's type methods. Numerical experiments show that these methods are not sensitive to changes in w, but require the Jacobian matrix to have purely imaginary eigenvalues.