Certification by the Karl Fischer method of the water content in SRM 2890, Water Saturated 1-Octanol, and the analysis of associated interlaboratory bias in the measurement process

The calibration of Karl Fischer instruments and reagents and the compensation for instrumental bias are essential to the accurate measurement of trace levels of water in organic and inorganic chemicals. A stable, nonhygroscopic standard, Water Saturated Octanol, which is compatible with the Karl Fischer reagents, has been prepared. This material, Standard Reference Material (SRM) 2890, is homogeneous and is certified to contain 39.24 +/- 0.85 mg water/mL (expanded uncertainty) of solution (47.3 +/- 1.0 mg water/g solution, expanded uncertainty) at 21.5 degrees C. The solubility of water in -octanol has been shown to be nearly constant between 10 degrees C and 30 degrees C (i.e., within 1% of the value at 21.5 degrees C). The results of an interlaboratory comparison exercise illustrate the utility of SRM 2890 in assessing the accuracy and bias of Karl Fischer instruments and measurements.     

ImmobilizedE. coli Alkaline Phosphatase

We have immobilized E.coli alkaline phosphatase (EC 3.1.3.1) by linking it covalently to sepharose 4B. This preparation has several advantages over the soluble enzyme. The immobilized enzyme is easily separable from other constituents in incubation mixtures. The immobilized enzyme can be reused repeatedly and is more stable than the soluble enzyme to heat treatment in the presence of 10 mM Mg²⁺. The insoluble and soluble phosphatases removed 75 and77%, respectively, of the inorganic phosphorus from casein. The immobilized enzyme inactivated two enzymes believed to be active in the phosphorylated state, acyl-CoA : cholesterol acyltransferase (ACAT) by 39% and NADPH-cytochrome P-450 reductase by 89%. The utility of immobilized alkaline phosphatase for studying the phosphorylation and dephosphorylation of soluble or membrane-bound enzymes and proteins is discussed.     

Compact,convex sets in R n and a new banach lattice. II.- Application: An approximation problem.

We develop a calculus structure in the Banach lattice introduced in a preceding paper, having in mind an approximation problem appearing in non-smooth optimization. We show that the essential results depend as much on the order structure as on the analytical one.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Semigroup identities in the monoid of two-by-two tropical matrices

We show that the monoid $M_{2}(\mathbb {T})$ of 2×2 tropical matrices is a regular semigroup satisfying the semigroup identity $$A^2B^4A^2A^2B^2A^2B^4A^2=A^2B^4A^2B^2A^2A^2B^4A^2.$$ Studying reduced identities for subsemigroups of $M_{2}(\mathbb {T})$ , and introducing a faithful semigroup representation for the bicyclic monoid by 2×2 tropical matrices, we reprove Adjan’s identity for the bicyclic monoid in a much simpler way.