The six semifield planes associated with a semifield flock

In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (a_ijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)²+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations.     

Comparison of the Temperature Effect on the π∗←n and π∗←π Electronic Transition Bands of NO<Subscript>3</Subscript><Superscript>−</Superscript>(aq)

The effect of temperature on the π∗←π transition band in the UV absorption spectrum of NO₃⁻(aq) centered at ≈200 nm was studied in the temperature range 10–70 ^∘C. The observed temperature independence of this band was in contrast to the significant influence of temperature on the nitrate π∗←n transition reported recently by us. However, taking into account the electronic states involved in both the transitions, it was concluded that this finding was in accordance with our previous assumption that interconversion between spectrally distinct (with respect to π∗←n band) nitrate species included the rupture/formation of hydrogen bond(s) in the hydration shell of the nitrate ion.     

Acyclic stereoselection. 35. Effect of cation on diastereofacial selectivity in aldol reactions of a chiral α-silyloxy ketone.

By an appropriate choice of cation, three of the four possible aldols from the reactions of the chiral α-silyloxy ketone 1 with aldehydes may be obtained. The $\text{Z}$, lithium enolate provides 6, the $\text{Z}$, boron enolate gives 7, and the $\text{E}$ magnesium enolate affords 8.     

Finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.

     

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.