Some theoretical implications of local optimization

This paper presents some theoretical results concerning the effectiveness of an approximate technique, known as local optimization, as applied to a wide class of problems.First, conditions are described under which the technique ensures exact solutions. Then, in regard to cases in which these conditions cannot be met in practice, a method is presented for estimating the probability that the approximate (locally optimal) solution delivered by such a technique is in fact the exact (globally optimal) solution.This probability may be viewed as a possible criterion of effectiveness in the design of neighborhoods for specific local optimization algorithms.     

Chemistry of alkenyl azlactones. I. Radiation-sensitive materials derived from azlactone-containing copolymers

2-Vinyl-4,4-disubstituted azlactones were shown to be effective comonomers in free radical addition polymerizations for purposes of subsequently preparing radiation-sensitive materials by attaching an unsaturated nucleophile. The azlactone-functional copolymers could be reacted with amine-, thiol-, and hydroxy-functional nucleophiles over the course of a few hours in solution at room temperature to effect covalent attachment of the nucleophile. The electron beam- and UV-sensitive materials were shown to be useful as photoresist and embossable video disk recording media.     

Second-order terms for the variances and covariances of the number of prime factors—Including the square free case

We obtain second-order terms for the variance and covariance of $\text{Ω(n)}$ and ω(n), the number of prime divisors counted with and without multiplicity, and connect these results to a formula of Renyi. We discuss the heuristic connection with the Landau-Sathe extension of the prime number theorem and develop new expansions for the mean and variance of ω(n) in the square free case.     

Correlations of functions of normal variables

Let (X₁, X₂,…, X_k, Y₁, Y₂,…, Y_k) be multivariate normal and define a matrix C by C_ij = cov(X_i, Y_j). If (i) (X₁,…, X_k) = (Y₁,…, Y_k) and (ii) C is symmetric positive definite, then 0 < varf(X₁,…, X_k) < ∞ corr(f(X₁,…, X_k),f(Y₁,…, Y_k)) > 0. Condition (i) is necessary for the conclusion. The sufficiency of (i) and (ii) follows from an infinite-dimensional version, which can also be applied to a pair of jointly normal Brownian motions.     

Use of the tandem-transfer technique in the rapid separation on ion-exchange resin papers of phenyl-alanine and tyrosine from mixtures of amino acids

Using the tandem-transfer technique (T-effect), the aromatic amino acids, phenylalanine and tyrosine, have been isolated from casein hydrolyzates and simultaneously separated from each other by one-step chromatography on cation-exchange papers. The total development time is about 80 min, using a 0.2M, pH-5.2 acetate buffer. Calculations of the optimum conditions for the separation are shown     

2,6-Bis(2-pyridyl)pyridine and alkyl derivatives.Their properties in the formation of ferrous and cobaltous colored complex cations

Terpyridine (2,6-bis-(2-pyridyl)-pyridine) and two alkyl substituted analogues of terpyridine have been investigated as organic complexing agents for use in spectrophotornetry. Terosine (2,6-bis-(2-pyridyl)-4-phenyl-pyridine) and terosole (2,6-bis- (4-methyl-pyridyl)-4-phenyl-pyridine) were the terpyndine analogues herein investigated.The determination has been made of the molecular extinction coefficient E, and the wavelength of maximum absorption lmax, of the three ligands terpyridyl, terosine and terosole both for the Fe(II) and the Co(II) chelation. The effect of substitutions in the 4,4', 4” carbon position of terpyndine on the values E and lmax has been shown.The unsubstituted terpyridine is not extracted from aqueous solution when complexed with either Fe(II) or Co(II), but in the case of terosine the complex may be extracted from aqueous solution by the multiple treatment by n-hexyl alcohol. With terosole the colored complex becomes extractable by this immiscible solvent in one operation.Interfering cations and anions are Cu(I), Ni(II), Co(II), F-, and ClO₄,-. A procedure is given preventing interference from Co (II) through the use of ethylenediamine as masking reagent for Co(II) when using terosine to complex Fe(II). The ClO₄- interference results from the formation of a very highly insoluble terosole perchlorate. Ions which may be present to the extent of 100 mg without interference are Mn(II), Al, Cr(III). the alkali and alkaline earth metals and Mg, PO₄^-3, P₂O₇^-4 C₂O₄^-2, Cl-, NO₃-, Ac- and SO₄^-2 among others.Terosole is the most sensitive iron reagent so far described having an E value of 26300 at wavelength of maximum absorption 575 mm.     

Separation of Bioactive Prostaglandins and their Metabolites by Reversed-Phase Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Prostaglandins are biological lipid mediators that control a variety of physiological and pathophysiological processes. They...     

Interlaboratory assessment of measurement precision and bias in the coulometric Karl Fischer determination of water

The precision and bias of the coulometric Karl Fischer ASTM method D1533-00 have been assessed in a collaborative ASTM round robin program for a group of 34 laboratories. The test materials used in this study included water saturated 1-octanol (WSO), water saturated 1-butanol (WSB), and a series of new and used transformer oil samples. Fundamental systematic biases have been demonstrated in the accuracy of the measurement of water in the WSO, WSB, and transformer oil samples. The systematic bias in the measurement of the WSO and WSB standards indicates that for some laboratories either the instruments were not accurate or the quantity of the standard was not measured accurately. A second type of systematic bias consisted of measurement errors associated with the selection of the Karl Fischer solvent that was used with each instrument, and this was superimposed upon the error in the measurement of the water in the standards. Using the statistical calculation method ASTM D 6300 the repeatability and reproducibility for water in transformer oil were found to be 7 mg/kg and 14 mg/kg respectively. The method detection limit of water was 8 mg/kg oil. The method bias was estimated based on the National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) 2890, WSO, since no suitable reference material for water in transformer oil was available for this study.