Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

On-column injection onto capillary columns. Part 2: Study of sampling conditions; practical recommendations

During one year continuous use of on-column injection, the typical advantages described in our first report have fully been confirmed. In addition the analysis of large sample volumes has proved promising. Only minor modifications have been applied to the on-column injector device. Broad evidence has been gathered showing that full separation efficiency of the capillary columns after on-column injection is attained only when cold trapping or the solvent effect, as band shortening mechanisms, are working- While, under the conditions of on-column injection, cold trapping is less efficient than with other injection techniques, the opposite holds true for the solvent effect. Compared with splitless injection, the danger of excessive solvent condensation on the column is increased. A working rule is presented for establishing the optimal chromatographic conditions for handling large sample volumes while ensuring full separation efficiency yet avoiding harm to the column.     

A statistical thermodynamic supermolecule-continuum study of ion hydration: Cell and shell methods

A theoretical study of ion hydration using the statistical thermodynamic supermolecule-continuum method is described. The cell and shell methods are used for configurational averaging. Enthalpies, free energies and entropies are calculated for Li⁺, Na⁺, K⁺, F^– and Cl^– each four coordinated with water. The results are in reasonable accord with experiment. A comparison of the site method, cell method and shell method results is presented. The supermolecule-continuum approach to solvent effects seems to be capable of accommodating essential features for the calculation of solvation energy and solvent effects on structure and properties.     

An electrochemical study of redox indicators : Part I. Substituted chrysoidines

The electrochemical oxidation of various substituted chrysoidines was studied by cyclic voltammetry, to determine which have stable oxidation products. Only 4-hydroxy-chrysoidine has a stable product; the apparent oxidation potential is 0.779 V vs. NHE. 4-Methoxy- and 4-ethoxy-chrysoidine rapidly lose methanol or ethanol, respectively, so that the 4-hydroxychrysoidine wave appears on subsequent scans. All the other chrysoidines studied are irreversible. The results indicate that a hydroxy group in the 4-position is necessary for stability; the 4-alkoxychrysoidines can achieve the stable quinoidal structure by cleavage of the alkoxy group after nucleophilic attack.     

Electrode processes in the oxidation of tetrahydroisoquinoline derivatives

The electrochemical oxidation of the alkaloid laudanosine (Ia) to O-methylflavinantine (II) has been studied in acetonitrile solvent. Using cyclic voltammetry, rotating disc voltammetry and preparative electrolyses on several alkaloids, simple aliphatic amines and aromatic compounds, some aspects of the mechanism of this coupling reaction are elucidated. The first anodic wave for laudanosine at platinum has E_p=0.55 V vs. Ag/Ag⁺. The electrode rapidly becomes partially passivated at potentials above 0.5 V. This is due to a film which “dissolves” below 0.5 V, at a rate independent of the potential. It is shown that the reaction (Ia)→(II) proceeds at 0.5 V by initial oxidation of the amine moiety. If acids such as sodium bicarbonate are added to the anolyte the amine is protonated causing the first wave to disappear. Oxidation at 1.1 V under these acidic conditions produces the same product, but more rapidly and in significantly higher yield because electrode filming and side reactions resulting from the amine oxidation are abrogated.     

The synthesis of cypridina etioluciferamine and the proof of structure of cypridina luciferin

An unambiguous synthesis of Cypridina etioluciferamine was accomplished in order to prove the structure of this important bioluminescent natural product. Several 2-aminopyrazine 1-oxides were synthesized in order to establish a spectroscopic method for determining the placement of substituents on the pyrazine nucleus of Cypridina etioluciferamine. Titanium tetrachloride was used to improve the yields of these compounds; for example, the yield of 2-amino-3-methyl-5-phenylpyrazine 1-oxide (19) from reaction of phenylglyoxal 1-oxime and α-aminopropionitrile was raised from 3% to 51% by the use of titanium tetrachloride. The pyrazine ring proton is found at τ 1·37 (DMSO-d₆). The isomeric 2-amino-3-methyl-6-phenylpyrazine 1-oxide (22) was similarly prepared and its pyrazine ring proton is found at τ 2·18. This large difference (0·81 ppm) in chemical shift was used to determine whether a 2-aminopyrazine 1-oxide was 5- or 6- substituted. Prepared in an analogous fashion were 2-amino-5-(indol-3-yl)-3-methylpyrazine 1-oxide (23) and 2-amino-5-(indol-3-yl)-3-(3-phthalimidopropyl)pyrazine 1-oxide (16). The structures of these compounds were verified by NMR spectroscopy. By treatment with Raney nickel and hydrogen gas, then 100% hydrazine hydrate, 16 was converted to 2-amino-3-(3-aminopropyl)-5-indol-3-ylpyrazine (5), isolated as the dihydrochloride. This compound, with the indole moiety definitely placed at C-5, is identical with Cypridina etioluciferamine dihydrochloride (IR, UV, TLC). These results show that the structures of Cypridina etioluciferamine and luciferin are correct as published.     

Preparation of apolar glass capillary columns by the barium carbonate procedure

As an extension of previous reports, the barium carbonate procedure has been optimized in detail for the preparation of apolar columns. The aim was to produce optimum overall column characteristics, and to maintain them unchanged under the prolonged influence of the highest possible temperature. The main parameters under optimization were glass variety, leaching of glass surface with aqueous HCl, and amount of barium carbonate deposited, while deactivation and coating were kept constant. The basic column characteristics were adsorption properties and thermostability of deactivation, acid/base behaviour and separation efficiency. They were determined by a new, quantitative testing procedure. Intense leaching was able to eliminate almost totally the differences between glass varieties and to create a well-defined glass surface. While untreated glass, leached glass, and barium carbonate treated glass showed specific weak points in the respective column quality, the combination of leaching and barium carbonate treatment yielded the highest and most stable quality. Some technical modifications of the preparation procedure are described, including deactivation in the gas phase, and use of pentane as a solvent for static coating.     

Analytical applications of picolinealdehyde salicyloylhydrazone: Spectrophotometric determination of nickel and zinc

With a view to the use of picolinealdehyde salicyloylhydrazone as analytical reagent, a study of the physical properties and chemical reactions of this substance has been carried out. It reacts with nickel (λ_max = 375 nm, ? = 3.9 × 10⁴M^?1cm^?1) or zinc (λ_max = 365 nm, ? = 4.8 × 10⁴M^?1cm^?1) to produce a yellow 1:2 complex in both cases. Spectrophotometric determinations of trace amounts of nickel and zinc have been established.