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.     

High performance liquid chromatographic separation of polar and non-polar chlorophyll pigments from algae using a wide pore polymeric octadecylsilica column

A method employing a wide pore polymeric reversed phase column has been developed for the separation of most of the chlorophylls and related compounds previously described as occurring in marine microalgae. The high selectivity toward molecular shape of this kind of stationary phase has enabled compounds of very similar structure, such as chlorophylls c₁, c₂ and Mg-divinylpheoporphyrin a₅ monomethyl ester, and chlorophyll a and the phytol-substituted chlorophyll c-like pigments, which commonly coelute on monomeric bonded phases, to be resolved in a single run. Some of these pigments, formerly thought to be a single compound, have, in fact, been demonstrated to be groups of two or more. The method has been successfully applied to both algal cultures and natural sea water samples. When visible light absorbance detection was used, the method proved suitable for separation of various carotenoids.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

New HPLC-chiral stationary phases for enantiomeric resolution of sulfoxides and selenoxides

Summary Enantiomers of several sulfoxides and some selenoxides can be easily separated by using a new chiral stationary phase (CSP-DACH-DNB) containing the 3,5-dinitrobenzoyl derivative of R,R-(-)1,2-diamino-cyclohexane as selector, covalently bonded to the siliceous matrix. The easy operative conditions and the high enantioselectivity values (α) allow a direct transfer of the analytical separations to a semi-preparative and preparative scale.     

High-Throughput Screening of Ten Microcystins and Nodularins, Cyanobacterial Peptide Hepatotoxins, by Reversed-Phase Liquid Chromatography-Electrospray Ionisation Mass Spectrometry

Liquid chromatography-electrospray ionisation mass spectrometry was evaluated in the high-throughput analysis of microcystins and nodularins, cyanobacterial peptide hepatotoxins. Extracts originating from cyanobacterial strains and field material were separated on a 30 mm × 4 mm I.D. Merck Purospher STAR RP-18e column using a rapid gradient of aqueous formic acid and acetonitrile, ionised by electrospray technique and analysed on a Micromass Quattro II triple-quadrupole mass spectrometer operated in the selected ion recording (SIR) mode. The total analysis time per sample was 2.8 min corresponding to 514 samples a day. The system showed good robustness during a series of 320 repetitive injections of a field sample containing three major microcystins.     

Chromatographic investigations of furocoumarins fromHeracleum genus fruits

Summary Furocoumarins from extracts ofHeracleum genus fruits were separated using normal and reversed phase TLC and HPLC and isolated in the milligram scale using overloaded systems of column chromatography. Binary or ternary solvents containing a polar modifier (methanol, diisopropyl ether or acetonitrile) were used as the mobile phases. Preliminary report on this work was presented at the 47th International Congress of Pharmaceutical Sciences of F.I.P. in Amsterdam. The Netherlands, 30 August–5 September 1987.     

Buckling of sandwich wide columns

The paper deals with the theoretical prediction of buckling loads for sandwich columns with metallic and laminated facings and foam or honeycomb core. The loading is a uniform axial compression, applied statically (very slowly) and suddenly with constant magnitude and infinite duration (step loading). The effect of length and boundary conditions is assessed and results are presented for the following cases: for a cantilever column, a simply supported column and a clamped column, for several lengths. Several fiber materials are used in the laminated facings. Two types of core were examined: alloy-foam or hexagonal glass/phenolic honeycomb. The facings are Boron/Epoxy, Graphite/Epoxy and Kevlar/Epoxy laminates with 0° orientation with respect to the column axis and a metallic one made out of aluminum. These various materials are employed to provide comparative data that can be used in design. Results, for the static case are generated by computer codes as well as by the use of closed form theoretical solutions. For the dynamic case, results are generated by the DYNA3D code.     

Separation of Monovinyl and Divinyl Protochlorophyllides Using C30 Reverse Phase High Performance Liquid Chromatography Column: Analytical and Preparative Applications

A new, high performance liquid chromatography method has been developed for the separation of monovinyl- and divinyl-protochlorophyllides, using commercially available, C₃₀ reverse phase column and isocratic elution. This method can be used both for analytical applications and preparative scale purification of monovinyl- and divinyl-protochlorophyllides using the same column where submilimolar concentrations of the crude protochlorophyllide extract can be separated in one run. The purity of the obtained protochlorophyllides was demonstrated by spectroscopic methods, as well by the formation of aggregates in toluene.