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.     

Single-molecule single crystals

Various approaches to the preparation and verification of single-molecule single crystals are discussed for polyethylene and poly (oxyethylene). Analytic tools are electron microscopy, electron diffraction, and differential scanning calorimetry. The main difficulty in producing a single-molecule single crystal is to keep crystals from joining during growth.     

Ramsey numbers for graphs with five vertices

The Ramsey numbers r(F¹, F²) are tabulated for essentially all but six pairs of graphs F¹ and F² with five vertices.     

Thermal addition of dibenzoylacetylene to cycloheptatriene and the photo-rearrangement of the thermal adduct

The reaction of cycloheptatriene (CHT) with dibenzoylacetylene (DBA), in refluxing toluene gave a mixture of products consisting of 6,7-dibenzoyltricyclo[3.2.2.0^2.4]nona-6,8-diene 6 and 3,4-dibenzoylbicyclo [3.2.2]nona-2,6,8-triene 7. Neat heating of a mixture of CHT and DBA around 95–100° gave besides, 6 and 7, small amounts of two dimers of DBA. Photolysis of 6 in benzene solution gave a lactonic, rearrangement product. 25. The structures of the various products have been established and reasonable mechanisms for their formation have been suggested.     

A convenient synthesis of cis and trans 4-tert-butoxycarbonyl-substituted cyclohexylglycine

A novel synthesis of cis and trans substituted 4-tert-butoxycarbonyl cyclohexylglycines via asymmetric aminohydroxylation of vinyl styrene followed by reduction of the aromatic ring and subsequent oxidation is reported.     

Mass spectrometric investigation of bimolecular compounds

Two points involving molecular structure have been investigated using mass spectrometry. First, mass spectra have been obtained that indicate a rapid means for differentiating bimolecular compounds from other structural isomers. Second, the mass spectrometric method has been used to evaluate bonding within bimolecular compounds. Quinone compounds have been reacted with dhydroxybenzene compounds to produce quinhydrone products, and upon mass spectrometric analysis, the quinhydrones decompose to regenerate derivatives of the starting materials. Evaluation of the decomposition products suggests that the hydroxyl hydrogens are involved in a resonance structure, and while in symmetrical quinhydrones, the hydroxyl hydrogens are probably associated equally with each reactant, unsymmetrical quinhydrones generate an unbalanced electronic distribution that eliminates the complete equivalency of the hydrogens.     

Electron-capture negative ionization calibrants for magnetic sector mass spectrometers

Fomblin [poly(perfluoropropylene oxide)], PFK (perfluorokerosene) and FC-43 (perfluorotributylamine) are investigated as mass calibrants in electron-capture negative ionization mass spectrometry on a magnetic sector hybrod mass spectrometer. This work provides exact negative ion mass tables of these three calibrants obtained using high-resolution peak matching of representative ions of the calibrants against ions of known mass. The suitability of these calibrants for full data system control in the negative ionization mode is demonstrated for the techniques of high-resolution scanning, selected ion recording and calibration of the quadrupole sector of a hybrid instrument.     

Self-assembling structures of long-chain phenyl glucoside influenced by the introduction of double bonds

Four long-chain phenyl glucoside amphiphiles possessing a saturated or unsaturated long alkyl chain group as the self-assembling unit of a highly organized molecular architecture were synthesized. Their self-assembling properties were investigated by EF-TEM, SEM, CD, FT-IR, and XRD. Compound 2 possessing one double bond in the lipophilic portion showed twisted helical fibers, which formed a bilayered structure with a 3.59 nm period, while compound 3 showed the helical ribbons and left-handed nanotubular structures with 150-200 nm inner diameters and ca. 20 nm of wall. Very interestingly, compound 4 possessing three double bonds showed a nanotubular structure with ca. 70 nm of inner diameter through a helical ribbon, which formed a loose bilayered structure with 4.62 nm. These results indicate that self-assembling properties strongly depend on the number of cis double bonds.     

Diels-Alder reactions of quinol lactones: a change of regioselectivity with stannic chloride catalysis

Lewis acid-mediated Diels-Alder reactions of quinol lactone 2 gave regioselectivity opposite to that of the uncatalyzed reaction. Compound 12 is proposed as the reactive intermediate generated by the reaction of 2 with stannic chloride.