Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Tandem purification of mouse IgM monoclonal antibodies produced in vitro using anion-exchange and gel fast protein liquid chromatography

A tandem chromatographic procedure was used to isolate rapidly mouse IgM monoclonal antibodies produced by cultivation of hybridomas in vitro. Hybridoma culture supernatants containing mouse IgM monoclonal antibodies were first chromatographed on an anion-exchange Mono Q column connected to a fast protein liquid chromatography system. This anion-exchange step offers the advantage of obtaining IgM antibodies in a concentrated form. The IgM-rich fractions from the Mono Q column were then injected on a gel filtration Superose 6 column equilibrated with a low-ionic strength buffer and eluted with a high-ionic strength buffer. Assessment of the purity of isolated IgM monoclonal antibodies was performed by sodium dodecyl sulphate polyacrylamide gel electrophoresis together with a Coomassie Brillant Blue R 250 staining technique. Assessment of the immunoreactivity of isolated IgM monoclonal antibodies was performed by an enzyme linked immunosorbent assay using a solid phase adsorbed antigen against which IgM monoclonal antibodies were directed. The chromatographic procedures described allows the rapid isolation of mouse IgM monoclonal antibodies produced in vitro at a high degree of purity and in an immunoreactive state.     

Laser desorption of DNA oligomers larger than one kilobase from cooled 4-nitrophenol

A unique matrix system consisting mostly of 4-nitrophenol has shown to be very effective for matrix-assisted laser desorption/ionization time-of-flight mass spectrometric analysis of large DNA oligomers when a cooled sample stage was used to prevent the sublimation of this matrix under vacuum. Using this 4-nitrophenol matrix with UV laser desorption, detection of picomole quantities of DNA oligomers containing up to approximately 800 nucleotides was routinely achieved. The effectiveness of this matrix was further demonstrated by the observation of a double-stranded DNA oligomer larger than 1000 base pairs, seen as a denatured single-stranded species, with a molecular ion mass exceeding 300 000 Da. The potential applications of 4-nitrophenol as a matrix for DNA sizing are discussed.     

SPECTRA AND EXTINCTION COEFFICIENTS OF NEAR-INFRARED ABSORPTION BANDS IN MEMBRANES OF Rhodobacter sphaeroides MUTANTS LACKING LIGHT-HARVESTING AND REACTION CENTER COMPLEXES

Abstract— Membranes from Rhodobacter (formerly Rhodopseudomonas) sphaeroides mutant strains that lack one or more of the bacteriochlorophyll a (BChl)-protein complexes were used to obtain spectra and molar extinction coefficients of the near-IR absorption bands. The strains examined were NF57 which lacks the B875 light-harvesting and reaction center complexes, and M21 which lacks the B800–850light-harvesting complex. The extinction coefficients obtained for the B800, B850 and B875 bands were 226 ± 10, 170 ± 5, and 118 ± 5 m M ^-1cm^-1, respectively, in reasonable agreement with values reported for detergent-isolated complexes (Clayton, R. K. and B. J. Clayton, Proc. Natl. Acad. Sci. USA 78 ,5583–5587, 1981). The results also demonstrated that detergent solubilization altered the spectra, causing a band broadening on the blue side of the B875 and B800 peaks. The data obtained from the analysis of the mutant strains were used for deconvolution of the BChl species in membranes of the wild-type. A short BASIC computer program for performing this deconvolution is included.     

Multi-residue method for rapid screening and confirmation of pesticides in crude extracts of fruits and vegetables using isocratic liquid chromatography with electrospray tandem mass spectrometry

A LC-MS-MS method capable of the quantitative determination of a range of pesticide residues present in crude extracts from a variety of fruit and vegetables has been developed. Isocratic LC conditions have been used in conjunction with electrospray ionisation tandem mass spectrometry to detect and identify up to 38 pesticides presented as various mixtures in different matrices. The utility of the method is demonstrated by the analysis of crude extracts, with no sample clean up, from grape, kiwi fruit, strawberry, spinach, lemon, peach and nectarine. Mean recoveries ranging from 63 to 96% with relative standard deviations < 20% were obtained for 30 of the 38 pesticides following analysis of organic produce fortified at concentrations between 0.01 and 0.8 mg/kg. Detected residues were quantified from interpolation against calibration data generated using matrix-matched standards that covered analyte concentration ranges between 0.005 and 0.8 microg/ml. Conditions suitable for the qualitative and quantitative confirmation of residues detected in samples are specified.     

The relationship between the Ritz variational method and Frobenius's method of solving Schrödinger's equation

The solution of a linear homogeneous differential equation (in particular the Schrödinger equation) by expansion of the solutions (wave functions) in a discrete complete set of function is considered. The coefficients of the expansion are determinable by either the Ritz variational (integral) method, or by a generalisation of Frobenius's (non-integral) method. Each method leads to an infinite matrix eigenvalue equation. It is shown that the integral and non-integral matrix equations are related by the overlap matrix of the set of basis functions. The effects of truncating the infinite matrices to finite order are described. A hybrid method of transformation to a matrix representation is proposed, which employs some techniques from each of the original methods.

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Zusammenfassung Die Lösung einer linearen homogenen Differentialgleichung (besonders der Schrödinger-Gleichung) durch Entwicklung der Lösungen (Wellenfunktionen) nach einem diskreten vollständigen Satz von Funktionen wird untersucht. Die Entwicklungskoeffizienten sind entweder durch die Variations-Methode (Integral-Methode) oder durch Verallgemeinerung der Methode von Frobenius (Methode ohne Integrale) bestimmbar. Beide Methoden führen zur einer unendlichen Matrix-Eigenwert-Gleichung. Es wird gezeigt, daß die Matrizengleichungen der beiden Verfahren durch die Überlappungsmatrix des Satzes von Basisfunktionen in Beziehung stehen. Es werden die Effekte beschrieben, die sich ergeben, wenn die Matrizen von unendlicher auf endliche Ordnung reduziert werden. Eine Hybridmethode zur Transformation in eine Matrixdarstellung wird vorgeschlagen, die einige Rechenoperationen aus jeder der Originalmethoden anwendet.

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Résumé On considère la résolution d'une équation différentielle linéaire homogène (en particulier l'équation Schrödinger) en développant les solutions (fonctions d'ondes) dans un groupe discret complet de fonctions. Les coefficients du développement peuvent être déterminés par la méthode de la variation de Ritz (intégral) ou par une généralisation de la méthode de Frobenius (non-intégral). Chaque méthode mène à une équation infinie matrice eigenvalue. On montre que les équations matrice, intégrales et non-intégrales, sont reliées par la matrice à recouvrement du groupe des fonctions fondamentales. On décrit les effects de tronquer les matrices infinies en ordre limité. On présente une méthode hybride de transformation à une représentation de matrice, qui utilise des techniques de chacune des méthodes originales.

     

An NMR study of some substituted 1,5-benzodiazepines and 1,5-benzothiazepines

The ¹H NMR spectra of a series of substituted 1,5-benzodiazepines and thiazepines are analysed by the LAOCN3 fitting program. The saturated molecules appear to exist in puckered chair conformations. The effect of increasing methyl substitution is a reduction in the amount of puckering with a flattening of the chair. Symmetrical substitution of the heterocyclic rings allows a ready inversion at room temperature whereas asymmetrical substitution stabilises the least hindered conformation. Variable temperature measurements are reported.     

A note on the numerical evaluation of finite integrals of oscillatory functions

A method is described for the numerical evaluation of integrals of the form ∫ _?1 ¹ f(x)K(m,x)dx, wheref(x) is smooth in [?1,1], whileK(m,x) is highly oscillatory for large values ofm.