Improved Gram–Schmidt Type Downdating Methods

The problem of deleting a row from a Q–R factorization (called downdating) using Gram–Schmidt orthogonalization is intimately connected to using classical iterative methods to solve a least squares problem with the orthogonal factor as the coefficient matrix. Past approaches to downdating have focused upon accurate computation of the residual of that least squares problem, then finding a unit vector in the direction of the residual that becomes a new column for the orthogonal factor. It is also important to compute the solution vector of the related least squares problem accurately, as that vector must be used in the downdating process to maintain good backward error in the new factorization. Using this observation, new algorithms are proposed. One of the new algorithms proposed is a modification of one due to Yoo and Park [BIT, 36:161–181, 1996]. That algorithm is shown to be a Gram–Schmidt procedure. Also presented are new results that bound the loss of orthogonality after downdating. An error analysis shows that the proposed algorithms’ behavior in floating point arithmetic is close to their behavior in exact arithmetic. Experiments show that the changes proposed in this paper can have a dramatic impact upon the accuracy of the downdated Q–R decomposition. AMS subject classification (2000) 65F20, 65F25     

Basic topological and geometric properties of Cesàro-Orlicz spaces

Necessary and sufficient conditions under which the Cesàro-Orlicz sequence spaceces _ϕ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spacesces _ϕ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements inces _ϕ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spacesces _ϕ are given.     

The mass spectra of some selenoureas and selenothiocarbamic esters

The mass spectra of five selenoureas and two selenothiocarbamic esters are reported and discussed. Fragmentation modes are compared with those reported for the ureas, thioureas, carbamates and thiocarbamates.     

The mass spectrometric fragmentation patterns of some biologically active 1,3,4-thiadiazoles

Mass spectra of some twelve derivatives of 1,3,4-thiadiazole are reported. The fragmentation scheme of the 1,3,4-thiadiazole ring is specific and indicative as to the structure. Derivatives of 5-phenyl-1,3,4-thiadiazoles show rearrangement to isothiocyanates.     

2,6-Dialkoxy-7-methylpurines

The preparation of unsymmetrical 2,6-dialkoxy-7-methylpurines (2), and 2-alkoxy-1,7-dialkyl-6-oxo-1,6-dihydropurines (5) is described. In contrast to1 and2, a facile thermal lactim-lactam rearrangement from hypoxanthines5 and7 into xanthines6 was observed.

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2,6-Dialkoxy-7-methylpurine

Zusammenfassung Die Darstellung von unsymmetrischen 2,6-Dialkoxy-7-methylpurinen (2) und 2-Alkoxy-1,7-dialkyl-6-oxo-1,6-dihydropurinen (5) wird beschrieben. Im Gegensatz zu den Verbindungen1 und2 erfolgt die thermische Lactim-Lactam-Umlagerung der Hypoxanthine5 und7 zu den Xanthinen6 glatt.

     

Radioactivity of honey from northern Poland

This work shows significant variations in the values of ²¹⁰Po in different analyzed Polish voivodeships. Statistical analysis of ²¹⁰Po activity concentrations in honey samples showed significant differences between place of honey collecting, kind of honey and morphological structure of plants from which bees collected nectar.

     

The mass spectra of halogeno derivatives of quinoxaline

The mass spectra of seventeen different quinoxaline halogeno derivatives are reported. The fragmentation mechanism is discussed.     

Bioaccumulation of uranium 234U and 238U in marine birds

In the paper was presented results of our study about uranium ²³⁴U and ²³⁸U radioactivity in the marine birds samples, collected in the Polish area of the southern Baltic Sea. We chose 11 species of sea birds: three species permanently residing at southern Baltic, four species of wintering birds and three species of migrating birds. The obtained results indicated that uranium is very irregularly distributed in organs and tissues of marine birds. The highest uranium content is characterized in liver, rest of viscera and feathers, the smallest in skin and muscles. The uranium concentration was higher for carnivorous species (long-tailed duck (C. hyemalis), common eider (S. mollissima), lower for species eating fish (great cormorant (P. carbo), common guillemot (U. aalge), red-throated diver (G. stellata) and razorbill (A. tarda)), but the biggest amounts for herbivorous species [tufted duck (A. fuligula) and eurasian coot (F. atra)]. About 63–67% of uranium, which was located in feathers of two species of marine birds: razorbill (A. tarda) and long-tailed duck (C. hymealis), was apparently adsorbed, which suggests that uranium adsorption on the feathers may be an important transfer from air to water.