Efficient polynomial reduction

H-bases are bases for polynomial ideals, characterized by the fact that their homogeneous leading terms are a basis for the associated homogeneous ideal. In the computation ofH-bases without term orders, an important task is to determine the orthogonal projection of a homogeneous polynomial to certain subspaces of homogeneous polynomials with respect to a given inner product. One way of doing so is to use an orthogonal basis of the subspace. In this paper, we present and study a method to efficiently compute such a basis for a particular but important inner product.     

Distribution of the inter and intra inertia in conditional MCA

Conditional Multiple Correspondence Analysis (MCA), where a control variable plays the role of a partition model, allows us to decompose global inertia into between inertia and within inertia. The problem is to assess when the conditioning variable gives different results with respect to the unconditional analysis. In this paper, we study the asymptotic distribution function of these inertias, which can allow us to determine whether conditioning is significant. Some simulations were performed to corroborate the established results.     

Repetition of chemistry from a recently retracted paper. A cautionary note

The base-catalyzed condensation reaction between (E)-4-phenylbut-2-enal and phenylpropargyl aldehyde recently reported in the literature to provide formylcyclobutadiene was repeated under the published conditions. The product obtained was identified as (E)-5-phenyl-2-((E)-styryl)pent-2-en-4-ynal rather than the reported 2-phenyl-3-styrylcyclobutadiene-1-carboxaldehyde. The structure assignment is supported by NMR and IR data and a x-ray structure of the crystalline alcohol obtained by Luche reduction.     

Protonation and deprotonation of hydroxamic acids. An MO ab initio study

Ab initio molecular orbital calculations with 4-31G//4-31G, 6-31G^*//4-31G and 6-31+G//4-31G basis sets have been used to examine the structure, relative energy, protonation and deprotonation of a series of seven hydroxamic acids in the gas phase. The results show that hydroxamic acids are predominantly in the E-TS form and that the most probable protonation site is the carbonyl oxygen atom, while deprotonation proceeds by loss of NH hydrogen.     

Synthesis,structure, and biological evaluation of novel N- and O-linked diinositols

Several O-and N-linked inositols and/or aminoinositols have been prepared by iterative opening of epoxides and aziridines derived from homochiral cyclohexadiene cis-diols. The three inositols and their intermediate conduritols (conduramines) were tested against several glycosidases (alpha- and beta-glucosidase, alpha- and beta-galactosidase, alpha- and beta-mannosidase) in an assay that measured the rate of hydrolysis of p-nitrophenolglycosides rather than the concentration of p-nitrophenolate. Somewhat surprisingly, the best inhibition was seen against beta-galactosidase with several of the compounds. The inositols linked through oxygen or nitrogen were subjected to calcium binding studies performed in NMR experiments. Detailed analysis of the title compounds by NMR spectroscopy has been performed, and full assignments were made. One of the attendant benefits of the preparation of these compounds has been expressed in the design and synthesis of new salen catalysts whose effectiveness has been compared with Jacobsen's catalyst in the epoxidation of styrene.     

The resolution of chromatograms with overlapping peaks by means of different statistical functions

The effectiveness of diverse functions of statistical distribution (log—normal, gamma and Weibull) is examined for the elucidation of chromatograms with overlapping peaks. A Gauss function and a modified Gauss function are used for comparison with the results obtained by the other functions. The generalized least-squares method is applied for adjustment; this is done automatically by the specially designed DAFNA program written in Fortran IV. The use of those functions in the resolution of experimental chromatograms is preceded by an outline of the difficulties involved in the elucidation of overlapping profiles.     

Closely spaced external standard: a universal method of achieving 5 ppm mass accuracy over the entire MALDI plate in axial matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Close deposition of the sample and external standard was used in axial matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) to achieve mass accuracy equivalent to that obtained with an internal standard across the entire MALDI plate. In this work, the sample and external standard were deposited by continuous deposition in separate traces, each approximately 200 micro m wide. The dependence of the mass accuracy on the distance between the sample and standard traces was determined across a MALDI target plate with dimensions of 57.5 mm x 57.0 mm by varying the gap between the traces from 100 micro m to 4 mm. During acquisition, two adjacent traces were alternately irradiated with a 200-Hz laser, such that the peaks in the resulting mass spectra combined the sample and external standard. Ion suppression was not observed even when the peptide concentrations in the two traces differed by more than two orders of magnitude. The five peaks from the external standard trace were used in a four-term mass calibration of the masses of the sample trace. The average accuracy across the whole plate with this method was 5 ppm when peaks of the sample trace had signal-to-noise ratios of at least 30 and the gap between the traces was approximately 100 micro m. This approach was applied to determining peptide masses of a reversed-phase liquid chromatographic (LC) separation of a tryptic digest of beta-galactosidase deposited as a long serpentine trace across the MALDI plate, with accuracy comparable to that obtainable using internal calibration. In addition, the eluent from reversed-phase LC separation of a strong cation-exchange fraction containing tryptic peptides from a yeast lysate along with the closely placed external standard was deposited on the MALDI plate. The data obtained in the MS and MS/MS modes on a MALDI-TOF/TOF mass spectrometer were combined and used in database searching with MASCOT. Since the significant score is a function of mass accuracy in the MS mode, database searching with high mass accuracy reduced the number of false positives and also added peptides which otherwise would have been eliminated at lower mass accuracy (false negatives).