Negative ion mode matrix-assisted laser desorption/ionisation time-of-flight mass spectrometric analysis of oligosaccharides using halide adducts and 9-aminoacridine matrix

9-Aminoacridine was established as a matrix for the detection of neutral oligosaccharides in negative ion mode matrix-assisted laser desorption/ionisation time-of-flight (MALDI-TOF) mass spectrometry. Sodium iodide proved to be a useful additive inducing formation of stable iodide adducts of the analytes, in particular for oligosaccharides with a degree of polymerisation (DP) of three and higher. Lower oligomers (DP <3) and monosaccharides show more stable adducts with chloride ions. After optimisation of the sample preparation procedure, limits of quantitation were determined for alpha-cyclodextrin and cellopentaose at 7 and 13 pmol, respectively, with a linear detector response over two concentration orders. The iodide additive could be successfully employed on MALDI-TOF mass spectrometers with vacuum and atmospheric pressure ion sources. The value of the new method to solve biological problems has been demonstrated by the analysis of a mixture of beta-glucane elicitors isolated from the cell walls of Phytophthora sojae.     

A conjugate-gradient optimization method invariant to nonlinear scaling

A conjugate-gradient optimization method which is invariant to nonlinear scaling of a quadratic form is introduced. The technique has the property that the search directions generated are identical to those produced by the classical Fletcher-Reeves algorithm applied to the quadratic form. The approach enables certain nonquadratic functions to be minimized in a finite number of steps. Several examples which illustrate the efficacy of the method are included.     

Stereospezifische Synthese cis/trans-disubstituierter Tetrahydrofurane

Multifidene 1 is a chemical messenger for male gametes of the brown alga Cutleria multifida. The synthesis of messenger analogues with a tetrahydrofurane ring will be reported. The general synthetic approach offers the possibility to prepare a great variety of stereospecific 2,3- and 3,4-cis/trans-disubstituted tetrahydrofurans.     

The numerical solution of fredholm integral equations with rapidly varying kernels

Approximating a solution to the Fredholm integral equation ø(x)=α(x) + ∫ ^b_aK(x, y)ø(y) dy by the Nyström method involves some numerical quadrature for approximating the integral, producing a linear system satisfied by approximate function values of ø. This paper discusses the use of generalized product-interpolatory formulas which model ø as one mth-degree polynomial on each subinterval and model K as a (possibly large) sequence of nth-degree polynomials. In cases where K is varying much more rapidly than ø this allows for ø to be sampled much less often than K. Since K is modeled as a sequence of polynomials, its frequent sampling does not require a prohibitive increase in the degree of the interpolating polynomials. Coefficient formulas and examples are given for the (m,n) cases (1,1), (1,2), (2,1) and (2,2).     

Product type quadrature formulas

This paper is concerned with the numerical approximation of integrals of the form _a ^b f(x)g(x)dx by means of a product type quadrature formula. In such a formula the functionf (x) is sampled at a set ofn+1 distinct points and the functiong(x) at a (possibly different) set ofm+1 distinct points. These formulas are a generalization of the classical (regular) numerical integration rules. A number of basic results for such formulas are stated and proved. The concept of a symmetric quadrature formula is defined and the connection between such rules and regular quadrature formulas is discussed. Expressions for the error term are developed. These are applied to a specific example.The work of the first author was supported in part by NIH Grant No. FRO 7129-01 and that of the second author in part by U.S. Army Ballistic Research Laboratories Contract DA-18-001-AMC-876 X.