Sodiation as a tool for enhancing the diagnostic value of MALDI‐TOF/TOF‐MS spectra of complex astaxanthin ester mixtures from Haematococcus pluvialis

The microalga Haematococcus pluvialis produces the pigment astaxanthin mainly in esterified form with a multitude of fatty acids, which results in a complex mixture of carotenol mono‐ and diesters. For rapid fingerprinting of these esters, matrix‐assisted laser desorption ionization time of flight mass spectrometry (MALDI‐TOF/TOF‐MS) might be an alternative to traditional chromatographic separation combined with MS. Investigation of ionization and fragmentation of astaxanthin mono‐ and diester palmitate standards in MALDI‐TOF/TOF‐MS showed that sodium adduct parent masses [M + Na]⁺ gave much simpler MS² spectra than radical / protonated [M]^+● / [M + H]⁺ parents. [M + Na]⁺ fragments yielded diagnostic polyene‐specific eliminations and fatty acid neutral losses, whereas [M]^+● / [M + H]⁺ fragmentation resulted in a multitude of non‐diagnostic daughters. For diesters, a benzonium fragment, formed by polyene elimination, was required for identification of the second fatty acid attached to the astaxanthin backbone. Parents were forced into [M + Na]⁺ ionization by addition of sodium acetate, and best signal‐to‐noise ratios were obtained in the 0.1 to 1.0 mM range. This method was applied to fingerprinting astaxanthin esters in a crude H. pluvialis extract. Prior to MALDI‐TOF/TOF‐MS, the extract was fractionated by normal phase Flash chromatography to obtain fractions enriched in mono‐ and diesters and to remove pheophytin a, which compromised monoester signals. All 12 types of all‐trans esterified esters found in LC were identified with MALDI‐TOF/TOF‐MS, with the exception of two minor monoesters. Copyright © 2013 John Wiley & Sons, Ltd.     

A pulse sequence for averaging the strong homonuclear scalar coupling in AB spin systems

A pulse sequence is proposed for the suppression of the strong homonuclear scalar coupling in the case of AB spin systems. The theoretical treatment is presented in terms of the average Hamiltonian theory in the case of aperiodic perturbations. The zero-order and the first-order correction terms in the full average Hamiltonian are calculated. It is shown that the chemical shift interaction for one of the spins is completely refocused and the conditions in which the interactions bilinear in spin operators are efficiently suppressed are analyzed.     

Unbounded divergence of simple quadrature formulas

Given a sequence of real or complex coefficients c_i and a sequence of distinct nodes t_i in a compact interval T, we prove the divergence and the unbounded divergence on superdense sets in the space C(T) of the simple quadrature formulas ∝_Tx(t)du(t) = Q_n(x) + R_n(x) and ∝_Tw(t)x(t)dt = Q_n(x) + R_n(x), where Q_n(x)=∑_i=1^m_n c_ix(t_i), ε C(T).The divergence (not certainly unbounded) for at most one continuous function of the first simple quadrature formula, with m_n = n and u(t) = t, was established by P. J. Davis in 1953.     

Effect of the interface on separation in multicapillary gas chromatography-based hyphenated techniques for speciation analysis of organometallic compounds

This paper reports the effect of transfer line (TL) internal diameter (i.d.) on gas chromatographic separation characteristics such as efficiency and speed, when a multicapillary (MC) column is used for speciation analysis of mercury. Five different TL consisting of fused-silica capillaries with 0.15, 0.20, 0.25, 0.32, and 0.53 mm i.d. are compared. The separation efficiency and total chromatographic run time are critically affected by the i.d. of the TL. Narrow capillaries (i.d.0.20 mm) produce minimum peak dispersion whereas wide capillaries result in narrow peaks and shorter chromatographic analysis times. A thermodynamic approach is proposed to describe the motion of the analytes through the separation column and TL. The model provides good agreement with the experimental data for high pressures (35 psig) and wide TL (0.25 mm i.d.).Dedicated to the memory of Wilhelm Fresenius     

A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems

We study the approximation of a multiscale reaction–diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro–macro flux conditions. Our target system has a typical structure for reaction–diffusion flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally e?cient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a fine bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions.     

Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits

This paper studies the distribution of particular weighted sums of Bernoulli random variables. The computing methods are applied to derive the probability distribution of the random amount of survivor credits to be shared among surviving participants in single-period tontine schemes. The effectiveness of this new arrangement can then be evaluated beyond the classical analysis based on crude approximations for the two first moments, only.