Mass spectrometric detection in narrow-bore (0.10 mm i.d.) capillary chromatography fast, sensitive and selective analysis of polychlorinated biphenyls

The combination of narrow-bore capillary gas chromatography with bench-top quadrupole mass spectrometric detection was evaluated for the determination of polychlorinated biphenyls (PCBs). The qualitative and quantitative performances of the system are illustrated by several analyses (PCB standards and human milk extracts). Capillary columns with different internal diameters (0.10, 0.18 and 0.22 mm, respectively) were compared for their ability to separate PCB congeners and the analysis time. Short run times (less than 7 min) were sufficient for complete separation of PCB congeners on a 0.10-mm internal diameter (I.D.) capillary column without any loss of resolution when compared with a 0.22 mm I.D. column. Good qualitative and quantitative data acquisition was possible with quadrupole mass spectrometer for run times of 8 min, but incomplete peak reading was observed when run times were reduced to 3-4 min. Selected ion monitoring and dwell times of 10 ms are necessary to obtain detection limits for individual PCB congeners as low as 0.4 pg microl(-1) for standard solutions and 0.2 ng g(-1) fat for milk extracts. By using cold splitless injection, relatively high volumes (1 microl) for narrow-bore capillaries could be injected without any peak distortion.     

A solid-state NMR study of the fast and slow dynamics of collagen fibrils at varying hydration levels

We report solid-state NMR investigations of the effect of temperature and hydration on the molecular mobility of collagen isolated from bovine achilles tendon. (13)C cross-polarization magic angle spinning (MAS) experiments were performed on samples at natural abundance, using NMR methods that detect motionally averaged dipolar interactions and chemical shift anisotropies and also slow reorientational processes. Fast motions with correlation times much shorter than 40 micro s scale dipolar couplings and chemical shift anisotropies of the carbon sites in collagen. These motionally averaged anisotropic interactions provide a measure of the amplitudes of the segmental motions expressed by a molecular order parameter. The data reveal that increasing hydration has a much stronger effect on the amplitude of the molecular processes than increasing temperature. In particular, the Cgamma carbons of the hydroxyproline residues exhibit a strong dependence of the amplitude of motion on the hydration level. This could be correlated with the effect of hydration on the hydrogen bonding structure in collagen, for which this residue is known to play a crucial role. The applicability of 1D MAS exchange experiments to investigate motions on the millisecond time-scale is discussed and first results are presented. Slow motions with correlation times of the order of milliseconds have also been detected for hydrated collagen.     

Gas chromatography–ion trap tandem mass spectrometry method for the analysis of methoxylated polybrominated diphenyl ethers in fish

Gas chromatography coupled to ion trap tandem mass spectrometry (GC–ITMS-MS) is proposed for the analysis of methoxylated polybrominated diphenyl ethers (MeO-PBDEs) in fish and shellfish. MS–MS operating parameters related to the isolation and fragmentation of the precursor ions were optimized to achieve maximum sensitivity and selectivity. This new method allows the determination of both MeO-PBDEs and PBDEs in a single run. Low limits of detection (0.4–2.5 pg injected) and high precision (RSD < 13%) were achieved. A sample treatment based on a selective pressurized liquid extraction (PLE) using Florisil as fat retainer was applied for the analysis of these compounds in fish samples. Method limits of quantification ranged from 0.11 to 0.95 ng g⁻¹ lipid weight for MeO-PBDEs and between 0.18 and 0.50 ng g⁻¹ lipid weight for PBDEs. In addition, good repeatability of the whole method was achieved (RSD < 15%). The suitability of the method was evaluated by analyzing a certified reference material (SRM 1945, whale blubber) with satisfactory results. The developed method was applied to the simultaneous analysis of MeO-PBDEs and PBDEs in fish and shellfish samples from the Mediterranean Sea.     

The Computational Complexity of Extrapolation Methods

This paper analyzes the cost of extrapolation methods for non-stiff ordinary differential equations depending on the number of digits of accuracy requested. Extrapolation of the explicit midpoint rule is applied for various number sequences. We show that for sequences with arithmetic growth, the cost of the method is polynomial in the number of digits of accuracy, while for sequences of numbers with geometric growth, the cost is super-polynomial with respect to the same parameter.     

Two fixed point theorems for generalized contractions with constants in complete metric space

In this paper we prove two fixed point theorems for generalized contractions with constants in complete metric space, which are generalizations of very recent results of Kikkawa and Suzuki.      

Polynomial cost for solving IVP for high-index DAE

We show that the cost of solving initial value problems for high-index differential algebraic equations is polynomial in the number of digits of accuracy requested. The algorithm analyzed is built on a Taylor series method developed by Pryce for solving a general class of differential algebraic equations. The problem may be fully implicit, of arbitrarily high fixed index and contain derivatives of any order. We give estimates of the residual which are needed to design practical error control algorithms for differential algebraic equations. We show that adaptive meshes are always more efficient than non-adaptive meshes. Finally, we construct sufficiently smooth interpolants of the discrete solution. AMS subject classification (2000) 34A09, 65L80, 68Q25     

Adaptivity and computational complexity in the numerical solution of ODEs

In this paper we analyze the problem of adaptivity for one-step numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating grids of minimal computational cost for which the local error is below a prescribed tolerance (optimal grids). The grids are generated by introducing an auxiliary independent variable τ and finding a grid deformation map, t=Θ(τ), that maps an equidistant grid {τ_j} to a non-equidistant grid in the original independent variable, {t_j}. An optimal deformation map Θ is determined by a variational approach. Finally, we investigate the cost of the solution procedure and compare it to the cost of using equidistant grids. We show that if the principal error function is non-constant, an adaptive method is always more efficient than a non-adaptive method.     

CONTRA: improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems.     

Lyapunov pairs for multi-valued semi-linear evolutions

We give here a characterization of a Lyapunov pair for a multi-valued semi-linear evolution equation on a Banach space by means of an appropriate lower contingent derivative. The contingent derivative introduced in this paper is related to a new concept of tangency introduced recently in [O. Cârj?, M. Necula, I.I. Vrabie, Necessary and sufficient conditions for viability for semilinear differential inclusions, Trans. Amer. Math. Soc. 361 (2009) 343-390]. As an application, we give a controllability result and a Lipschitz estimate of the corresponding minimum time function under a Petrov-like condition.