Pathology of infinite systems of linear first order differential equations with constant coefficients

Summary The properties of solutions of finite systems are analyzed and it is shown by examples how these properties may be distorted and ultimately lost in passing from finite to infinite systems. To Enrico Bompiani on his Scientific Jubilee This research was supported in part by United States Army through its Office of Ordnance Research under Grant DA-ORD-12. — Most of the results have been presented to various organisations such as Section A of the American Association for the Advancement of Science and mathematics colloquia at the universities of Leningrad, Moscow, and Toronto.     

Mass spectrometry of onium compounds—XX: Ionisation potential in structural assignment of some gaseous molecules

The ionisation potentials for a series of thiazolo[3,2-a]pyridinium-3-oxides are reduced by about 1.7 to 1.8eV on introduction of an 8-OH group. The gaseous species from the former compounds are ascribed a mesoion, structure while the hydroxy-derivatives are rearranged to non charged molecules.     

A domain embedding preconditioner for the Lagrange multiplier system

Finite element approximations for the Dirichlet problem associated to a second-order elliptic differential equation are studied. The purpose of this paper is to discuss domain embedding preconditioners for discrete systems. The essential boundary condition on the interior interface is removed by introducing Lagrange multipliers. The associated discrete system, with a saddle point structure, is preconditioned by a block diagonal preconditioner. The main contribution of this paper is to propose a new operator, constructed from the -inner product, for the block of the preconditioner corresponding to the multipliers.

     

Models of fragmentations induced by electron attachment to protonated peptides

Invoking a number of theoretical levels ranging from HF/STO-3G to CCSD(T)/aug-cc-pVQZ, we have made a detailed survey of six potential energy surfaces (NH4+, NH4*, [CH3CONHCH3]H+, [CH3CONHCH3]H*, [HCONHCH2CONH2]H+, [HCONHCH2CONH2]H*). In conjunction with this, ab inito direct dynamics calculations have been conducted, tracing out several hundred reaction trajectories to reveal details of the electron-capture dissociation mechanism. The model calculations suggest the possibility of a bimodal pattern where some of the radicals, formed upon recombination, dissociate almost directly within one picosecond, the remaining radicals being subject to complete energy redistribution with a subsequent dissociation occurring at the microsecond timescale. Both processes give rise to c and z backbone fragments, resulting from cleavage of N-Calpha bonds of the peptide chain.     

Proton mobility and stability of water clusters containing the bisulfate anion, HSO4(-)(H2O)n

Bisulfate water clusters, HSO(4)(-)(H(2)O)(n), have been studied both experimentally by a quadrupole time-of-flight mass spectrometer and by quantum chemical calculations. For the cluster distributions studied, there are some possible "magic number" peaks, although the increase in abundance compared to their neighbours is small. Experiments with size-selected clusters with n = 0-25, reacting with D(2)O at a center-of-mass energy of 0.1 eV, were performed, and it was observed that the rate of hydrogen/deuterium exchange is lower for the smallest clusters (n < 8) than for the larger (n > 11), with a transition taking place in the range n = 8-11. We propose that the protonic defect of the bisulfate ion remains rather stationary unless the degree of hydration reaches a given level. In addition, it was observed that H/D scrambling becomes close to statistically randomized for the larger clusters. Insight into this size dependency was obtained by B3LYP/6-311++G(2d,2p) calculations for HSO(4)(-)(H(2)O)(n) with n = 0-10. In agreement with experimental observations, these calculations suggest pronounced effectiveness of a 'see-saw mechanism' for pendular proton transfer with increasing HSO(4)(-)(H(2)O)(n) cluster size.     

Spectroscopic Identification of a Bidentate Binding Motif in the Anionic Magnesium–CO2 Complex ([ClMgCO2]−)

A magnesium complex incorporating a novel metal–CO₂ binding motif is spectroscopically identified. Here we show with the help of infrared photodissociation spectroscopy that the complex exists solely in the [ClMg(η²‐O₂C)]^? form. This bidentate double oxygen metal–CO₂ coordination has previously not been observed in neutral nor in charged unimetallic complexes. The antisymmetric CO₂ stretching mode in [ClMg(η²‐O₂C)]^? is found at 1128 cm^?1, which is considerably redshifted from the corresponding mode in bare CO₂ at 2349 cm^?1, suggesting that the CO₂ moiety has a considerable negative charge (～1.8 e^?). We also employed electronic structure calculations and kinetic analysis to support the interpretation of the experimental results.     

Electrokinetic migration of acidic drugs across a supported liquid membrane

Electrokinetic cross membrane extraction of acidic drugs was demonstrated for the first time. The acidic drugs were extracted from an alkaline aqueous donor solution (300 microl), through a thin supported liquid membrane of 1-heptanol sustained in the pores of the wall of a porous hollow fiber, and into an aqueous alkaline acceptor solution (30 microl) present inside the lumen of the hollow fiber by the application of a d.c. electrical potential. The negative electrode was placed in the donor solution, and the positive electrode was placed in the acceptor solution. Optimal extractions were accomplished with 1-heptanol as the supported liquid membrane, with 50 V as the driving force, and with pH 12.0 in both the donor and acceptor solutions, respectively (NaOH). Equilibrium extraction conditions were obtained after 5 min of operation with the whole assembly agitated at 1200 rpm. Eleven different acidic drugs were extracted with recovery values between 8 and 100%, and initial data supported that electrokinetic cross membrane extraction provided repeatable data and linear response between original donor concentration and final acceptor concentration of the acidic model compounds.     

Structure elucidation of unsaturated fatty acids after vicinal hydroxylation of the double bonds by negative electrospray ionisation low-energy tandem mass spectrometry

A method for determining the positions of double bonds in unsaturated fatty acids by use of negative electrospray ionisation low-energy tandem mass spectrometry is described. First, a vicinal hydroxylation of the double bonds of mono- and poly-unsaturated fatty acids was performed. Low-energy collision activation dissociation of the deprotonated molecules produced structurally informative ions formed by a-cleavages relative to the hydroxyl groups. Abundant fragment ions that confirmed the positions of all hydroxyl groups, and thus the positions of the double bonds in the native fatty acids, were observed in the spectra of derivatised mono-, di-, and tri-unsaturated fatty acids. Two types of ions were observed, called [alpha'(n)](-) and [alpha(n)](-). The letter n indicates the positions of the hydroxyl groups. The structurally diagnostic ions [alpha'(n)](-) were produced by cleavages distal to the hydroxyl-groups with the charge retained on the carboxylate. [alpha'(n)](-) ions originating from all hydroxyl-groups were observed in the spectra of modified mono-, di-, and tri-unsaturated fatty acids. Initial proton transfer of a hydroxyl proton to the carboxylate with subsequent cleavages proximal to the hydroxyl groups, relative to the carboxylate, resulted in the two structurally diagnostic [alpha(n)](-) ions. In hydroxylated fatty acids having two or more double bonds in their native structure, [alpha(n)](-) ions originating only from the two final hydroxyl-groups were observed. The formation of all ions of [alpha'(n)](-) and [alpha(n)](-) type can be rationalised by a six-membered transition state. Hydroxylated deprotonated tetra-, penta-, and hexa-unsaturated fatty acids also produced [alpha'(n)](-) ions indicating the positions of most of the hydroxyl-groups, whereas the [alpha(n)](-) ions were observed as described above. The method described offers a simple approach to the determination of the positions of double bonds in unsaturated fatty acids, and is an alternative to utilising di-lithiated fatty acids. The method should also be applicable when fatty acids are constituents of more complex molecules such as phospholipids.     

Kinetic aspects of hollow fiber liquid-phase microextraction and electromembrane extraction

In this paper, extraction kinetics was investigated experimentally and theoretically in hollow fiber liquid-phase microextraction (HF-LPME) and electromembrane extraction (EME) with the basic drugs droperidol, haloperidol, nortriptyline, clomipramine, and clemastine as model analytes. In HF-LPME, the analytes were extracted by passive diffusion from an alkaline sample, through a (organic) supported liquid membrane (SLM) and into an acidic acceptor solution. In EME, the analytes were extracted by electrokinetic migration from an acidic sample, through the SLM, and into an acidic acceptor solution by application of an electrical potential across the SLM. In both HF-LPME and EME, the sample (donor solution) was found to be rapidly depleted for analyte. In HF-LPME, the mass transfer across the SLM was slow, and this was found to be the rate limiting step of HF-LPME. This finding is in contrast to earlier discussions in the literature suggesting that mass transfer across the boundary layer at the donor–SLM interface is the rate limiting step of HF-LPME. In EME, mass transfer across the SLM was much more rapid due to electrokinetic migration. Nevertheless, mass transfer across the SLM was rate limiting even in EME. Theoretical models were developed to describe the kinetics in HF-LPME, in agreement with the experimental findings. In HF-LPME, the extraction efficiency was found to be maintained even if pH in the donor solution was lowered from 10 to 7–8, which was below the pK_a-value for several of the analytes. Similarly, in EME, the extraction efficiency was found to be maintained even if pH in the donor solution increased from 4 to 11, which was above the pK_a-value for several of the analytes. The two latter experiments suggested that both techniques may be used to effectively extract analytes from samples in a broader pH range as compared to the pH range recommended in the literature.