A uniform asymptotic expansion for the Jacobian elliptic functions n(u,k)

The usual two term approximation for the Jacobian elliptic functions n (u, k) when the modulusk is close to unity (see for example [3], [4], [5]) is shown to be nonuniform when |u|K, whereK is the quarter period. The nonuniformity is shown to be weak, with the remainder term becoming of the same order as the last retained term in the approximation. A formal application of the method of matched asymptotic expansions is then used to obtain a uniformly valid two term expansion fors n(u, k). Uniform expansions forc n(u, k) andd n(u, k) can also be developed in a similar manner.

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Zusammenfassung Wir zeigen, daß die übliche zweigliedrige Entwicklung der Jacobischen elliptischen Funktions n(u, k) fürk1 (siehe zum Beispiel [3], [4], [5]) nicht uniform ist, falls |u|K, woK die Viertelperiode ist. Es wird gezeigt, daß diese Nichtuniformität schwach ist wo der Restterm dieselbe Ordnung annimmt wie der letzte Term in der Entwicklung. Eine formale Anwendung der Methode der Matched Asymptotic Expansions wird dann benutzt um eine uniform gültige zweigliedrige Entwicklung fürs n(u, k) zu erhalten. Uniforme Entwicklungen fürc n(u, k) undd n(u, k) erhält man in analoger Weise.

     

Use of reference pools to compare the qualitative and quantitative determination of polychlorinated biphenyls by packed and capillary gas chromatography with electron capture detection. Part 1. Serum

Serum for reference pools of in vivo polychlorinated biphenyls (PCBs) was obtained from four goats that had received one dose (100 mg kg-1) of a selected technical Aroclor (AR) (1016, 1242, 1254 or 1260) and were allowed to recover for 30 d. These pools were used to assess the differences in an analytical method that determines and quantifies PCBs using packed-column gas chromatography (PCGC) (quantified on the basis of mean mass percent. data for grouped PCB peaks) and capillary-column gas chromatography (CCGC) (quantified on the basis of percent. composition data for specific congeners). With CCGC, results were statistically significantly different (p less than or equal to 0.0002) from results with PCGC for ARs 1016, 1242 and 1254 but not for AR 1260 (p = 0.23). When comparing these gas chromatographic methods using bovine serum spiked in vitro with the same ARs at 17-25 p.p.b., it was found that the methods were not statistically significantly different for any of the ARs (p = 0.30-0.92). Levels of serum PCB determined by the two methods for 12 persons, divided into two groups according to exposure, were compared using the paired t-test. Group 1 consisted of three persons with dietary and/or environmental exposure; one with dietary and/or environmental exposure in addition to occupational exposure dating back 20 years. Group 2 consisted of eight persons with recent occupational exposure.(ABSTRACT TRUNCATED AT 250 WORDS)     

The infrared spectra (600-150 cm−1 of pyridine N-oxide complexes of metal(II) halides and mixed-ligand (pyridine N-oxide—dimethylsulphoxide) complexes of copper(II) halides

The infrared spectra of the complexes [M(pyO)(H₂O)Cl₂] (M = Mn, Fe, Co, Ni, Cu; pyO = pyridine N-oxide) have been determined. Assignments of ν M-Opy, νM-OH₂ and ν M-Cl are made by observing the effects of deuterating the coordinated pyO and H₂O and replacing chloride by bromide in the Mn(II) complex. Assignments of metal—ligand modes in the mixed ligand complexes [M(pyO)(dmso)X₂] (dmso = dimethylsulphoxide) are made by comparison with the spectra of (ML₂X₂] (L = pyO, dmso) and by observing the effects of deuteration of pyO and dmso. Structural aspects of the spectra are discussed.     

Analysis of a mixture of polychlorinated biphenyls and chlorinated pesticides in human serum by column fractionation and dual-column capillary gas chromatography with electron capture detection

An analytical method is presented for precise identification and quantitation of 29 specific polychlorinated biphenyl (PCB) congeners and 15 chlorinated pesticides in human serum. Analyte surrogates PCB 30, PCB 204, 2,2',4,4',5,5'-hexabromo-biphenyl, perthane, alpha-hexachlorocyclohexane, and dichlorobenzophenone were added to each sample. The serum was extracted with an organic solvent and separated by adsorption chromatography into 3 elution fractions for high-resolution gas chromatographic analysis. Each fraction was analyzed by dual-column capillary chromatography followed by electron capture detection. Two capillary columns, DB-5 and DB-1701, with different polarities were used to increase selectivity for each analyte. Quantitation was performed by selecting 2 sets of calibration standard mixtures and 1,2-dichloronaphthalene as an internal standard. Mean recoveries ranged from 39 to 126% for selected analytes and from 31 to 88% for surrogates. Detection limits for specific congeners and pesticides are reported. Typical chromatographic profiles of calibration standard mixtures, as well as a human sample, are illustrated. Verification of each analyte is assessed, and results of analyses of selected human samples and quality control criteria used to ensure data validity also are presented.     

A note on the global asymptotic stability of the unreacting state in a simple model for quadratic autocatalysis with linear decay

In this note we consider a reaction-diffusion problem which describes a simple model chemical reaction scheme for quadratic autocatalysis with linear decay. We show that withk>1 (wherek is a parameter measuring the relative strength of the decay step to the autocatalytic step) the dimensionless unreacting state 1, 0 is globally asymptotically stable, with 1+0(t ^–1/2) and 0(t ^–1/2 e ^–(k–1)t) ast-. Here and are the concentrations of the reactant and the autocatalyst respectively, andt is time. The casek<1 has been considered in detail by Merkin et al. [1].     

Determination of paraquat in marijuana by reversed-phase paired-ion high performance liquid chromatography.

A sensitive and selective method is described for the quantitative determination of paraquat in marijuana. Paraquat is extracted from finely ground plant material with hydrochloric acid with sonification, and the resulting acidic solution is extracted with chloroform:isopropanol (9:1) and evaporated to dryness. The residue is reconstituted with aqueous phosphate buffer pH 7.0; the solution is passed through a C-18 SEP-PAK TM and is analyzed with high performance liquid chromatography, using a reversed-phase column and an "ion pairing" reagent in the mobile phase. The recovery of paraquat in laboratory-spiked material varied from 90-97%. Results obtained with confiscated, field-sprayed marijuana by the procedure described were in excellent agreement with those obtained with a well-established ultraviolet procedure. The calculated limit of detection with this method is 2 ng of paraquat.     

Influence of bilayer fluctuations on the steric interactions between polymer-grafted bilayers

Abstract

We propose a mechanism, through which the low membrane bending rigidity changes the steric polymer repulsion between polymer-grafted bilayers. We calculate the energy of a polymer chain trapped between two thermally undulating surfaces. The proposed treatment is in terms of de Gennes' theory of fluctuations in liquid crystals, later developed by Helfrich for membranes. We show that the confinement energy of the polymer increases due to membrane fluctuations. Also, the repulsive forces between soft polymer-grafted bilayers can extend further from the surface than the height of the polymer layer.     

PEG-covered lipid surfaces: bilayers and monolayers

In this review paper we survey the ways in which various micropipet techniques have been used to study the mechanochemical and interactive features of lipid bilayer vesicles and monolayer-coated gas bubbles. Special emphasis will be made on characterizing the barrier properties of grafted PEG layers and how a hierarchical approach that uses a short barrier and extended ligand allows us to start to mimic nature's own solution to the problem of ubiquitous repulsion and specific attraction. The information gained from such studies not only characterizes the membrane and other lipid surfaces and their intersurface interactions from a fundamental materials science perspective, but also provides essential materials property data that are required for the successful design and deployment of lipid-based carriers and other capsules in applications involving this so-called ‘stealthy’ surface.