Studies of phthalic acid and related compounds by positive- and negative-ion chemical ionization tandem mass spectrometry (± CI/MS/MS)

The positive- and negative-ion chemical ionization (± CI) behavior of phthalic acid and four related compounds (phthalic anhydride, phthalide, biphthalyl, and anthraquinone-2-carboxyIic acid) are characterized by tandem mass spectrometry with low-energy collisionally activated dissociation. Principal fragmentation pathways have been established, and molecular and fragment ions arising from these compounds have been differentiated from adduct and dimer ions, as well as from ions due to impurities. The ubiquitous nature of these compounds in analytical samples makes it important to identify the corresponding ions, and thus to be able to exclude them from consideration in the identification of other sample components.     

Superselection rules in quantum theory: Part II. Subensemble selection

A dynamical analysis of standard procedures for subensemble selection is used to show that the state restriction violation proposal in Part I of the paper cannot be realized by employing familiar correlation schemes. However, it is shown that measurement of an observable not commuting with the superselection operator is possible, a violation of the observable restrictions. This is interpreted as supporting the position that each of these restrictions is sufficient but not necessary for the superselection rule. The results do constitute a proposal for superselection rule violation in theories requiring both restrictions, e.g., the axiomatic treatment by Bogolubov, Logunov, and Todorov. It is also concluded that superselection rules place restrictions on procedures for selective state preparations using correlations. More generally, it is conjectured that a mathematically conceivable decomposition of a given density operator does not necessarily represent a possibility for partitioning of the corresponding ensemble into subensembles by any physically realizable means.     

Synthesis and characterization of a solvatochromic,lipophilic fluorescent oxazone: 1-Pentyl-7-dimethylamino-3H-phenoxazine-3-one

Olivetol and 4-nitroso-N,N-dimethylaniline were combined under reflux in acetic acid to produce 1-pentyl-7-dimethylamino-3H-phenoxazine-3-one (1-PDMPO). The fluorescent behavior of the purified compound in a variety of solutions and samples was investigated. Excitation and emission spectra in pure solvents and mixtures of solvents demonstrate solvatochromism, indicating that the fluorescence response of this compound is affected by its environment. Nonpolar, aprotic solvents as well as protic, polar solvents diminish fluorescent emission in the spectral regions examined, and trends in the fluorescence decary lifetimes measured in five pure solvents are consistent with these intensity changes. The anisotropy excitation spectrum taken in glycerol for 1-PDMPO at –15°C appears to be consistent with the presence of a single electronic state upon excitation, with anisotropy values approaching 0.35 over 400–600 nm. Fluorescence emission is also diminished at low acid concentrations in methanol, with smaller decreases observed in more highly concentrated basic solutions. Emission peaks in aqueous sodium dodecyl sulfate solutions, extruded egg phosphatidylcholine vesicles, and fatty acid free bovine serum albumin suspensions all lie above 600 nm, with emission in the albumin suspension displaying a broad shoulder extending to 800 nm. The fluorescent properties of this compound suggest that it or structural homologues may have utility as fluorescent biological probes.Presented in part at the Biophysical Society Meeting, Washington, DC (February 1993).     

Mass spectral studies of unsaturated carboxylic acids—I: Some cyclic and acyclic βγ-unsaturated acids

The mass spectra of a series of βγ-unsaturated cyclic and acyclic carboxylic acids are reported. Metastable ion studies and precise mass measurements have been employed in demonstrating that the ten compounds studied conform to one or other of two generalised fragmentation pathways.     

Superconvergence for galerkin methods for the two point boundary problem via local projections

The two point boundary problemy'-a(x)y–b(x)y=-f(x), o<x<1,y(0)=y(1)=0, is first solved approximately by the standard Galerkin method, (Y, ) + (aY+bY, )=(f, ), ₁ ⁰ (r, ), for a function Y ₁ ⁰ (r, ), the space ofC ¹-piecewise--degree-polynomials vanishing atx=0 andx=1 and having knots at {x ₀ ,x ₁ , ...,x _M }=. ThenY is projected locally into a polynomial of higher degree by means of one of several projections. It is then shown that higher-order convergence results locally, provided thaty is locally smooth and is quasi-uniform.This research was supported in part by the National Science Foundation.     

Characterizing binary simplical matroids

In an earlier paper we defined a class of matroids whose circuit are combinatorial generalizations of simple polytopes; these matroids are the binary analogue of the simplical geometrics of Crapo and Rota. Here we find necessary and sufficient conditions for a matroid to be isomorphic to such a binary simplical matroid.     

A constructive proof of Tucker's combinatorial lemma

Tucker's combinatorial lemma is concerned with certain labellings of the vertices of a triangulation of the n-ball. It can be used as a basis for the proof of antipodal-point theorems in the same way that Sperner's lemma yields Brouwer's theorem. Here we give a constructive proof, which thereby yields algorithms for antipodal-point problems. Our method is based on an algorithm of Reiser.