The use of stable carbon isotope analysis to detect the abuse of testosterone in cattle.

The use of stable carbon isotope analysis to detect the administration of anabolic steroids to cattle was investigated. Samples were extracted by solid-phase extraction on C18 cartridges. Stable isotope ratios (13C:12C) were measured by gas chromatography-isotope ratio mass spectrometry (GC-IRMS) of the underivatised extracts. A programmed temperature vaporiser (PTV) injector was installed in the GC-IRMS system, which conferred a number of advantages. First, it allowed large volumes of sample to be injected whilst the injector liner was cool. The solvent was subsequently vented to the atmosphere prior to transfer of the sample to the GC column. Thus a significantly greater amount of sample could be presented for analysis, thereby increasing the sensitivity. Second, by this means virtually all the solvent could be removed prior to analysis. This eliminates solvent peak tailing, which can be a major problem in GC-IRMS. Finally, the PTV allowed the use of higher initial GC oven temperatures, which in turn facilitated the analysis of underivatised steroids by reducing the GC run time and improving the chromatographic peak shape. The carbon isotope composition of 5 beta-androstane-3 alpha,17 alpha-diol, the major metabolite of testosterone found in bovine bile, was measured in bile samples from untreated cattle and from cattle injected intramuscularly with testosterone or a mixture of testosterone esters. There was considerable inter-animal variation in the values obtained and there was no significant difference between samples from treated and untreated animals. However, when the isotopic composition of the metabolite was normalised with respect to that of an endogenous reference compound (cholesterol) in the same sample, the difference between treated and untreated animals become statistically significant.     

Quantum efficiency of the 2537 A. Photolysis of a mixed phenyl–methyl polysiloxane

The ultraviolet (λ = 2537 A.) photolysis of a degassed mixed phenyl and methyl polysiloxane liquid is examined in terms of gas and crosslinking yields. Results are compared to the published values obtained by ionizing irradiation of this type of molecule. It is shown that ultraviolet radiation is less efficient by two orders of magnitude in producing decomposition (i.e., gaseous products) than is ionizing radiation. The comparisons for crosslinking efficiencies are less certain, but the yields seem to have much more similar values in this case based on a spectroscopic estimation of crosslinking (i.e., analysis for substituted phenylcyclohexadiene formation). The gas quantum yields were ?H₂ = 2.6 × 10^?5, ?CH₄ = 0.63 × 10^?5, ?C₂H₆ ≈ 0.12 × 10^?5, and ?C₂H₂ ≈ 0.06 × 10^?5.     

Stereoisomeric effects on mass spectra—I. A Review

The unimolecular reactions that give rise to mass spectra are controlled by spatial relationships and energy considerations. In molecules that contain a heteroatom, elimination reactions, involving bond-making as well as breaking, are often prominent, e.g. loss of water from alcohols. The ease of such reactions depends on spatial relationships in the molecule, and the resultant ion intensities in the spectra of geometric isomers can consequently be correlated with differences in geometry and hence furnish a basis for assigning structures. Processes that do not involve bond-making do not have such rigorous geometric requirements, but depend rather on attainment of a transition state defined in terms of a minimum energy content. Common product ions from stereoisomeric hydrocarbons seem often to arise via a common transition state. When this condition holds, the difference between the enthalpies of the isomers is reflected in the relative appearance potentials and–though the cause-and-effect relationship here is less direct and more readily obscured by other factors–relative intensities of the common product derived from the isomers. In both classes of processes, the spectra of stereoisomers can be simplified and made more distinctive by lowering source temperature and ionizing voltage.     

History of the Development and Growth of Thermosetting Polymers

Fibrous proteins are cross-linked through the disulfide linkages of cystine; animal and vegetable proteins can be cross-linked by the reaction of tannic acid, chromic acid, or formaldehyde; and natural rubber can be vulcanized by heating with sulfur. However, most thermosetting polymers are synthetic polymers. These include saturated polyesters (Glyptals) synthesized by Smith in 1901, phenolic plastics produced by Baekeland in 1907, urea and melamine plastics produced by John and Henkel in 1918 and 1935, alkyds patented by Kienle in 1933, glycol maleates patented by Ellis in 1937, and epoxy resins patented by Schlack in 1933. Many of these developments were made prior to the advent of commercial synthetic thermoplastics. However, because their fabrication is more labor intensive than that of thermoplastics, thermosetting plastics now account for less than 20% of all plastics produced. Nevertheless, over 2.5 million tons of these thermosets are produced annually and the use of these cross-linked plastics continues to grow.     

Uniqueness of highly representative surface embeddings

Let Σ be a (connected) surface of “complexity” κ; that is, Σ may be obtained from a sphere by adding either ½κ handles or κ crosscaps. Let ρ ≥ 0 be an integer, and let Γ be a “ρ-representative drawing” in Σ; that is, a drawing of a graph in Σ so that every simple closed curve in Σ that meets the drawing in < ρ points bounds a disc in Σ. Now let Γ′ be another drawing, in another surface Σ′ of complexity κ′, so that Γ and Γ′ are isomorphic as abstract graphs. We prove that. (i) If ρ ≥ 100 log κ/ log log κ (or ρ ≥ 100 if κ ≤ 2) then κ′ ≥ κ, and if κ′ = κ and Γ is simple and 3-connected there is a homeomorphism from Σ to Σ′ taking Γ to Γ′, and. (ii) if Γ is simple and 3-connected and Γ′ is 3-representative, and ρ ≥ min (320, 5 log κ), then either there is a homeomorphism from Σ to Σ′ taking Γ to Γ′, or κ′ ≥ κ + 10^-4 ρ². © 1996 John Wiley & Sons, Inc.     

Nonlinear two-point boundary value problems with multiple solutions

In the first part of this paper we study the convergence of finite difference methods to approximate the maximal solution of problems of the form:u+f (x, u)=0, with boundary conditions eitheru(0)=u(b)=0 oru(0)=u (b)=0, 0<b1. The functionf(x, u) satisfies several conditions that are explicitly given in § 1. This work extends earlier results of Parter (see references at the end).Since this problem has in general more than one solution we develop in the second part two algorithms to approximate solutions characterized by the number of their zeros in (0, 1). We include in the last Section numerical results and some additional comments on the implementation of the algorithms on a digital computer.The research of this author was supported by the Office of Naval Research under contract N^o N-0014-67-A-0128-004.Part of this research was carried on while this author was visiting the Mathematics Research Center, University of Wisconsin, during the summer of 1969.     

Nowhere-zero 6-flows

We prove that every graph with no isthmus has a nowhere-zero 6-flow, that is, a circulation in which the value of the flow through each edge is one of ±1, ±2,…, ±5. This improves Jaeger's 8-flow theorem, and approaches Tutte's 5-flow conjecture.     

A note on convergence of the multigrid V-cycle

Several recent papers have discussed the convergence of the multigrid V-cycle. In particular there are several results for the symmetric case: where the numbers of smoothings before the fine-to-coarse transfer and after the coarse-to-fine transfer are the same. In most instances, the smoother H=I?E^-1A has been limited to the case where E is positive definite and the eigenvalues h of H satisfy 0?h?1. In this note we extend these results to asymmetric V-cycles and the case where -b?h?1 with 0<b<1.     

Cycles in dense digraphs

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?

We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:

• when V(G) is the union of two cliques
• when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.