Paley graphs satisfy all first-order adjacency axioms

A graph satisfies Axiom n if, for any sequence of 2n of its points, there is another point adjacent to the first n and not to any of the last n. We show that, for each n, all sufficiently large Paley graphs satisfy Axiom n. From this we conclude at once that several properties of graphs are not first order, including self-complementarity and regularity.     

A Model of the Dynamics of the Third World War — An Exercise in Technology Transfer

The paper discusses two scenarios for a Third World War in Europe, and argues that it is often convenient to supplement a scenario by a formal model. The problems of creating such a model are examined, and a model is formulated for land, air, and sea combat in Europe and the Atlantic, using the System Dynamics approach, which has not hitherto been widely employed for military analysis.The model confirms the results of the two scenarios, and its use for the analysis of alternative force configurations is illustrated. Some implications in the interpretation of Soviet military literature are discussed, and the paper ends with speculations on the role and value of such models.     

The reaction of atomic oxygen O(3P) with isobutane

The reaction of O(³P) atoms with isobutane has been studied by using the discharge-flow system described previously [1]. The rate constant was measured from determinations of the isobutane concentration in the presence of an excess of O atoms and is given by k₁ = (7.9 ± 1.4) × 10⁷ dm³/mol·s at 307 K. In order to explain the observed reaction products, the mechanism requires that the principal process be the successive abstraction of H atoms from isobutane and from the t-butyl radical to give isobutene. A minor part of the reaction between O(³P) and the t-butyl radical gives the t-butoxy radical, which decomposes to acetone. The branching ratios are .     

Preparation and properties of a soluble polymeric aquo ion of molybdenum(V)

An orange/brown ionic and polymeric Mo(V) ion (Mo to Na ratio 2.3:1), soluble in H₂O to give stable solutions at pH～6, with UV visible spectrum λ_max 318nm, ?(per Mo) 330OM^?1 cm^?1, has been prepared and partially characterised. Various properties are described, including the conversion to the well established Mo(V) aquo dimer, MO₂O₄²⁺, on adjustment of [H⁺] to 0.17–0.50 M, I=0.50 M (H/LiClO₄). First-order rate constants, k_obs(25°C), determined by conventional spectrophotometry give a good fit to the empirical rate law,     

Bootstrapping the photon

A nontechnical review is given of a topological bootstrap theory, with emphasis on theraison d'être for an electromagnetism whose fine-structure constant is of order10 ^?2.     

Event shapes in deep inelastic lepton-hadron scattering

The structure of hadronic final states in deep inelastic scattering expected from QCD is analyzed in terms of the shape parameters H_l and C_l. We find that the effects of the fragmentation of quarks and gluons into hadrons are typically governed by $\text{√s = [Q}{}^2\text{(1/x?1)]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. For √s?30 GeV, the distributions of events in H₂ and C₂ should allow a test of the perturbative QCD prediction of three-jet events.     

The single basis filter diagonalization method: a rapid multidimensional data processing scheme

A new way to apply the filter diagonalization method (FDM) that results in a large increase in the speed of calculation of multidimensional NMR spectra is presented. The speed increase is accompanied by slight differences in spectral lineshapes, although frequency estimates remain essentially identical. For contoured spectra, the method does not result in appreciable differences from the full FDM calculation. Optimal parameter sets for an FDM calculation can be estimated far more rapidly, which makes the FDM more straightforward to employ in practice. The performance of the method versus the full FDM was investigated for both model and experimental signals. The effect of noise on the method was also studied.     

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.