Improved Proton Decoupling in NMR Spectroscopy of Crystalline Solids Using the SPINAL-64 Sequence

Summary.  The performance of three different spin decoupling schemes, CW, TPPM, and SPINAL-64 is compared, by recording proton decoupled ¹³C NMR spectra of a crystalline glycine sample, with 20% isotopic labelling. At a magnetic field of B ₀ = 14.1 T, the two phase modulated pulse schemes, TPPM and SPINAL-64, are shown to give decisively better results than CW decoupling, and the SPINAL-64 sequence is found to perform better than TPPM. It is suggested that in NMR of crystalline solids, SPINAL-64 offers a viable and competitive alternative to the well established TPPM decoupling technique, especially at higher magnetic fields. Corresponding author. E-mail: thomas.braeuniger@durham.ac.uk Received May 6, 2002; accepted May 22, 2002     

Cataloguing the graphs on 10 vertices

We describe the production of a catalogue of all the nonisomorphic graphs on 10 vertices by means of a computer program. The basic program generated all the nonisomorphic graphs with a given degree sequence. Some tables, derived from the catalogue, concerning the numbers of automorphisms of these graphs are given at the end of the paper.     

Achiral plane trees

Harary and Robinson showed that the number a_n of achiral planted plane trees with n points coincides with the number p_n of achiral plane trees with n points, for n ? 2. They posed the problem of finding a natural structural correspondence which explains this coincidence. In the present paper this problem is answered by constructing two-to-one correspondences from certain sets of binary sequences to each of the sets of trees concerned, giving a structural basis for the equation 2a_n = 2p_n. Answers are also supplied to similar correspondence-type problems of Harary and Robinson, concerning planted plane trees, and achiral rooted plane trees. In addition, each of these four types of plane trees are counted with numbers of points and endpoints as the enumeration parameters. The results all show a symmetry with respect to the number of endpoints which is not shared by the set of all plane trees.     

Synthesis and Characterization of Chitosan/ Dextran-Based Hydrogels for Surgical Use

A series of hydrogels were formed from the reaction between an amine functionalized succinyl chitosan and an oxidized dextran. The properties and rate of formation of the gel were related to both the amine and aldehyde levels of the precursors. These levels could be readily changed by altering the reaction conditions, and allowed good control of the gel properties. Oxidation of the dextran with periodate was accompanied by chain scission and a large reduction in molecular weight. The gel showed excellent haemostatic properties and reduction of adhesions in animal models.     

Number of labeled 4-regular graphs

Several operations on 4-regular graphs and pseudographs are analyzed and equations are obtained relating the numbers of these graphs on given numbers of labeled points. These equations are used recursively to find the numbers of 4-regular graphs on up to 13 labeled points.     

Almost all cubic graphs are Hamiltonian

In a previous article the authors showed that at least 98.4% of large labelled cubic graphs are hamiltonian. In the present article, this is improved to 100% in the limit by asymptotic analysis of the variance of the number of Hamilton cycles with respect to populations of cubic graphs with fixed numbers of short odd cycles.     

A new enthalpy-increment calorimeter enthalpy increments for n-hexane

A water-cooled heat-exchange calorimeter for the measurement of enthalpy increments of fluids up to 700 K and 15 MPa has been constructed. Novel features of the design ensure that heat leaks are small, well controlled, and easily measured. The results of 90 test runs on steam gave enthalpy increments in agreement with steam tables to within 0.5 per cent. The calorimeter has been used to measure enthalpy increments of n-hexane up to 573.2 K and 12.67 MPa, and the results are compared with the Starling modification of the BWR equation of state. Overall agreement of 115 measurements with the BWRS equation is 0.97 per cent. In the critical region BWRS values differ from experiment by up to 4 per cent.     

Asymptotic Enumeration of Convex Polygons

A polygon is an elementary (self-avoiding) cycle in the hypercubic lattice ^dtaking at least one step in every dimension. A polygon on ^dis said to be convex if its length is exactly twice the sum of the side lengths of the smallest hypercube containing it. The number ofd-dimensional convex polygonsp_{n, d}of length 2nwithd(n)→∞ is asymptoticallywherer=r(n, d) is the unique solution ofr coth r=2n/d−1andb(r)=d(r coth r−r²/sinh² r). The convergence is uniform over alld?ω(n) for any functionω(n)→∞. Whendis constant the exponential is replaced with (1−d⁻¹)^2d. These results are proved by asymptotically enumerating a larger class of combinatorial objects calledconvex proto-polygonsby the saddle-point method and then finding the asymptotic probability a randomly chosen convex proto-polygon is a convex polygon.     

Meyniel's conjecture holds for random graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In this paper, we show that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph , which improves upon existing results showing that asymptotically almost surely the cop number of is provided that for some . We do this by first showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. This will also be used in a separate paper on random d‐regular graphs, where we show that the conjecture holds asymptotically almost surely when . © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 396–421, 2016     

A critique of Segal's chronometric theory

The Segal Chronometric theory is examined, with particular attention given to the role of a physical measurement in the theory. A calculation of the red shift in Segal's theory in the geometrical optics limit yields the resultz=0, in contradiction to Segal's resultz=tan² (/2), and the disagreement is shown to arise from the unphysical nature of Segal's theory of measurement. An argument is also presented to show that the postulates on which Segal's theory is based are inconsistent when massive particles are introduced into the Segal universe.