A microcomputer program for estimation of copolymerization reactivity ratios

A user-friendly program has been developed to estimate copolymerization reactivity ratios based on a nonlinear minimization algorithm. The use of an optimal experimental design for copolymerization when the Mayo–Lewis model applies is presented. The applicability of the program is demonstrated using actual and simulated experimental data.     

Comparison of cryoscopic determinations of purity of benzene by thermometric and calorimetric procedures

Workers at the National Bureau of Standards and elsewhere have been conscious of the discordant results sometimes yielded by two methods for determining purity employing the same physical principle. A comparison was made on samples of benzene by the thermometeric method, by which a stirred sample is frozen at nearly constant rate, and by the calorimetric method, by which a frozen sample is melted in stages by the addition of accurately controlled increments of energy under adiabatic conditions.Benzene, purified by single crystal formation and of very high purity, was contaminated in known amounts by n-heptane and samples of the same level of purity determined by both procedures. Great care was taken to submit samples of the same composition to the different groups employing the two different methods. Further, the actual degree of contamination of the benzene was unknown to both groups until final values of the purity were submitted. Results of this comparison showed that the large divergence between the two methods that had characterized earlier comparisons is not displayed. The differences between the analyses on all three samples are roughly of the order of the statistically estimated uncertainties of the averages and less than deviations between individual experiments by one method. Comparison of the methods with absolute values of purity could not be made because of contamination of the highly purified sample of benzene with supposedly chemically adsorbed water from the borosilicate glass walls.     

On forced oscillations of a simple model for a novel wave energy converter

The dynamics of a simple model for an ocean wave energy converter is discussed. The model for the converter is a hybrid system consisting of a pair of harmonically excited mass–spring–dashpot systems and a set of four state-dependent switching rules. Of particular interest is the response of the model to a wide spectrum of harmonic excitations. Partially because of the piecewise-smooth dynamics of the system, the response is far more interesting than the linear components of the model would suggest. As expected with hybrid systems of this type, it is difficult to establish analytical results, and hence, with the assistance of an extensive series of numerical integrations, an atlas of qualitative results on the limit cycles and other forms of bounded oscillations exhibited by the system is presented. In addition, the presence of unstable limit cycles, the stabilization of the unforced system using low-frequency excitation, the peculiar nature of the response of the system to high-frequency excitation, and the implications of these results on the energy harvesting capabilities of the wave energy converter are discussed.     

Extensions of homomorphisms to dense extensions of semigroups

Gluskin [2] has shown that if α is an isomorphism of a weakly reductive semigroup S onto a semigroup T, if V is a dense extension of S and T is densely embedded in W then α extends uniquely to an isomorphism of V into W. Here we consider the problem of extending epimorphisms and as a consequence of a few simple observations obtain as the main theorem a homomorphism of Ω(S), for any semisimple semigroup S, into the product of the translational hulls of the principal factors of S. A few consequences are considered.     

Kinetic analysis of the disproportionation of aqueous glyoxal

Rates of disproportionation of 0.015–0.4 mM aqueous glyoxal toglycolic acid were measured at 0.24–75 mM NaOH and constant ionic strength, leading to the empirical rate expression r = (a₁[OH^?] + a₂[OH^?]²) [G_T]/(1 + a₃[OH^?]), where [G_T] is the total glyoxal concentration. These results were confirmed in bicarbonate/carbonate buffer and at 2–20 mM [G_T]. The rate form is in contradiction to earlier work on glyoxal, which suggested a second-order dependence on [OH^?], but agrees with the rate equation for phenylglyoxal disproportionation. The kinetic data can be explained by a mechanism postulating the presence of monohydrated and dihydrated forms of glyoxal in equilibrium, with the rate-limiting steps being intramolecular hydride ion transfers to the unhydrated carbonyl carbon of the mono- and divalent anions of glyoxal monohydrate.     

Automated processing of the single-lead electrocardiogram for the detection of obstructive sleep apnoea

A method for the automatic processing of the electrocardiogram (ECG) for the detection of obstructive apnoea is presented. The method screens nighttime single-lead ECG recordings for the presence of major sleep apnoea and provides a minute-by-minute analysis of disordered breathing. A large independently validated database of 70 ECG recordings acquired from normal subjects and subjects with obstructive and mixed sleep apnoea, each of approximately eight hours in duration, was used throughout the study. Thirty-five of these recordings were used for training and 35 retained for independent testing. A wide variety of features based on heartbeat intervals and an ECG-derived respiratory signal were considered. Classifiers based on linear and quadratic discriminants were compared. Feature selection and regularization of classifier parameters were used to optimize classifier performance. Results show that the normal recordings could be separated from the apnoea recordings with a 100% success rate and a minute-by-minute classification accuracy of over 90% is achievable.