Ultrasonic spectroscopic evaluation of the ring‐opening metathesis polymerization of dicyclopentadiene

An in situ ultrasonic spectroscopy technique was used to study the ring‐opening metathesis polymerization of dicyclopentadiene catalyzed by bis(tricyclohexylphosphine)benzylidene ruthenium dichloride. A reaction cell employing a flexible poly(ethylene terephthalate) window for pulse echo ultrasonic spectroscopy was used to monitor the polymerization. The changes in the density, wave speed, acoustic modulus, and attenuation were all simultaneously monitored. In comparison with Fourier transform infrared (FTIR) spectroscopy data, the changes in the density, velocity, and modulus only accurately measured the rate constant for the metathesis of the cyclopentyl unsaturation. The ultrasonic values were within 6% of the values determined by FTIR. The activation energy for metathesis of the cyclopentyl unsaturation was 84 kJ mol^?1, following first‐order kinetics. Rate constants for the polymerization of the norbornyl unsaturation could not be determined by ultrasound. The gel point, vitrification, and qualitative information about the reaction rate could be determined from the change in the attenuation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1323–1333, 2003     

Optimal entropic uncertainty relation for successive measurements in quantum information theory

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in the literature on the sum of entropie uncertainties of two observables which are measured on distinct but identically prepared ensembles of systems. In the case of a two-dimensional Hilbert space, the optimum bound for successive measurements of two-spin components, is seen to be strictly greater than the optimal bound for the case when they are measured on distinct ensembles, except when the spin components are mutually parallel or perpendicular     

Invariant Dissipative Mechanisms for the Spatial Motion of Rods Suggested by Artificial Viscosity

The introduction of artificial viscosity into the partial differential equations of mechanics is often useful for both analytic and numerical studies. The traditional forms of artificial viscosity, originally designed to treat problems for fluids, when applied to problems for solids often lead to equations describing material properties that are not invariant under rigid motions. Consequently, for rapidly rotating bodies, artificial viscosity could produce serious errors. In this paper it is shown how to introduce artificial viscosity in a properly invariant way, and that the resulting systems have a rich and attractive structure, which beckons analysis.     

Angular correlations in the decays of two unstable identical particles with close momenta

For the decay of two identical particles with close momenta, the angular correlations between the directions of emission of decay products are considered on the basis of the model of independent single-particle sources emitting unstable unpolarized particles of nonzero spin. These correlations reflect spin correlations that are caused by quantum-statistics and final-state-interaction effects. A general theory of angular correlations in the decays of two arbitrarily polarized particles (resonances) is constructed.     

Measurement of the differential cross section and of the tensor and vector analyzing powers for the fragmentation of 4.5-GeV/c deuterons on beryllium in the reaction involving proton emission at an angle of 80 mrad

The invariant differential cross section, the tensor analyzing power A _yy , and the vector analyzing power A _y for the reaction ⁹Be(d, p)X are measured at an initial deuteron momentum of 4.5 GeV/c and a proton detection angle of about 80 mrad. The data obtained for the differential cross section are consistent with the results of measurements at 3.5 and 5.78 GeV/c and a proton emission angle of 2.5°. The values found for the tensor analyzing power A _yy are compared with similar data obtained previously for the deuteron-fragmentation process occurring on a carbon target at various values of the initial deuteron momentum and leading to proton emission at zero angle. The data on the differential cross section for the reaction ⁹Be(d, p)X can be satisfactorily described within the relativistic impulse approximation by using standard deuteron wave functions; however, the approach based on this conceptual framework proves to be inadequate in dealing with data on the tensor analyzing power. These results indicate that it is necessary either to change the method for describing the relativistic deuteron or to take into account additional mechanisms.     

Enclosure results for quasilinear systems of variational inequalities

In this paper we consider systems of quasilinear elliptic variational inequalities, and prove the existence of minimal and maximal (in the set theoretical sense) solutions within some ordered interval of an appropriately defined pair of sub- and supersolutions. We show that the notion of sub- and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub-supersolutions for (variational) equations. For weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved.     

Stability and Nonlinear Deformation of Cylindrical Grids

The general stability of single-layer cylindrical grids is studied in linear and nonlinear formulations. Dependence of the general buckling load on the geometry and stiffness parameters of a grid is established in an analytical form. Such grids are numerically analyzed for stability. It is established that the general buckling load is much less than the local buckling load. Typical general buckling modes are found. It is shown that such grids are weakly sensitive to imperfections     

Unforeseen formation of 2-bromo-3-hydroxybenzaldehyde by bromination of 3-hydroxybenzaldehyde

Contrary to literature reports, bromination of 3-hydroxybenzaldehyde can afford both 2-bromo-5-hydroxybenzaldehyde and 2-bromo-3-hydroxybenzaldehyde, but 4-bromo-3-hydroxybenzaldehyde was not detected. 2-Bromo-3-hydroxybenzaldehyde was converted into 2-(benzyloxy)-1-bromo-5-methoxy-7-methylnaphthalene. X-ray crystallographic analysis supports the identity of 2-bromo-3-hydroxybenzaldehyde.