The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Quantum NOT operation and integrability in two-level systems

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different “average” systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.     

A new microwave dielectric method for studying photoinitiated chain radical polymerization processes

Measurements of both real and imaginary parts of the dielectric constant at a fixed microwave frequency have been performed on n-butyl acrylate/poly(n-butyl acrylate) mixtures. The dielectric constant of the mixtures has been compared with that of neat n-butyl acrylate during UV photoinitiated polymerization. The values of the imaginary part of the dielectric constant thus obtained have allowed determination of the instantaneous monomer concentration and verified the kinetic equation for the photoinitiated polymerization process. The limits of validity of the method as well as its capability of providing detailed kinetic information are also discussed.     

The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

Letters to the editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chief, Chandler Davis.     

Search of theH particle in antiproton-nuclear interactions

The proposal of hunting theH-particle taking advantage of antiproton annihilation at rest on³He is discussed. The obtained K^* beam should allow one to obtain a flux ofΞ ^? with momentum low enough to optimize the fusion probability (ΞN) to give anH. The experimental apparatus to detectH-events as the only missing mass of the fully reconstructed reaction¯p ³He →KKπ ⁺ H is the OBELIX Spectrometer at LEAR. A detailed Monte Carlo simulation of the overall acceptance of OBELIX for the above reaction is performed. The obtained final rate shows the feasibility of the experiment also in a not dedicated detector like OBELIX.     

Mössbauer and infrared spectroscopic studies of novel mixed valence states in cobaltous ferrocyanides and ferricyanides

Novel mixed valence states have been obtained by the treatment of cobaltous ferrocyanides (Co⁺²Fe^II) and ferricyanides (Co⁺²Fe^III) in an ozone flow. The CN stretching bands occur at 2085 cm^–1 for Co⁺²Fe^II and at 2160 cm^–1 for Co⁺²Fe^III. After the ozonization process of Co⁺²Fe^II, an intense band approximately at 2125 cm^–1 is detected. This intermediate band must correspond to a mixed valence state of the type: Fe^II–CN–Co²⁺–NC–Fe^III Mössbauer spectra recorded in situ during the ozonization of Co⁺²Fe^II show the presence of two components: a doublet with isomer shift and quadrupole splitting values close to the cobalti ferricyanide and a very broad line for the mixed valence state. From the Mössbauer and infrared spectra of the aged samples of the Co⁺²Fe^II after ozonization, a relaxation process to the initial state of the samples is observed but the mixed valence state is stable.     

Thermogravimetric analysis of polycarbonates and polythiocarbonates with chlorinated aromatic side-rings

The thermal stability and kinetics parameters of polycarbonates and polythiocarbonates derived from diphenols with chlorinated aromatic side-rings were studied. The polycarbonates exhibited a higher thermal stability than the polythiocarbonates, except for polythiocarbonate Ib, which displayed similar behaviour to that of the analogous polycarbonate. The kinetic parameters of the thermal decomposition were determined by using the Arrhenius relationship and a computer program. In the considered temperature range, all the polymers degraded in a single stage with first-order kinetics.

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Zusammenfassung Es wurde die thermische Stabilität und die kinetischen Parameter von aus Diphenolen mit chlorierten aromatischen Nebenringen abgeleiteten Polycarbonate und Polythiocarbonate untersucht. Polycarbonate zeigen eine höhere thermische Stabilität als Polythiocarbonate. Eine Ausnahme bildet das Polythiocarbonat Ib, das in seinem Verhalten den Polycarbonaten gleicht. Mittels der Arrheniusschen Gleichung und einem Rechnerprogramm wurden die kinetischen Parameter der thermischen Zersetzung ermittelt. Im untersuchten Temperaturbereich zersetzen sich alle Polymere in einer einstufigen Reaktion erster Ordnung.

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The authors acknowledge financial support from the Dirección de Investigación of the Pontificia Universidad Católica de Chile.     

Reactivity of methyl mandelate-Ti(IV)-enediolate: oxidative homocoupling versus aldol and direct Mannich-type syn-diastereoselective condensation

[reaction: see text] Methyl mandelate undergoes quantitative oxidative homocoupling on treatment with TiCl4/amine at room temperature. In the presence of ArCHO, quantitative syn-diastereoselective aldol condensation takes over the dimerization, whereas exclusive Mannich-type syn-diastereoselective reaction is observed in the presence of both ArCHO and PhNH2. The subsequent reactions of the title intermediate do not depend on how it is generated.     

A more convenient and general procedure for O-monobenzylation of diols via stannylenes: a critical reevaluation of the Bu2SnO method

A more consistent, straightforward, and economical protocol for generation of stannylene species and their reaction with BnBr leading to products of O-monobenzylation of diols has been set. It has shown to be specially indicated for substrates bearing vicinal trans 1,2-diol moieties on cyclohexane backbones, which are more resistant to these transformations. Such protocol has been successfully applied to myo-inositol derivatives and acyclic diols.