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.     

Whole body vibration in mountain-rescue operations

In mountain-rescue operations injured people are generally exposed to vibrations and shocks that can be potential causes of physical conditions worsening. Such vibrations can derive both from patient's body manipulations (e.g. when it is being loaded and immobilized on a stretcher) and from forces coming from the transport devices and vehicles. Despite the general feeling that during this kind of operations the levels of transmitted vibrations to the injured can be quite large and potentially dangerous, there is practically no study in literature providing reliable parameters (i.e. measurements) to support or dismiss these beliefs. This paper reports the results of a measurement campaign carried-out in order to outline, identify and quantify the excitations a human body is exposed to, during typical transportation phases related to mountain-rescue operations. The work mainly presents and discusses the experimental setup with the aim of focusing on the problems related to this kind of measurements; the results of the experimental campaign carried-out for the measurement of the vibrations undergone by a human body during a simulated rescue operation are presented and discussed as well. Such simulation includes three phases of transportation: on a hand-held stretcher, on an ambulance and on a helicopter. The work is not intended to supply a complete characterization and analysis of vibrations transmission during any rescue operation but just to provide a preliminary overview and to define a measurement method that can be applied for a more comprehensive characterization. With such aims measurements were carried out in on-field situations stated as “typical” by rescue experts and data then analyzed both with standard procedures and algorithms (e.g. ISO 2631s weighting curves) and with the commonly used statistical indexes; in the analysis it is important to be aware that standardized measurement procedures and indexes, created to verify comfort or health-risks of workers, might not fit the case of a generic patient who experienced a serious mountain accident. The work includes also a laboratory activity mainly related to mechanical characterization of the stretcher used in the field tests. The most interesting result of the study is the comparison of the vibration levels in the various rescue phases that, even when using different indicators, shows that the most critical issue is due to hand transportation despite the bad judgment usually expressed for helicopter flight.     

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.     

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.     

Molecular recognition and crystal energy landscapes: an X-ray and computational study of caffeine and other methylxanthines

We introduce a new approach to crystal-packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom-atom contacts, and on the study of crystal energy landscapes over many computer-generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid-state phase behavior of caffeine and several methylxanthines (purine-2,6-diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X-ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine-water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono- and dimethylxanthines (theophylline, theobromine, and the 1,7-isomer, for which we present a single-crystal X-ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.