Unexpected ring expansion of an enantiopure imidazoline carbene ligand

[reaction: see text] We report an unexpected ring expansion reaction of an enantiopure fenchone-derived imidazolinium salt during attempts to form copper complexes of the corresponding imidazoline carbene ligand. A N,N'-difenchyl piperazinone was formed in low yield together with the difenchyl-substituted five-membered urea.     

A Range-Compaction Heuristic for Graph Coloring

This paper presents a novel heuristic for graph coloring that works on a range of colors and iteratively tries to make this range more compact. This range-compaction heuristic also has a pressure component and an annealing schedule for it. The value of this component is empirically quantified. This algorithm is evaluated on a wide range of DIMACS benchmark graphs, and found to be competitive with state-of-the-art algorithms in terms of solution quality and run time.     

Precovers

Let be an abstract class (closed under isomorpic copies) of left R-modules. In the first part of the paper some sufficient conditions under which is a precover class are given. The next section studies the -precovers which are -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left R-modules. Especially, several sufficient conditions for the existence of -torsionfree and -torsionfree -injective covers are presented.     

On the Existence of Relative Injective Covers

Let be a hereditary torsion theory for the category -mod of unital left -modules over an associative ring with an identity element. The purpose of this note is to prove that if the associated Gabriel filter consists of finitely presented left ideals, then every module has a -injective cover and if contains a cofinal subset of finitely presented left ideals, then every module has a -torsionfree -injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results.     

Charge/radical site initiation versus coulombic repulsion for cleavage of multiply charged ions. Charge solvation in poly(alkene glycol) ions

Electrospray ionization of poly(ethylene glycol) (PEG) followed by separation with Fourier-transform mass spectrometry traps (PEG100 + nH)n+ ions. Both collisionally activated dissociation (CAD) and electron capture dissociation (ECD) of these ions (n = 5, 6, 7) produce PEGx fragment ions in which the x values correspond closely to those for an equal distribution of charges in the linear polymer ion, e.g., for n = 7, near x = 1, 17, 34, 50, 67, 83, and 100. However, positions intermediate between these charges should represent the maximum coulombic repulsion, so this is not a specific driving force for fragmentation, which is instead consistent with charge site (CAD) or radical site (ECD) initiation. These conclusions were confirmed by studies of a variety of other poly(alkene glycol) polymers. For these, the ECD spectra of the protonated species are consistent with the predicted charge solvation by the ion's oxygen atoms.     

Electron capture dissociation of gaseous multiply charged ions by Fourier-transform ion cyclotron resonance

Fourier-transform ion cyclotron resonance instrumentation is uniquely applicable to an unusual new ion chemistry, electron capture dissociation (ECD). This causes nonergodic dissociation of far larger molecules (42 kDa) than previously observed (<1 kDa), with the resulting unimolecular ion chemistry also unique because it involves radical site reactions for similarly larger ions. ECD is highly complementary to the well known energetic methods for multiply charged ion dissociation, providing much more extensive protein sequence information, including the direct identification of N- versus C-terminal fragment ions. Because ECD only excites the molecule near the cleavage site, accompanying rearrangements are minimized. Counterintuitively, cleavage of backbone covalent bonds of protein ions is favored over that of noncovalent bonds; larger (>10 kDa) ions give far more extensive ECD if they are first thermally activated. This high specificity for covalent bond cleavage also makes ECD promising for studying the secondary and tertiary structure of gaseous protein ions caused by noncovalent bonding.     

Synchronization of trajectories in canonical molecular-dynamics simulations: observation, explanation, and exploitation

For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system.     

Spatiotemporal control of cardiac alternans

Electrical alternans are believed to be linked to the onset of life-threatening ventricular arrhythmias and sudden cardiac death. Recent studies have shown that alternans can be suppressed temporally by dynamic feedback control of the pacing interval. Here we investigate theoretically whether control can suppress alternans both temporally and spatially in homogeneous tissue paced at a single site. We first carry out ionic model simulations in a one-dimensional cable geometry which show that control is only effective up to a maximum cable length that decreases sharply away from the alternans bifurcation point. We then explain this finding by a linear stability analysis of an amplitude equation that describes the spatiotemporal evolution of alternans. This analysis reveals that control failure above a critical cable length is caused by the formation of standing wave patterns of alternans that are eigenfunctions of a forced Helmholtz equation, and therefore remarkably analogous to sound harmonics in an open pipe. We discuss the implications of these results for using control to suppress alternans in the human ventricles as well as to probe fundamental aspects of alternans morphogenesis. (c) 2002 American Institute of Physics.