Localizability of the embedding problem with symplectic kernel

In this paper we consider the question of how much information is supplied by local solutions to a global embedding problem for the special case in which the normal subgroup belonging to the given group extension is the projective symplectic group PSp(2m, q). It is proved that for suitable Galois extensions K of a given number field k (which constitute part of the data of the embedding problem), the local solutions in a sense determine whether or not an extension K ? K, Galois over k, with $\text{G(}\text{L}\text{K}\text{) ≈ PSp(2m, q)}$, represents a global solution to the embedding problem.     

Combined phase singularity and wavefront analysis for optical maps of ventricular fibrillation

Much of the research into the mechanisms of ventricular fibrillation (VF) employs high-resolution mapping of electrical activation and recovery patterns. We previously developed a method for analyzing electrically mapped VF patterns that was based on identifying individual VF wavefronts. We now introduce a related method designed to take into account the information on repolarization that is present in optically mapped VF data. The new method first converts raw fluorescence data to an angular variable that tracks the phase of the mapped tissue through the depolarization-repolarization cycle. We define wavefronts in this context as isolines of phase that terminate either at boundaries or at singular points within the phase field. These singularities are the pivots of functional reentry and are important determinants of VF patterns. We parameterize VF by constructing data structures that describe wavefronts and singularities and also maintain wavefront-wavefront, wavefront-singularity, and singularity-singularity relationships. We describe one important application of this parameterization, which is to identify, localize, and characterize the importance of occurrences of propagation block during VF.     

Fetal MEG redistribution by projection operators

The fetal magnetoencephalogram (fMEG) is measured in the presence of large interference from the maternal and fetal magnetocardiograms. This interference can be efficiently attenuated by orthogonal projection of the corresponding spatial vectors. However, the projection operators redistribute the fMEG signal among sensors. Although redistribution can be readily accounted for in the forward solution, visual interpretation of the fMEG signal topography is made difficult. We have devised a general, model-independent method for correction of the redistribution effect that utilizes the assumption that we know in which channels the fMEG should be negligible (such channels are distant from the known fetal head position). In a simplified case where the fMEG can be explained by equivalent current dipoles, the correction can also be obtained from fitting the dipoles to the fMEG signal. The corrected fMEG signal topography then corresponds to the dipole forward solution, but without orthogonal projection. We illustrate the redistribution correction on an example of experimentally measured flash evoked fMEG.     

Modelling of kink nucleation and propagation along steps of finite length

A discrete model for kink nucleation and propagation along steps of finite length is developed. The step velocities were calculated as a function of the step length, the first order rate constants, k_s and k_K, for kink nucleation and propagation respectively, and a kink interaction parameter. The two limiting kinetic regimes of short and long steps as well as the intermediate transitional regime were considered. For very short steps, S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, the velocity varied directly with the number of sites S. Steps which met the criterion S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, were shown to have velocities on the order (2k_Kk_s)^{$\text{1}\text{2}$}, independent of step length. Step velocities were constant over large ranges of the kink interaction parameter. The steps were shown to be “sharp” for zero or attractive kink interaction, but with sufficiently large kink repulsion very diffuse steps could be formed. The density of kinks and numbers of kinks nucleated along an atom row were also calculated.     

Direct summands of class groups

Let G be a finite abelian group, and F a global field of characteristic prime to the order of G. Then there exists a finite extension of F whose class group has a direct summand isomorphic to G.     

Directional Preferences of Approach of Nucleophiles to Sulfonium Ions

An analysis of the crystal environments of sulfonium ions shows that short nonbonded contacts (secondary bonds) to sulfur tend to occur along the extensions of the C-S primary bonds. Non-bonded contacts to the C (a)-atoms of sulfonium ions are not especially short and do not show any striking directional preference, except in sulfonium ions derived from methionine where a specific intramolecular interaction between a carboxyl O-atom and the C (γ)-atom may represent an incipient stage of the internal nucleophilic displacement leading to formation of homoserine and mercaptan.     

Tetrameric Cubic Structures of Two Solvated Lithium Enolates

The structures of the crystalline lithium enolates derived from 3, 3-dimethyl-2-butanone and from cyclopentanone have been determined by X-ray analysis. Both structures are tetrameric aggregates based on a Li₄O₄-cube, each Li⁺-ion being additionally bonded to the O-atom of a tetrahydrofuran solvent molecule.     

Oxidation of Organometallic Compounds

Stable organometallic compounds, notably of the later transition metals (groups VI–VIII), usually are characterized by closed shell electron configurations (typically 18-electron valence shells) which are destabilized by electron addition or removal. One-electron oxidation of such compounds results in the formation of unstable radical ions, whose characteristic reactivity patterns include susceptibility to nucleophilic attack, disproportionation, and metal-carbon bond dissociation. Two-electron oxidation may result in dissociation or oxidation of the organic ligand. In this review studies on the chemical and electrochemical oxidations of metal carbonyls, metal-olefin complexes, and alkyl transition-metal compounds are described. The studies encompass the following themes: (1) The kinetics and thermodynamics of the initial redox steps; (2) The characterization and reactivity patterns of the resulting oxidation products; (3) The synthetic and catalytic applications of organometallic redox processes.