Oka's principle for holomorphic submersions with sprays

We classify, up to a local isometry, all non-K?hler almost K?hler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost K?hler 4-manifolds satisfy the third curvature condition of A. Gray. We use our local classification to show that, in the compact case, the third curvature condition of Gray is equivalent to the integrability of the corresponding almost complex structure. Received: 1 October 2001 / Published online: 17 June 2002     

Internalism, externalism, and beyond: 19th-century British algebra

This paper discovers the roots of symbolical algebra in a three-quarters-of-a-century British discussion of sound reasoning, general terms, and signs—a discussion in which mathematical and philosophical elements were freely and perhaps inseparably intermingled. It establishes, in particular, a link between early-19th-century symbolical algebra and nominalism. Opening with a review of recent attacks on the rigid internal/external dichotomy, which underlies much of the modern history of science, the paper also serves as an example of the fertility of suspending the dichotomy in pursuit of earlier mathematical subcultures.     

Isomer shifts in Zr2Fe and Zr3Fe

The⁵⁷Fe isomer shifts in the crystalline compounds Zr₂Fe and Zr₃Fe are calculated. We use the standard first-principles linear-muffin-tin-orbital formalism in the atomic sphere approximation (LMTO-ASA) to obtain the electronic structure of the compounds. The electronic structure of pure Fe was also calculated with the same formalism, where the local spin density approximation for the exchange correlation term is used. We found that the calculated isomer shift values are in good agreement with the experimental values for Zr₂Fe and Zr₃Fe found in the literature.     

The equality of fractal dimension and uncertainty dimension for certain dynamical systems

[MGOY] introduced the uncertainty dimension as a quantative measure for final state sensitivity in a system. In [MGOY] and [P] it was conjectured that the box-counting dimension equals the uncertainty dimension for basin boundaries in typical dynamical systems. In this paper our main result is that the box-counting dimension, the uncertainty dimension and the Hausdorff dimension are all equal for the basin boundaries of one and two dimensional systems, which are uniformly hyperbolic on their basin boundary. When the box-counting dimension of the basin boundary is large, that is, near the dimension of the phase space, this result implies that even a large decrease in the uncertainty of the position of the initial condition yields only a relatively small decrease in the uncertainty of which basin that initial point is in.Research in part supported by AFOSR and by the Department of Energy (Scientific Computing Staff Office of Energy Research)     

Composition of extraction products from alkylated high-sulphur coals

Products of reductive and non-reductive methylation of two high-sulphur coals (Mequinenza and Illinois No. 6) have been extracted by dichloromethane. It has been established that the efficiency of the transformation of coal to the products soluble in CH₂Cl₂ is higher for coals subjected to non-reductive methylation by the Liotta method than for those after reduction in the potassium/liquid ammonia system. The extracts and the extraction residues were subjected to elemental analysis, IR spectroscopy, and AP-TPR (Atmospheric Pressure-Temperature Programmed Reduction) measurements. It has been shown that the main species undergoing extraction by CH₂Cl₂ are aliphatic compounds or aromatic structures of low degree of condensation. The effect of the extraction on the sulphur groups in coal has been discussed.     

The cardinalities of the Green classes of the free objects in varieties of bands

We compute the cardinalities of the Green classes of the free objects in the varieties of bands. We also compare the cardinalities obtained and analyse the “collapsing” of the finitely generated free objects. We deduce corresponding results for varieties of band monoids.     

Indole-2,3-quinodimethanes: Generation, reactivity and regioselective control of intermolecular Diels-Alder reactions

N-acylindole-2,3-quinodimethanes generated at low temperature from the N-acyl-2,3-bis (bromomethyl)indoles undergo a variety of cycloadditions including the reversible chelotropic reaction with sulphur dioxide to yield the unreported 1,3-dihydrothieno[3,4-b]indole-2,2-dioxide 9. Successful attempts to control the regioselectivity of reactions with unsymmetrical dienophiles are described.     

Classical conformational analysis of strained organic molecules. I. [l,m,n]Propellanes with l,m,n equal to 2, 3, and 4

Classical conformational analysis was applied to the study of the variation of heats of formation (HOF ) and geometrical parameters of small-ring propellanes. As expected, the calculated HOF is the smallest for [4,4,4] propellane I and the largest for [2,2,2]propellane X. In spite of the different trends exhibited by the strain energy components, the calculated HOF values may be reproduced within a simple additivity scheme. The calculated bridgehead–bridgehead bond length is the longest for [2,2,2]propellane (1.655 Å), lowers with increasing molecular size, and is equal to 1.558 Å for [4,4,4]propellane. In agreement with experimental findings the latter value is significantly larger than the standard value of 1.54 Å typical for unstrained hydrocarbons. Other calculated geometrical parameters as well as HOF values cannot be compared with experimental and/or theoretical results since there is a lack of reliable experimental data. Surprisingly, [2,2,2]propellane was found to be more flexible than the less strained bicyclo[2,2,2]octane.