Cayley hypersurfaces

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, that generalize the Cayley surface.     

Endomorphism valued cohomology and gauge-neutral matter

For several physically interesting Calabi-Yau manifolds, we count and parametrize gauge-neutral matter particles occurring in corresponding superstring compactifications. To this end, we use the technique of exact and spectral sequences and then describe and discuss our results in the more familiar tensor notation.Supported by the Robert A. Welch Foundation and the NSF Grant: PHY 8605978. On leave of absence from the Ruder Bokovi Institute, Bijenika 54, YU-41000 Zagreb, Croatia, Yugoslavia     

Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras

Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case sl(2,C)$\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$, there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter.     

Excitation of analytes and enhancement of emission intensities in a d.c. plasma jet: a critical review leading to proposed mechanistic models

Experimental data and theoretical criteria are used to critically review existing models for analyte emission enhancement in the 3-electrode d.c. plasma (DCP). The analytical zone is characterized as a non-optically thin recombining plasma in partial thermodynamic equilibrium (PTE). Spectrochemical excitation the authors ascribe largely to: (1) argon resonance line radiative transport; (2) inversion of optically pumped argon states; (3) inversion of analyte populations by Franck-Condon collisions with argon; (4) energy cascading in analytes via a multitude of channels. Adding an easily ionized element (EIE): (1) induces additional resonance line radiative transfer; (2) raises electron densities in cooler, analyte-rich plasma margins; (3) locally increases argon optical absorption cross sections via Stark broadening; (4) redistributes ohmic heating. Coupling between the proposed mechanisms is non-linear. Relationships between radiative transfer and collisional redistribution and (1) background suppression by EIE and (2) analyte emission enhancement by helium are also examined. Similarities between DCP and inductively coupled plasma (ICP) excitation mechanisms are noted and practical implications are addressed.     

An edge-of-the-wedge theorem for hypersurface CR functions

The classical edge-of-the-wedge theorem for holomorphic functions is generally false for CR functions. However, it is true on Levi-indefinite hypersurfaces for wedges pointing in null directions.     

What is Q-Curvature?

Branson’s Q-curvature is now recognized as a fundamental quantity in conformal geometry. We outline its construction and present its basic properties.     

Extended magnetic reconnection across the dayside magnetopause

The extent of where magnetic reconnection (MR), the dominant process responsible for energy and plasma transport into the magnetosphere, operates across Earth's dayside magnetopause has previously been only indirectly shown by observations. We report the first direct evidence of X-line structure resulting from the operation of MR at each of two widely separated locations along the tilted, subsolar line of maximum current on Earth's magnetopause, confirming the operation of MR at two or more sites across the extended region where MR is expected to occur. The evidence results from in-situ observations of the associated ion and electron plasma distributions, present within each magnetic X-line structure, taken by two spacecraft passing through the active MR regions simultaneously.