Formal Adjoints and a Canonical Form for Linear Operators

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.Comment: 3 page

The Research of Thomas P. Branson

The Midwest Geometry Conference 2007 was devoted to the substantial mathematical legacy of Thomas P. Branson who passed away unexpectedly the previous year. This contribution to the Proceedings briefly introduces this legacy. We also take the opportunity of recording his bibliography. Thomas Branson was on the Editorial Board of SIGMA and we are pleased that SIGMA is able to publish the Proceedings.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A study of marine luminescence signatures, part 1

Fluorescent excitation and emission spectral data on chlorophyll and Gelbstoff in natural sea waters from the Atlantic, Gulf, and Pacific coasts show that algae particulates are totally absorbing over much of the near ultraviolet and visible spectra and act approximately as quantum counters; plant pigments absorb energy and transfer a large portion to chlorophyll where some fraction is emitted as chlorophyll fluorescence. Gelbstoff data do not exhibit quantum counter action because of their low concentration. It is concluded that luminescence data of natural sea waters are useful in monitoring algal and Gelbstoff as well as pollutant concentrations

Global MHD Simulations of Neptune's Magnetosphere

A global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large-scale reconfiguration of magnetic topology and plasma distribution. During the “pole-on” magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole-on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning “off” and “on” when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations

Electrostatic Contributions of Aromatic Residues in the Local Anesthetic Receptor of Voltage-Gated Sodium Channels

Antiarrhythmics, anticonvulsants, and local anesthetics target voltage-gated sodium channels, decreasing excitability of nerve and muscle cells. Channel inhibition by members of this family of cationic, hydrophobic drugs relies on the presence of highly conserved aromatic residues in the pore-lining S6 segment of the fourth homologous domain of the channel. We tested whether channel inhibition was facilitated by an electrostatic attraction between lidocaine and {pi} electrons of the aromatic rings of these residues, namely a cation-{pi} interaction. To this end, we used the in vivo nonsense suppression method to incorporate a series of unnatural phenylalanine derivatives designed to systematically reduce the negative electrostatic potential on the face of the aromatic ring. In contrast to standard point mutations at the same sites, these subtly altered amino acids preserve the wild-type voltage dependence of channel activation and inactivation. Although these phenylalanine derivatives have no effect on low-affinity tonic inhibition by lidocaine or its permanently charged derivative QX-314 at any of the substituted sites, high-affinity use-dependent inhibition displays substantial cation-{pi} energetics for 1 residue only: Phe1579 in rNaV1.4. Replacement of the aromatic ring of Phe1579 by cyclohexane, for example, strongly reduces use-dependent inhibition and speeds recovery of lidocaine-engaged channels. Channel block by the neutral local anesthetic benzocaine is unaffected by the distribution of {pi} electrons at Phe1579, indicating that our aromatic manipulations expose electrostatic contributions to channel inhibition. These results fine tune our understanding of local anesthetic inhibition of voltage-gated sodium channels and will help the design of safer and more salutary therapeutic agents