Boundary controllability of Maxwell's equations with nonzero conductivity inside a cube, I: Spectral controllability

AbstractThis is a first paper in a series of two. In both papers, we consider the question of control of Maxwell's equations in a homogeneous medium with positive conductivity by means of boundary surface currents. The domain under consideration is a cube, where the conductivity is allowed to take on any nonnegative value. An additional restriction imposed in order to make this problem more suitable for practical implementations is that the controls are applied over only one face of the cube. In this paper, the method of moments is employed to establish spectral controllability for the above case (meaning that any finite combination of eigenfunctions is controllable). In the companion paper [S.S. Krigman, C.E. Wayne, Boundary controllability of Maxwell's equations with nonzero conductivity inside a cube, II: Lack of exact controllability and controllability for very smooth solutions, J. Math. Anal. Appl. (2006), doi:10.1016/j.jmaa2006.02.102] it will be established, by modifying the calculations in [H.O. Fattorini, Estimates for sequences biorthogonal to certain complex exponentials and boundary control of the wave equation, in: New Trends in Systems Analysis, Proceedings of the International Symposium, Versailles, 1976, in: Lecture Notes in Control and Inform. Sci., vol. 2, Springer, Berlin, 1977, pp. 111–124], that exact controllability fails for this geometry regardless of the size of the conductivity term. However, we will also establish in [S.S. Krigman, C.E. Wayne, Boundary controllability of Maxwell's equations with nonzero conductivity inside a cube, II: Lack of exact controllability and controllability for very smooth solutions, J. Math. Anal. Appl. (2006), doi:10.1016/j.jmaa2006.02.102] controllability of solutions that are smooth enough that the Fourier coefficients of their initial data decay at a suitable exponential rate

Pathogenesis of trimethyltin neuronal toxicity. Ultrastructural and cytochemical observations.

The ultrastructural cytopathologic and cytochemical effects of trimethyltin (TMT) neurotoxicity were delineated in hippocampal and pyriform neurons of acutely intoxicated adult rats. TMT produced neuronal necrosis that preferentially involved hippocampal formation pyriform cortex. The first subcellular alterations were multifocal collection of dense-cored vesicles and tubules and membrane-delimited vacuoles in the cytoplasm of the perikaryon and proximal dendrite. Ultrastructural cytochemical examination revealed that the vesicles and tubules had acid phosphatase activity analagous to Golgi-associated endoplasmic reticulum (GERL). Shortly after the appearance of the GERL-like vesicles and tubules, autophagic vacuoles and polymorphic dense bodies accumulated in the neuronal cytoplasm. Some dense bodies appeared to arise from the dense-cored tubules. Neuronal necrosis was characterized by increased electron density of the cytoplasm and large, electron-dense intranuclear masses. Alterations of mitochondria and other organelles were not observed in the early stages of cell injury. No light- or electron-microscopic alterations were found in liver or kidney. Comparable subcellular alterations were observed in adult and neonatal rats chronically intoxicated with TMT. A series of other trialkyl and tricyclic tins and dimethyltin did not produce similar pathologic findings. The GERL-like accumulations are unique in neuronal cytopathology. These findings suggests that GERL and autophagy play an important role in the pathogenesis of TMT-induced neuronal injury

The Grizzly, October 9, 2008

Biden and Palin Hold Their Ground in 2008 Debate • Pimps Up, Ho\u27s Down: Hip-Hop Music and Modern Women • Indian Temple Stampede Kills Hundreds, Injures Others • Hollywood Mourns Legend Paul Newman • Earth Shattering Stock Market Fall Shakes Nation • Spotlight on Sally Rousse: Dance Artistry at its Finest • Ursinus in Tuebingen Students Travel to Berlin, Munich • Introducing the Gender Wage Gap • Opinions: Democratic and Republican Extremes at Ursinus College; Zack\u27s Dining: Why Wait? • Women\u27s Rugby in for Incredible Season • UC Men\u27s Rugby: Sport with Quickly Growing Popularityhttps://digitalcommons.ursinus.edu/grizzlynews/1771/thumbnail.jp

The Grizzly, October 23, 2008

Professors\u27 Performance to Jazz Up Your Friday Night • Cafe Nia Event Brings Spirit of Poetry to Homecoming • Active Minds to Spread Mental Health Awareness at UC • Safe to Use Internet to Play Doctor? • UC Popularity Growing Steadily • Stand Up: STAND Rallies Ursinus Students for Darfur • Another Night of Artistry in Philadelphia • Omega Chi Blood Drive Takes the UC Campus by Storm, Highest Turnout Yet • Alpha Paintball Company: Fun for the Whole Family • Assassins Players Still on the Lookout • Opinions: GSA Members Call for Respect; Breakaway Presents Ten Minute Play Festival, Take Two • Senior Spotlight: Lisa Clark, Senior Women\u27s Soccer Playerhttps://digitalcommons.ursinus.edu/grizzlynews/1772/thumbnail.jp

The Grizzly, November 20, 2008

Adding Machine Makes Explosive Debut on UC Campus • Active Minds Encourages Students to Relax: Stop Stressing! • Creative Writing Author John Holman Visits UC Students • Is the Economy Affecting Your Waistline? • More Bailout News: AIG • Inside the Busy Life of Senior Laura Ng • Plummer Speaks About Importance of Election • Ottinger Fights Child Illiteracy in Cold • Play n Trade: New Store for Gamers • Letter to the Editor • Sunny Review • Dracula\u27s Ball Recap: Ideal Halloween Destination • Hockey Prepares for On-Campus Nationals This Weekendhttps://digitalcommons.ursinus.edu/grizzlynews/1776/thumbnail.jp