Statistics and characterization of matrices by determinant and trace

The Ramanujan Journal - Answering a question of Erdös, Komlós proved in 1968 that almost all $$n\times n$$ Bernoulli matrices are nonsingular as $$n\rightarrow \infty $$ . In this paper,...     

An organometallic inhibitor for glycogen synthase kinase 3

Replacing natural products with kinetically inert metal complexes may lead to a new class of therapeutics in which a metal center plays the role of an innocent bystander, organizing the orientation of the organic ligands in the receptor space. As an example of this approach, a ruthenium complex is described that copies the binding mode of indolocarbazole protein kinase inhibitors and serves as a reversible, low-nanomolar inhibitor for glycogen synthase kinase 3 (GSK-3).     

Spectral analysis of eigenparameter dependent boundary value transmission problems

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces.     

Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale Invited Paper

We review some of the recent advances in the development of subwavelength plasmonic devices for ma- nipulating light at the nanoscale, drawing examples from our own work in metal-dielectric-metal (MDM) plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switch- ing in MDM plasmonie waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.     

Temperature dependent energy relaxation time in AlGaN/AlN/GaN heterostructures

The two-dimensional (2D) electron energy relaxation in Al_0.25Ga_0.75N/AlN/GaN heterostructures was investigated experimentally by using two experimental techniques; Shubnikov-de Haas (SdH) effect and classical Hall Effect. The electron temperature (T_e) of hot electrons was obtained from the lattice temperature (T_L) and the applied electric field dependencies of the amplitude of SdH oscillations and Hall mobility. The experimental results for the electron temperature dependence of power loss are also compared with the current theoretical models for power loss in 2D semiconductors. The power loss that was determined from the SdH measurements indicates that the energy relaxation of electrons is due to acoustic phonon emission via unscreened piezoelectric interaction. In addition, the power loss from the electrons obtained from Hall mobility for electron temperatures in the range T_e > 100 K is associated with optical phonon emission. The temperature dependent energy relaxation time in Al_0.25Ga_0.75N/AlN/GaN heterostructures that was determined from the power loss data indicates that hot electrons relax spontaneously with MHz to THz emission with increasing temperatures.