We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions or also po
sitions with infinitely many pieces. For lower bounds, we present specific infinite positions with transfinite game values of omega, omega^2, omega^2 times k, and omega^3. By embedding trees into chess, we show that there is a computable infinite chess position that is a win for white if the players are required to play according to a deterministic computable strategy, but which is a draw without that restriction. Finally, we prove that every countable ordinal arises as the game value of a position in infinite three-dimensional chess, and consequently the omega one of infinite three-dimensional chess is as large as it can be, namely, true omega one.
We characterize the terahertz detection mechanism in antenna-coupled metallic single-walled carbon nanotubes. At low temperature, 4.2 K, a peak in the low-frequency differential resistance is observed at zero bias current due to non-Ohmic contacts. T
his electrical contact nonlinearity gives rise to the measured terahertz response. By modeling each nanotube contact as a nonlinear resistor in parallel with a capacitor, we determine an upper bound for the value of the contact capacitance that is smaller than previous experimental estimates. The small magnitude of this contact capacitance has favorable implications for the use of carbon nanotubes in high-frequency device applications.
