Degenerate complex Hessian equations on compact K\"ahler manifolds

Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $m\in \mathbb{N}$ such that $1\leq m \leq n$. We prove that any $(\omega,m)$-sh function can be approximated from above by smooth $(\omega,m)$-sh functions. A potential theory for the complex Hessian equation is also developed which generalizes the classical pluripotential theory on compact K\"ahler manifolds. We then use novel variational tools due to Berman, Boucksom, Guedj and Zeriahi to study degenerate complex Hessian equations

A New Transmitted Reference Pulse Cluster Based Ultra-Wideband Transmitter Design

An energy efficient ultra-wideband (UWB) transmitter based on the novel transmitted reference pulse cluster (TRPC) modulation scheme is presented. The TRPC-UWB transmitter integrates, namely, wideband active baluns, wideband I-Q modulator based up-conversion mixer, and differential to single-ended converter. The integrated circuits of TRPC-UWB front end is designed and implemented in the 130-nm CMOS process technology. the measured worst-case carrier leakage suppression is 22.4 dBc, while the single sideband suppression is higher than 31.6 dBc, operating at the frequency from 3.1 GHz to 8.2 GHz. With adjustable data rate of 10 to 300 Mbps, the transmitter achieves a high energy efficiency of 38.4 pJ/pulse.Comment: 4 page, 8 figure