The Lichnerowicz theorem on CR manifolds

We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.Comment: 21 page

On the boundary behavior of the holomorphic sectional curvature of the Bergman metric

We obtain a conceptually new differential geometric proof of P.F. Klembeck's result that the holomorphic sectional curvature of a strictly pseudoconvex domain approaches (in the boundary limit) the constant sectional curvature of the Bergman metric of the unit ball.Comment: 14 page

On the pseudohermitian sectional curvature of a strictly pseudoconvex CR manifold

We study the pseudohermitian sectional curvature of a CR manifold.Comment: 29 page

Upper Bound on the Capacity of Discrete-Time Wiener Phase Noise Channels

A discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. An upper bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. If the oversampling factor grows as $\text{SNR}^\alpha$ for $0\le \alpha \le 1$, then the capacity pre-log is at most $(1+\alpha)/2$ at high SNR.Comment: 5 pages, 1 figure. To be presented at IEEE Inf. Theory Workshop (ITW) 201

A rigorous definition of mass in special relativity

The axiomatic definition of mass in classical mechanics, outlined by Mach in the second half of 19th century and improved by several authors, is simplified and extended to the theory of special relativity. According to the extended definition presented here, the mass of a relativistic particle is independent of its velocity and coincides with the rest mass, i.e., with the mass defined in classical mechanics. Then, force is defined as the product of mass and acceleration, both in the classical and in the relativistic framework.Comment: to be published in Il Nuovo Cimento

Lower Bound on the Capacity of Continuous-Time Wiener Phase Noise Channels

A continuous-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A lower bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. The capacity pre-log depends on the oversampling factor, and amplitude and phase modulation do not equally contribute to capacity at high SNR.Comment: Extended version of a paper submitted to ISIT 2015. 9 pages and 1 figure. arXiv admin note: text overlap with arXiv:1411.039

Jacobi fields of the Tanaka-Webster connection on Sasakian manifolds

We build a variational theory of geodesics of the Tanaka-Webster connection on a strictly pseudoconvex CR manifold.Comment: 52 page

Capacity Outer Bound and Degrees of Freedom of Wiener Phase Noise Channels with Oversampling

The discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A novel outer bound on the capacity with an average input power constraint is derived as a function of the oversampling factor. This outer bound yields the degrees of freedom for the scenario in which the oversampling factor grows with the transmit power $P$ as $P^{\alpha}$. The result shows, perhaps surprisingly, that the largest pre-log that can be attained with phase modulation at high signal-to-noise ratio is at most $1/4$.Comment: 5 pages, 1 figure, Submitted to Intern. Workshop Inf. Theory (ITW) 201

Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.Comment: 5 pages, 2 figures. Accepted for presentation at ISIT 201