In this paper, we revisit the problem of finding the average capacity of the Gaussian feedback channel. First, we consider the problem of finding the average capacity of the analog colored Gaussian noise channel where the noise has an arbitrary spectral density. We introduce a new approach to the problem where we solve the problem over a finite number of transmissions and then consider the limi...

Let us look at a special type of context sensitive grammars, the so-called Definite Clause Grammars, or DCG, as described by Pereira and Warren (l980). The following question seems natural here: every context sensitive language be described by meeins of a definite clause grammar ? The question must be answered in the eiffirmative, as can be seen by simu­ lating Turing machines or better Markov ...

We consider the non-definite linear functionals Ln[f ] = ∫ IR w(x)f (n)(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.

We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. show this can be rigorously addressed by a smooth and local adiabatic mapping procedure to number conserving Hamiltonian. In contrast generic fermionic pairing Hamiltonian, such always constructed for bosons. Our approach shows non-conserving classifi...

A possible solution for the problem of non-existence of universal time is given by utilizing Gödel’s incompleteness theorem [2]. In a recent book [1], Barbour presented a thought that time is an illusion, by noting that Wheeler-DeWitt equation yields the non-existence of time, whereas time around us looks flowing. However, he does not seem to have a definite idea or formal way to actualize his ...