In this talk we present the Riccati inequality and equality for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results are based on earlier work on the Kalman-Yakubovich-Popov inequality in [AKP1]. The main theorems are closely related to the results of Yu.M. Arlinskĭı [ARL]. The main difference is that we do not assume the original ...

The model elimination calculus is a linear, refutationally complete calculus for first order clause logic. We show how to extend this calculus with aframeworkfor theory reasoning. Theory reasoning m~ans to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model e...

The TCP-Friendly Rate Control (TFRC) protocol manifests strong equality towards competing TCP or TCPfriendly flows. Although the RFC 3448 suggests that TFRC is suitable for multimedia, this equality is a great disadvantage in the case of transmitting multimedia over the TFRC. The TFRC emulates TCP-like congestion control using the TCP throughput equation. In the paper, we substitute the TCP thr...

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty produc...

Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, G̊) = Z(G̊) by introducing the bridge tree of a connected graph. Since this...

The model elimination calculus is a linear, refutationally complete calculus for rst order clause logic. We show how to extend this calculus with a framework for theory reasoning. Theory reasoning means to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model e...

Model Evolution is a lifted version of the propositional DPLL procedure for first-order logic with equality. This paper combines and extends the essentials of the latest Model Evolution variants with and without theory reasoning into a new calculus. The new calculus is described in detail. The main results reported here are the calculus’ completeness under (unavoidable) conditions, and its appl...

In systems driven away from equilibrium, the velocity correlation function and the linear-response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems...