The periodontal ligament (PDL) is a soft biological tissue which shows a strongly nonlinear and time dependent mechanical behavior. Recent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be described well by the separable quasi linear viscoelasticity theory which is usually used in tissue biomechanics. Therefore, P...

The success of superposition-based theorem proving in first-order logic relies in particular on the fact that the superposition calculus is able to decide well-known classical decidable fragments of first-order logic and has been successful in identifying new decidable classes. In this paper, we extend this story to the hierarchic combination of linear arithmetic and first-order superposition. ...

We study nonlinear dispersive wave systems described by hyperbolic PDE’s in Rd and difference equations on the lattice Zd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pas...

The hierarchical superposition based theorem proving calculus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arithmetic. In particular, we develop new effective version...

The paper studies the problem of reachability for linear systems in the presence of uncertain input disturbances that may also be interpreted as the action of an adversary in a game-theoretic setting. It emphasizes the differences between reachability under open-loop and closed-loop control. The situation when observations arrive at given isolated instances of time, leads to problems of anticip...

We present a method to solve the inverse problem in pulsed photothermal radiometry sPPTRd that exploits advantages of truncated singular value decomposition sT-SVDd while imposing a non-negativity constraint to the solution. The presented method is a hybrid in the sense that it expresses the solution vector as a linear superposition of right singular vectors, but with a non-negative constraint ...