We discuss solvability issues of H−/H2/∞ optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standardH−/H2/∞ optimization problem for which we discuss possible solution approaches. Using an appropriate definition of th...

Context uniication is a natural variant of second order uniica-tion that represents a generalization of word uniication at the same time. While second order uniication is wellknown to be undecidable and word uniication is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidab...

In this paper, the time and norm optimal control problems of controlled heat equations with a weight function are considered. For the time optimal problems, we study the following two cases: one is for equations with multi-domain control under null controllability, and the other is for equations under approximate null controllability. We prove the solvability, and obtain the bang-bang principle...

We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded real space. We first introduce four new Theorems for a set of periodic Functions with irrational periods, based on which we then use a trigonometric substituti...

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems with time-independent Hamiltonians. The mapping of dynamics can be performed in any dimension, for an arbitrary number of interacting particles and for any t...

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant ...

Recent empirical 9, 2] studies have shown that many interesting cost-based abduction problems can be solved eeciently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network ow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction prob...

Abstract. Let L = divA∇ be a real, symmetric second order elliptic operator with bounded measurable coefficients. Consider the elliptic equation Lu = 0 in a bounded Lipschitz domain Ω of R. We study the relationship between the solvability of the L Dirichlet problem (D)p with boundary data in L(∂Ω) and that of the L regularity problem (R)q with boundary data in W (∂Ω), where 1 < p, q < ∞. It is...