This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the result...

This article investigates the solvability of volume integral equations arising in elastodynamic scattering by penetrable obstacles. The elasticity tensor and mass density are allowed to be smoothly heterogeneous inside the obstacle and may be discontinuous across the background-obstacle interface, the background elastic material being homogeneous. Both materials may be anisotropic, within certa...

In this paper, we study properties such as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of underlying graph. We show that graded simplicity algebra can be connected via algebra. Moreover, use Gelfand–Kirillov dimension a classification solvability.

We consider the problem of combining procedures that decide solvability of (dis)uniication problems over disjoint equational theories. Partial answers to the following questions are given: Which properties of the component theories imply intractability in the sense that there cannot be a polynomial combination algorithm, assuming P 6 = NP? Which general properties of the component theories guar...

All applications of equational uniication in the area of term rewriting and theorem proving require algorithms for general E-uniica-tion, i.e., E-uniication with free function symbols. On this background, the complexity of general E-uniication algorithms has been investigated for a large number of equational theories. For most of the relevant cases, the problem of deciding solvability of genera...

A kernel of a directed graph is a set of vertices without edges between them, such that every other vertex has a directed edge to a vertex in the kernel. A digraph possessing a kernel is called solvable. We show that solvability of digraphs is equivalent to satisfiability of theories of propositional logic. Based on a new normal form for such theories, this equivalence relates finitely branchin...

Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the known queries that separate FPC from Ptime, nearly nothing was known about the limitations of its expressive power. In our first main result we show that the e...

We’ve shown that if a solution exists, it’s unique (though only up to an additive constant for the Neumann boundary condition; in this case there’s also a requirement on g). We’ve also shown other interesting properties possessed by any solution, e.g., the maximum principle and the mean value property. Existence is actually the toughest issue. On certain special domains like rectangles and circ...

We prove local solvability for large classes of operators of the form