We have recast the problem of t ru th maintenance in a setting of algebraic equations over Boolean lattices. If a method of labeling propositions to justi fy them according to some reasoning agent's constraints of belief happens to conform to the postulates of Boolean lattices, the labeling system can be reformulated as an algebraic equation solving system. A l l t ru th maintenance systems kno...

In this paper we consider the supervisory control problem through language equation solving. The equation solving approach allows to deal with more general topologies and to find a largest supervisor which can be used as a reservoir for deriving an optimal controller. We introduce the notions of solutions under partial controllability and partial observability, and we show how supervisory contr...

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The effective Hamiltonian governing the time evolution of the composed system are derived from the master equation. Two examples, the dissipative two-level system an...

and we are going to determine all the possible dynamics of this type of equation. Also, we can say that generically there are two different T-periodic solutions. In this equation we emphasize the following antecedents. First, in 1975, there appeared a paper written by N. G. Lloyd [5] about complex solutions of a real Riccati equation. This study was continued in a 1984 paper by H. S. Hassan [3]...

The equation solving problem is to derive the behavior of the unknown component X knowing the joint behavior of the other components (or the context) C and the specification of the overall system S. The component X can be derived by solving the Finite State Machine (FSM) equation C ◊ X ∼ S, where ◊ is the parallel composition operator and ∼ is the trace equivalence or the trace reduction relati...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

We consider the family of active scalar equations on the plane and study the dynamics of two centrally symmetric patches. We focus on the two-dimensional Euler equation written in the vorticity form and consider its truncated version. For this model, a non-linear and non-local evolution equation is studied and a family of stationary solutions {y(x, λ)}, x ∈ [−1, 1], λ ∈ (0, λ0) is found. For th...