Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the derivation trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.

x until it reaches a xed point. In order to determine whether an argument is a xed point, f x is compared with x. In the case of grammar analysis problems, the rst components of the elements of the grammar analysis problems are always the nonterminals of the given grammar. It follows that the rst components of the elements of f x and x are always equal, and that equality depends just on the sec...

We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations X = f (X) is equal to the least fixed-point of a linear system obtained by “linearizing” the polynomials of f in a certain way. Our proofs rely on derivation tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first use...

We present a new derivation of the momentum exchange algorithm first introduced by Ladd [12], to compute the flow force and torque on a submerged body. The starting point of our derivation is to consider the time derivative of the total momentum of a virtual fluid system that replaces the submerged body in the real problem. The new derivation gives, in turn, some correction terms to the origina...

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

Let n ∈ N − {1}, and let A be a Banach algebra. An additive map D : A → A is called n-Jordan derivation if D(a) = D(a)a + aD(a)a + ...+ aD(a)a+ aD(a), for all a ∈ A. Using fixed point methods, we investigate the stability of n–Jordan derivations (n–Jordan ∗−derivations) on Banach algebras (C∗−algebras). Also we show that to each approximate ∗−Jordan derivation f in a C∗− algebra there correspon...

When compared to the vast amount of research on domain engineering and building product lines, relatively little work has been dedicated to the derivation of individual products from product lines. Existing approaches to product derivation have been developed in isolation with different aims and purposes. The definition of a generic product derivation approach applicable to every domain may not...