The main objective of this paper is to study the qualitative behavior for a class of nonlinear rational difference equation. We study the local stability, periodicity, Oscillation, boundedness, and the global stability for the positive solutions of equation. Examples illustrate the importance of the results Keywords— Difference equation, stability, oscillation, boundedness, globale stability an...

It is shown that the boundedness problem for a certain class of basic object nets and a corresponding class of multiset rewriting systems is decidable. To achieve this result Dickson’s Lemma for a certain class of multisets, and a modified Karp Miller algorithm, is applied. This presents another class of nets with different decidability behaviour for reachability and boundedness.

In this paper, we propose a progression semantics for firstorder answer set programs. Based on this new semantics, we are able to define the notion of boundedness for answer set programming. We prove that boundedness coincides with the notions of recursion-free and loop-free under program equivalence, and is also equivalent to first-order definability of answer set programs on arbitrary structu...

We consider the vector-valued extension of the Fefferman–Stein– Strömberg sharp maximal inequality under growth condition. As an application we obtain a vector-valued extension of the boundedness of the commutator. Furthermore, we prove the boundedness of the commutator. 2000 Mathematics Subject Classification: Primary 42B35; Secondary 42B25.

We study the boundedness problem for monadic least fixed points as a decision problem. While this problem is known to be undecidable in general and even for syntactically very restricted classes of underlying first-order formulae, we here obtain a decidability result for the boundedness issue for monadic fixed points over arbitrary first-order formulae in restriction to acyclic structures.

We prove that Rado’s Boundedness Conjecture from Richard Rado’s 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado’s Boundedness Conjecture: if a1, a2, and a3 are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution t...

In this paper we extend the traditional Dung framework for argumentation with cardinality constraints over the set of warranted arguments. This results in a new definition for argumentation semantics wherein arguments within an extension are both in some sense consistent and compliant with the constraints imposed on the system. After discussing the theoretical aspects of such a resource-bounded...

A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is χ-bounded if there exists a function f : N → N such that for all graphs G ∈ G, and all induced subgraphs H of G, we have that χ(H) ≤ f(ω(H)). We prove that proper homogeneous sets, clique-cutsets, and amalgams together preserve χ-boundedness. More precisely, we show that if G and G∗ a...

P/T nets with reset and transfer arcs can be seen as counter-machines with some restricted set of operations. Surprisingly, several problems related to boundedness are harder for Reset nets than for the more expressive Transfer nets. Our main result is that boundedness is undecidable for nets with three reset arcs, while it is decidable for nets with two resetable places.