In this paper we obtain some results about a class of functions ̺ : Ω → R+, where Ω is an open set of R, which are related to the distance function from a fixed subset S̺ ⊂ ∂Ω. We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function ̺.

In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of ...

In mathematics, various representations of real numbers have been investigated, such as nested interval representations, Cauchy sequences, ... • The effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. • However, the primitive recursive (p.r., for short) versions of these representations can lead to different ...

We show that the index set complexity of the computably categorical structures is Π1-complete, demonstrating that computable categoricity has no simple syntactic characterization. As a consequence of our proof, we exhibit, for every computable ordinal α, a computable structure that is computably categorical but not relatively ∆α-categorical.

We consider partition function games and introduce new definitions of the core that include the effects of externalities. We assume that all players behave rationally and that all stable outcomes arising are consistent with the appropriate generalised concept of the core. The result is a recursive definition of the core where residual subgames are considered as games with fewer players and with...

We introduce a basis of rational polynomial-like functions P 0 ,. .. , P n−1 for the free module of functions Z/nZ → Z/mZ. We then characterize the subfamily of congruence preserving functions as the set of linear combinations of the functions lcm(k) P k where lcm(k) is the least common multiple of 2,. .. , k (viewed in Z/mZ). As a consequence , when n ≥ m, the number of such functions is indep...

We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+ βyn)/(1 + yn−1) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a+ byn)/(A+Byn−1), when th...

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

We prove, in primitive recursive arithmetic, an extension of a theorem established by Milliken and independently by Neget~il and R6dl on partitions of fixed rank partitions of a finite set. In this way we depict the preservation of structure under partitions of the outcomes of substitution systems, which can also undergo various stage transitions.