The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic t...

The edge-bandwidth problem is an analog of the classical bandwidth problem, in which one has to label the edges of a graph by distinct integers such that the maximum difference of labels of any two incident edges is minimized. We prove tight bounds on the edge-bandwidth of hypercube and butterfly graphs and complete k-ary trees which extend and improve on previous known results. We also provide...

The role of symmetry in ring theory is universally recognized. most directly definable universal relation a symmetric set isomorphism. This article develops certain structure bipolar fuzzy subrings, including quotient ring, homomorphism, and We define (?,?)-cut investigate the algebraic attributions this phenomenon. also support prove various important properties relating to concept. Additional...

In this paper we introduce a notion of divisibility and primality on k-ary trees and we nd a relation between indecomposable preex code and prime trees. This relation allows to work on trees instead than directly on preex codes. In this way we can prove a density theorem for indecomposable preex codes and we can give an algorithm to test the indecomposability of a maximal preex code.

In this paper, we present an involution on some kind of colored k-ary trees which provides a combinatorial proof of a combinatorial sum involving the generalized Catalan numbers Ck,γ(n) = γ kn+γ ( kn+γ n ) . From the combinatorial sum, we refine the formula for k-ary trees and obtain an implicit formula for the generating function of the generalized Catalan numbers which obviously implies a Van...

We prove that any IN-rational sequence s = (s n) n1 of nonnega-tive integers satisfying the Kraft strict inequality P n1 s n k ?n < 1 is the enumerative sequence of leaves by height of a rational k-ary tree. We give an eecient algorithm to get a k-ary rational tree. Particular cases of this result had been previously proven. We give some partial results in the case of equality. Especially we so...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergr...