An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...

In this paper, we will discuss the concept of almost sure convergence for specic groups of fuzzyrandom variables. For this purpose, we use the type of generalized Chebyshev inequalities.Moreover, we show the concept of almost sure convergence of weighted average pairwise NQDof fuzzy random variables.

Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...

pair of interlacing bights, A 1 and A 2. Let A 1 be between a 1 and a 2 and A 2 , between b 1 and b 2 , where a 1 , a 2 , b 1 and b 2 are four distinct vertices on J such that they are external vertices of attachment on J or one of s and t. Further assume that U has the least number of blocks of overlapping B PQ-bridges. Assume that B 1 , B 2 ,. . ., B l are so so ordered that if i < j (for 1 i...

For a given support L ∈ Fn qm and a polynomial g ∈ Fqm [x] with no roots in Fqm , we prove equality between the q–aryGoppa codesΓq ( L,N(g ) ) =Γq ( L,N(g )/g ) whereN(g ) denotes thenorm of g , that is gq +···+q+1. In particular, for m = 2, that is, for a quadratic extension, we get Γq ( L,gq ) = Γq ( L,gq+1 ) . If g has roots in Fqm , then we do not necessarily have equality and we prove that...

The ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P , Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P ′ which is isomorphic to P , and the complement of P ′ in V is isomorphic toQ. Conversely, we prove that every extension of...