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...

The concept of function permeates most branches of modern mathematics: from analysis, algebra and logic to probability and mathematical physics. However, the set-theoretic conception of function as a particular mathematical object (specifically, as a set of ordered pairs satisfying conditions of totality and single valuedness) was a long time in development. Indeed, historians generally cite th...

Let (At | i e I) be an indexed family of nonempty intervals of a linearly ordered set {L, <). Let (/, E) be the intersection graph of (̂ 4, | I G / ) , that is {i,j}eE if and only if At n At J= 0 . In [6], R. Rado considered the following sentence R(K), where K is a cardinal number. If Chr(J, E n |V]) ^ K for all ; £ / , |J| ^ K + , then Chr(/ , E) < K. He proved (see [6, Theorem 2]) that R(K) h...

recently, cho et al. [y. j. cho, r. saadati, s. h. wang, common xed point theorems on generalized distance in ordered cone metric spaces, comput. math. appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. in this paper, we prove some new xed point and common xed point theorems by using the distance in ordere...

Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ < g in Pp iif(p) < g(p) for all p £ P. We prove that if P and Q are finite, connected partially ordered sets and Pp = Q<¡ then Psg. Is a partially ordered set determined by its order-preserving mappings? L. M. Gluskin [4] has shown that the set of order-preserving mappings of a part...

A Latin square of order n is an n by n array in which every row and column is a permutation of a set N of n elements. Let L = [li,j ] and M = [mi,j ] be two Latin squares of even order n, based on the same N -set. Define the superposition of L onto M to be the n by n array A = (li,j ,mi,j). When n is even, L and M are said to be nearly orthogonal if the superposition of L onto M has every order...

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

We show there is a unique maximal positive variety of languages which does not contain the language (ab)∗. This variety is the unique maximal positive variety satisfying the two following conditions: it is strictly included in the class of rational languages and is closed under the shuffle operation. It is also the largest proper positive variety closed under length preserving morphisms. The or...

We introduce a new generalization of Alan Day’s doubling construction. For ordered sets L and K and a subset E ⊆ ≤L we define the ordered set L ?E K arising from inflation of L along E by K. Under the restriction that L and K are finite lattices, we find those subsets E ⊆ ≤L such that the ordered set L ?E K is a lattice. Finite lattices that can be constructed in this way are classified in term...

We introduce a new generalization of Alan Day’s doubling construction. For ordered sets L and K and a subset E ⊆ ≤L we define the ordered set L ?E K arising from inflation of L along E by K. Under the restriction that L and K are finite lattices, we find those subsets E ⊆ ≤L such that the ordered set L ?E K is a lattice. Finite lattices that can be constructed in this way are classified in term...