In this section we will talk about some simple algorithms for looking up items in a sorted list. Broadly speaking, an algorithm is a group of instructions that completely characterize the process of converting a set of inputs into desired outputs. To illustrate this concept, we shall solve a basic search problem. Let L = {l1, l2, . . . , lK} denote a set of ordered objects, where lk precedes lk...

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...

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G,⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex W -definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two conseq...

We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentago...

Given an ordered eld K we compute the natural valuation and skeleton of the ordered multiplicative group K in terms of those of the ordered additive group K We use this computation to provide necessary and su cient conditions on the value group v K and residue eld K for the L equivalence of the above mentioned groups We then apply the results to exponential elds and describe v K in that case Fi...

We introduce the notion of ideal, prime ideal, lter, fuzzy ideal, fuzzy prime ideal, fuzzy lter of ordered $Gamma$-semiring and study their properties and relations between them. We characterize the prime ideals and lters of ordered $Gamma$-semiring with respect to fuzzy ideals and fuzzy l- ters respectively.

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

The set of isotopy classes ordered n-component links in the 3-sphere is acted on by symmetric group via permutation components. intrinsic symmetry link, S(L), defined to be elements that preserve type L as an unoriented link. study these groups was initiated 1969, but question whether or not every subgroup arises intrinisic some link has remained open. We provide counterexamples; particular, if...