From the more than two hundred partial orders for fuzzy numbers proposed in literature, only a few are total. In this article, we introduce notion of admissible order equipped with order, i.e., total which refines order. particular, it is given special attention to by Klir and Yuan 1995. Moreover, propose method construct on terms linear defined intervals considering strictly increasing upper d...

A sequence of integers in an interval of length x is called admissible if for each prime there is a residue class modulo the prime which contains no elements of the sequence. The maximum number of elements in an admissible sequence in an interval of length x is denoted by %∗(x). Hensley and Richards showed that %∗(x) > π(x) for large enough x. We increase the known bounds on the set of x satisf...

1 Prologue Ordinals made their entrance in proof theory through Gentzen's second consistency proof for Peano Arithmetic by transsnite induction up to " 0 , the latter being applied only to decidable predicates (cf. Gentzen 1938]). Gentzen's constructive use of ordinals as a method of analyzing formal theories has come to be a paradigm for much of proof theory from then on, particularly as exemp...

Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let ρ ∗(x) be the size of the largest admissible set in [1, x]. The Prime k-tuples Conjecture states that any for any admissible set, there are infinitely many n such that n+b1, n+b2, . . . n+bk are simultaneously prime. In 1974, Hensley and Richards ...

The distribution behavior of ofloxacin enantiomers was examined in the aqueous and organic solvent of a two-phase system containing chiral selector L-tartarate. The effect of extraction equilibrium time, buffer pH, organic solvents and length of alkyl chain of L-tartarate on the partition coefficients and enantioselectivity of racemic ofloxacin were investigated, respectively. The L-tartara...