$q$-analogue triangular numbers and distance geometry

Weighted triangular approximation of fuzzy numbers q

In this paper, we use the weighted distance between fuzzy numbers to investigate the approximation of arbitrary fuzzy numbers by weighted distance. We then discuss properties of the approximation strategy including continuity, translation invariance, scale invariance and identity and give an application to the generation of fuzzy partitions. 2006 Elsevier Inc. All rights reserved.

A q-ANALOGUE OF GENERALIZED STIRLING NUMBERS

We investigate a kind of q-analogue which involves a unified generalization of Stirling numbers as a limiting case with q→1. Some basic properties and explicit formulas will be derived, and certain applications related to previously known results will be discussed.

Triangular numbers and elliptic curves

Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solutions (r, s, t) in the function field Q(m, n) of the pair of equations r(r + 1)/2 = ms(s + 1)/2 r(r + 1)/2 = nt(t + 1)/2. } It turns out that infinitely many solutions exist. Several examples will be given.

. CO / 0505548 . ON q - EULER NUMBERS AND q - SALIÉ NUMBERS

Carlitz q-Bernoulli Numbers and q-Stirling Numbers

a+ dpZp = {x ∈ X | x ≡ a (mod dp N )}, where a ∈ Z lies in 0 ≤ a < dp , see [1-21]. The p-adic absolute value in Cp is normalized so that |p|p = 1/p. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C or a p-adic number q ∈ Cp. If q ∈ Cp, then we assume |q − 1|p < p − 1 p−1 , so that q = exp(x log q) for |x|p ≤ 1. We use the notation [x]q = [x :...