Algebraic theory of Colombeauʼs generalized numbers

Theory of Generalized Bernoulli-Hurwitz Numbers for the Algebraic Functions of Cyclotomic Type

This is an integral of a differential of first kind on C which does not vanish at ∞. The integral converges everywhere. If g = 0 the inverse funcion of (1.2) is −1/ sin(u). As is well-known, if g = 1 the inverse function of (1.2) is just the Weierstrass function ℘(u) with ℘(u) = 4℘(u) − 4 (or ℘(u) = 4℘(u) − 4). The Bernoulli numbers {B2n} are the coefficients of the Laurent expansion of −1/ sin...

On the algebraic numbers computable by some generalized Ehrenfest urns

This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls are drawn and their colors is changed according to the number of black balls among them.The limiting behaviour of the composition of the urn when both the tim...

On generalized fuzzy numbers

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Algebraic Numbers and Algebraic Integers

c © W W L Chen, 1984, 2013. This chapter originates from material used by the author at Imperial College London between 1981 and 1990. It is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage an...

Addition two generalized fuzzy numbers