Recursive real numbers

A real-time recursive dynamic model for vehicle driving simulators

This paper presents the Real-Time Recursive Dynamics (RTRD) model that is developed for driving simulators. The model could be implemented in the Driving Simulator. The RTRD can also be used for off-line high-speed dynamics analysis, compared with commercial multibody dynamics codes, to speed up mechanical design process. An overview of RTRD is presented in the paper. Basic models for specific ...

Recursive definitions on surreal numbers

Let No be Conway’s class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some ‘tameness’ and uniformity conditions, f must satisfy some interesting properties; in particular, the supremum of the class ̆ x ∈ No : f (x) ≥ 0 ̄ is actually an element of No. As an application, I will prove that concatenation function x ...

Some properties of fuzzy real numbers

In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove  Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

Real Recursive Functions and Real Extensions of Recursive Functions

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...

Real-Time Recursive Procedures