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One one type of ud-preserving mapping

Milan Pasteka

Abstract

In this paper a class of mappings on unit interval is constructed. These mapping preserve uniform distribution and theirs iterations form a sequence which is Buck uniformly distributed. In the third part some prorties of these mappings are proven.

One one type of ud-preserving mapping

Abstract

In this paper a class of mappings on unit interval is constructed. These mapping preserve uniform distribution and theirs iterations form a sequence which is Buck uniformly distributed. In the third part some prorties of these mappings are proven.
Paper Structure (3 sections, 3 theorems, 27 equations)

This paper contains 3 sections, 3 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Mapping
  3. Monotonicity and Derivative of $T_{\boldsymbol{\pi}}$

Key Result

Theorem 1

Suppose that the permutations $\pi_i$ are cyclic of the length $m_i$. Let $\alpha \in [0.1)$, then the sequence of iterations $\{v(n)\}$, where $v(n)=T^n(\alpha)$ is Buck's uniformly distributed modulo $1$.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3