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Simple close curve magnetization and application to Bellman's lost in the forest problem

Theophilus Agama

Abstract

In this paper, we introduce and develop the notion of simple closed-curve magnetization. We provide an application to the Bellman lost in the forest problem by assuming special geometric conditions between the hiker and the boundary of the forest.

Simple close curve magnetization and application to Bellman's lost in the forest problem

Abstract

In this paper, we introduce and develop the notion of simple closed-curve magnetization. We provide an application to the Bellman lost in the forest problem by assuming special geometric conditions between the hiker and the boundary of the forest.

Paper Structure

This paper contains 5 sections, 4 theorems, 48 equations.

Table of Contents

  1. Introduction and problem statement
  2. Simple close curves with magnetic boundaries
  3. Connected and isomorphic simple close curves with magnetic boundaries
  4. Application to Bellman's lost in the forest problem
  5. A sketch partial solution

Key Result

Proposition 2.4

Every simple closed curve $\mathcal{C}$ in $\mathbb{R}^n$ with magnetic boundary is uniquely determined by their magnetic boundary $\mathcal{C}_{\mathcal{B}}$ up to constant dilates of their magnets.

Theorems & Definitions (12)

  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Proposition 2.4
  • proof
  • Theorem 2.5
  • proof
  • Theorem 2.6
  • proof
  • Definition 3.1
  • ...and 2 more