ON DIFFERENTIABLE MAPPINGS,

Abstract

This article contains mathematical proofs of three theorems on differentiable mappings. Theorems 1 and 2 establish the character of behavior of a mapping near an individual point at which the Jacobian is not equal to zero. Theorem 3 asserts that if the Jacobian is positive (is negative) at some point, then it is positive (is negative) also on a set of positive size, and the image of this set is also set of positive size.

Document Details

Document Type
Technical Report
Publication Date
Jun 12, 1964
Accession Number
AD0602348

Entities

People

  • A. M. Rodniinskii

Organizations

  • National Air and Space Intelligence Center

Tags

DTIC Thesaurus Topics

  • Behavior And Behavior Mechanisms
  • Personality

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.