The Jacobian matrix and global univalence of mappings

  title={The Jacobian matrix and global univalence of mappings},
  author={David Gale and H. Nikaido},
  journal={Mathematische Annalen},
Nonconvexities in Univalence
Conditions under which the set need not be convex are presented, demonstrating first that the set can be diffeomorphic to a convex set and, second, that theset can have holes inside of it.
Domains of unicity
The Gale–Nikaido theorem claims that if the Jacobian of a mapping F is a P-matrix at every point of K and K is a closed rectangular region in R n , then F is globally univalent on K . Under the more
On the Hicksian Laws of Comparative Statics for the Hicksian Case: the Path-Following Approach Using an Alternative Homotopy
The paper discusses an approach to comparative statics in the large by making use of a homotopy continuation method. This is based on the path-following approach presented by the author which is in
Algebraic Univalence Theorems for Nonsmooth Functions
Abstract A well known univalence result due to D. Gale and H. Nikaido (1965, Math. Ann. 159, 81–93) asserts that if the Jacobian matrix of a differentiable function from a closed rectangle K in R n
P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems
This paper first explores reaction systems and derive results which provide a deep connection between system structure and the P matrix property, then examines a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process and characterize conditions which ensure that the P Matrix property survives the negative feedback.
CP-rays in simplicial cones
The concept of regularity is generalized using this property of every interior point of the triangle being a CP-point, and extended to simplicial cones in ℝn, and necessary and sufficient conditions for this property to hold in them are derived.
Existence and uniqueness of solutions for the generalized linear complementarity problem
Cottle and Dantzig (Ref. 1) showed that the generalized linear complementarity problem has a solution for anyq∈Rm ifM is a vertical blockP-matrix of type (m1,...,mn). They also extended known


is regular and schlicht in the unit circle, then we may say, for convenience, that $f(z)$ is a function of the class $k$ . If $f(z)$ is a function of the class $k$ and maps the unit circle on a
Linear Inequalities And Related Systems
The description for this book, Linear Inequalities and Related Systems. (AM-38), will be forthcoming.
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