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Abstract: In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of ...

ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...

Abstract: This paper is a survey of some results on Newton's method as applied to the implicit function theorem, homotopy methods, and Bezout's theorem. An application to macroeconomics is also ...

Until now we have considered methods for computing derivatives that work directly on the function being differentiated. However, this is not always possible. For example, if the function can only be ...

Adjoint algorithmic differentiation is an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Often the differentiation does not cover the full pricing ...

Automatic differentiation is a transformation of the computational graph associated with the algorithmic implementation of a mathematical function. It breaks it down into atomistic primitive ...

ABSTRACT: In this paper, the dynamical behaviors of a modified Leslie-Gower predator-prey model incorporating fear effect and prey refuge are investigated. We delve into the construction of the model ...