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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 ...

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 ...

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 ...

Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

ABSTRACT: The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and ...

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 ...

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 ...