The counterexamples presented here are the first of this kind for notions of differentiability that satisfy a chain rule. Their context arises naturally from requiring differentiability of crucial ...

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 ...

1 Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria. 2 Department of Industrial Mathematics and Statistics, Ebonyi State University, Abakaliki, Nigeria. where a, b, ...

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: 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 ...

Recall that an indefinite integral (or antiderivative) is so called as it provides a family of solutions with a constant term. It is called indefinite as the constant \(c\) can take any real value, ...

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 ...