Results 1 to 10 of about 10,375 (259)

A Geometric Solution to the Jacobian Problem

Journal of New Theory, 2018
In this article given a geometric solution to the well-known Jacobian problem. The twodimensionalpolynomial Keller map is considered in four-dimensional Euclidean space R4. Used the conceptof parallel. A well-known example of Vitushkin is also considered.
Kerimbayev Rashid Konyrbayevich
doaj   +3 more sources

Dicritical divisors and Jacobian problem

Indian Journal of Pure and Applied Mathematics, 2010
A complex polynomial \(f:\mathbb{C}^{2}\rightarrow \mathbb{C}\) gives rise to a rational map from the projective plane to the projective line (by compactifying \(\mathbb{C}^{2}\) and \(\mathbb{C}\) to the projective spaces). Removing its points of indeterminacy (by blowing up) at points on the line at infinity we get a complex surface on which the map ...
Shreeram S Abhyankar, Abhyankar Shreeram S   +1 more
exaly   +3 more sources

A combinatorial analogue of the Jacobian problem in automata networks

Advances in Applied Mathematics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mau-Hsiang Shih
exaly   +3 more sources

Jacobian Conjecture as a Problem on Integral Points on Affine Curves

Vietnam Journal of Mathematics, 2021
It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then for some $n\gg 1$ there exists a counterexample $F\in \mathbb{Z}[X]^n$ of the form $F_i(X)=X_i+ (a_{i1}X_1+\dots ...
Van Chau Nguyen
exaly   +3 more sources

Surjective polynomial maps, and a remark on the jacobian problem

Manuscripta Mathematica, 1990
The authors prove the following theorem: ``If R is an affine domain (a domain that is either finitely generated as a ring, or finitely generated as an algebra over a subfield) but not a field, and if f: \(R^ m\to R^ m\) is a surjective polynomial map over R, then f is bijective, and its inverse is also a polynomial map over R.''
Lou Van Den Dries, Van Den Dries Lou
exaly   +3 more sources

A Note on the Jacobian Problem of Coifman, Lions, Meyer and Semmes

Journal of Fourier Analysis and Applications, 2023
AbstractCoifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$\mathcal {H}^1({\mathbb {R}}^n)$$ H
Sauli Lindberg
exaly   +5 more sources

Efficient Jacobian Computations for Complex ECT/EIT Imaging

Mathematics
The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography.
Markus Neumayer, Thomas Suppan, Thomas Bretterklieber, Hannes Wegleiter, Colin Fox   +4 more
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Attacking Jacobian Problem Using Resultant Theory

مجلة بغداد للعلوم, 2022
     This paper introduces a relation between resultant and the Jacobian determinant by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:
Alaa Jony, Shawki Al-Rashed
doaj   +1 more source

Per-unit Scheme for Integrated Solution of Hybrid Power-water Flow Problem

Journal of Modern Power Systems and Clean Energy, 2023
When applying the widely-used Newton-Raphson (N-R) method to the integrated solution of the hybrid power-water flow problem of the power-water integrated energy system (PW-IES), it is found that there are numerical differences among Jacobian elements ...
Xia Zhao, Hong Tan, Luo Wang, Mingyi Sun
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Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian [PDF]

AUT Journal of Mathematics and Computing, 2022
It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton’s method. Newton’s method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution ...
Mohammad Ali Mehrpouya
doaj   +1 more source