Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
A brief history of the Jacobian
View through CrossRef
In his pioneering work, Jacobi discovered two remarkable identities related to the Jacobian. The first one asserts that the Jacobian has a divergence structure. The second one, that some vector fields involving the cofactors of the Jacobian are divergence free. We illustrate the fundamental impact of these properties on research, from the times of Jacobi to our days.
World Scientific Pub Co Pte Ltd
Title: A brief history of the Jacobian
Description:
In his pioneering work, Jacobi discovered two remarkable identities related to the Jacobian.
The first one asserts that the Jacobian has a divergence structure.
The second one, that some vector fields involving the cofactors of the Jacobian are divergence free.
We illustrate the fundamental impact of these properties on research, from the times of Jacobi to our days.
Related Results
Inverse Jacobian and related topics for certain superelliptic curves
Inverse Jacobian and related topics for certain superelliptic curves
Given an elliptic curve E over the complex numbers (CC) given by y^2 = x^3 + ax + b, there exists a lattice L in CC such that the group E(CC) of complex points on E is isomorphic ...
A Jacobian‐free Newton–Krylov method for thermalhydraulics simulations
A Jacobian‐free Newton–Krylov method for thermalhydraulics simulations
SummaryThe current paper is focused on investigating a Jacobian‐free Newton–Krylov (JFNK) method to obtain a fully implicit solution for two‐phase flows. In the JFNK formulation, t...
Learning a Resolution-Consistent Jacobian Field for Bio-Inspired Rigid-Soft Finger
Learning a Resolution-Consistent Jacobian Field for Bio-Inspired Rigid-Soft Finger
Bio-inspired tendon-driven rigid-soft coupled dexterous fingers exhibit strong nonlinearity and configuration-dependent sensitivity, making accurate modeling challenging. In discre...
Tropicalization of the universal Jacobian
Tropicalization of the universal Jacobian
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process o...
Fundamental Limits of Inferring Dynamical Gene Regulatory Models from Single-Cell Data
Fundamental Limits of Inferring Dynamical Gene Regulatory Models from Single-Cell Data
Abstract
A long-standing goal in systems biology is to construct computational models that capture gene regulatory dynamics. On the one hand, graph-based regulatory...
Dimensionally Homogeneous Jacobian and Condition Number
Dimensionally Homogeneous Jacobian and Condition Number
This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f...
Studies on register-based family history of cardiovascular disease : from preclinical to recurrent disease
Studies on register-based family history of cardiovascular disease : from preclinical to recurrent disease
<p dir="ltr"><b>Background</b></p><p dir="ltr">Family history of coronary heart disease (CHD) is a known risk-factor for incident atherosclerotic card...
Studies on register-based family history of cardiovascular disease : from preclinical to recurrent disease
Studies on register-based family history of cardiovascular disease : from preclinical to recurrent disease
<p dir="ltr"><b>Background</b></p><p dir="ltr">Family history of coronary heart disease (CHD) is a known risk-factor for incident atherosclerotic card...