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NeuroImage: Clinical, 2014 Gray matter atrophy provides important insights into neurodegeneration in multiple sclerosis (MS) and can be used as a marker of neuroprotection in clinical trials. Jacobian integration is a method for measuring volume change that uses integration of the
Sridar Narayanan +2 more
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THE JACOBIAN CONJECTURE IS TRUE
Journal of New Theory, 2017 – We are talking about famous the Jacobian conjecture. Let f and g be polynomials dependent from two variables over the field K zero characteristics, f(x,y),g(x,y)∈K[x,y]
Kerimbayev Rashid Konyrbayevich
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Tropicalization of the universal Jacobian [PDF]
Épijournal de Géométrie Algébrique, 2022 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 of tropicalization of the universal compactified Jacobian over the moduli ...
Margarida Melo +3 more
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St. Petersburg Polytechnical University Journal: Physics and Mathematics, 2023 In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented
Golubkov Valentin, Garbaruk Andrey
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PLANAR HARMONIC MAPPINGS WITH A GIVEN JACOBIAN
Проблемы анализа, 2023 The article is devoted to the study of the Jacobians of sense-preserving harmonic mappings in the unit disk of the complex plane. The main result is a criterion for an infinitely differentiable positive function to be a Jacobian of some sense-preserving
S. Yu. Graf, I. A. Nikitin
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Sensors, 2020 Sarcopenia is defined as muscle mass and strength loss with aging. As places, such as South Korea, Japan, and Europe have entered an aged society, sarcopenia is attracting global attention with elderly health.
Yeoun-Jae Kim +2 more
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Of Commutators and Jacobians [PDF]
, 2021 I discuss the prescribed Jacobian equation $Ju=\det\nabla u=f$ for an unknown vector-function $u$, and the connection of this problem to the boundedness of commutators of multiplication operators with singular integrals in general, and with the Beurling operator in particular. A conjecture of T. Iwaniec regarding the solvability for general datum $f\in
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An extension to the planar Markus–Yamabe Jacobian conjecture
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We extend the planar Markus–Yamabe Jacobian conjecture to differential systems having Jacobian matrix with eigenvalues with negative or zero real parts.
Marco Sabatini
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The Jacobian conjecture for symmetric Jacobian matrices
Journal of Pure and Applied Algebra, 2004 Let \(F = (F_1,\ldots,F_n) : \mathbb C^n \longrightarrow \mathbb C^n\) be a polynomial map and \(J(F) = (\partial F_i/\partial x_j)\) the Jacobian matrix of \(F\). The Jacobian conjecture asserts that \(F\) is invertible if det\((J(F)) \in \mathbb C^*\).
van den Essen, Arno, Washburn, Sherwood
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Observations on the Computation of Eigenvalue and Eigenvector Jacobians
Algorithms, 2019 Many scientific and engineering problems benefit from analytic expressions for eigenvalue and eigenvector derivatives with respect to the elements of the parent matrix.
Andrew J. Liounis +2 more
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