Picard-vessiot theory and the Jacobian problem
There are two definitions of Picard-Vessiot extension of partial differential fields, defined respectively in [\textit{E. R. Kolchin}, Proc. Am. Math. Soc. 3, 596--603 (1952; Zbl 0047.33303)] and in [\textit{M. van der Put} and \textit{M. Singer}, Galois theory of linear differential equations. Grundlehren der Mathematischen Wissenschaften 328. Berlin:
Crespo, Teresa, Hajto, Zbigniew
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Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient [PDF]
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions are obtained for
Bouchut, Francois +2 more
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Iterative Solutions to the Inverse Geometric Problem for Manipulators with no Closed Form Solution [PDF]
A set of new iterative solutions to the inverse geometric problem is presented. The approach is general and does not depend on intersecting axes or calculation of the Jacobian.
Pål Johan From, Jan Tommy Gravdahl
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Partitioned semi-implicit methods for simulation of biomechanical fluid-structure interaction problems [PDF]
This article is published under a CC BY licence. The Version of Record is available online at: http://dx.doi.org/10.1088/1742-6596/745/3/032020.This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an ...
González Acedo, Ignacio +3 more
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Quantitative Estimates on Jacobians for Hybrid Inverse Problems
We consider $ $-harmonic mappings, that is mappings $U$ whose components $u_i$ solve a divergence structure elliptic equation ${\rm div} ( \nabla u_i)=0$, for $i=1,\ldots,n $. We investigate whether, with suitably prescribed Dirichlet data, the Jacobian determinant can be bounded away from zero.
Alessandrini, G., NESI, Vincenzo
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A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method [PDF]
In this article, we apply three numerical methods to study the L∞-convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side.
M. Bahi, M. Beggas, N. Nesba, A. Imtiaz
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The problem of inverse kinematics is essential to consider while dealing with the robot’s mechanical structure in almost all applications. Since the solution of the inverse kinematics problem is very complex, many research efforts have been working
Wael Mohammed Elawady +2 more
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Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 1: Model description and Jacobian calculation [PDF]
Our global understanding of clouds and aerosols relies on the remote sensing of their optical, microphysical, and macrophysical properties using, in part, scattered solar radiation.
J. Loveridge +6 more
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Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities [PDF]
This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as polynomial optimization by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions.
Guo, Feng, Wang, Li, Zhou, Guangming
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This paper presents a method to directly extract the Jacobian matrix of a power system’s power flow (PF) equations in polar coordinates (termed as DEJMP method). This method is designed to reduce the computational complexity of the extraction process and
Zhongliang Lyu +4 more
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