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Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian conjecture [PDF]
Linear Algebra and its Applications, 1996 Let \(F:K^n\to K^n\) be a polynomial map, \(F(x)= (F_1(x), \dots, F_n(x))\), and \(J(F)= ({\partial F_i \over \partial x_j})\) be the Jacobian matrix. \(J(F)\) is called strongly nilpotent if \(J(F)(x_1) \cdot \cdots \cdot J(F) (x_n)=0\) for all \(x_1, \dots, x_n\in K^n\). It is proved that the following conditions are equivalent: 1.
Essen, A. van den +1 more
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Topology optimization of three-translational degree-of-freedom spatial compliant mechanism
Advances in Mechanical Engineering, 2019 Considering that the Jacobian matrix maps the velocity of the joint space of the robot to the end velocity of the Cartesian space, a novel topology optimization approach is proposed in this article for the design of three-translational degree-of-freedom ...
Dachang Zhu, Yanping Feng, Wanghu Zhan
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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
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Factor Price Equalization : Geometrical Conditions [PDF]
, 1998 This paper presents a geometrical approach to the univalence problem for a system of cost functions. We present a natural (almost tautological) extension of a geometrical theorem due to McKenzie: our sufficient condition is related to the non ...
Fujimoto, Takao, Ranade, Ravindra R.
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Nuclear Engineering and Technology, 2017 This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems.
Manuele Aufiero, Massimiliano Fratoni
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Sparsing in Real Time Simulation [PDF]
, 2003 Modelling of mechatronical systems often leads to large DAEs with stiff components. In real time simulation neither implicit nor explicit methods can cope with such systems in an efficient way: explicit methods have to employ too small steps and implicit
Bornemann, Folkmar, Schiela, Anton
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Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms [PDF]
, 2001 We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations.
Nepomechie, Rafael I.
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Application of seeding and automatic differentiation in a large scale ocean circulation model [PDF]
Modeling, Identification and Control, 2005 Computation of the Jacobian in a 3-dimensional general ocean circulation model is considered in this paper. The Jacobian matrix considered in this paper is square, large and sparse.
Frode Martinsen, Dag Slagstad
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, 2013 In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients.
Liu, Tingting, Yang, Chenyang
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A note on large gauge transformations in double field theory [PDF]
, 2015 We give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. This result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required, equivalent to ...
Naseer, Usman
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