نتایج جستجو برای: jacobian rank
تعداد نتایج: 77374 فیلتر نتایج به سال:
Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's method, which works when the Mordell-Weil ...
We present a method for calculating the envelope surface of a parametric solid object swept along a path in three-dimensional space. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the Jacobian of the defining function has a rank-deficiency condition. Using the rank deficiency condition, we determine a set of square sub-Jacobian determin...
We study the barycentric straightening of simplices in higher rank irreducible symmetric spaces of non-compact type. We show that, for an n-dimensional symmetric space of rank r ≥ 2 (excluding S L(3,R)/S O(3) and S L(4,R)/S O(4)), the p-Jacobian has uniformly bounded norm, provided p ≥ n − r + 2. As a consequence, for the corresponding non-compact, connected, semisimple real Lie group G, in deg...
Preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite (SPD) Jacobian. Following the theoretical work in [1] we start from a given approximation of the inverse of the initial Jacobian, and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems arising in the Picard-Newton solution of...
This paper discusses deriving geometric jacobians and identifying and analyzing the kinematic singularities for two 6 DOF arm robots. First we show the direct kinematics and D-H parameters derived for these two arms. The Geometric jacobian is computed for Barrett WAM and Smokie OUR. By analyzing the jacobian matrices we find the configurations at which J is rank deficient and derive the kinemat...
In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the dens...
According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve Γ, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of Γ. It is proven that, for a generic X , the Abel-Jacobi map of the family of elliptic sextics...
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