We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f+F)~x when / has vanishing strict derivative. In this paper, we present an inverse mapping theorem for set-valued maps F acting from a complete metric space I toa linear space Y with a (translation) invariant metric. We prove that, for any function f: X -> Y with "vanishing strict deri...

Abstraet--Jacobians are used in robotics for motion planning and control. They are also used in algorithms that determine linkage parameter errors of robots and in algorithms that determine pair variable corrections for accurate motion. Most applications require that the inverse of the Jacobian be obtained. The causes of singularities in Jacobians and a procedure to detect their presence are gi...

In this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. Conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. Numerical examples are presented to illustrate the proposed method.

Given n + 1 points in Rd with nonnegative weights, the inverse 1-median problem with variable coordinates consists in changing the coordinates of the given points at minimum cost such that a prespecified point in Rd becomes the 1-median. The cost is proportional to the increase or decrease of the corresponding point coordinate. In case that the distances between points are measured by the recti...

This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution correspond...

A bstract I study the behavior of gauge-invariant gluon bi-local operator with space- like separation at large longitudinal distances. Performing Fourier transform, also calculate pseudo and quasi PDF low Bjorken x compare it leading next-to-leading twist approximation. show that pseudo-PDF quasi-PDF are very different this regime higher corrections come in not as inverse powers P but B .

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix (L) of a simple, undirected graph is proposed. The nature of the underlying sub-problems is studied in detail by means of an elegant interplay between L and the effective resistance distance (Ω). Closed forms are provided for a novel two-stage process that helps compute the p...

1.1 Singular values and matrix inversion For non-symmetric matrices, the eigenvalues and singular values are not equivalent. However, they share one important property: Fact 1 A matrix A, NxN, is invertible iff all of its singular values are non-zero.