The kinematic analyses, of manipulators and other robotic devices composed of mechanical links, usually depend on the solution of sets of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of equations and to give bounds on the number of solutions. These solution methods have also led to an understanding of how special choices of ...

In this paper we study the inverse problem of determining the unknown leading coefficient k 1⁄4 kðxÞ of the linear Sturm–Liouville operator Au 1⁄4 ðkðxÞu0ðxÞÞþ qðxÞuðxÞ, x 2 ð0; 1Þ, from boundary measurements, when u0ðxÞ or/and u00ðxÞ vanishes at several, called singular, points of the interval ð0; 1Þ. As a result the considered inverse problem has simultaneously different types (moderate or se...

We study the left-invertibility of infinite matrices indexed by metric spaces with polynomial growth. Under different conditions on the rows and the columns, we prove that being bounded-below in lp for some 1 ≤ p ≤ ∞, implies that there is a left-inverse which is bounded in lq, for all 1 ≤ q ≤ ∞. In particular, this applies to matrices with polynomial decay, indexed by discrete groups of polyno...

A function from the group GL(2, R) to itself is called polynomial if it can be written as some product of constant functions, the identity function, and the function that maps every element to its inverse. We give a necessary topological condition for a function to be polynomial. As a consequence we prove that transposition is not polynomial. Mathematics Subject Classification 2000. 08A40 (20G20)

A polynomial is determined by its roots and its leading coefficient. If you set the roots in motion, the critical points will move too. Using only tools from the undergraduate curriculum, we find an inverse square law that determines the velocities of the critical points in terms of the positions and velocities of the roots. As corollaries we get the Polynomial Root Dragging Theorem and the Pol...

In the heat-bath Glauber dynamics for the Ising model on the lattice, physicists believe that the spectral gap of the continuoustime chain exhibits the following behavior. For some critical inversetemperature βc, the inverse-gap is O(1) for β < βc, polynomial in the surface area for β = βc and exponential in it for β > βc. This has been proved for Z except at criticality. So far, the only under...

In this work we consider planar quasihomogeneous vector fields and we show, among other qualitative properties, how to calculate all the inverse integrating factors of such C systems. Additionally, we obtain a necessary condition in order to have analytic inverse integrating factors and first integrals for planar positively semi-quasihomogeneous vector fields which is related with the existence...

We have two main results. 1. Let P : Kn → Kn be a polynomial map with constant nonzero Jacobian, where K is any extension of Q. Then, P has a polynomial inverse if and only if the range of P contains a cartesian product of n universal Hilbert sets. 2. Let P : K → K be a polynomial map with constant nonzero Jacobian, where K is an algebraic number field. Then, P is invertible for “almost all” ra...

This paper is to present a geometrical proof of the plane Jacobian conjecture for rational polynomials by an approach of Newton-Puiseux data and geometry of rational surfaces. The obtained result shows that a polynomial map F = (P, Q) : C −→ C with PxQy − PyQx ≡ const. 6= 0 has a polynomial inverse if the component P is a rational polynomial, i.e. if the generic fiber of P is the 2-dimensional ...

This paper deals with closed form solutions for the inverse and forward position analyses of a 3-SPR parallel mechanism, which can be used to form the main body of a 5-DOF hybrid robot manipulator. In the inverse position analysis, a fourth order polynomial equation has been formulated, leading to four set of solutions of limb lengths for a given position of the reference point on the platform....