In the theory of 2 D Ginzburg-Landau vortices, Jacobian plays a crucial role for detection topological singularities. We introduce related distributional quantity, called global that can detect both interior and boundary vortices map u . point out several features Jacobian, in particular, we prove an important stability property. This property allows us to study model arising thin ferromagnetic...

A rational map $\phi: \mathbb{P}_k^m \dashrightarrow \mathbb{P}_k^n$ is defined by homogeneous polynomials of a common degree $d$. We establish linear bound in terms $d$ for the number $(m-1)$-dimensional fibers $\phi$, using ideals minors Jacobian matrix. In particular, we answer affirmatively Question~11 arXiv:1511.02933v2.

A neural map algorithm has been employed to control a five-joint pneumatic robot arm and gripper through feedback from two video cameras. The pneumatically driven robot arm (SoftArm) employed in this investigation shares essential mechanical characteristics with skeletal muscle systems. To control the position of the arm, 200 neurons formed a network representing the three-dimensional workspace...

The order of accuracy of the node-centered finite volume methods is analyzed, and the analysis is based on an exact derivation of the numerical errors in one dimension. The accuracy for various types of grids are considered. Numerical simulations and analysis are performed for both a hyperbolic and a eliptic case, and the results agree. The impact of weakly imposed boundary conditions is analyz...

As is well-known, there exist nonconstant holomorphic maps from the plane into the Riemann sphere P minus two points, the simplest example of which is an explicit realization of the uniformization map given by applying the exponential map and then composing with a Mobius transformation taking 0 and∞ to the two given punctures. Likewise, we can map the plane into the sphere minus one point by si...

Near a nonresonant, elliptic fixed point, a symplectic map can be transformed into Birkhoff normal form. In these coordinates, the dynamics is represented entirely by the Lagrangian ‘‘frequency map’’ that gives the rotation number as a function of the action. The twist matrix, given by the Jacobian of the rotation number, describes the anharmonicity in the system. When the twist is singular the...

This paper examines the standard map with sawtooth nonlinearity when the eigenvalues of the Jacobian lie on the unit circle. This is an area-preserving map of the torus to itself that is linear except on a line on which it is discon-tinuous. We discuss the closure of the set of images of the discontinuity and present numerical evidence that its Lebesgue measure is positive. Moreover, we present...

In this paper we consider degree theory for mappings u from one compact smooth n-dimensional manifold X to a connected compact smooth manifold Y of the same dimension. These are manifolds without boundary and which are oriented. The classical degree counts the "number of times" Y is covered by u(X), taking into account algebraic multiplicity. For instance, if u E C 1 and y E Y is a regular valu...