Homotopy algorithms are a class of methods for solving systems of nonlinear equations that are globally convergent with probability one. All homotopy algorithms are based on the construction of an appropriate homotopy map and then the tracking of a curve in the zero set of this homotopy map. The fundamental linear algebra step in these algorithms is the computation of the kernel of the homotopy...

in this work are studied the jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

In many contexts, there is a need to construct C maps from a given reference domain to a family of deformed domains. In our case, the motivation comes from the application of the Arbitrary Lagrangian Eulerian (ALE) method and also the reduced basis element method. In these methods, the maps are used to construct the grid-points needed on the deformed domains, and the corresponding Jacobian of t...

We investigate the occurrence of coarse macroscopic states in an agent-based model of consumer lock-in. The system studied here is a modification of an existing model by Garlic and Chli [24] and it serves as a prototypical Ising-type sociological system with binary state variables and spatially-dependent agent parameters. In the regime of globally-coupled agents with independent identically-dis...

We consider the kinematics of a mobile manipulator that consists of a non-holonomic (or holonomic) mobile platform and a holonomic manipulator mounted atop of the platform. At any fixed time instant and with fixed initial state of the platform these kinematics are viewed as a map from a Hilbert space of controls and manipulator’s joint positions into a taskspace of the mobile manipulator, and c...

This paper proposes two novel methods to simply Logarithmic Maximum a posteriori (Log-MAP) algorithm for turbo codes in the Third Generation Partnership Project Long Term Evolution (3GPP LTE). Firstly, we exploit a new function to replace the logarithmic term in the Jacobian logarithmic function based on Taylor series, which has the best approximated accuracy compared with the existing methods....

In this paper, for the genus-2 hyperelliptic curve y2 = x5 − αx (α = ±2) defined over finite fields of characteristic five, we construct a distortion map explicitly, and show the map indeed gives an input for which the value of the Tate pairing is not trivial. Next we describe a computation of the Tate pairing by using the proposed distortion map. Furthermore, we also see that this type of curv...

a watermarking scheme for Grayscale image is proposed based on a family of the chaotic maps and discrete cosine transform. Jacobian Elliptic mapis employed to encrypt of watermarked logo. Piecewise nonlinear chaotic map is also used to determine the location of DCT coefficients for the watermark embedding. The purpose of this algorithm is to improve the shortcoming of watermarking such as small...

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map AL:C → J̄ , which maps C into its compactified Jacobian, and form its pullback map A L : Pic J̄ → J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, points of multipli...