Let f = (f1, f2) be a regular sequence of affine curves in C. Under some reduction conditions achieved by composing with some polynomial automorphisms of C, we show that the intersection number of curves (fi) in C 2 equals to the coefficient of the leading term x in g2, where n = deg fi (i = 1, 2) and (g1, g2) is the unique solution of the equation yJ(f) = g1f1 + g2f2 with deg gi ≤ n−1. So the ...

We present a completed list of polynomial dominanting maps of C2 with branched value curve isomorphic to the complex line C, up to polynomial automorphisms. AMS Classification : 14 E20, 14 B25. 1. Let f : C −→ C be a polynomial dominanting map, Close(f(C)) = C, and denote by degf the geometric degree of f the number of solutions of the equation f = a for generic points a ∈ C. The branched value...

We give a solution to the weak Schottky problem for genus five Jacobians with vanishing theta null, answering question of Grushevsky and Salvati Manni. More precisely, we show that if principally polarized abelian variety dimension has null quadric tangent cone rank at most three, then it is in Jacobian locus, up extra irreducible components. employ degeneration argument, together study ramific...

This paper describes a mobile robot equipped with a sonar sensor array, Werrimbi, in a guided feature based map building task in an indoor environment. Common indoor landmarks such as planes, corners and edges are located and classified with a multiple transducer sensor array. Accurate odometry information is derived from a pair of narrow unloaded encoder wheels. Discrete sonar observations are...

In the field of optimal transport theory, an optimal map is known to be a gradient map of a potential function satisfying cost-convexity. In this paper, the Jacobian determinant of a gradient map is shown to be log-concave with respect to a convex combination of the potential functions when the underlying manifold is the sphere and the cost function is the distance squared. The proof uses the n...

In this paper, kinematic modeling and singularity and stiffness analysis of a 3-d.o.f. redundant parallel manipulator have been elaborated in detail. It is known that, contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled non-linear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting...