We consider the problem of finding a singularity of a differentiable vector field X defined on a complete Riemannian manifold. We prove a unified result for the existence and local...
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
For an ideal I R[x] given by a set of generators, a new semidefinite characterization of its real radical I(VR(I)) is presented, provided it is zero-dimensional (even if I is not...
Jean B. Lasserre, Monique Laurent, Philipp Rostals...
Smale's 17th Problem asks "Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the s...
This paper considers the least-square online gradient descent algorithm in a reproducing kernel Hilbert space (RKHS) without explicit regularization. We present a novel capacity i...