We have developed a novel experimental procedure that allows us to quantify how polarization effects determine the passive mode locking of an optical fiber figure-eight laser. Based on our measurements, we have performed numerical simulations demonstrating that the nonlinear switching within this laser operates in a manner contrary to that described by the conventional theory of passive mode lo...

In this paper, we first describe how we can arrange any bodies on Figure-Eight without collision in a dense subset of [0, T ] after showing that the self-intersections of Figure-Eight will not happen in this subset. Then it is reasonable for us to consider the existence of generalized solutions and non-collision solutions with Mixed-symmetries or with Double-Eight constraints, arising from Figu...

The purpose of this study was to assess the benefits of a 3 T scanner and an eight-channel phased-array head coil for acquiring three-dimensional PRESS (Point REsolved Spectral Selection) proton (H-1) magnetic resonance spectroscopic imaging (MRSI) data from the brains of volunteers and patients with brain tumors relative to previous studies that used a 1.5 T scanner and a quadrature head coil....

We prove that torsion free subgroups of PGL2(C) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the title.

The exact relationship between knot theory and non-euclidean geometry was a puzzle that survived more than 100 years. The histories of the two subjects were clearly intertwined; Carl Friedrich Gauss was a pioneer and did much to popularize both fields. After Gauss their two histories diverge a little, although taken together the list of luminaries in the two fields reads like a mathematical and...

OBJECTIVE To address the question of how the CNS generates muscle activation patterns for complex gestures, we have chosen to study a figure-eight movement. We hypothesized that the well defined rhythmic aspect of this figure will provide further insights into the temporal features of multi-muscular commands. METHODS Subjects performed, as fast as possible, figure-eights initiated in the cent...

CONTENTS We address the problem of topologically characterising simple

We establish results concerning the profinite completions of 3-manifold groups. In particular, we prove that the complement of the figure-eight knot SrK is distinguished from all other compact 3-manifolds by the set of finite quotients of its fundamental group. In addition, we show that if M is a compact 3-manifold with b1(M) = 1, and π1(M) has the same finite quotients as a free-by-cyclic grou...