We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The two formulas use the related notions of “Wheels” and “Wheeling”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from...

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [5, 9], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its i...

We study the rational Kontsevich integral of torus knots. We construct explicitely a series of diagrams made of circles joined together in a tree-like fashion and colored by some special rational functions. We show that this series codes exactly the unwheeled rational Kontsevich integral of torus knots, and that it behaves very simply under branched coverings. Our proof is combinatorial. It use...

Recent developments in grinding have opened up new avenues for finishingof hard and brittle materials with Nano-surface finish, high tolerance and accuracy.Grinding with super abrasive diamond wheels is an excellent way to produce ultraprecision surface finish. However, super abrasive diamond grits need higher bondingstrength while grinding, which metal-bonded grinding wheels ca...

In our paper we present an innovative locomotion concept for rough terrain based on six motorized wheels. Using rhombus configuration, the rover named Shrimp has a steering wheel in the front and the rear, and two wheels arranged on a bogie on each side. The front wheel has a spring suspension to guarantee optimal ground contact of all wheels at any time. The steering of the rover is realized b...

Chromium(III)-based wheels close-pack on the Ag(110) surface forming a quasi-hexagonal 2D network following direct sublimation in ultra high vacuum (UHV). Wheels organization and chemical integrity have been proved through in situ Scanning Tunneling Microscopy (STM) and X-ray Photoelectron Spectroscopy (XPS) studies.

In this paper, the chromaticity of K3-gluings of two wheels is studied. For each even integer n ≥ 6 and each odd integer 3 ≤ q ≤ [n/2] all K3-gluings of wheels Wq+2 and Wn−q+2 create an χ-equivalent class.

Mobile robotics is a growing trend in recent years as mobile robots are being used in service as well as industrial sectors. This paper introduces a novel design of a mobile robot platform for use in constrained workplaces. The constrained environments are nothing but congested places, for example hospitals, ware houses, offices, shop floors where various equipments and machineries are to be ar...