We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoo-Witt theorem, the Harish-Chandra isomorphism, the Duuo isomorphism, the Kirillov formula and some minor Fourier-analysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjectu...

Development on the design concept using OmniWheels to provide three degree-of-freedom (d.o.f) in a single spherical joint is presented in this paper. The purpose of this design is to provide the industrial robots that have limited movement flexibility with additional d.o.f in order to carry tasks that require complicated trajectories. In addition, this compact single joint will be installed as ...

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...

The paper introduces mathematical models of a skid steered mobile platform for robotics. The platform consists of a rectangular steel construction with four wheels. Two banks of two drive wheels on each side are linked to two DC electrical motors via chain on sprocket drive and gearing. The two drive assemblies for the left and right banks are identical but they operate independently to steer t...

The paper discusses the redesign of the second version of the Mantis hybrid leg-wheel mobile robot, conceived for surveillance and inspection tasks in unstructured indoor and outdoor environments. This small-scale ground mobile robot is characterized by a main body equipped with two front actuated wheels, a passive rear axle and two rotating legs. Motion on flat and even ground is purely wheele...

Example Commercial Web servers typically maintain a ‘hit count’ component that records how many times each URL is accessed by clients over a period of time. To reduce latency, a Web server process does not maintain the hit counts in a file on disk but rather in a memoryresident table. Moreover, to increase throughput, Web server processes are often multi-threaded [HS98]. Therefore, public metho...