On finite Thurston type orderings of braid groups

We prove that for any finite Thurston-type ordering $<_{T}$ on the braid group\ $B_{n}$, the restriction to the positive braid monoid $(B_{n}^{+},<_{T})$ is a\ well-ordered set of order type $\omega^{\omega^{n-2}}$. The proof uses a combi\ natorial description of the ordering $<_{T}$. Our combinatorial description is \ based on a new normal form for positive braids which we call the \C-normal fo\ rm. It can be seen as a generalization of Burckel's normal form and Dehornoy's \ $\Phi$-normal form (alternating normal form).Comment: 25 pages, 2 figures; proof of Theorem 1 is correcte

Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology

All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly and the geometrical significance of continuous and discrete labels is elucidated. As a corollary we gain insight into the (in general non-trivial) topology of the reduced phase space. The classification covers basically all 2D metrics of Lorentzian signature with a (local) Killing symmetry.Comment: 39 pages, 22 figures, uses AMSTeX, extended version of former chapter 7 (Gravitational Kinks) now available as gr-qc/9707053, problem with figure 6 fixe

Directly patterned substrate-free plasmonic 'nanograter' structures with unusual Fano resonances

The application of three-dimensional (3D) plasmonic nanostructures as metamaterials,nano-antennas, and other devices faces challenges in producing metallic nanostructures with easily definable orientations, sophisticated shapes and smooth surfaces that are operational in the optical regime and beyond. Here, we demonstrate that complex 3D nanostructures can be readily achieved with focused-ion-beam irradiation-induced folding and examine the optical characteristics of plasmonic “nanograter” structures that are composed of free-standing Au films.These 3D nanostructures exhibit interesting 3D hybridization in current flows and exhibit unusual and well-scalable Fano resonances at wavelengths ranging from 1.6 to 6.4 μm. Upon the introduction of liquids of various refractive indices to the structures, a strong dependence of the Fano resonance is observed, with spectral sensitivities of 1400 nm and 2,040 nm per refractive-index-unit (RIU) under figures of merit of 35.0 and 12.5, respectively, for low-order and high-order resonance in the near-infrared region. This work indicates the exciting, increasing relevance of similarly constructed 3D free standing nanostructures in the research and development of photonics and metamaterials

An algorithm for the SAT problem via inclusion-exclusion: SATINEX

This paper proposes an algorithm that decides the Satisfiability of any conjunctive formula #PHI# with k clauses on n variables. The method checks whether the number of models of the negation of #PHI# is strictly lower than 2&quot;n. This counting is computed by using the inclusion-exclusion principle. We propose an elementary counting algorithm in time O(2&quot;kn) that is improved after using combinatorial arguments. (orig.)SIGLEAvailable from TIB Hannover: RN 7886(98) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Computation of the ordinal of braids

There exists a linear ordering on braids coming from left distributivity assumptions. The restriction of this order to positive braids is a wellordering. We present here some tools and an effective algorithm for the computation of the rank of any positive braid in this wellordering. (orig.)Available from TIB Hannover: RN 7886(97) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman