Three dimensional field theories from infinite dimensional lie algebras

A procedure for constructing topological actions from centrally extended Lie groups is introduced. For a \km\ group, this produces \3al \cs, while for the \vir\ group the result is a new \3al \tft\ whose physical states satisfy the \vir\ \wi. This \tft\ is shown to be a first order formulation of two dimensional induced gravity in the chiral gauge. The extension to $W_3$-gravity is discussed.Comment: 11 pages, USC-92/01

A-models in three and four dimensions

We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary conditions. It plays a role in 3d mirror symmetry as well as in the physical approach to the geometric Langlands duality. A similar TFT can be defined in four dimensions.Comment: 16 pages, late

Hygrothermomechanical evaluation of transverse filament tape epoxy/polyester fiberglass composites

The static and cyclic load behavior of transverse filament tape (TFT) fiberglass/epoxy and TFY fiberglass/polyester composites, intended for use in the design of low-cost wind turbine blades, are presented. The data behavior is also evaluated with respect to predicted properties based on an integrated hygrothermomechanical response theory. Experimental TFT composite data were developed by the testing of laminates made by using composite layups typical of those used for the fabrication of TFT fiberglass wind turbine blades. Static properties include tension, compression, and interlaminar shear strengths at ambient conditions and at high humidity/elevated temperature conditions after a 500 hour exposure. Cyclic fatigue data were obtained using similar environmental conditions and a range of cyclic stresses. The environmental (temperature and moisture) and cyclic load effects on composite strength degradation are subsequently compared with the predictions obtained by using the composite life/durability theory. The results obtained show that the predicted hygrothermomechanical environmental effects on TFT composites are in good agreement with measured data for various properties including fatigue at different cyclic stresses

A new Truncated Fourier Transform algorithm

Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is comparable to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.Comment: 8 pages, submitted to the 38th International Symposium on Symbolic and Algebraic Computation (ISSAC 2013

A Lattice Formulation of Two Dimensional Topological Field Theory

We propose a non-perturbative criterion to investigate whether supersymmetric lattice gauge theories preserving partial SUSY can have the desired continuum limit or not. Since the target continuum theories of the lattice models are extended supersymmetric gauge theories including the topological field theory (TFT) as a special subsector, the continuum limits of them should reproduce the properties of the TFT. Therefore, whether the property of the TFT can be recovered at the continuum limit becomes a non-perturbative criterion. Then we accept it as a criterion. In this paper, among the topological properties, we investigate the BRST cohomology on the two dimensional ${\mathcal N}=(4,4)$ CKKU lattice model without moduli fixing mass term. We show that the BRST cohomology in the target continuum theory cannot be realized from the BRST cohomology on the lattice. From this result, we obtain the possible implication that the ${\mathcal N} = (4,4)$ CKKU model cannot recover the target continuum theory if the non-perturbative effects are taken into account.Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTeX, no figure, typos corrected, references adde