Open/closed string topology and moduli space actions via open/closed Hochschild actions

In this paper we extend our correlation functions to the open/closed case. This gives rise to actions of an open/closed version of the Sullivan PROP as well as an action of the relevant moduli space. There are several unexpected structures and conditions that arise in this extension which are forced upon us by considering the open sector. For string topology type operations, one cannot just consider graphs, but has to take punctures into account and one has to restrict the underlying Frobenius algebras. In the moduli space, one first has to pass to a smaller moduli space which is closed under open/closed duality and then consider covers in order to account for the punctures

The geometry of the double gyroid wire network: quantum and classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.Comment: pdflatex 9 Figures. Minor changes, some typos and formulation

Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the Gyroid wire network

We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)-commutative geometries. By selecting gauging data, these geometries are realized by matrices through an explicit construction or a Kan extension. We describe the changes in gauge via the action of a re-gauging groupoid. It acts via matrices that give rise to a noncommutative 2-cocycle and hence to a groupoid extension (gerbe). We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of re-gaugings. In the commutative case, we deduce that the extended symmetries act via a projective representation. This yields isotypical decompositions and super-selection rules. We apply these results to the primitive cubic, diamond, gyroid and honeycomb wire networks using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the G(yroid) and the honeycomb systems

Industrial applications of multiaxial warp knit composites

Over the past few years, multiaxial warp knit (MWK) fabrics have made significant inroads into the industrial composites arena. This paper examines the use of MWK fabrics in industrial composite applications. Although the focus is on current applications of MWK fabrics in composites, this paper also discusses the physical properties, advantages and disadvantages of MWK fabrics. The author also offers possibilities for the future of MWK fabrics in the industrial composites arena

Conservation of the first and second adiabatic invariants

Calculation of changes in energy and equatorial pitch angles of geomagnetically trapped particles assuming conservation of first and second adiabatic invariant

Arc Operads and Arc Algebras

Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to Penner of a space closely related to Riemann's moduli space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras, where the entire BV structure is realized simplicially. Furthermore, our basic operad contains the cacti operad up to homotopy, and it similarly acts on the loop space of any topological space. New operad structures on the circle are classified and combined with the basic operad to produce geometrically natural extensions of the algebraic structure of BV algebras, which are also computed.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper15.abs.htm

Quantum Cohomology of a Product

The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between strata classes is given. This operation is a version of the Kuenneth formula for quantum cohomology. In addition, rank one CohFT's are studied, and a generalization of Zograf's formula for Weil-Petersson volumes is suggested.Comment: AMSTex file, 30 pages. Figures (hard copies) available from Yu. Manin. Main paper by M. Kontsevich, Yu. Manin, appendix by R. Kaufman

Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation

Functional studies on oligotropha carboxidovorans molybdenum–copper CO dehydrogenase produced in escherichia coli

The Mo/Cu-dependent CO dehydrogenase (CODH) from Oligotropha carboxidovorans is an enzyme that is able to catalyze both the oxidation of CO to CO2 and the oxidation of H2 to protons and electrons. Despite the close to atomic resolution structure (1.1 Å), significant uncertainties have remained with regard to the reaction mechanism of substrate oxidation at the unique Mo/Cu center, as well as the nature of intermediates formed during the catalytic cycle. So far, the investigation of the role of amino acids at the active site was hampered by the lack of a suitable expression system that allowed for detailed site-directed mutagenesis studies at the active site. Here, we report on the establishment of a functional heterologous expression system of O. carboxidovorans CODH in Escherichia coli. We characterize the purified enzyme in detail by a combination of kinetic and spectroscopic studies and show that it was purified in a form with characteristics comparable to those of the native enzyme purified from O. carboxidovorans. With this expression system in hand, we were for the first time able to generate active-site variants of this enzyme. Our work presents the basis for more detailed studies of the reaction mechanism for CO and H2 oxidation of Mo/Cu-dependent CODHs in the future