Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Electrospinning of continuous nanofiber bundles and twisted nanofiber yarns

Spinning is a prehistoric technology in which endless filaments, shorter fibers or twisted fibers are put together to produce yarns that serve as key element to assemble multifarious structural designs for diverse functions. Electrospinning has been regarded as the most effective and versatile technology to produce nanofibers with controlled fiber morphology, dimension and functional components from various polymeric materials (Dersch et al., 2007, Frenot and Chronakis, 2003, Schreuder-Gibson et al., 2002). However, most electrospun fibers are produced in the form of randomly-oriented nonwoven fiber mats (Doshi and Reneker, 1995, Madhavamoorthi, 2005). The relatively low mechanical strength and difficulty in tailoring the fibrous structure have restricted their applications. With the rapid development in nanoscience and nanotechnology, yarns composed of nanofibers may uncover new opportunities for development of well-defined three dimensional nano fibrous architectures. This chapter focuses on recent research and advancement in electrospinning of nanofiber bundles and nanofiber yarns. The preparation, morphology, mechanical properties and potential applications of these fibrous materials are discussed in details.

Strip twisted electrospun nanofiber yarns: Structural effects on tensile properties

Nanofiber yarns with controlled twist levels were prepared by twisting a narrow fibrous strip cut directly from electrospun nanofiber mats. The effects of fiber morphology, diameter and orientation, as well as the yarn twist level on the yarn tensile properties were examined. For the yarns made from randomly oriented fine uniform nanofibers (e.g., diameter 359 nm) and beaded nanofibers, the tensile strength increased with increasing the yarn twist level. Higher fiber diameter (e.g., 634 nm) led to the tensile strength having an initial increase and then decrease trend. The modulus increased with the twist level for all the yarns studied. However, the elongation at break increased initially with the twist level and subsequently decreased. The orientation of aligned fibers within the fiber strip greatly influenced the yarn tensile properties. When the fibers were oriented along the fiber length direction, both tensile strength and modulus were the largest.

Twisted things : playing with time

Twisted Things: Playing with Time is a film script and exegesis. The script, a murder mystery, slips between contemporary Melbourne and Melbourne in 1959 during the making of, ‘On the Beach’. The exegesis explores history by considering Melbourne in 1959, glamour and image, and the cinema of time.

Highly-twisted, continuous nanofibre yarns prepared by a hybrid needle-needleless electrospinning technique

Nanofibres prepared by electrospinning have shown enormous potential for various applications. They are obtained predominantly in the form of nonwoven fibre webs. The 2-dimensional nonwoven feature and fragility have considerably confined their further processing into fabrics through knitting or weaving. Nanofibre yarns, which are nanofibre bundles with continuous length and a twist feature, show improved tensile strength, offering opportunities for making 3-dimensional fibrous materials with precisely controlled fibrous architecture, porous features and fabric dimensions. Despite a few techniques having been developed for electrospinning nanofibre yarns, they are chiefly based on the needle electrospinning technique, which often has low nanofibre productivity. In this study, we for the first time report a nanofibre yarn electrospinning technique which combines both needle and needleless electrospinning. A rotating intermediate ring collector was employed to directly collect freshly-electrospun nanofibres into a fibrous cone, which was further drawn and twisted into a nanofibre yarn. This novel system was able to produce high tenacity yarn (tensile strength 128.9 MPa and max strain 222.1%) at a production rate of 240 m h^-1, with a twist level up to 4700 twists per metre. The effects of various parameters, e.g. position of the electrospinning units, operating conditions and polymer concentration, on nanofibre and yarn production were examined.

Lula and Brazil: investors twisted logic

Investors were wrong to believe in change for the better; Brazil is stuck for at least two years

Tinkertoys for the twisted D-series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gaiotto duality for the twisted A(2N-1) series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Two-phase flow patterns and pressure drop inside horizontal tubes containing twisted-tape inserts

This paper presents an experimental study on two-phase flow patterns and pressure drop of R134a inside a 15.9 mm ID tube containing twisted-tape inserts. Experimental results were obtained in a horizontal test section for twisted-tape ratios of 3, 4, 9 and 14, mass velocities ranging from 75 to 250 kg/m(2) s and saturation temperatures of 5 and 15 degrees C. An unprecedented discussion on two-phase flow patterns inside tubes containing twisted-tape inserts is presented and the flow pattern effects on the frictional pressure drop are carefully discussed. Additionally, a new method to predict the frictional pressure drop during two-phase flow inside tubes containing twisted-tape inserts is proposed. (C) 2012 Elsevier Ltd. All rights reserved.

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

Multiparameter twisted Weyl algebras

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.