Relevant bibliographies by topics / Transverse knots and links

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Transverse knots and links'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Transverse knots and links"

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OGASA, EIJI. "THE INTERSECTION OF SPHERES IN A SPHERE AND A NEW GEOMETRIC MEANING OF THE ARF INVARIANT." Journal of Knot Theory and Its Ramifications 11, no. 08 (December 2002): 1211–31. http://dx.doi.org/10.1142/s0218216502002104.

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Let [Formula: see text] be a 3-sphere embedded in the 5-sphere S5 (i = 1,2). Let [Formula: see text] and [Formula: see text] intersect transversely. Then the intersection [Formula: see text] is a disjoint collection of circles. Thus we obtain a pair of 1-links, C in [Formula: see text], and a pair of 3-knots, [Formula: see text] in S5 (i = 1, 2). Conversely let (L1, L2) be a pair of 1-links and (X1, X2) be a pair of 3-knots. It is natural to ask whether the pair of 1-links (L1, L2) is obtained as the intersection of the 3-knots X1 and X2 as above. We give a complete answer to this question. Our answer gives a new geometric meaning of the Arf invariant of 1-links. Let f : S3 → S5 be a smooth transverse immersion such that the self-intersection C consists of double points. Suppose that C is a single circle in S5. Then f-1(C) in S3 is a 1-knot or a 2-component 1-link. There is a similar realization problem. We give a complete answer to this question.
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DING, FAN, and HANSJÖRG GEIGES. "LEGENDRIAN KNOTS AND LINKS CLASSIFIED BY CLASSICAL INVARIANTS." Communications in Contemporary Mathematics 09, no. 02 (April 2007): 135–62. http://dx.doi.org/10.1142/s0219199707002381.

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It is shown that Legendrian (respectively transverse) cable links in S3 with its standard tight contact structure, i.e. links consisting of an unknot and a cable of that unknot, are classified by their oriented link type and the classical invariants (Thurston–Bennequin invariant and rotation number in the Legendrian case, self-linking number in the transverse case). The analogous result is proved for torus knots in the 1-jet space J1(S1) with its standard tight contact structure.
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Chmutov, S., S. Jablan, K. Karvounis, and S. Lambropoulou. "On the link invariants from the Yokonuma–Hecke algebras." Journal of Knot Theory and Its Ramifications 25, no. 09 (August 2016): 1641004. http://dx.doi.org/10.1142/s0218216516410042.

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In this paper, we study properties of the Markov trace tr[Formula: see text] and the specialized trace [Formula: see text] on the Yokonuma–Hecke algebras, such as behavior under inversion of a word, connected sums and mirror imaging. We then define invariants for framed, classical and singular links through the trace [Formula: see text] and also invariants for transverse links through the trace tr[Formula: see text]. In order to compare the invariants for classical links with the Homflypt polynomial, we develop computer programs and we evaluate them on several Homflypt-equivalent pairs of knots and links. Our computations lead to the result that these invariants are topologically equivalent to the Homflypt polynomial on knots. However, they do not demonstrate the same behavior on links.
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Vance, Katherine. "Tau invariants for balanced spatial graphs." Journal of Knot Theory and Its Ramifications 29, no. 09 (August 2020): 2050066. http://dx.doi.org/10.1142/s0218216520500662.

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In 2003, Ozsváth and Szabó defined the concordance invariant [Formula: see text] for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of [Formula: see text] for knots in [Formula: see text] and a combinatorial proof that [Formula: see text] gives a lower bound for the slice genus of a knot. Recently, Harvey and O’Donnol defined a relatively bigraded combinatorial Heegaard Floer homology theory for transverse spatial graphs in [Formula: see text], extending HFK for knots. We define a [Formula: see text]-filtered chain complex for balanced spatial graphs whose associated graded chain complex has homology determined by Harvey and O’Donnol’s graph Floer homology. We use this to show that there is a well-defined [Formula: see text] invariant for balanced spatial graphs generalizing the [Formula: see text] knot concordance invariant. In particular, this defines a [Formula: see text] invariant for links in [Formula: see text]. Using techniques similar to those of Sarkar, we show that our [Formula: see text] invariant is an obstruction to a link being slice.
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Bode, B., M. R. Dennis, D. Foster, and R. P. King. "Knotted fields and explicit fibrations for lemniscate knots." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2202 (June 2017): 20160829. http://dx.doi.org/10.1098/rspa.2016.0829.

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We give an explicit construction of complex maps whose nodal lines have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids where all strands follow the same transverse (1, ℓ) Lissajous figure, and are therefore a subfamily of spiral knots generalizing the torus knots. We then prove that such maps exist and are in fact fibrations with appropriate choices of parameters. We describe how this may be useful in physics for creating knotted fields, in quantum mechanics, optics and generalizing to rational maps with application to the Skyrme–Faddeev model. We also prove how this construction extends to maps with weakly isolated singularities.
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Ito, Tetsuya. "Braids, chain of Yang–Baxter like operations, and (transverse) knot invariants." Journal of Knot Theory and Its Ramifications 27, no. 11 (October 2018): 1843009. http://dx.doi.org/10.1142/s0218216518430095.

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We introduce a notion of a chain of Yang–Baxter like operations. This is a sequence of solutions of an asymmetric variant of the Yang–Baxter equation and is a multi-operator generalization of (bi)rack/quandles. We discuss knot and link invariants coming from a chain of Yang–Baxter like operations, and give potential applications. Among them, we define a cocycle invariant for transverse links.
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Xie, C., S. Y. Haffert, J. de Boer, M. A. Kenworthy, J. Brinchmann, J. Girard, I. A. G. Snellen, and C. U. Keller. "A MUSE view of the asymmetric jet from HD 163296." Astronomy & Astrophysics 650 (June 2021): L6. http://dx.doi.org/10.1051/0004-6361/202140602.

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Context. Jets and outflows are thought to play important roles in regulating star formation and disk evolution. An important question is how the jets are launched. HD 163296 is a well-studied Herbig Ae star that hosts proto-planet candidates, a protoplanetary disk, a protostellar jet, and a molecular outflow, which makes it an excellent laboratory for studying jets. Aims. We aim to characterize the jet at the inner regions and check if there are large differences with the features at large separations. A secondary objective is to demonstrate the performance of Multi Unit Spectroscopic Explorer (MUSE) in high-contrast imaging of extended line emission. Methods. MUSE in the narrow field mode (NFM) can provide observations at optical wavelengths with high spatial (∼75 mas) and medium spectral (R ∼ 2500) resolution. With the high-resolution spectral differential imaging technique, we can characterize the kinematic structures and physical conditions of jets down to 100 mas. Results. We detect multiple atomic lines in two new knots, B3 and A4, at distances of < 4″ from the host star with MUSE. The derived Ṁjet/Ṁacc is about 0.08 and 0.06 for knots B3 and A4, respectively. The observed [Ca II]/[S II] ratios indicate that there is no sign of dust grains at distances of < 4″. Assuming the A4 knot traced the streamline, we can estimate a jet radius at the origin by fitting the half width half maximum of the jet, which sets an upper limit of 2.2 au on the size of the launching region. Although MUSE has the ability to detect the velocity shifts caused by high- and low-velocity components, we found no significant evidence of velocity decrease transverse to the jet direction in our 500 s MUSE observation. Conclusions. Our work demonstrates the capability of using MUSE NFM observations for the detailed study of stellar jets in the optical down to 100 mas. The derived Ṁjet/Ṁacc, no dust grain, and jet radius at the star support the magneto-centrifugal models as a launching mechanism for the jet.
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Coe, Tom, Jim Mackey, and Hyde Marine. "Controlling Oil Spills in Fast Currents with the Flow∼Diverter." International Oil Spill Conference Proceedings 2003, no. 1 (April 1, 2003): 833–41. http://dx.doi.org/10.7901/2169-3358-2003-1-833.

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ABSTRACT Sixty nine percent (645 million tons annually) of the oil transported in United States waters is on waterways where currents routinely exceed one knot. Conventional skimmers and booms lose their effectiveness when current speeds exceed 1 knot. The US Coast Guard recognized that this threat could not be easily controlled, and so they initiated a project that led to the successful development of a novel spill control device, the Oil Spill Flow~Diverter. The Flow~Diverter system is effective at diverting and converging oil at speeds up to 5+ knots. In more moderate currents it can also be used in place of an anchor, towboat or outrigger arm to deploy and position the outboard end of a deflection boom. It may also have application to dispersant and in-situ burn operations. The diverter is a unique stable catamaran design that consists of two hulls each comprised of symmetrical foils with integral buoyancy. The foils are pinned to a rigid connecting structure such that they can pivot but always remain parallel to each other. Two or more diverter catamarans can be connected together with cables to increase the total sweep width of the system. Two control lines are anchored to shore or secured to a boat and are used to deploy the system by adjusting the foils’ angle to the oncoming water. With the control lines securely anchored, the system is launched into the current and “flies out” into a stable operating position. It remains in equilibrium, balanced by the hydrodynamic lift forces of the passing water and the tension in the lines. The foils create a strong transverse surface current downstream to achieve the desired diversion and consolidation affect on floating oil. Unlike most skimmers and deflection boom, the diverters are not adversely affected as currents increase. The oil is diverted by the same lateral distance irrespective of the current or speed of advance. This paper presents the development of the Flow~Diverter prototype, its testing and operational evaluations. Several applications of the diverter technology in various response tactics are discussed. Use of the Diverter during a recent US Coast Guard Spill Exercise on the Ohio River is also presented. Production model enhancements are presented that will enhance performance in 7+ knot currents and shallow water applications.
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Sebastian, K. L. "Knots and links." Resonance 11, no. 3 (March 2006): 25–35. http://dx.doi.org/10.1007/bf02835965.

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Radovic, Ljiljana, and Slavik Jablan. "Meander knots and links." Filomat 29, no. 10 (2015): 2381–92. http://dx.doi.org/10.2298/fil1510381r.

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We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with n ? 16 crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.
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Dissertations / Theses on the topic "Transverse knots and links"

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Tovstopyat-Nelip, Lev Igorevich. "Braids, transverse links and knot Floer homology:." Thesis, Boston College, 2019. http://hdl.handle.net/2345/bc-ir:108376.

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Thesis advisor: John A. Baldwin
Contact geometry has played a central role in many recent advances in low-dimensional topology; e.g. in showing that knot Floer homology detects the genus of a knot and whether a knot is fibered. It has also been used to show that the unknot, trefoil, and figure eight knot are determined by their Dehn surgeries. An important problem in 3-dimensional contact geometry is the classification of Legendrian and transverse knots. Such knots come equipped with some classical invariants. New invariants from knot Floer homology have been effective in distinguishing Legendrian and transverse knots with identical classical invariants, a notoriously difficult task. The Giroux correspondence allows contact structures to be studied via purely topological constructs called open book decompositions. Transverse links are then braids about these open books, which in turn may be thought of as mapping tori of diffeomorphisms of compact surfaces with boundary having marked points, which we refer to as pointed monodromies. In the first part of this thesis, we investigate properties of the transverse invariant in knot Floer homology, in particular its behavior for transverse closures of pointed monodromies possessing certain dynamical properties. The binding of an open book sits naturally as a transverse link in the supported contact manifold. We prove that the transverse link invariant in knot Floer homology of the binding union any braid about the open book is non-zero. As an application, we show that any pointed monodromy with fractional Dehn twist coefficient greater than one has non-zero transverse invariant, generalizing a result of Plamenevskaya for braids about the unknot. In the second part of this thesis, we define invariants of Legendrian and transverse links in universally tight lens spaces using grid diagrams, generalizing those defined by Ozsvath, Szabo and Thurston. We show that our invariants are equivalent to those defined by Lisca, Ozsvath, Szabo and Stipsicz for Legendrian and transverse links in arbitrary contact 3-manifolds. Our argument involves considering braids about rational open book decompositions and filtrations on knot Floer complexes
Thesis (PhD) — Boston College, 2019
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Wiest, Bertold. "Knots, links, and cubical sets." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263657.

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Montemayor, Anthony. "On Nullification of Knots and Links." TopSCHOLAR®, 2012. http://digitalcommons.wku.edu/theses/1158.

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Motivated by the action of XER site-specific recombinase on DNA, this thesis will study the topological properties of a type of local crossing change on oriented knots and links called nullification. One can define a distance between types of knots and links based on the minimum number of nullification moves necessary to change one to the other. Nullification distances form a class of isotopy invariants for oriented knots and links which may help inform potential reaction pathways for enzyme action on DNA. The minimal number of nullification moves to reach a è-component unlink will be called the è-nullification number. This thesis will demonstrate the relationship of the nullification numbers to a variety of knot invariants, and use these to solve the è-nullification numbers for prime knots up to 10 crossings for any è. A table of nullification numbers for oriented prime links up to 9 crossings is also presented, but not all cases are solved. In addition, we examine the families of rational links and torus links for explicit results on nullification. Nullification numbers of torus knots and a subfamily of rational links are solved. In doing so, we obtain an expression for the four genus of said subfamily of rational links, and an expression for the nullity of any torus link.
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Lipson, Andrew Solomon. "Polynomial invariants of knots and links." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303206.

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Bettersworth, Zachary S. "Nullification of Torus Knots and Links." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1626.

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Knot nullification is an unknotting operation performed on knots and links that can be used to model DNA recombination moves of circular DNA molecules in the laboratory. Thus nullification is a biologically relevant operation that should be studied. Nullification moves can be naturally grouped into two classes: coherent nullification, which preserves the orientation of the knot, and incoherent nullification, which changes the orientation of the knot. We define the coherent (incoherent) nullification number of a knot or link as the minimal number of coherent (incoherent) nullification moves needed to unknot any knot or link. This thesis concentrates on the study of such nullification numbers. In more detail, coherent nullification moves have already been studied at quite some length. This is because the preservation of the previous orientation of the knot, or link, makes the coherent operation easier to study. In particular, a complete solution of coherent nullification numbers has been obtained for the torus knot family, (the solution of the torus link family is still an open question). In this thesis, we concentrate on incoherent nullification numbers, and place an emphasis on calculating the incoherent nullification number for the torus knot and link family. Unfortunately, we were unable to compute the exact incoherent nullification numbers for most torus knots. Instead, our main results are upper and lower bounds on the incoherent nullification number of torus knots and links. In addition we conjecture what the actual incoherent nullification number of a torus knot will be.
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Pham, Van Anh. "Loop Numbers of Knots and Links." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1952.

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This thesis introduces a new quantity called loop number, and shows the conditions in which loop numbers become knot invariants. For a given knot diagram D, one can traverse the knot diagram and count the number of loops created by the traversal. The number of loops recorded depends on the starting point in the diagram D and on the traversal direction. Looking at the minimum or maximum number of loops over all starting points and directions, one can define two positive integers as loop numbers of the diagram D. In this thesis, the conditions under which these loop numbers become knot invariants are identified. In particular, the thesis answers the question when these numbers are invariant under flypes in the diagram D.
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Ozawa, Makoto. "Tangle decompositions of knots and links /." Electronic version of summary, 1999. http://www.wul.waseda.ac.jp/gakui/gaiyo/2848.pdf.

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Manfredi, Enrico <1986&gt. "Knots and links in lens spaces." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amsdottorato.unibo.it/6265/1/manfredi_enrico_tesi.pdf.

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The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.
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Manfredi, Enrico <1986&gt. "Knots and links in lens spaces." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amsdottorato.unibo.it/6265/.

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The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.
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Tosun, Bulent. "Legendrian and transverse knots and their invariants." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44880.

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In this thesis, we study Legendrian and transverse isotopy problem for cabled knot types. We give two structural theorems to describe when the (r,s)- cable of a Legendrian simple knot type K is also Legendrian simple. We then study the same problem for cables of the positive trefoil knot. We give a complete classification of Legendrian and transverse cables of the positive trefoil. Our results exhibit many new phenomena in the structural understanding of Legendrian and transverse knots. we then extend these results to the other positive torus knots. The key ingredient in these results is to find necessary and sufficient conditions on maximally thickened contact neighborhoods of the positive torus knots in three sphere.
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Books on the topic "Transverse knots and links"

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Knots and links. Houston, Tex: Publish or Perish, 1990.

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Knots and links. Providence, R.I: AMS Chelsea Pub., 2003.

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Wiest, Bertold. Knots, links, and cubical sets. [s.l.]: typescript, 1997.

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András, Stipsicz, and Szabó Zoltán 1965-, eds. Grid homology for knots and links. Providence, Rhode Island: American Mathematical Society, 2015.

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Flapan, Erica, Allison Henrich, Aaron Kaestner, and Sam Nelson, eds. Knots, Links, Spatial Graphs, and Algebraic Invariants. Providence, Rhode Island: American Mathematical Society, 2017. http://dx.doi.org/10.1090/conm/689.

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Fiedler, Thomas. Gauss diagram invariants for knots and links. Dordrecht: Kluwer Academic Publishers, 2001.

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Ghrist, Robert W., Philip J. Holmes, and Michael C. Sullivan. Knots and Links in Three-Dimensional Flows. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0093387.

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Fiedler, Thomas. Gauss Diagram Invariants for Knots and Links. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9785-2.

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Ghrist, Robert W. Knots and links in three-dimensional flows. Berlin: Springer, 1997.

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Fiedler, Thomas. Gauss Diagram Invariants for Knots and Links. Dordrecht: Springer Netherlands, 2001.

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Book chapters on the topic "Transverse knots and links"

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Fomenko, A. T., and S. V. Matveev. "Knots and Links." In Algorithmic and Computer Methods for Three-Manifolds, 179–205. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-0699-5_8.

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Monastyrsky, Michael. "Knots, Links, and Physics." In Riemann, Topology, and Physics, 167–81. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-0-8176-4779-7_16.

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Kassel, Christian, and Vladimir Turaev. "Braids, Knots, and Links." In Graduate Texts in Mathematics, 47–91. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-68548-9_2.

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Åström, Alexander, and Christoffer Åström. "Projections of Knots and Links." In Handbook of the Mathematics of the Arts and Sciences, 1–31. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70658-0_16-1.

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Kassel, Christian. "Knots, Links, Tangles, and Braids." In Graduate Texts in Mathematics, 241–74. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0783-2_10.

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Abrosimov, Nikolay, and Alexander Mednykh. "Geometry of knots and links." In Topology and Geometry, 433–54. Zuerich, Switzerland: European Mathematical Society Publishing House, 2021. http://dx.doi.org/10.4171/irma/33-1/20.

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Åström, Alexander, and Christoffer Åström. "Projections of Knots and Links." In Handbook of the Mathematics of the Arts and Sciences, 665–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-319-57072-3_16.

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Meliani, Z., and O. Hervet. "Knots in Relativistic Transverse Stratified Jets." In Astrophysics and Space Science Proceedings, 79–83. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14128-8_12.

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Przytycki, Józef H. "From Goeritz Matrices to Quasi-alternating Links." In The Mathematics of Knots, 257–316. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15637-3_9.

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Kindermann, Philipp, Stephen Kobourov, Maarten Löffler, Martin Nöllenburg, André Schulz, and Birgit Vogtenhuber. "Lombardi Drawings of Knots and Links." In Lecture Notes in Computer Science, 113–26. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73915-1_10.

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Conference papers on the topic "Transverse knots and links"

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Lescop, Christine. "On configuration space integrals for links." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2002. http://dx.doi.org/10.2140/gtm.2002.4.183.

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STASIAK, ANDRZEJ. "QUANTUM-LIKE PROPERTIES OF KNOTS AND LINKS." In Proceedings of the International Conference on Knot Theory and Its Ramifications. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792679_0030.

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Starrett, John. "The Pendulum Weaves All Knots and Links." In EXPERIMENTAL CHAOS: 7th Experimental Chaos Conference. AIP, 2003. http://dx.doi.org/10.1063/1.1612264.

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Przytycki, Jozef H. "Skein module deformations of elementary moves on links." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2003. http://dx.doi.org/10.2140/gtm.2002.4.313.

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MEDNYKH, ALEXANDER D. "Trigonometric identities and geometrical inequalities for links and knots." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0032.

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Stanford, Theodore. "Some computational results on mod 2 finite-type invariants of knots and string links." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2004. http://dx.doi.org/10.2140/gtm.2002.4.363.

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GODA, Hiroshi. "SOME ESTIMATES OF THE MORSE-NOVIKOV NUMBERS FOR KNOTS AND LINKS." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0005.

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BUNIY, ROMAN V., and THOMAS W. KEPHART. "GLUEBALLS AND THE UNIVERSAL ENERGY SPECTRUM OF TIGHT KNOTS AND LINKS." In Proceedings of the 32nd Coral Gables Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701992_0001.

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KAWAMURA, TOMOMI. "LOWER BOUNDS FOR THE UNKNOTTING NUMBERS OF THE KNOTS OBTAINED FROM CERTAIN LINKS." In Proceedings of the International Conference on Knot Theory and Its Ramifications. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792679_0013.

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Ito, Tetsuya, and Keiko Kawamuro. "On the self-linking number of transverse links." In Interactions between low-dimensional topology and mapping class groups. Mathematical Sciences Publishers, 2015. http://dx.doi.org/10.2140/gtm.2015.19.157.

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Reports on the topic "Transverse knots and links"

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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2020. http://dx.doi.org/10.55461/ytgv8834.

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Abstract:
Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining functionality in the aftermath of moderate to strong earthquakes, referred to as “resiliency” in earthquake engineering research. Moreover, the associated construction philosophy is being modernized with the utilization of accelerated bridge construction (ABC) techniques, which strive to reduce the impact of construction on traffic, society, economy and on-site safety. This report presents two bridge systems that target the aforementioned issues. A study that combined numerical and experimental research was undertaken to characterize the seismic performance of these bridge systems. The first part of the study focuses on the structural system-level response of highway bridges that incorporate a class of innovative connecting devices called the “V-connector,”, which can be used to connect two components in a structural system, e.g., the column and the bridge deck, or the column and its foundation. This device, designed by ACII, Inc., results in an isolation surface at the connection plane via a connector rod placed in a V-shaped tube that is embedded into the concrete. Energy dissipation is provided by friction between a special washer located around the V-shaped tube and a top plate. Because of the period elongation due to the isolation layer and the limited amount of force transferred by the relatively flexible connector rod, bridge columns are protected from experiencing damage, thus leading to improved seismic behavior. The V-connector system also facilitates the ABC by allowing on-site assembly of prefabricated structural parts including those of the V-connector. A single-column, two-span highway bridge located in Northern California was used for the proof-of-concept of the proposed V-connector protective system. The V-connector was designed to result in an elastic bridge response based on nonlinear dynamic analyses of the bridge model with the V-connector. Accordingly, a one-third scale V-connector was fabricated based on a set of selected design parameters. A quasi-static cyclic test was first conducted to characterize the force-displacement relationship of the V-connector, followed by a hybrid simulation (HS) test in the longitudinal direction of the bridge to verify the intended linear elastic response of the bridge system. In the HS test, all bridge components were analytically modeled except for the V-connector, which was simulated as the experimental substructure in a specially designed and constructed test setup. Linear elastic bridge response was confirmed according to the HS results. The response of the bridge with the V-connector was compared against that of the as-built bridge without the V-connector, which experienced significant column damage. These results justified the effectiveness of this innovative device. The second part of the study presents the HS test conducted on a one-third scale two-column bridge bent with self-centering columns (broadly defined as “resilient columns” in this study) to reduce (or ultimately eliminate) any residual drifts. The comparison of the HS test with a previously conducted shaking table test on an identical bridge bent is one of the highlights of this study. The concept of resiliency was incorporated in the design of the bridge bent columns characterized by a well-balanced combination of self-centering, rocking, and energy-dissipating mechanisms. This combination is expected to lead to minimum damage and low levels of residual drifts. The ABC is achieved by utilizing precast columns and end members (cap beam and foundation) through an innovative socket connection. In order to conduct the HS test, a new hybrid simulation system (HSS) was developed, utilizing commonly available software and hardware components in most structural laboratories including: a computational platform using Matlab/Simulink [MathWorks 2015], an interface hardware/software platform dSPACE [2017], and MTS controllers and data acquisition (DAQ) system for the utilized actuators and sensors. Proper operation of the HSS was verified using a trial run without the test specimen before the actual HS test. In the conducted HS test, the two-column bridge bent was simulated as the experimental substructure while modeling the horizontal and vertical inertia masses and corresponding mass proportional damping in the computer. The same ground motions from the shaking table test, consisting of one horizontal component and the vertical component, were applied as input excitations to the equations of motion in the HS. Good matching was obtained between the shaking table and the HS test results, demonstrating the appropriateness of the defined governing equations of motion and the employed damping model, in addition to the reliability of the developed HSS with minimum simulation errors. The small residual drifts and the minimum level of structural damage at large peak drift levels demonstrated the superior seismic response of the innovative design of the bridge bent with self-centering columns. The reliability of the developed HS approach motivated performing a follow-up HS study focusing on the transverse direction of the bridge, where the entire two-span bridge deck and its abutments represented the computational substructure, while the two-column bridge bent was the physical substructure. This investigation was effective in shedding light on the system-level performance of the entire bridge system that incorporated innovative bridge bent design beyond what can be achieved via shaking table tests, which are usually limited by large-scale bridge system testing capacities.
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