Relevant bibliographies by topics / Knots and links in $S^3$

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

Academic literature on the topic 'Knots and links in $S^3$'

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Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Knots and links in $S^3$"

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Manion, Andrew. "The rational Khovanov homology of 3-strand pretzel links." Journal of Knot Theory and Its Ramifications 23, no. 08 (2014): 1450040. http://dx.doi.org/10.1142/s0218216514500400.

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The 3-strand pretzel knots and links are a well-studied source of examples in knot theory. However, while there have been computations of the Khovanov homology and Rasmussen s-invariants of some sub-families of 3-strand pretzel knots, no general formula has been given for all of them. We give a formula for the unreduced Khovanov homology, over the rational numbers, of all 3-strand pretzel links. We also compute generalized s-invariants of these links.
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MULAZZANI, MICHELE. "ALL LINS-MANDEL SPACES ARE BRANCHED CYCLIC COVERINGS OF S3." Journal of Knot Theory and Its Ramifications 05, no. 02 (1996): 239–63. http://dx.doi.org/10.1142/s0218216596000175.

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In this paper we show that all Lins-Mandel spaces S (b, l, t, c) are branched cyclic coverings of the 3-sphere. When the space is a 3-manifold, the branching set of the covering is a two-bridge knot or link of type (l, t) and otherwise is a graph with two vertices joined by three edges (a θ-graph). In the latter case the singular set of the space is always composed by two points with homeomorphic links. The first homology groups of the Lins-Mandel manifolds are computed when t=1 and when the branching set is a knot of genus one. Furthermore the family of spaces has been extended in order to contain all branched cyclic coverings of two-bridge knots or links.
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KODA, YUYA. "LINKS AND SPINES." Journal of Knot Theory and Its Ramifications 21, no. 03 (2012): 1250027. http://dx.doi.org/10.1142/s0218216511009674.

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We define two kinds of invariants of links in closed 3-manifolds, the s-complexity(s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S3 and ℝP3, which provide upper bounds for the invariants.
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Planat, Michel, Raymond Aschheim, Marcelo Amaral, and Klee Irwin. "Universal Quantum Computing and Three-Manifolds." Symmetry 10, no. 12 (2018): 773. http://dx.doi.org/10.3390/sym10120773.

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A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 ’s obtained from Dehn fillings are explored.
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GE, MO-LIN, LU-YU WANG, KANG XUE, and YONG-SHI WU. "AKUTZU-WADATI LINK POLYNOMIALS FROM FEYNMAN-KAUFFMAN DIAGRAMS." International Journal of Modern Physics A 04, no. 13 (1989): 3351–73. http://dx.doi.org/10.1142/s0217751x89001370.

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By employing techniques familiar to particle physicists, we develop Kauffman’s state model for the Jones polynomial, which uses diagrams looking like Feynman diagrams for scattering, into a systematic, diagrammatic approach to new link polynomials. We systematize the ansatz for S matrix by symmetry considerations and find a natural interpretation for CPT symmetry in the context of knot theory. The invariance under Reidemeister moves of type III, II and I can be imposed diagrammatically step by step, and one obtains successively braid group representations, regular isotopy and ambient isotopy invariants from Kauffman’s bracket polynomials. This procedure is explicitiy carried out for the N=3 and 4 cases. N being the number of particle labels (or charges). With appropriate symmetry ansatz and with annihilation and creation included in the S matrix, we have obtained link polynomials which generalize the definition of the Akutzu-Wadati polynomials from closed braids to any oriented knots or links with explicit invariance under Reidemeister moves.
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RANKIN, STUART, ORTHO FLINT, and JOHN SCHERMANN. "ENUMERATING THE PRIME ALTERNATING KNOTS, PART I." Journal of Knot Theory and Its Ramifications 13, no. 01 (2004): 57–100. http://dx.doi.org/10.1142/s0218216504003044.

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The enumeration of prime knots has a long and storied history, beginning with the work of T. P. Kirkman [9,10], C. N. Little [14], and P. G. Tait [19] in the late 1800's, and continuing through to the present day, with significant progress and related results provided along the way by J. H. Conway [3], K. A. Perko [17, 18], M. B. Thistlethwaite [6, 8, 15, 16, 20], C. H. Dowker [6], J. Hoste [1, 8], J. Calvo [2], W. Menasco [15, 16], W. B. R. Lickorish [12, 13], J. Weeks [8] and many others. Additionally, there have been many efforts to establish bounds on the number of prime knots and links, as described in the works of O. Dasbach and S. Hougardy [4], D. J. A. Welsh [22], C. Ernst and D. W. Sumners [7], and C. Sundberg and M. Thistlethwaite [21] and others. In this paper, we provide a solution to part of the enumeration problem, in that we describe an efficient inductive scheme which uses a total of four operators to generate all prime alternating knots of a given minimal crossing size, and we prove that the procedure does in fact produce them all. The process proceeds in two steps, where in the first step, two of the four operators are applied to the prime alternating knots of minimal crossing size n to produce approximately 98% of the prime alternating knots of minimal crossing size n+1, while in the second step, the remaining two operators are applied to these newly constructed knots, thereby producing the remaining prime alternating knots of crossing size n+1. The process begins with the prime alternating knot of four crossings, the figure eight knot. In the sequel, we provide an actual implementation of our procedure, wherein we spend considerable effort to make the procedure efficient. One very important aspect of the implementation is a new way of encoding a knot. We are able to assign an integer array (called the master array) to a prime alternating knot in such a way that each regular projection, or plane configuration, of the knot can be constructed from the data in the array, and moreover, two knots are equivalent if and only if their master arrays are identical. A fringe benefit of this scheme is a candidate for the so-called ideal configuration of a prime alternating knot. We have used this generation scheme to enumerate the prime alternating knots up to and including those of 19 crossings. The knots up to and including 17 crossings produced by our generation scheme concurred with those found by M. Thistlethwaite, J. Hoste and J. Weeks (see [8]). The current implementation of the algorithms involved in the generation scheme allowed us to produce the 1,769,979 prime alternating knots of 17 crossings on a five node beowulf cluster in approximately 2.3 hours, while the time to produce the prime alternating knots up to and including those of 16 crossings totalled approximately 45 minutes. The prime alternating knots at 18 and 19 crossings were enumerated using the 48 node Compaq ES-40 beowulf cluster at the University of Western Ontario (we also received generous support from Compaq at the SC 99 conference). The cluster was shared with other users and so an accurate estimate of the running time is not available, but the generation of the 8,400,285 knots at 18 crossings was completed in 17 hours, and the generation of the 40,619,385 prime alternating knots at 19 crossings took approximately 72 hours. With the improvements that are described in the sequel, we anticipate that the knots at 19 crossings will be generated in not more than 10 hours on a current Pentium III personal computer equipped with 256 megabytes of main memory.
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OHTSUKI, TOMOTADA. "INVARIANTS OF KNOTS DERIVED FROM EQUIVARIANT LINKING MATRICES OF THEIR SURGERY PRESENTATIONS." International Journal of Mathematics 20, no. 07 (2009): 883–913. http://dx.doi.org/10.1142/s0129167x09005583.

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The quantum U(1) invariant of a closed 3-manifold M is defined from the linking matrix of a framed link of a surgery presentation of M. As an equivariant version of it, we formulate an invariant of a knot K from the equivariant linking matrix of a lift of a framed link of a surgery presentation of K. We show that this invariant is determined by the Blanchfield pairing of K, or equivalently, determined by the S-equivalent class of a Seifert matrix of K, and that the "product" of this invariant and its complex conjugation is presented by the Alexander module of K. We present some values of this invariant of some classes of knots concretely.
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Cautis, Sabin, Aaron D. Lauda, and Joshua Sussan. "Curved Rickard complexes and link homologies." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 769 (2020): 87–119. http://dx.doi.org/10.1515/crelle-2019-0044.

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AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).
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Jablan, Slavik, Ljiljana Radović, and Radmila Sazdanović. "Knots and links in architecture." Pollack Periodica 7, Supplement 1 (2012): 65–76. http://dx.doi.org/10.1556/pollack.7.2012.s.6.

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Lassen, Augusto E., Rogerio Riffel, Ana L. Chies-Santos, et al. "The metal-poor dwarf irregular galaxy candidate next to Mrk 1172." Monthly Notices of the Royal Astronomical Society 506, no. 3 (2021): 3527–39. http://dx.doi.org/10.1093/mnras/stab1838.

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ABSTRACT In this work, we characterize the properties of the object SDSS J020536.84−081424.7, an extended nebular region with projected extension of 14 × 14 kpc2 in the line of sight of the ETG Mrk 1172, using unprecedented spectroscopic data from MUSE. We perform a spatially resolved stellar population synthesis and estimate the stellar mass for both Mrk 1172 (1 × 1011 M⊙) and our object of study (3 × 109 M⊙). While the stellar content of Mrk 1172 is dominated by an old (∼10 Gyr) stellar population, the extended nebular emission has its light dominated by young to intermediate age populations (from ∼100 Myr to ∼1 Gyr) and presents strong emission lines such as H β; [O iii] λλ4959, 5007 Å; H α; [N ii] λλ6549, 6585 Å; and [S ii] λλ6717, 6732 Å. Using these emission lines, we find that it is metal poor (with Z ∼ 1/3 Z⊙, comparable to the LMC) and is actively forming stars (0.70 M⊙ yr−1), especially in a few bright clumpy knots that are readily visible in H α. The object has an ionized gas mass ≥3.8 × 105 M⊙. Moreover, the motion of the gas is well described by a gas in circular orbit in the plane of a disc and is being affected by interaction wtih Mrk 1172. We conclude that SDSS J020536.84−081424.7 is most likely a dwarf irregular galaxy (the dIGal).
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Dissertations / Theses on the topic "Knots and links in $S^3$"

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Cho, Karina Elle. "Enhancing the Quandle Coloring Invariant for Knots and Links." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/228.

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Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and the number of these colorings is called the quandle coloring invariant. We strengthen the quandle coloring invariant by considering a graph structure on the space of quandle colorings of a knot, and we call our graph the quandle coloring quiver. This structure is a categorification of the quandle coloring invariant. Then, we strengthen the quiver by decorating it with Boltzmann weights. Explicit examples of links that show that our enhancements are proper are provided, as well as background information in quandle theory.
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Garza, César. "Examples of hyperbolic knots with distance 3 toroidal surgeries in S³." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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Krishna, Siddhi. "Taut foliations, positive braids, and the L-space conjecture:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108731.

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Thesis advisor: Joshua E. Greene<br>We construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a positive 3-braid knot K in S^3, where r &lt; 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. We adapt our techniques to construct taut foliations in every closed 3-manifold obtained along r-framed Dehn surgery along a positive 1-bridge braid, and indeed, along any positive braid knot, in S^3, where r &lt; g(K)-1. These are the only examples of theorems producing taut foliations in surgeries along hyperbolic knots where the interval of surgery slopes is in terms of g(K)<br>Thesis (PhD) — Boston College, 2020<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Mathematics
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Gutierrez, Quispe Robert Gerson. "Aspectos de la teoría de nudos." Bachelor's thesis, 2019. http://hdl.handle.net/11086/14649.

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Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.<br>Los nudos, tal cual aparecen en nuestra vida cotidiana, son un objeto de estudio en la Matemática. La Teoría de Nudos es la rama de la Matemática que se encarga de su estudio. Un problema central es el de poder decir si dos nudos dados son equivalentes o no. Los matemáticos, en la búsqueda de responder esta pregunta, entre otras, han desarrollado diversas técnicas y herramientas en esta área de estudio. En este trabajo se hace un recorrido en el estudio de la Teoría de Nudos, comenzando con las definiciones más elementales, hasta llegar a estudiar herramientas sofisticadas como el polinomio de Alexander, el grupo de un nudo y las matrices de Seifert, entre otros. En los dos últimos capítulos se investigan los dos temas siguientes: nudos virtuales y presentaciones de Wirtinger. En este último se hace un aporte, dando una nueva familia infinita de presentaciones de Wirtinger no geométricas.<br>The knots we usually see in our lifes are studied in mathematics in the branch called Knot Theory. A main problem is to decide whether two knots are equivalent or not. Many tools and techniques have been developed by mathematicians in order to answer this and other related questions. In this work, we study Knot Theory from the beginning, with definitions and elementary notions, until some sophisticated concepts and tools like the Alexander polynomial, the knot group and Seifert matrices, among others. In the last two chapters, we work on the following two particular subjects: virtual knots and Wirtinger presentations. In this last one, we made a small contribution by presenting a new infinite family of Wirtinger presentations which are not geometric.<br>Fil: Gutierrez Quispe. Robert Gerson. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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Books on the topic "Knots and links in $S^3$"

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

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1974-, Nelson Sam, ed. Quandles: An introduction to the algebra of knots. American Mathematical Society, 2015.

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Flapan, Erica. Knots, molecules, and the universe: An introduction to topology. American Mathematical Society, 2015.

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Prasolov, V. V. Knots, links, braids and 3-manifolds: An introduction to the new invariants in low-dimensional topology. American Mathematical Society, 1997.

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Knots, links, braids, and 3-manifolds: An introduction to the new invariants in low-dimensional topology. American Mathematical Society, 1997.

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Jaco, William H., Hyam Rubinstein, Craig David Hodgson, Martin Scharlemann, and Stephan Tillmann. Geometry and topology down under: A conference in honour of Hyam Rubinstein, July 11-22, 2011, The University of Melbourne, Parkville, Australia. American Mathematical Society, 2013.

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1978-, Usher Michael, ed. Low-dimensional and symplectic topology. American Mathematical Society, 2011.

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Introduction to 3-maniflods. AMS, 2014.

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Book chapters on the topic "Knots and links in $S^3$"

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Karalashvili, O. "On Links Embedded into Surfaces of Heegaard Splittings of S 3." In Topics in Knot Theory. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1695-4_16.

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

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

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Przytycki, Józef H. "From Goeritz Matrices to Quasi-alternating Links." In The Mathematics of Knots. 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. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73915-1_10.

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Furusho, Hidekazu. "Galois Action on Knots II: Proalgebraic String Links and Knots." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37031-2_20.

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Chbili, Nafaa. "From Alternating to Quasi-Alternating Links." In Knots, Low-Dimensional Topology and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_8.

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Kozlov, Dmitri. "Knots and Links As Form-Generating Structures." In Mathematics and Modern Art. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24497-1_10.

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Sulkowska, Joanna I., and Piotr Sułkowski. "Entangled Proteins: Knots, Slipknots, Links, and Lassos." In Springer Series in Solid-State Sciences. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76596-9_8.

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Schücker, Thomas. "Knots and Their Links with Biology and Physics." In Geometry and Theoretical Physics. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76353-3_11.

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Conference papers on the topic "Knots and links in $S^3$"

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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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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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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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Moeneclaey, Bart, Jochen Verbrugghe, Elad Mentovich, Paraskevas Bakopoulos, Johan Bauwelinck, and Xin Yin. "A 64 Gb/s PAM-4 Transimpedance Amplifier for Optical Links." In Optical Fiber Communication Conference. OSA, 2017. http://dx.doi.org/10.1364/ofc.2017.tu2d.3.

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Proesel, Jonathan E., Clint L. Schow, and Alexander V. Rylyakov. "Ultra Low Power 10- to 25-Gb/s CMOS-Driven VCSEL Links." In Optical Fiber Communication Conference. OSA, 2012. http://dx.doi.org/10.1364/ofc.2012.ow4i.3.

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Pontaza, Juan P., Mohan Kotikanyadanam, Piet Moeleker, Raghu G. Menon, and Shankar Bhat. "Fairing Evaluation Based on Numerical Simulation." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83883.

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It is well established that strakes are effective at suppressing vortex-induced vibrations (VIV). Fairings are an attractive alternative to helical strakes, because they are a low drag VIV suppression solution. The paper presents an evaluation of a fairing design, based on numerical simulations — to be complemented at a later stage with current tank testing. This paper documents the computational fluid dynamics (CFD) and finite element analysis (FEA) of the evaluation: (1) 3-D CFD in the laboratory scale: 4.5 inch pipe, 3 ft/s current speed, (2) 3-D CFD in the full scale: 14 inch riser, 4 knots current speed, and (3) 3-D FEA of the full-scale fairing module latching mechanism, under service loads corresponding to 4 knots current speed. The analysis results show that the fairing design (1) is effective at suppressing VIV, (2) yields a low drag coefficient (0.52 at Re ∼ 106), and (3) its latching mechanism is adequate for use in calm sea states with 4 knots current speeds.
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von Lindeiner, J. B., J. D. Ingham, A. Wonfor, J. Zhu, R. V. Penty, and I. H. White. "100 Gb/s Uncooled DWDM using Orthogonal Coding for Low-cost Datacommunication Links." In Optical Fiber Communication Conference. OSA, 2014. http://dx.doi.org/10.1364/ofc.2014.m2e.3.

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Ledentsov, N., Ł. Chorchos, V. A. Shchukin, V. P. Kalosha, J. P. Turkiewicz, and N. N. Ledentsov. "Development of VCSELs and VCSEL-based Links for Data Communication beyond 50Gb/s." In Optical Fiber Communication Conference. OSA, 2020. http://dx.doi.org/10.1364/ofc.2020.m2a.3.

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Redwan, B., V. Kösek, C. Begher, et al. "Links-transaxillärer minimal-invasiver Zugang für die Resektion und Rekonstruktion der Brustwirbelkörper BWK2 und 3." In DACH-Jahrestagung Thoraxchirurgie. Georg Thieme Verlag KG, 2019. http://dx.doi.org/10.1055/s-0039-1694216.

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Papistas, Ioannis A., and Vasilis F. Pavlidis. "Comparative study of crosstalk noise due to inductive links on heterogeneous 3-D ICs." In 2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO). IEEE, 2017. http://dx.doi.org/10.1109/nemo.2017.7964271.

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