Relevant bibliographies by topics / Torus knot

Academic literature on the topic 'Torus knot'

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Published: 9 March 2023

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Journal articles on the topic "Torus knot"

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Lee, Sangyop. "Knot types of twisted torus knots." Journal of Knot Theory and Its Ramifications 26, no. 12 (October 2017): 1750074. http://dx.doi.org/10.1142/s0218216517500742.

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Dean introduced twisted torus knots, which are obtained from a torus knot and a torus link by splicing them together along a number of adjacent strands of each of them. We study the knot types of these knots.
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Lee, Sangyop. "Twisted torus knots T(p,q,p − kq,−1) which are torus knots." Journal of Knot Theory and Its Ramifications 29, no. 09 (August 2020): 2050068. http://dx.doi.org/10.1142/s0218216520500686.

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A twisted torus knot is a torus knot with some consecutive strands twisted. More precisely, a twisted torus knot [Formula: see text] is a torus knot [Formula: see text] with [Formula: see text] consecutive strands [Formula: see text] times fully twisted. We determine which twisted torus knots [Formula: see text] are a torus knot.
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Lee, Sangyop. "Composite Knots Obtained by Twisting Torus Knots." International Mathematics Research Notices 2019, no. 18 (December 9, 2017): 5744–76. http://dx.doi.org/10.1093/imrn/rnx282.

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Abstract A twisted torus knot is obtained from a torus knot by performing full twists on some adjacent strands of the torus knot. Morimoto constructed infinitely many twisted torus knots which are composite knots and he conjectured that his knots are all of composite twisted torus knots. We show that his conjecture is almost true by giving a complete list of such twisted torus knots.
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OZAWA, MAKOTO. "SATELLITE DOUBLE TORUS KNOTS." Journal of Knot Theory and Its Ramifications 10, no. 01 (February 2001): 133–42. http://dx.doi.org/10.1142/s0218216501000779.

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We characterize satellite double torus knots. Especially, if a satellite double torus knot is not a cable knot, then it has a torus knot companion. This answers Question 12 (a) raised by Hill and Murasugi in [4].
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Amoranto, Evan, Brandy Doleshal, and Matt Rathbun. "Additional cases of positive twisted torus knots." Journal of Knot Theory and Its Ramifications 26, no. 12 (October 2017): 1750078. http://dx.doi.org/10.1142/s021821651750078x.

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A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in [Formula: see text], the genus 2 Heegaard surface for [Formula: see text]. Primitive/primitive and primitive/Seifert knots lie in [Formula: see text] in a particular way. Dean gives sufficient conditions for the parameters of the twisted torus knots to ensure they are primitive/primitive or primitive/Seifert. Using Dean’s conditions, Doleshal shows that there are infinitely many twisted torus knots that are fibered and that there are twisted torus knots with distinct primitive/Seifert representatives with the same slope in [Formula: see text]. In this paper, we extend Doleshal’s results to show there is a four parameter family of positive twisted torus knots. Additionally, we provide new examples of twisted torus knots with distinct representatives with the same surface slope in [Formula: see text].
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SATOH, SHIN. "VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS." Journal of Knot Theory and Its Ramifications 09, no. 04 (June 2000): 531–42. http://dx.doi.org/10.1142/s0218216500000293.

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Any ribbon torus-knot in 4-space is naturally associated with a virtual knot. We investigate a relationship between ribbon torus-knots and virtual knots from this viewpoint. We also give a new example of a non-classical virtual knots which can not be detected by the group and the Z-polynomial.
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BAADER, SEBASTIAN. "Unknotting sequences for torus knots." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 1 (July 6, 2009): 111–16. http://dx.doi.org/10.1017/s0305004109990156.

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AbstractThe unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this paper we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.
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NAKAMURA, INASA. "BRAIDING SURFACE LINKS WHICH ARE COVERINGS OVER THE STANDARD TORUS." Journal of Knot Theory and Its Ramifications 21, no. 01 (January 2012): 1250011. http://dx.doi.org/10.1142/s0218216511009650.

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We consider a surface link in the 4-space which can be presented by a simple branched covering over the standard torus, which we call a torus-covering link. Torus-covering links include spun T2-knots and turned spun T2-knots. In this paper we braid a torus-covering link over the standard 2-sphere. This gives an upper estimate of the braid index of a torus-covering link. In particular we show that the turned spun T2-knot of the torus (2, p)-knot has the braid index four.
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Tran, Anh T. "The strong AJ conjecture for cables of torus knots." Journal of Knot Theory and Its Ramifications 24, no. 14 (December 2015): 1550072. http://dx.doi.org/10.1142/s0218216515500728.

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The AJ conjecture, formulated by Garoufalidis, relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been confirmed for all torus knots, some classes of two-bridge knots and pretzel knots, and most cable knots over torus knots. The strong AJ conjecture, formulated by Sikora, relates the A-ideal and the colored Jones polynomial of a knot. It was confirmed for all torus knots. In this paper we confirm the strong AJ conjecture for most cable knots over torus knots.
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ABE, TETSUYA. "AN ESTIMATION OF THE ALTERNATION NUMBER OF A TORUS KNOT." Journal of Knot Theory and Its Ramifications 18, no. 03 (March 2009): 363–79. http://dx.doi.org/10.1142/s021821650900694x.

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We give a lower bound for the alternation number of a knot by using the Rasmussen s-invariant and the signature of a knot. Then, we determine the torus knots with alternation number one and show that many torus knots are "far" from the alternating knots. As an application, we determine the almost alternating torus knots, solving a conjecture due to Adams et al.
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Dissertations / Theses on the topic "Torus knot"

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Barker, Stephen J. "Interchanging Two Notations for Double-torus Links." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/2616.

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Knot theory is a relatively young branch of mathematics, still less than a century old. The development of the Jones polynomial in 1984 led to increased activity in knot theory. Though work is constantly being done in this field, notably the classification of torus knots, double-torus knots are still lacking such a complete understanding. There exists two notations, those of Rick Norwood and of Peter Hill, that describe knots on the double-torus. The ambition of this thesis is to begin to make the case that it is possible to render these two notations interchangeable. Illustrating this will require examining the two notations and finding a way to change one into the other, then check if this process is reversible. If not, then proceed to develop a method that works to convert the second notation back to the first.
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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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OBERTI, CHIARA. "Induction effects of torus knots and unknots." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/87792.

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In questa tesi si analizzano gli effetti di induzione di un campo sorgente stazionario nella forma di un filamento a nodo o non-nodo torico. Studi simili sono stati compiuti per geometrie rettilinee, circolari o elicoidali, ma poco o nulla è noto per geometrie e topologie più complesse. I nodi torici sono un raro esempio di curve spaziali chiuse con topologia non banale che ammettono una descrizione matematicamente semplice; per questo rappresentano un interessante caso da studiare. Inoltre, poiché i nodi torici sono anche un buon modello matematico per studiare strutture di campo intrecciate, questo lavoro offre utili informazioni per svariate applicazioni possibili, dalle scienze fisiche (fisica del sole e astrofisica, dinamica vorticosa, fisica della fusione) alla tecnologia (telecomunicazioni, progettazione di nuovi materiali, analisi di dati). Il lavoro è organizzato in 4 capitoli. Nel capitolo 1 presentiamo uno studio esaustivo di proprietà geometriche e topologiche dei nodi/non-nodi torici. Usando una parametrizzazione standard, dimostriamo l'esistenza e determiniamo la posizione di punti di flesso per una data configurazione critica, e prescriviamo la condizione per rimuovere la singolarità associata alla torsione nel punto di flesso. Mostriamo che in prima approssimazione la lunghezza cresce linearmente con il numero di avvolgimenti ed è proporzionale al numero minimo di incroci. Prendendo il numero di avvolgimento, definito come rapporto tra gli avvolgimenti meridiani e quelli longitudinali, come misura di complessità topologica, ne analizziamo l'influenza su varie proprietà globali, quali lunghezza, curvatura, torsione totale e distorsione. Nel capitolo 2 analizziamo l'influenza del numero di avvolgimento e di altre proprietà geometriche su induzione, energia ed elicità. Per far questo si assume che il filamento fisico abbia sezione trasversale infinitesima e si usa la legge di Biot-Savart adattata alla particolare parametrizzazione scelta. Si studiano le linee di campo indotto per numerosi nodi/non-nodi torici su vari piani trasversali. Si mostra che l'intensità del campo indotto dipende linearmente dal numero di avvolgimenti longitudinali. Si forniscono maggiorazioni e minorazioni per l'energia e una stima dell'elicità in termini del numero di distorsione. Nel capitolo 3 compariamo i contributi d'induzione locali e globali in relazione al numero di avvolgimento, derivando espansioni asintotiche della funzione integranda. Mostriamo che i termini locali di ordine principale in generale non sono sufficienti a fornire accurate informazioni globali; tuttavia, mostriamo che per alcuni valori del numero di avvolgimento i comportamenti locali e globali sono in buon accordo. Nel capitolo 4 analizziamo gli effetti del numero di avvolgimento sull'auto-induzione per punti asintoticamente vicini al campo sorgente. Poiché al limite l'integrale di Biot-Savart diventa singolare, lo regolarizziamo applicando la prescrizione analitica di Moore e Saffman (1972). Mentre al primo ordine l'auto-induzione è proporzionale alla curvatura locale, determiniamo l'influenza del numero di avvolgimento sui termini successivi, mostrando che i suoi effetti sono comparabili con quelli dati da una distribuzione di campo sorgente sulla sezione trasversale finita del filamento.
The induction effects due to a steady source field in the shape of a torus knot or unknot filament are analysed in detail. Similar studies for rectilinear, circular or helical geometries have been done in the past, but very little is known for more complex geometries and topologies. Torus knots provide a rare example of closed, space curves of non-trivial topology, that admit a mathematically simple description; for this reason they represent an interesting case study to consider. Moreover, since torus knots are also a good mathematical model for studying braided field line structures, the present work provides useful information for a wide range of possible applications, from physical sciences (solar physics and astrophysics, vortex dynamics, fusion physics) to technology (telecommunication, new materials design, data analysis). The work is organized in 4 chapters. In chapter 1 we present a comprehensive study of geometric and topological properties of torus knots and unknots. By using a standard parametrization, we demonstrate the existence, and determine the location, of inection points for a given critical configuration, and prescribe the condition for removing the singularity associated with torsion at the inflection point. We show that, to first approximation, total length grows linearly with the number of coils, and it is proportional to the minimum crossing number of the knot type. By taking the winding number, given by the ratio between meridian and longitudinal wraps, as measure of topological complexity of the knot, we analyse its influence on several global quantities, such as total length, curvature, torsion and writhe. In chapter 2 we analyse the influence of the winding number and other geometric properties on induction, energy and helicity. This is done by assuming the physical filament of infinitesimally small cross-section and by using the Biot-Savart law adapted for the particular parametrization chosen. Field line patterns of the induced field are obtained for a large family of knots/unknots on several cross-sectional planes. The intensity of the induced field is shown to depend linearly on the number of toroidal coils. We provide bounds on energy, and an estimate of helicity in terms of writhe. In chapter 3 we compare local and global induction contributions in relation to the winding number, by providing asymptotic expansions of the integrand function. We show that in general local leading order terms are not sufficient to provide accurate global information; nevertheless, for some values of the winding number local and global behaviours are found to be in good agreement. In chapter 4 we investigate the influence of the winding number on the binormal component of the self-induction a point asymptotically near to the source field. Since in the limit the Biot-Savart integral becomes singular, we apply the analytical prescription of Moore and Saffman (1972) to regularize it. While to leading order the self-induction is proportional to local curvature, we derive an integral formula for next terms, including higher order local terms together with non-local terms, and we study its dependence on the winding number by showing that the dominant contribution is generally given by non-local terms.
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Ameur, Kheira. "Polynomial quandle cocycles, their knot invariants and applications." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001813.

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Bellanco, Olivia. "Articulation topologique de la clinique." Thesis, Paris 8, 2018. http://www.theses.fr/2018PA080039.

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Nous retracerons le parcours de la topologie dans l’enseignement lacanien : de la topologie algébrique, nous traiterons des figures topologiques (tore, bande de Mœbius, bouteille de Klein, cross-cap) pour en arriver à la topologie nodale dont le paradigme est le nœud borroméen. Nous considérerons alors les conséquences théoriques qu’elle implique : de l’inconscient freudien ou l’inconscient symbolique nous passerons à l’inconscient réel et l’une-bévue, et du symptôme nous envisagerons le sinthome et sa logique. Nous affinerons ainsi le double rapport du sujet au signifiant et à la jouissance mettant en avant l’importance du corps pris comme vivant. Pour ce faire, nous étudierons plus précisément le rapport du sujet au trou, manque fondamental qui le constitue, à la fois extérieur et intérieur. Nous verrons comment, dans son creux et dans ses bords, le sujet y loge sa singularité, son « x ». Nous l’articulerons à la clinique afin de révéler l’apport qu’elle représente dans la pratique
We will trace the course of topology in Lacan’s teaching: from algebraic topology, where we will deal with topological surfaces (torus, Moebius strip, Klein bottle, cross-cap) we will reach topology whose paradigm is the Borromean knot. We will then consider the theoretical consequences implied: from the Freudian unconscious or symbolic unconscious we will move to the real unconscious and the une-bévue, and from the symptom we will consider the sinthome and its logic. We will refine the dual relationship of the subject to signifier and Jouissance, and highlight the importance of the body as living. To do this, we will study more precisely the relationship of the subject to the hole, a fundamental lack that constitutes him, both exterior and interior. We will see how, in its hollow and its edges, the subject lodges its singularity, its "x". We will link it to clinic to reveal the contribution of topology in practice
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Hill, Peter Clifford. "On double-torus knots." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0011/NQ35186.pdf.

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Irvine, Robin. ""Los toros guapos" - "good-looking bulls" : animal life, ethics and professional know-how on an Andalusian bull-breeding estate." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/15550.

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This thesis take the form of an ethnographic exploration of a bull-breeding estate called Partido de Resina (formerly Pablo Romero) in the countryside near Seville in Andalusia. The estate, founded in 1885, produces fighting bulls for taurine events in Southern France, Spain and Portugal. At the heart of the thesis is the life cycle of the fighting animals, every chapter being anchored to a particular point in the bull-breeding calendar and the lives of the stock. Each chapter draws out specific qualities of the world of the bulls from the perspective of Partido de Resina, rooting the bulls and their people in a wider Spanish and Andalusian landscape and history, with a focus on technical know-how and everyday ethics after the 2008 financial crisis. The professionals who care for the Partido de Resina bulls, cows, and calves are the human protagonists of this project; their working routines, hopes, concerns, and stories described through their interactions with the animals which they look after. The core anthropological argument in the thesis is to show how different ethnographically salient forms of life emerge on and around the estate, sometimes weighted towards individual animals, sometimes towards bits of taurine bodies, or breeds, types, lineages, cohorts, and other groupings of stock. The varied, dynamic presence of animal life is contextualised in the literature of the 'animal turn' in anthropology, which has drawn non- human life into the ethnographic foreground. A case is made for a nuanced and contextual ethnographic attention to animal life and interiority as it emerges in the field, without an a priori emphasis on animal personhood or subjectivity. In foregrounding the qualities and concerns encountered and worked through during both routine livestock maintenance and extraordinary, definitive events like bullfights, the emergent, multiple character of taurine forms of existence become apparent.
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Romuald, Camille. "Des Muscles Moléculaires dans tous leurs Etats aux Noeuds Moléculaires inédits à Cavité Modulable." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20167.

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Cette thèse est dédiée à la conception de machines moléculaires pH-sensibles inédites de type muscles et nœuds moléculaires. Le premier muscle moléculaire pH-sensible a été synthétisé de manière très directe, et publié en 2008, en utilisant une stratégie en deux étapes: 1) fermeture des axes encapsulés par cycloaddition 1,3-dipolaire de type Huisgen catalysée par le cuivre (I), 2) méthylation des triazoles formés en triazoliums, capables d'être reconnus par les macrocycles DB24C8. Deux états étirés ou contractés, déclenchés par simple variation de pH, permettent le contrôle de l'orientation et de la distance entre les deux « stoppeurs » glucidiques non reliés de manière covalente. Des stations pyridiniums amides mono ou disubstitués inédites ont également été utilisées pour la synthèse de muscles moléculaires de plus large amplitude à effets co-conformationnels induits. Lors de la contraction du muscle par carbamoylation des ammoniums, la différence de localisation des macrocycles autour des stations pyridiniums amides, dépendante de la substitution des amides, engendre deux effets très différents : rôle de frein moléculaire de la DB24C8 ou basculement conformationnel impressionnant des chaises des mannopyranoses. Une étude méthodologique a été menée afin de classer les stations moléculaires rencontrées dans ce manuscrit, selon leurs affinités respectives pour la DB24C8, et a conduit à la conception d'un muscle moléculaire oscillant dont l'état varie continuellement entre contracté et semi-contracté en fonction de la température et de la nature du solvant. Enfin, différentes stratégies de synthèse ont été explorées pour obtenir des nœuds moléculaires inédits en forme de double lasso par cyclisation de synthons dimères de rotaxanes. Un double lasso dont la vitesse de rotation et la taille de la cavité peuvent être modulées en fonction du pH a ainsi été obtenu
This thesis is devoted to the synthesis of pH-sensitive molecular muscles and knots. The first molecular muscle has been readily synthesized and published in 2008, using a two-step strategy: 1) end-capping of the interlocked axles by copper(I)-catalyzed Huisgen alkyne-azide 1,3-dipolar cycloaddition, 2) methylation of triazoles to triazoliums, which are able to interact with the macrocycle DB24C8. Two stretched and contracted states, triggered by variation of pH, allow the control of the distance and of the orientation of the two glucidic ends, which are not covalently linked. Novel mono- and disubstituted pyridinium amide stations have been used for the synthesis of large-amplitude molecular muscles, whose translation of the macrocycles trigger a second co-conformational induced effect. In fact, upon contraction of the molecular muscle, using carbamoylation of the ammoniums, the slight different localizations of the macrocycles around the pyridinium amides (depending on their mono- or disubstitution) trigger two very different effects. The first one is a molecular break played by the DB24C8, whereas the second one is a flipping of the chair-like conformation of the mannopyranosyl ends. A methodologic study was then carried out with the aim to determine the relative affinity of the new described molecular stations for the DB24C8, and led to the synthesis of a molecular muscle which oscillates from the contracted to the semi-contracted co-conformation, depending on solvent and temperature. Eventually, different routes to very new double-lasso molecular knots were investigated from a molecular muscle building-block. One molecular knotted machine has been obtained, and has a double-lasso structure, whose rotation and size of its cavity can both been modulated by variation of pH
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Henri, Delphine. "Production et consommation textiles à Tours aux XVe et XVIe siecles : Approche archéologique." Thesis, Tours, 2015. http://www.theses.fr/2015TOUR2019/document.

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La découverte à Tours de plus de six mille fragments de textiles dans la même fosse, à l’extérieur du rempart qui longe la berge de la Loire (site 69 « place Anatole France »), a permis d’étudier tout le processus du travail textile, du fil au rejet. La quasi-totalité des éléments examinés sont en drap de laine, grande industrie en Europe aux 15e – 16e siècles. Tout comme pour les soieries, moins bien conservées, l’étude s’est attachée à déterminer s’il s’agit de produits tourangeaux. Le traitement des draps de laine, augmentant leur résistance, a permis l’observation des formes, dont quelques pièces de vêtements isolées. Les pièces vestimentaires ont été découpées pour produire lacets et chausses avec une fréquence qui incite à voir dans le rejet la vidange d’un atelier de fripier. Ce corpus et l’analyse de chartes concernant la ville de Tours ouvrent un aperçu de la vie quotidienne dans une capitale de la fin du Moyen Âge, où les habitants relativement fortunés sont vêtus de bon drap et, malgré l’interdiction, de vêtements et accessoires de soie
The discovery in Tours of a set of almost 6000 pieces in the same pit, located just outside the city walls along the Loire River ("place Anatole France") provides an opportunity to study the entire process of textile work. The fragments studied are mostly wool cloth, which was a significant commercial production on the 15th - 16th centuries. As for remains of silk which are less well preserved, the study attempted to determine if they were produced in Tours. Among the shapes of wool remains, remarkably preserved, were a few clear parts of garments. Textiles were re-used to fashion laces and hoses in such a high frequency that the corpus is interpreted as the emptying of a second-hand clothes dealer shop. This corpus, combined with law texts regarding Tours, provides a picture of a late medieval capital city, where bourgeoisie wore good broadcloth and, contrary to law, silk dress accessories
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Hok, Jean-Marc. "1-cocycles pour les n-tresses fermées dans le tore solide qui sont des nœuds et algorithmes de calculs." Thesis, Toulouse 3, 2021. http://www.theses.fr/2021TOU30022.

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Ce manuscrit est un travail qui s'inscrit dans le cadre de la topologie, de l'algèbre, de la combinatoire et de la programmation. Plus précisément, c'est une thèse en théorie des noeuds. L'objectif de ce travail est de fournir une famille d'invariants permettant de distinguer les 4-tresses qui sont des noeuds (une famille particulière de noeuds) dans le tore solide S1 × D2. La construction et le calcul de ces invariants utilise des notions élémentaires de la théorie des nœuds mais la preuve du théorème principal d'invariance nécessite des connaissances plus poussées en théorie des singularités. La compréhension du programme de calcul qui implémente ces invariants en Sagemath implique d'avoir des bases en programmation Python et en algorithmique (Programmation Orientée Objet, fonctions récursives, dictionnaires, etc...)
This manuscript is a work within the scope of topology, algebra, combinatorics and programming. More precisely, it is a thesis in knot theory. The main goal of this manuscript is to provide a family of invariants that can distinguish 4-braids that are knots (a particular family of knots) in the solid torus S1×D2. The construction and the computation of these invariants use knot theory basics but the proof of the main invariance theorem requires more advanced knowledge in singularity theory. The understanding of the computational program that implements these invariants in Sagemath requires basic knowledge of Python programming and algorithmics (Oriented-Object Programming, recursive function theory, dictionaries, etc...)
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Books on the topic "Torus knot"

1

Hikami, Kazuhiro. Torus knot and minimal model. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2003.

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Hill, Peter Clifford. On double-Torus knots. Toronto: University of Toronto, 1998.

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Spring, Michael. Great European itineraries: Everything you need to know to plan your own memorable vacation. Garden City, N.Y: Doubleday, 1987.

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Tort Law Update (5th 1994 Spokane & Seattle, Wash.). 5th Annual Tort Law Update: Strictly "need to know". [Seattle, Wash: Washington State Trial Lawyers Association, 1994.

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Sondra, Jamieson, ed. Historic Knoxville and Knox County: City center, neighborhoods, and parks : a walking and touring guide. Norris, Tenn: Laurel Place, 1990.

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Tort Law Update (1st 1990 SeaTac, Wash.). 1st Annual Tort Law Update: What you don't know can hurt you and your client. [Seattle, WA?]: Washington State Trial Lawyers Association, 1990.

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Popper, Adrienne. Summer camps and teen tours: Everything parents and kids should know. New York: Pocket Books, 1988.

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Gindlesperger, James. So you think you know Gettysburg?: The stories behind the monuments and the men who fought one of America's most epic battles. Winston-Salem, N.C: John F. Blair, 2010.

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Mark, Gorney, ed. Risk, liability and malpractice: What every plastic surgeon needs to know. [Philadelphia]: Elsevier Saunders, 2011.

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Suzanne, Gindlesperger, ed. So you think you know Gettysburg?: The stories behind the monuments and the men who fought one of America's most epic battles. Winston-Salem, N.C: John F. Blair Publisher, 2010.

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Book chapters on the topic "Torus knot"

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Murasugi, Kunio. "Torus Knots." In Knot Theory & Its Applications, 132–51. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4719-3_8.

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Pandey, Vipul Kumar, and Bhabani Prasad Mandal. "BRST Qantization on Torus Knot." In XXII DAE High Energy Physics Symposium, 513–16. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73171-1_120.

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Damiani, Celeste. "Towards a Version of Markov’s Theorem for Ribbon Torus-Links in $$\mathbb {R}^4$$." In Knots, Low-Dimensional Topology and Applications, 309–28. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_15.

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Diamantis, Ioannis. "An Alternative Basis for the Kauffman Bracket Skein Module of the Solid Torus via Braids." In Knots, Low-Dimensional Topology and Applications, 329–45. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_16.

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Tyurina, S. D. "Closure of Drinfeld’s Associator and the Kontsevich Integral for (2,n)-Torus Knots." In Proceedings of the Second ISAAC Congress, 1079–89. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0271-1_31.

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Tyurina, Svetlana, and Alexander Varchenko. "Finite-order Invariants for (n, 2)-Torus Knots and the Curve $${Y^2}={X^3}+{X^2}$$." In Notions of Positivity and the Geometry of Polynomials, 401–3. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0142-3_21.

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Mahieu, Rilke. "‘We're not coming from Mars; we know how things work in Morocco!’ How diasporic Moroccan youth resists political socialisation in state-led homeland tours." In The Microfoundations of Diaspora Politics, 202–19. London: Routledge, 2021. http://dx.doi.org/10.4324/9781003191261-11.

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Mee, Nicholas. "The Gordian Knot." In Celestial Tapestry, 235–47. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851950.003.0023.

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Chapter 22 includes a brief survey of knots and their uses. The nineteenth-century physicist Lord Kelvin suggested that atoms might be knots in the aether. This idea led to the development of knot theory as a branch of mathematics. Knots are classified by their crossing number. As the crossing number increases, the number of prime knots rises rapidly. This chapter explains an important class of knots known as torus knots that can be produced by winding a string around a torus. Knots that are formed of more than one component are known as links.
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"Representations and the colored Jones polynomial of a torus knot." In Chern-Simons Gauge Theory: 20 Years After, 153–71. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/amsip/050/08.

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"Torus Knots." In Crafting Conundrums, 50–66. A K Peters/CRC Press, 2014. http://dx.doi.org/10.1201/b17578-7.

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Conference papers on the topic "Torus knot"

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Xufeng, Zhang, and Luo Jianshu. "A New Torus Knot EFIE." In 2007 International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications. IEEE, 2007. http://dx.doi.org/10.1109/mape.2007.4393674.

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Kumar, S. Vinoth, and A. R. Harish. "Trefoil torus knot antenna with boresight radiation pattern." In 2017 IEEE International Conference on Antenna Innovations & Modern Technologies for Ground, Aircraft and Satellite Applications (iAIM). IEEE, 2017. http://dx.doi.org/10.1109/iaim.2017.8402575.

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Kumar, S. Vinoth, and A. R. Harish. "Dual mode bandpass filter using trefoil torus knot resonator." In 2015 IEEE MTT-S International Microwave and RF Conference (IMaRC). IEEE, 2015. http://dx.doi.org/10.1109/imarc.2015.7411408.

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Kumar, S. Vinoth, and A. R. Harish. "Two-port 3D printed trefoil torus knot antenna with pattern diversity." In 2018 3rd International Conference on Microwave and Photonics (ICMAP). IEEE, 2018. http://dx.doi.org/10.1109/icmap.2018.8354587.

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Kumar, S. Vinoth, and A. R. Harish. "Generation of circularly polarized conical beam pattern using (3, 8) torus knot antenna." In 2017 11th European Conference on Antennas and Propagation (EUCAP). IEEE, 2017. http://dx.doi.org/10.23919/eucap.2017.7928724.

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Golbus, Peter, Robert W. McGrail, Tomasz Przytycki, Mary Sharac, and Aleksandar Chakarov. "Tricolorable torus knots are NP-complete." In the 47th Annual Southeast Regional Conference. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1566445.1566503.

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Syrmos, G., R. Rassai, and R. W. Newcomb. "Semistate Equations for Solid-Holed Torus Knots." In 1989 American Control Conference. IEEE, 1989. http://dx.doi.org/10.23919/acc.1989.4790545.

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Balutoiu, Maria anca, Alexandru Gradinaru, Alin Moldoveanu, Florica Moldoveanu, Anakarina Nazare, Andrei Lapusteanu, and Mireille Radoi. "LIBQUEST - A CHALLENGE TO READ BOOKS THROUGH FUN." In eLSE 2021. ADL Romania, 2021. http://dx.doi.org/10.12753/2066-026x-21-065.

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We live in a time period when technology is advancing at an incredible speed. What seemed to be almost science fiction twenty years ago nowadays is becoming or has already become reality. As a result, our activities (especially the activities of young people) have started to shift more and more towards the digital world. If our parents used to read books in order to spend their free time when they were in their 20s, nowadays young people prefer in their free time to play a mobile game rather than to read a book. Even though they know reading books can be more useful and even more entertaining than a mobile phone game, people tend to choose the smartphone activity because of the easiness of reaching the desired action. This paper presents the current status of the LibQuest prototype, an application part of Lib2Life research project, that enables the possibility to combine reading with fun and technology, aiming to remind people how important and fun reading can be. Inside virtual libraries, which reproduce real life libraries, people can solve quests (such as RPG quests), can take part in virtual tours or can participate to custom cultural events. All these actions (whether we talk about quests, tours or cultural events) can be created by an admin of the library or can be also created by users of the application. Tours and cultural events can take place only in the virtual world, while quests, in order to be more exciting, can take place in both the virtual world and the real world.
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Wilkomirsky, Michèle. "Design Journey: A View from the Global South." In LINK 2022. Tuwhera Open Access, 2022. http://dx.doi.org/10.24135/link2022.v3i1.189.

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In 1984 the Travesías was incorporated as a preponderant activity in the study plan for all the Architecture and Design workshops at the Pontificia Universidad Católica de Valparaíso from Chile. The voyages are study tours of professors and students whose purpose is to build together a work of design construction and light duration somewhere in America. The equation of the journey is always open: the place, the number of resources and impediments make it an adventure. But it is not an adventure without measure, but that of allowing ourselves to be surprised by some dimension of America that we do not know or believe we know, and then we feel in direct experience. The Travesías project constitutes the last of the inventions of the school, which, together with the Phalène, Ciudad Abierta and the churches built by the Work Workshops in the south of Chile, has been developing to fulfil the vision of inhabiting this American continent. It was to realize a utopia, of itself the unrealizable. However, the saying of poetry and the doing of design propose the fit of life, work, and study. The first step was forty years ago with the founding of the Institute of Architecture, and ten years ago, the passage of the e Travesías that go out to tour the continent. These steps are not intermediaries for other purposes; if not so that our days are simultaneous to our work, and thus, we reach the present. After almost 20 years of experiencing these Travesías, we still ask ourselves about our poetic destiny as a vision of this America not discovered but founded as a gift. The journey, unlike the class in the classroom, incorporates the life of the student, their customs and social ties, as well as their personal characteristics, values, attitudes and knowledge of life. This can only be appreciated and evidenced through uprooting pedagogy in the classroom. Then, once the student is subjected to an extraordinary life regime, it will be precisely his most intimate thoughts and actions that will remain in all evidence, a situation that is difficult to obtain in the traditional and regulated structure that constitutes teaching in the classroom to this day. This presentation illustrates the last Design Travesía, held in November of the present year and the continuous question about our global south.
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