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This chapter uses the work of Charles Taylor to frame the way in which time operates in the early Gothic. Taylor follows Friedrich Schiller in describing the cleavage between the modern and pre-modern worlds as the difference between ‘naïve’ enchantment and ‘sentimental’ disenchantment (‘radical reflexivity’, as Taylor terms it). Enchanted subjectivity was ‘porous’, meaning that the self had no defences beyond magic to regulate against animistic intrusions. Modern subjectivity, by contrast, is ‘buffered’. For Taylor, the Romantic period was that moment in which the process of disenchantment completed itself as a widely accepted, scarcely noted, norm. From across the unbridgeable divide of radical reflexivity, Gothic writers imagine encounters with an enchanted world where time is represented either as ‘kairotic knots’ affording glimpses into higher times that radically shift the subjectivity of the protagonist, or as senseless repetitions undermining the linear logic of modern character development. The chapter demonstrates how this dynamic plays out in three canonical Gothic texts: Ann Radcliffe’s The Mysteries of Udolpho, Gottfried Bürger’s ‘Lenore’ and S. T. Coleridge’s ‘Christabel’.
We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as complex as possible in the sense of Borel reducibility. These algebraic structures are important for their connections with the theory of knots, links and braids. In particular, Joyce showed that a quandle can be associated with any knot, and this serves as a complete invariant for tame knots. However, such a classification of tame knots heuristically seemed to be unsatisfactory, due to the apparent difficulty of the quandle isomorphism problem. Our result confirms this view, showing that, from a set-theoretic perspective, classifying tame knots by quandles replaces one problem with (a special case of) a much harder problem.
We construct prime amphicheiral knots that have free period 2. This settles an open question raised by the second-named author, who proved that amphicheiral hyperbolic knots cannot admit free periods and that prime amphicheiral knots cannot admit free periods of order > 2.
We give simple homological conditions for a rational homology 3-sphere
to have infinite order in the rational homology cobordism group
, and for a collection of rational homology spheres to be linearly independent. These translate immediately to statements about knot concordance when
is the branched double cover of a knot, recovering some results of Livingston and Naik. The statements depend only on the homology groups of the 3-manifolds, but are proven through an analysis of correction terms and their behavior under connected sums.
Guanxi is one of the most popular topics in Chinese and Western scholarship concerning social ties in China. However, several problems in research on guanxi persist, and multiple debates are still ongoing without much consensus in sight. This study has two goals. First, we offer a systematic review of the current literature on guanxi, especially by differentiating guan dyads from xi networks. This reconceptualization of guanxi enables us to clarify the concept of guanxi by differentiating its two dimensions. Second, based on this literature review, we propose a redirection of future research on guanxi such that guan dyads and xi networks are not examined in isolation; rather, their holistic and dynamic interaction is the most fruitful avenue for future research, especially the four mechanisms of their interaction. The proposed reconceptualization and redirection are our two contributions to the literature.
Meloidogyne paranaensis is responsible for considerable losses in coffee production. Because of the distribution of this species in the main Coffea arabica producing regions, there is a need for management practices to ensure the sustainability of coffee production. In this work, we evaluated the agronomic performance of resistant clones of the Conilon coffee cultivar Vitoria Incaper 8142 in areas infested by M. paranaensis in the west region of Minas Gerais, Brazil. Clones 2V, 3V, and 6V presented the lowest number of nematodes per gram of roots and were considered resistant to M. paranaensis. All other clones were considered tolerant to this nematode, and one had good vegetative growth but allowed nematode reproduction. Clones of Vitoria Incaper 8142 of C. canephora represent an alternative to coffee production in areas infested by M. paranaensis including areas traditionally cultivated with C. arabica.
We consider fluid dynamics and solutions. We define the ideal fluid and viscous fluid dynamics (governed by the Navier–Stokes equations) and their relativistic generalizations. The notion of vorticity and fluid helicity is defined, and the wave of small fluid fluctuations is found. Finally, we define fluid vortices and knotted solutions.
In the search for alternative practices to chemical soil fumigation (CSF), anaerobic soil disinfestation (ASD) has proven to be a promising tool for soil-borne pest management and crop production improvement. The ASD treatment with composted poultry litter (CPL) and molasses (M, a labile carbon source) was identified as an effective approach for a biologically based soil disinfestation system in tomato (Solanum lycopersicum L.) production in Florida. However, environmental and food-safety concerns are associated with animal manure-based amendments, which led to the exploration of composted yard waste (CYW) as a potential substitute for CPL in ASD application. In this study, field trials were conducted in Citra and Immokalee, FL to examine the effects of ASD using CYW, CPL and M compared with a commercially available microbial amendment system on root-knot nematodes, weeds, fruit yield and quality of fresh-market tomato. Treatments included (1) ASD with CPL (11 Mg ha−1) and M (6.9 m3 ha−1) (ASD0.5), (2) ASD with CYW (26.9 Mg ha−1) and M (CYW1 + M), (3) ASD with CYW (13.5 Mg ha−1) and M (CYW0.5 + M), (4) Soil Symphony Amendment (SSA), (5) CYW (26.9 Mg ha−1) alone (CYW1) and (6) a combination of CYW1 + SSA, in comparison with (7) untreated control and (8) CSF (Pic-Clor 60 at 224 kg ha−1). Cumulative soil anaerobiosis was greater in ASD0.5 compared with all the other treatments. The root-knot nematode gall index ratings on the tomato crop were significantly lower in CSF, ASD0.5, CYW1 + M and CYW0.5 + M than untreated control in Citra. Although CYW1 and SSA alone had a moderately suppressive effect on weed coverage and root-knot nematodes, their positive impact on crop performance was limited when used alone. ASD0.5, CYW1 + M and CSF had significantly higher marketable and total fruit yields than untreated control in both locations, while all treatments showed promising results in the Immokalee trial in comparison with untreated control. In general, few differences in major fruit quality attributes were found. Although using CYW in ASD was not as effective as CPL in creating soil anaerobic conditions, the enhanced crop performance in CYW1 + M and CYW0.5 + M suggests the potential of using CYW as an alternative source of organic amendment in combination with M to achieve benefits similar to those obtained with CPL-based ASD.
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However, there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known ‘leakage-free’ entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.
We define a homology theory of virtual links built out of the direct sum of the standard Khovanov complex with itself, motivating the name doubled Khovanov homology. We demonstrate that it can be used to show that some virtual links are non-classical, and that it yields a condition on a virtual knot being the connect sum of two unknots. Further, we show that doubled Khovanov homology possesses a perturbation analogous to that defined by Lee in the classical case, and we define a doubled Rasmussen invariant. This invariant is used to obtain various cobordism obstructions; in particular, it is an obstruction to sliceness. Finally, we show that the doubled Rasmussen invariant contains the odd writhe of a virtual knot and use this to show that knots with non-zero odd writhe are not slice.
A knot group has weight one, so is normally generated by a single element called a weight element of the knot group. A meridian is a typical weight element, but some knot groups admit other weight elements. We show that for some infinite classes of three-strand pretzel knots and all prime knots with up to eight crossings, the knot groups admit weight elements that are not automorphic images of meridians.
Fragments of two robust wool textiles with an unusual knotted blue pile were recovered from a Period I (late Flavian) fort ditch at Vindolanda. Their knotted structure — unknown hitherto in the western Roman provinces and only partially paralleled in the eastern — is discussed, together with questions about their possible production centre and actual function. The Supplementary Material available online (https://doi.org/10.1017/S0068113X18000259) contains technical details of the textiles, an investigation of the raw materials and a comparison of the wools used.
In this paper, we obtain a new result for overtwisted contact
-surgery. We also give a counterexample to a conjecture by James Conway on overtwistedness of manifolds obtained by contact surgery.
The Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define twisted Burau maps and use them to compute twisted Alexander polynomials.
PHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline locally in a tensor product B-spline, and then apply the de-Boor algorithm to evaluate the PHT-spline at a certain parameter pair. We perform analysis about computational complexity and memory costs. The results show that our algorithm takes about the same order of computational costs while requires much less amount of memory compared with the Bézier representations. We give an example to illustrate the effectiveness of our algorithm.
Based on polyhedral splines, some multivariate splines of different orders with given supports over arbitrary topological meshes are developed. Schemes for choosing suitable families of multivariate splines based on pre-given meshes are discussed. Those multivariate splines with inner knots and boundary knots from the related meshes are used to generate rational spline shapes with related control points. Steps for up to C2-surfaces over the meshes are designed. The relationship among the meshes and their knots, the splines and control points is analyzed. To avoid any unexpected discontinuities and get higher smoothness, a heart-repairing technique to adjust inner knots in the multivariate splines is designed.
With the theory above, bivariate C1-quadratic splines over rectangular meshes are developed. Those bivariate splines are used to generate rational C1-quadratic surfaces over the meshes with related control points and weights. The properties of the surfaces are analyzed. The boundary curves and the corner points and tangent planes, and smooth connecting conditions of different patches are presented. The C1–continuous connection schemes between two patches of the surfaces are presented.
We give a method for constructing a Legendrian representative of a knot in
which realizes its maximal Thurston–Bennequin number under a certain condition. The method utilizes Stein handle decompositions of
, and the resulting Legendrian representative is often very complicated (relative to the complexity of the topological knot type). As an application, we construct infinitely many knots in
each of which yields a reducible 3-manifold by a Legendrian surgery in the standard tight contact structure. This disproves a conjecture of Lidman and Sivek.
We apply the concept of braiding sequences to link polynomials to show polynomial growth bounds on the derivatives of the Jones polynomial evaluated on S1 and of the Brandt–Lickorish–Millett–Ho polynomial evaluated on [–2, 2] on alternating and positive knots of given genus. For positive links, boundedness criteria for the coefficients of the Jones, HOMFLY and Kauffman polynomials are derived. (This is a continuation of the paper ‘Applications of braiding sequences. I’: Commun. Contemp. Math.12(5) (2010), 681–726.)