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Autore: Grafiati

Pubblicato: 8 giugno 2024

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1

Jiang, Jackson, Ita Suzana Mat Jais, Andrew Kean Tuck Yam, Duncan Angus McGrouther e Shian Chao Tay. "A Biomechanical Comparison of Different Knots Tied on Fibrewire Suture". Journal of Hand Surgery (Asian-Pacific Volume) 22, n. 01 (16 febbraio 2017): 65–69. http://dx.doi.org/10.1142/s0218810417500113.

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Background: Synthetic sutures such as Fiberwire used in flexor tendon repairs have high tensile strength. Proper application allows early mobilisation, decreasing morbidity from repair rupture and adhesions while preserving range of motion. Suture stiffness can cause poorer knot holding, contributing to gapping, peritendinous adhesions or rupture. Previous studies recommended more throws in knots tied on Fiberwire to prevent knot slippage. These larger knots are voluminous and prominent. In tendon repairs they can cause “catching”, increase friction and work of flexion. Other studies advocated certain complicated knots as being more secure. We evaluated several knots and their biomechanical properties with the aim of finding a compact knot with less potential for slippage to maximise strength potential of flexor tendon repairs using Fiberwire. Methods: A series of different knots tied on Fiberwire 4-0 sutures were pulled to failure on a mechanical tester. Mean tensile strengths, knot volumes and tensile strength to knot volume ratios were compared. Results: Tensile strengths and knot volume increased with more throws and loops. Four variations of the square knot (the 4=4=1, 2=2=2=2, 1=1=1=1=1, 2=1=1=1=1 knots) had tensile strengths greater than 35N. The specialised anti-slip knot had highest tensile strength and suture volume but lower strength-to-volume ratio. Conclusions: The anti-slip knot had highest tensile strength but it also had the highest volume. The greater strength of repair may not translate into improved clinical outcome. The 1=1=1=1=1 knot has superior knot strength-to-volume ratio with good knot strength adequate for early active mobilisation in flexor tendon repairs.

2

Manso, Rubén, J. Paul McLean, Adam Ash e Alexis Achim. "Estimation of individual knot volumes by mixed-effects modelling". Canadian Journal of Forest Research 50, n. 2 (febbraio 2020): 81–88. http://dx.doi.org/10.1139/cjfr-2019-0038.

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We present a new method to estimate individual knot volumes based on a knot geometry model coupled with observations on branch characteristics. X-ray computer tomography and image analysis were used to measure the volume and geometry of 424 knots of Sitka spruce (Picea sitchensis (Bong.) Carrière). Knot geometry can be described mathematically by deriving functions for relative vertical position, diameter, and slope dependent on radial position in the stem. These functions were parameterized using “seemingly unrelated regression” and mixed-modelling techniques. This provided a base model for typical knots. To estimate individual knot volume, we used available data for branch diameter and insertion angle to obtain conditional predictions. We imputed the most likely knot trajectory, as relative vertical position cannot be measured on branches. The model explained up to 96% of the variability in knot volume by incorporating the branch measurements, in contrast to the 43% explained using the typical knot model. Knot volume assessment based only on conditional predictions of diameter and marginal predictions of vertical position also accounted for 96% of the variability. Therefore, measurements of branch diameter alone would be enough to obtain highly precise predictions of individual knot volume. This estimator is a first step towards a knot model to be used for the management of Sitka spruce in Great Britain.

3

CHO, JINSEOK, e JUN MURAKAMI. "THE COMPLEX VOLUMES OF TWIST KNOTS VIA COLORED JONES POLYNOMIALS". Journal of Knot Theory and Its Ramifications 19, n. 11 (novembre 2010): 1401–21. http://dx.doi.org/10.1142/s0218216510008443.

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For a hyperbolic knot, an ideal triangulation of the knot complement corresponding to the colored Jones polynomial was introduced by Thurston. Considering this triangulation of a twist knot, we find a function which gives the hyperbolicity equations and the complex volume of the knot complement, using Zickert's theory of the extended Bloch group and the complex volume. We also consider a formal approximation of the colored Jones polynomial. Following Ohnuki's theory of 2-bridge knots, we define another function which comes from the approximation. We show that this function is essentially the same as the previous function, and therefore it also gives the same hyperbolicity equations and the complex volume. Finally we compare this result with our previous one which dealt with Yokota theory, and, as an application to Yokota theory, present a refined formula of the complex volumes for any twist knots.

4

YOKOTA, YOSHIYUKI. "ON THE COMPLEX VOLUME OF HYPERBOLIC KNOTS". Journal of Knot Theory and Its Ramifications 20, n. 07 (luglio 2011): 955–76. http://dx.doi.org/10.1142/s021821651100908x.

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5

BAKER, KENNETH L. "SURGERY DESCRIPTIONS AND VOLUMES OF BERGE KNOTS I: LARGE VOLUME BERGE KNOTS". Journal of Knot Theory and Its Ramifications 17, n. 09 (settembre 2008): 1077–97. http://dx.doi.org/10.1142/s0218216508006518.

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By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery descriptions for these knots on minimally twisted chain links.

6

Aptekarev, Alexander Ivanovich. "Hyperbolic volume of 3-d manifolds, A-polynomials, numerical hypothesis testing". Keldysh Institute Preprints, n. 52 (2023): 1–36. http://dx.doi.org/10.20948/prepr-2023-52.

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We continue our study of the connections between the hyperbolic volume of the complement of a knot in the three dimensional sphere with topological invariants of this knot. This time we pay attention to A(M,L) parametrization for the affine variety with casp, produced by a knot (so-called A-polynomials). Then, using the known expressions of A-polynomials for number of knots we present results of the numerical tests for the conjectures on asymptotics of solutions of q-difference equations connected with the hyperbolic volume of these knots.

7

Ito, Noboru, e Yusuke Takimura. "Crosscap number of knots and volume bounds". International Journal of Mathematics 31, n. 13 (28 novembre 2020): 2050111. http://dx.doi.org/10.1142/s0129167x20501116.

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In this paper, we obtain the crosscap number of any alternating knots by using our recently-introduced diagrammatic knot invariant (Theorem 1). The proof is given by properties of chord diagrams (Kindred proved Theorem 1 independently via other techniques). For non-alternating knots, we give Theorem 2 that generalizes Theorem 1. We also improve known formulas to obtain upper bounds of the crosscap number of knots (alternating or non-alternating) (Theorem 3). As a corollary, this paper connects crosscap numbers and our invariant with other knot invariants such as the Jones polynomial, twist number, crossing number, and hyperbolic volume (Corollaries 1–7). In Appendix A, using Theorem 1, we complete giving the crosscap numbers of the alternating knots with up to 11 crossings including those of the previously unknown values for [Formula: see text] knots (Tables A.1).

8

Ben Aribi, Fathi. "The L2-Alexander invariant is stronger than the genus and the simplicial volume". Journal of Knot Theory and Its Ramifications 28, n. 05 (aprile 2019): 1950030. http://dx.doi.org/10.1142/s0218216519500305.

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We study how the genus, the simplicial volume and the [Formula: see text]-Alexander invariant of Li and Zhang can detect individual knots among all others. In particular, we use various techniques coming from hyperbolic geometry and topology to prove that the [Formula: see text]-Alexander invariant contains strictly more information than the pair (genus, simplicial volume). Along the way, we prove that the [Formula: see text]-Alexander invariant detects the figure-eight knot [Formula: see text], the twist knot [Formula: see text] and an infinite family of cables on the figure-eight knot.

9

Ji, Airu, Julie Cool e Isabelle Duchesne. "Using X-ray CT Scanned Reconstructed Logs to Predict Knot Characteristics and Tree Value". Forests 12, n. 6 (1 giugno 2021): 720. http://dx.doi.org/10.3390/f12060720.

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Research Highlights: Stand density was connected with wood quality and lumber production to develop a predictive model to better estimate tree value. Background and Objectives: The available standing wood volume in British Columbia (BC), Canada has consistently decreased since 1990. Better understanding the link between stand growth conditions, knot characteristics, the sawmilling process and product quality is essential in making informed forest management decisions and efficiently utilizing wood. The overall objective was to investigate and predict the impact of tree growth as affected by stand density on knot characteristics, lumber volume and value recoveries for two conifer species, two types of sawmills and three economic scenarios. Materials and Methods: Seventy-two amabilis fir and western hemlock trees were harvested from three stands located on Vancouver Island, BC. Sawlogs were scanned using an X-ray computed tomography (CT) scanner and images were processed to extract knot characteristics and reconstruct three-dimensional (3D) log models. The effects of three diameter at breast height (DBH) classes (30, 40 and 50 cm) and three stand densities on knot characteristics, including knot volume, number of knots, average knot area and knot/tree volume ratio, as well as the simulated lumber volume and value recoveries from two types of sawmills (i.e., Coastal and Interior) under three economic scenarios (i.e., baseline, optimistic, and pessimistic) were investigated. Results: As expected, the knot characteristics of both species increased with the DBH. The difference of knot distribution between amabilis fir and western hemlock suggests that the latter is more sensitive to growth site conditions. The sawmilling simulations revealed that the Coastal mill produced a lower lumber volume due to the type of products manufactured and the primary breakdown patterns being used. Conclusions: The developed linear mixed effects models based on the knot characteristics and tree features could predict the value of a standing tree and can be used for estimating preharvest stand value of similar Coastal Hem-Fir forests.

10

LE, THANG T. Q., e ANH T. TRAN. "ON THE VOLUME CONJECTURE FOR CABLES OF KNOTS". Journal of Knot Theory and Its Ramifications 19, n. 12 (dicembre 2010): 1673–91. http://dx.doi.org/10.1142/s0218216510008534.

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We establish the volume conjecture for (m, 2)-cables of the figure 8 knot, when m is odd. For (m, 2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev invariant). There are many cases when the volume conjecture for cables of the figure 8 knot is false if one considers all the colors, but holds true if one restricts the colors to a subset of the set of positive integers.

11

Fan, Miaomiao, Jiangzhou Li, Kuai Dai, Meiju Liu, Wenbing Zhou, Limeng Zhang e Shan Lin. "Root-Knot Density as a New Index Can Quantitatively Diagnose the Damage of Root Nematodes to Plant Growth". Agronomy 13, n. 1 (30 dicembre 2022): 136. http://dx.doi.org/10.3390/agronomy13010136.

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Root-knot nematode disease occurs frequently due to continuous monocropping and excessive water and nitrogen input. The disease degree and gall index are often used to evaluate the damage of root-knot disease. However, the weak correlation between these two indicators to tobacco leaf dry weight has often been reported. The objective of this study was to verify whether the use of the root-knot density (RKD)—the root-knot number per unit root weight or volume—as a new indicator could describe the damage of root-knot disease to tobacco growth and yield quantitatively. A total of 3000 tobacco plants from 60 independent plots were classified according to the damage symptom of leaves in situ. A total of 6 plants in each plot were selected and sampled to represent six damage levels in a total of 360 plants. The responding roots were taken out with a root auger. The dry weight of the leaves, stems, roots and root knots as well as the root volume, root-knot number and volume, disease degree, and gall index were determined for all 360 plants separately. Our results showed that: (1) the disease degree and gall index of the root-knot nematodes had a weak negative correlation with the tobacco leaf dry weight while the leaf dry weight and the dry weight, volume, and number of root knots were not correlated; (2) the root dry weight, volume, and length of roots with a diameter ≥ 2 mm were significantly positively correlated with the leaf dry weight; (3) the RKD of roots with a diameter ≥ 2 mm was significantly negatively correlated with the leaf dry weight; and (4) the dry weight of the leaves, stems, and roots decreased significantly with the increase in the average RKD of roots with a diameter ≥ 2 mm in the reclassified groups, which was significantly positively correlated with the average reclassified disease degree and gall index. Our results highlighted that the proposed RKD in this paper can be used to evaluate the damage degree of root-knot disease quantitatively as a new indicator in future research and the practical diagnosis of root-knot nematodes.

12

Cho, Jinseok. "Connected sum of representations of knot groups". Journal of Knot Theory and Its Ramifications 24, n. 03 (marzo 2015): 1550020. http://dx.doi.org/10.1142/s0218216515500200.

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When two boundary-parabolic representations of knot groups are given, we introduce the connected sum of these representations and show several natural properties including the unique factorization property. Furthermore, the complex volume of the connected sum is the sum of each complex volumes modulo iπ2 and the twisted Alexander polynomial of the connected sum is the product of each polynomials with normalization.

13

Meyerhoff, Robert. "A Lower Bound for the Volume of Hyperbolic 3-Manifolds". Canadian Journal of Mathematics 39, n. 5 (1 ottobre 1987): 1038–56. http://dx.doi.org/10.4153/cjm-1987-053-6.

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The motivation for this paper was the work of Thurston and Jørgensen on volumes of hyperbolic 3-manifolds. They prove, among other things, that the set of all volumes of complete hyperbolic 3-manifolds is well-ordered. In particular, there is a hyperbolic 3-manifold which has minimum volume among all complete hyperbolic 3-manifolds. Further, there is a minimum volume member in the collection of complete hyperbolic 3-manifolds with one cusp; and similarly for n cusps. Computer studies to date show that the manifold obtained by performing (5,1) Dehn surgery on the figure-eight knot in the 3-sphere is the leading candidate for the minimum volume hyperbolic 3-manifold. Its volume is about 0.98. The leading one-cusp minimum volume candidate is the figure-eight knot complement in the 3-sphere. Its volume is about 2.03.

14

Blair, Ryan, Heidi Allen e Leslie Rodriguez. "Twist number and the alternating volume of knots". Journal of Knot Theory and Its Ramifications 28, n. 01 (gennaio 2019): 1950016. http://dx.doi.org/10.1142/s0218216519500160.

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It was previously shown by the first author that every knot in [Formula: see text] is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot [Formula: see text] to be the minimum volume of any link [Formula: see text] in a natural class of alternating, hyperbolic links such that [Formula: see text] is ambient isotopic to a component of [Formula: see text]. Our main result shows that the alternating volume of a knot is coarsely equivalent to the twist number of a knot.

15

Mäkinen, Harri, Heikki Korpunen, Antti Raatevaara, Jere Heikkinen, Juha Alatalo e Jori Uusitalo. "Predicting knottiness of Scots pine stems for quality bucking". European Journal of Wood and Wood Products 78, n. 1 (20 novembre 2019): 143–50. http://dx.doi.org/10.1007/s00107-019-01476-x.

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AbstractStem shapes and wood properties are typically unknown at the time of harvesting. To date, approaches that integrate information about past tree growth into the harvesting and bucking process are rarely used. New models were developed and their potential demonstrated for stem bucking procedures for cut-to-length harvesters that integrate information about external and internal stem characteristics detected during harvesting. In total 221 stems were sampled from nine Scots pine (Pinus sylvestris L.) stands in Finland. The widths of rings 11−20 from the pith were measured using images taken from the end face of each butt log. The total volume of knots in each whorl was measured by using a 4D X-ray log scanner. In addition, 13 stems were test sawn, and the diameters of individual knots were measured from the sawn boards. A model system was developed for predicting the horizontal diameter of the thickest knot for each whorl along a stem. The first submodel predicts the knot volume profile from the stem base upwards, and the second submodel converts the predicted knot volume to maximum knot diameter. The results showed that the knottiness of stems of a given size may vary greatly depending on their early growth rate. The developed system will be used to guide logging operations to achieve more profitable bucking procedures.

16

Kou, Su-Peng. "Kelvin wave and knot dynamics on entangled vortices". International Journal of Modern Physics B 31, n. 31 (10 dicembre 2017): 1750241. http://dx.doi.org/10.1142/s0217979217502411.

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In this paper, starting from Biot–Savart mechanics for entangled vortex-membranes, a new theory — knot physics — is developed to explore the underlying physics of quantum mechanics. Owning to the conservation conditions of the volume of knots on vortices in incompressible fluid, the shape of knots will never be changed and the corresponding Kelvin waves cannot evolve smoothly. Instead, the knot can only be split. The knot-pieces evolve following the equation of motion of Biot–Savart equation that becomes Schrödinger equation for probability waves of knots. The classical functions for Kelvin waves become wave-functions for knots. The effective theory of perturbative entangled vortex-membranes becomes a traditional model of relativistic quantum field theory — a massive Dirac model. As a result, this work would help researchers to understand the mystery in quantum mechanics.

17

Jejjala, Vishnu, Arjun Kar e Onkar Parrikar. "Deep learning the hyperbolic volume of a knot". Physics Letters B 799 (dicembre 2019): 135033. http://dx.doi.org/10.1016/j.physletb.2019.135033.

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Aptekarev, A. I., T. V. Dudnikova e D. N. Tulyakov. "Recurrence Relations and Asymptotics of Colored Jones Polynomials". Lobachevskii Journal of Mathematics 42, n. 11 (novembre 2021): 2580–95. http://dx.doi.org/10.1134/s1995080221110056.

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Abstract We consider $$q$$-difference equations for colored Jones polynomials. These sequences of polynomials are invariants for the knots and their asymptotics plays an important role in the famous volume conjecture for the complement of the knot to the $$3$$d sphere. We give an introduction to the theory of hyperbolic volume of the knots complements and study the asymptotics of the solutions of $$q$$-recurrence relations of high order.

19

Barbosa, Marcela Cordeiro, Jason Street, Frank C. Owens e Rubin Shmulsky. "The Effect of Multiple Knots in Close Proximity on Southern Pine Lumber Properties". Forest Products Journal 69, n. 4 (1 gennaio 2019): 278–82. http://dx.doi.org/10.13073/fpj-d-19-00027.

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Abstract Lumber grade rules address well-spaced single-knot and combination-knot sizes. Information is lacking, however, with respect to multiple knots in close proximity. The term “well-spaced” appears to lack quantitation. This research investigates the effect that knots in close proximity (not necessarily combination knots) have on the strength properties of southern yellow pine (SYP; Pinus spp.) lumber. This study attempts to use a statistical model to determine the modulus of rupture (MOR) for SYP having multiple knots in close proximity using variables including the knot diameter (KD), amount of clear wood (CW) present, knot area (KA), and modulus of elasticity (MOE) of the lumber. This study investigated specimens of 2 by 4-inch SYP dimensional lumber exhibiting multiple knots in close proximity. The basic density (D) was determined by dividing the entire specimen weight by its volume. Third-point bending tests were used in flatwise orientation to quantify the MOR and MOE. There were significant correlations among all parameters analyzed. Multiple regression analysis with one dependent variable, MOR, and three independent variables, KD, MOE, and D, resulted in a coefficient of determination value (r2) of 0.702. When using only the MOE to predict MOR, an r2 value of 0.564 was found.

20

Futer, David, Efstratia Kalfagianni e Jessica S. Purcell. "Jones polynomials, volume and essential knot surfaces: a survey". Banach Center Publications 100 (2014): 51–77. http://dx.doi.org/10.4064/bc100-0-3.

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ADAMS, COLIN. "TRIPLE CROSSING NUMBER OF KNOTS AND LINKS". Journal of Knot Theory and Its Ramifications 22, n. 02 (febbraio 2013): 1350006. http://dx.doi.org/10.1142/s0218216513500065.

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A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot and link has a triple crossing projection and then investigate c3(K), which is the minimum number of triple crossings in a projection of K. We obtain upper and lower bounds on c3(K) in terms of the traditional crossing number and show that both are realized. We also relate triple crossing number to the span of the bracket polynomial and use this to determine c3(K) for a variety of knots and links. We then use c3(K) to obtain bounds on the volume of a hyperbolic knot or link. We also consider extensions to cn(K).

22

Champanerkar, Abhijit, Ilya Kofman e Jessica S. Purcell. "Density spectra for knots". Journal of Knot Theory and Its Ramifications 25, n. 03 (marzo 2016): 1640001. http://dx.doi.org/10.1142/s0218216516400010.

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We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this study to new quantum density spectra associated to quantum invariants, such as Jones polynomials, Kashaev invariants and knot homology. We also propose related conjectures motivated by geometrically and diagrammatically maximal sequences of knots.

23

ORTIZ-NAVARRO, JUAN. "A VOLUME FORM ON THE KHOVANOV INVARIANT". Journal of Knot Theory and Its Ramifications 21, n. 04 (aprile 2012): 1250032. http://dx.doi.org/10.1142/s0218216511009844.

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The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This defines a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister moves to give an invariant volume on the Khovanov homology. In this paper, its construction and invariance under these moves is demonstrated. Also, some examples of the invariant are presented for particular choices for the bases of homology groups to obtain a numerical invariant of knots and links. In these examples, the algebraic torsion seen in the Khovanov chain complex when homology is computed over ℤ is recovered.

24

Belley, Denis, Isabelle Duchesne, Steve Vallerand, Julie Barrette e Michel Beaudoin. "Computed tomography (CT) scanning of internal log attributes prior to sawing increases lumber value in white spruce (Picea glauca) and jack pine (Pinus banksiana)". Canadian Journal of Forest Research 49, n. 12 (dicembre 2019): 1516–24. http://dx.doi.org/10.1139/cjfr-2018-0409.

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The increased pressure on timber supply due to a reduced forest land base urges the development of new approaches to fully capture the value of forest products. This paper investigates the effects of knowing the position of knots on lumber volume, value, and grade recoveries in curve sawing of 31 white spruce (Picea glauca (Moench) Voss) and 22 jack pine (Pinus banksiana Lamb.) trees. Internal knot position was evidenced by X-ray computed tomography (CT) imaging, followed by the application of a knot-detection algorithm allowing log reconstruction for use as input in the Optitek sawing simulation software. Comparisons of the three levels of sawing optimization (sweep up, shape optimized, and knot optimized) revealed that considering internal knots before log sawing (e.g., knot optimized) generated 23% more lumber value for jack pine and 15% more for white spruce compared with the traditional sweep-up sawing strategy. In terms of lumber quality, the knot-optimized strategy produced 38% more pieces of grade No. 2 and better in jack pine and 15% more such pieces in white spruce compared with the sweep-up strategy. These results indicate a great potential to increase manufacturing efficiency and profitability by implementing the CT scanning technology, which should aid in developing a strong bioeconomy based on an optimized use of wood.

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RAMIREZ-LOSADA, ENRIQUE. "BRANCHED COVERINGS OF S3 AND VOLUME ZERO KNOTS". Journal of Knot Theory and Its Ramifications 13, n. 05 (agosto 2004): 703–8. http://dx.doi.org/10.1142/s021821650400338x.

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Dąbkowski, Mieczysław K., Józef H. Przytycki e Amir A. Togha. "Non-Left-Orderable 3-Manifold Groups". Canadian Mathematical Bulletin 48, n. 1 (1 marzo 2005): 32–40. http://dx.doi.org/10.4153/cmb-2005-003-6.

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AbstractWe show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of S3 branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of S3 branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the 52 knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.

27

Ballas, Samuel A. "Finite volume properly convex deformations of the figure-eight knot". Geometriae Dedicata 178, n. 1 (22 gennaio 2015): 49–73. http://dx.doi.org/10.1007/s10711-015-0043-2.

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CHO, JINSEOK, e JUN MURAKAMI. "SOME LIMITS OF THE COLORED ALEXANDER INVARIANT OF THE FIGURE-EIGHT KNOT AND THE VOLUME OF HYPERBOLIC ORBIFOLDS". Journal of Knot Theory and Its Ramifications 18, n. 09 (settembre 2009): 1271–86. http://dx.doi.org/10.1142/s0218216509007464.

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We calculate certain limits of the colored Alexander invariant of the figure-eight knot for some cases and show that this limit is related to the volume of hyperbolic orbifolds whose singular set is the figure-eight knot.

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Stabile, Guglielmo, Stefania Carlucci, Lucia De Bonis, Felice Sorrentino, Luigi Nappi e Giuseppe Ricci. "Umbilical Cord Knots: Is the Number Related to Fetal Risk?" Medicina 58, n. 6 (25 maggio 2022): 703. http://dx.doi.org/10.3390/medicina58060703.

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True knots of the umbilical cord (UC) are a rare occurrence and are reported in 0.4–1.2% of deliveries. The compression of true knot of the UC can cause obstruction of the fetal circulation, leading to intra-uterine growth retardation or fetal death. Predisposing factors for the genesis of the true UC knot are numerous and include all the conditions, which lead to a relatively large uterine volume. This situation may predispose to free and excessive fetal movements. Although not all true knots lead to perinatal complications, they have been associated with adverse pregnancy outcomes, including fetal distress, fetal hypoxia, intra-uterine growth restriction (IUGR), long-term neurological damage, caesarean delivery and stillbirth. We present a rare case of operative delivery with vacuum in a multiparous woman at term of pregnancy with a double true knot of the UC. As in most cases, the diagnosis was made after delivery, as there were no fetal symptoms during pregnancy. Some authors assume that 3D power sonography may be useful in the diagnosis of true UC knots. However, 3D power Doppler cannot be considered as a definitive method. There are no specific prenatal indications to induce the physician to look for ultrasound signs suggestive of umbilical true knot. Some studies argue that cases of fetal death and fetal risk are directly related to the number of knots. We also support this thesis, even if further observational and retrospective studies are needed to demonstrate it.

30

Ham, Ji-Young, Joongul Lee, Alexander Mednykh e Aleksei Rasskazov. "On the volume and Chern–Simons invariant for 2-bridge knot orbifolds". Journal of Knot Theory and Its Ramifications 26, n. 12 (ottobre 2017): 1750082. http://dx.doi.org/10.1142/s0218216517500821.

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Abstract (sommario):

This paper extends the work by Mednykh and Rasskazov presented in [On the structure of the canonical fundamental set for the 2-bridge link orbifolds, Universität Bielefeld, Sonderforschungsbereich 343, Discrete Structuren in der Mathematik, Preprint (1988), pp. 98–062, www.mathematik.uni-bielefeld.de/sfb343/preprints/pr98062.ps.gz ]. By using their approach, we derive the Riley–Mednykh polynomial for a family of [Formula: see text]-bridge knot orbifolds. As a result, we obtain explicit formulae for the volumes and Chern–Simons invariants of orbifolds and cone-manifolds on the knot with Conway’s notation [Formula: see text].

31

SOTEROS, C. E., D. W. SUMNERS e S. G. WHITTINGTON. "LINKING OF RANDOM p-SPHERES IN Zd". Journal of Knot Theory and Its Ramifications 08, n. 01 (febbraio 1999): 49–70. http://dx.doi.org/10.1142/s0218216599000067.

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Abstract (sommario):

We consider the number of embeddings of k p-spheres in Zd, with p+2≤d≤2p+1, stratified by the p-dimensional volumes of the spheres. We show for p+2<d that the number of embeddings of a fixed link type of k equivolume p-spheres grows with increasing p-dimensional volume at an exponential rate which is independent of the link type. For d=p+2 we derive similar results both for links of unknotted p-spheres and for "augmented" links where each component p-sphere can have any knot type, and similar but weaker results when the spheres are of specified knot type.

32

Adams, Colin, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang, Kate O’Connor, Natalia Pacheco-Tallaj e Yi Wang. "TG-Hyperbolicity of virtual links". Journal of Knot Theory and Its Ramifications 28, n. 12 (ottobre 2019): 1950080. http://dx.doi.org/10.1142/s0218216519500809.

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Abstract (sommario):

We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.

33

Ewer, MS, MK Ali, HR Gibbs e J. Swafford. "Nodus migrans: the case of the migrating knot". American Journal of Critical Care 1, n. 2 (1 settembre 1992): 108–10. http://dx.doi.org/10.4037/ajcc1992.1.2.108.

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Abstract (sommario):

Flow-directed pulmonary artery catheters provide important information regarding intravascular volume status, cardiac function and vascular resistance. We describe an unusual complication of pulmonary artery catheterization in which a knot formed at the distal end was torn away from the catheter body and migrated from its original position in the right subclavian vein to a distal branch of the right pulmonary artery. Careful attention to insertion and withdrawal techniques could prevent this potentially serious complication.

34

Murakami, Hitoshi, e Jun Murakami. "The colored Jones polynomials and the simplicial volume of a knot". Acta Mathematica 186, n. 1 (2001): 85–104. http://dx.doi.org/10.1007/bf02392716.

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35

LI, WEIPING, e WEIPING ZHANG. "AN L2-ALEXANDER INVARIANT FOR KNOTS". Communications in Contemporary Mathematics 08, n. 02 (aprile 2006): 167–87. http://dx.doi.org/10.1142/s0219199706002088.

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Abstract (sommario):

In this paper, in an attempt to extend an earlier work of Lück, we construct a knot invariant with parameter in C* by using the fundamental L2-representation of the fundamental group of the knot complement, which may be thought of as an L2-analogue of the usual Alexander polynomial of the knot in S3. When restricted to U(1) parameters, we interpret this invariant in terms of the U(1) twisted L2-Reidemeister torsion. We also show that this L2-invariant depends only on the norm |t| for t ∈ C*. In particular, this implies an unexpected rigidity property of the U(1) twisted L2-torsion on a knot complement. A possible relationship with the volume conjecture is discussed.

36

Khoi, Vu The. "Seifert volumes and dilogarithm identities". Journal of Knot Theory and Its Ramifications 23, n. 05 (aprile 2014): 1450025. http://dx.doi.org/10.1142/s0218216514500254.

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37

Ohtsuki, Tomotada. "On the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings". International Journal of Mathematics 28, n. 13 (dicembre 2017): 1750096. http://dx.doi.org/10.1142/s0129167x17500963.

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Abstract (sommario):

We give presentations of the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings. As the volume conjecture states, the leading terms of the expansions present the hyperbolic volume and the Chern–Simons invariant of the complements of the knots. As coefficients of the expansions, we obtain a series of new invariants of the knots. This paper is a continuation of the previous papers [T. Ohtsuki, On the asymptotic expansion of the Kashaev invariant of the [Formula: see text] knot, Quantum Topol. 7 (2016) 669–735; T. Ohtsuki and Y. Yokota, On the asymptotic expansion of the Kashaev invariant of the knots with 6 crossings, to appear in Math. Proc. Cambridge Philos. Soc.], where the asymptotic expansions of the Kashaev invariant are calculated for hyperbolic knots with five and six crossings. A technical difficulty of this paper is to use 4-variable saddle point method, whose concrete calculations are far more complicated than the previous papers.

38

Dubois, Jérôme. "A volume form on the SU(2)–representation space of knot groups". Algebraic & Geometric Topology 6, n. 1 (12 marzo 2006): 373–404. http://dx.doi.org/10.2140/agt.2006.6.373.

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39

Dijkgraaf, Robbert, Hiroyuki Fuji e Masahide Manabe. "The volume conjecture, perturbative knot invariants, and recursion relations for topological strings". Nuclear Physics B 849, n. 1 (agosto 2011): 166–211. http://dx.doi.org/10.1016/j.nuclphysb.2011.03.014.

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40

Dalhatu, A. K., A. A. Khan e Z. D. Umar. "Study of Root-Knot Problems in Ajiwa Dam Area, Katsina State, Nigeria". International Journal of Environment 4, n. 1 (22 febbraio 2015): 204–9. http://dx.doi.org/10.3126/ije.v4i1.12189.

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Abstract (sommario):

The present study was undertaken to observe the root-knot problems in Ajiwa dam area, Katsina state. Surveys were done to determine the level of infestation, incidence, intensity and frequency of root-knot disease and to identify the root-knot nematodes associated with vegetables. The study showed that root-knot disease incidence in the area was fairly very high. Of the fields visited, about 42% fields were infested. Incidence of the disease in different fields and on different vegetables showed wide variation. Short pepper and tomato were most affected crops followed by onion, lettuce and carrot. Spinach was less affected. Two species M. incognita and M. javanica of root-knot nematodes were identified. M. incognita showed highest frequency (71.4%) and was dominant species in the studied area. M. javanica has lowest frequency (28.5%).DOI: http://dx.doi.org/10.3126/ije.v4i1.12189International Journal of Environment Volume-4, Issue-1, Dec-Feb 2014/15, Page: 204-209

41

Park, Hyungjun, e Joo-Haeng Lee. "Adaptive B-spline volume representation of measured BRDF data for photorealistic rendering". Journal of Computational Design and Engineering 2, n. 1 (6 dicembre 2014): 1–15. http://dx.doi.org/10.1016/j.jcde.2014.11.001.

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Abstract (sommario):

Abstract Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically performs approximate B-spline volume lofting, which decomposes the problem into three sub-problems of multiple B-spline curve fitting along u-, v-, and w-parametric directions. Especially, it makes the efficient use of knots in the multiple B-spline curve fitting and thereby accomplishes adaptive knot placement along each parametric direction of a resulting B-spline volume. The proposed method is quite useful to realize efficient data reduction while smoothing out the noises and keeping the overall features of BRDF data well. By applying the B-spline volume models of real materials for rendering, we show that the B-spline volume models are effective in preserving the features of material appearance and are suitable for representing BRDF data.

42

Eftekhar, Behzad, e Andrew Hunn. "Ventriculoperitoneal shunt blockage due to spontaneous knot formation in the peritoneal catheter". Journal of Neurosurgery: Pediatrics 1, n. 2 (febbraio 2008): 142–43. http://dx.doi.org/10.3171/ped/2008/1/2/142.

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Abstract (sommario):

✓The authors report the third case of ventriculoperitoneal shunt blockage due to spontaneous knot formation in the peritoneal catheter that had been placed in a 3.5-year-old boy 8 months earlier. On surgical exploration a double knot was found 10 cm from the distal end of the peritoneal catheter. Although the underlying mechanism remains unknown, the authors used the analogy of related physical studies and true knot formation in the umbilical cord and determined the possible causes as related to the catheter, volume and configuration of the abdomen, and kinetics of the catheter movements. If further study should reveal a significantly higher incidence of this complication, the authors suggest further in vitro studies, designed to investigate the optimal characteristics and safe range of length of peritoneal catheters in different situations.

43

Liu, Shengbo, Pengyuan Fu, Lei Yan, Jian Wu e Yandong Zhao. "Detection of Surface Defects in Logs Using Point Cloud Data and Deep Learning". International Journal of Circuits, Systems and Signal Processing 15 (19 luglio 2021): 607–16. http://dx.doi.org/10.46300/9106.2021.15.67.

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Deep learning classification based on 3D point clouds has gained considerable research interest in recent years.The classification and quantitative analysis of wood defects are of great significance to the wood processing industry. In order to solve the problems of slow processing and low robustness of 3D data. This paper proposes an improvement based on littlepoint CNN lightweight deep learning network, adding BN layer. And based on the data set made by ourselves, the test is carried out. The new network bnlittlepoint CNN has been improved in speed and recognition rate. The correct rate of recognition for non defect log, non defect log and defect log as well as defect knot and dead knot can reach 95.6%.Finally, the "dead knot" and "loose knot" are quantitatively analyzed based on the "integral" idea, and the volume and surface area of the defect are obtained to a certain extent,the error is not more than 1.5% and the defect surface reconstruction is completed based on the triangulation idea.

44

Naschie, M. S. El. "Knot Complement with a Three Sphere Volume as a Model for e (∞ ∞) Spacetime". Chaos, Solitons & Fractals 9, n. 10 (ottobre 1998): 1787–88. http://dx.doi.org/10.1016/s0960-0779(98)00136-2.

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45

LI, WEIPING, e QINGXUE WANG. "ON THE GENERALIZED VOLUME CONJECTURE AND REGULATOR". Communications in Contemporary Mathematics 10, supp01 (novembre 2008): 1023–32. http://dx.doi.org/10.1142/s0219199708003149.

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Abstract (sommario):

In this paper, by using the regulator map of Beilinson-Deligne on a curve, we show that the quantization condition posed by Gukov is true for the SL2(ℂ) character variety of the hyperbolic knot in S3. Furthermore, we prove that the corresponding ℂ*-valued closed 1-form is a secondary characteristic class (Chern-Simons) arising from the vanishing first Chern class of the flat line bundle over the smooth part of the character variety, where the flat line bundle is the pullback of the universal Heisenberg line bundle over ℂ* × ℂ*. Based on this result, we give a reformulation of Gukov's generalized volume conjecture from a motivic perspective.

46

Garoufalidis, Stavros, e Alan W. Reid. "Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds". Journal of Topology and Analysis 10, n. 01 (15 dicembre 2017): 1–25. http://dx.doi.org/10.1142/s1793525318500024.

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Abstract (sommario):

We construct infinitely many examples of pairs of isospectral but non-isometric [Formula: see text]-cusped hyperbolic [Formula: see text]-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada’s method in the cusped setting, and so in addition our pairs are finite covers of the same degree of a 1-cusped hyperbolic 3-orbifold (indeed manifold) and also have the same complex length spectra. Finally we prove that any finite volume hyperbolic 3-manifold isospectral to the figure-eight knot complement is homeomorphic to the figure-eight knot complement.

47

Penner, M., C. Robinson e D. Burgess. "Pinus resinosa product potential following initial spacing and subsequent thinning". Forestry Chronicle 77, n. 1 (1 febbraio 2001): 129–39. http://dx.doi.org/10.5558/tfc77129-1.

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Abstract (sommario):

A trial was initiated in 1953 to investigate the effect of initial tree spacing on red pine (Pinus resinosa Ait.) volume production. Approximately three decades later, in 1982, thinning treatments were added to compare the effects of thinning and initial spacing on volume production. After 45 growing seasons from planting, total volume production (cut + standing volume) mainly was independent of initial spacing and thinning intensity except at the widest (4.3 m +) spacing treatments. Both initial spacing and thinning affected quadratic mean diameter, standing volume and basal area. Knot size was affected by initial spacing with trees at an initial spacing of 3.0 m or wider having a significant number of stems failing to meet utility pole standards due to excessive, large knots. At the time of sampling, 1998, the higher initial densities (1.2 and 1.5 m-spacing) were undergoing significant mortality and falling behind the lower initial spacings in terms of total volume production. In addition, trees at the narrowest spacing were more prone to snow and ice damage. Thinning reduced the time required to meet sawlog and utility pole specifications. The initial spacings ranging from 1.8 to 2.4 m resulted in good growth with high utility pole potential and little mortality. Lower initial spacings required thinning to prevent mortality and maintain good diameter growth. Key words: red pine, density management, volume production, product mixtures

48

Alexiou, Margaret. "On σκορδαψός: gut-knot or eyesore? A tribute to BMGS". Byzantine and Modern Greek Studies 40, n. 1 (aprile 2016): 49–54. http://dx.doi.org/10.1017/byz.2015.6.

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Forty years ago, I contributed my first independent article to Volume 1 of Byzantine and Modern Greek Studies, ‘The lament of the Virgin in Byzantine literature and modern Greek folksong’. For this fortieth anniversary issue, dedicated to A. A. M. Bryer, I have, as in the closing words of Theodore Prodromos’ seventh letter to Aristenos (Πεϱὶ Γλώττης), nothing to offer but μικϱαῖς ἀντιδεξιοῦσα σταγόσι, καὶ ταύταις θολεϱαῖς (‘meagre and murky drops’),1 further sullied with speculation on possible meanings of a single rare word: skordapsos. Does it mean ‘gut-knot’ or ‘eyesore’? Is it a vulgar form of chordapsos, an affliction of the intestines (attested in early medical texts)? Or is it a later vernacular term for ‘eye disease’, for which garlic (skordo) was, and remains, a known curative? And does it matter?

49

Garoufalidis, Stavros, e Yueheng Lan. "Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2–bridge knot". Algebraic & Geometric Topology 5, n. 1 (22 maggio 2005): 379–403. http://dx.doi.org/10.2140/agt.2005.5.379.

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50

NAGASAWA, MICHIYASU, e KATSUHIKO SATO. "DENSITY PERTURBATIONS BY GLOBAL TEXTURES". International Journal of Modern Physics D 01, n. 02 (gennaio 1992): 427–37. http://dx.doi.org/10.1142/s0218271892000239.

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The dynamical evolution of global textures is studied. The evolution equation of a texture field is solved numerically and the effect of cosmic expansion is explicitly introduced. The process of knot collapse is traced and the knot number at conformal time, τ, per comoving volume is 0.01~0.02/τ3. The density perturbations by textures are investigated by a clustering analysis. High density clusters have large-scale correlation and extend widely, which enables the formation of large-scale structures. Moreover, the initial fluctuations by textures show the highly non-Gaussian spatial distribution. Thus they produce the density perturbations which may yield the cosmological structures in the universe.