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Статті в журналах з теми "Toroidal embedding"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Nakamoto, Atsuhiro, Katsuhiro Ota, and Kenta Ozeki. "Book Embedding of Toroidal Bipartite Graphs." SIAM Journal on Discrete Mathematics 26, no. 2 (January 2012): 661–69. http://dx.doi.org/10.1137/100794651.

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2

Kang, Ming-Hsuan, and Jing-Wen Gu. "Toroidal Spectral Drawing." Axioms 11, no. 3 (March 16, 2022): 137. http://dx.doi.org/10.3390/axioms11030137.

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Анотація:

We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the torus.

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3

Barthel, Senja. "On chirality of toroidal embeddings of polyhedral graphs." Journal of Knot Theory and Its Ramifications 26, no. 08 (May 22, 2017): 1750050. http://dx.doi.org/10.1142/s021821651750050x.

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We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a nonsplit link due to [2, 3]. Building on this and using the chirality of torus knots and links [9, 10], we prove that the nontrivial embeddings of simple 3-connected planar graphs in the standard torus are chiral. For the case that the spatial graph contains a nontrivial knot, the statement was shown by Castle et al. [5]. We give an alternative proof using minors instead of the Euler characteristic. To prove the case in which the graph embedding contains a nonsplit link, we show the chirality of Hopf ladders with at least three rungs, thus generalizing a theorem of Simon [12].

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4

Ford, T. J. "The Toroidal Embedding Arising From an Irrational Fan." Results in Mathematics 35, no. 1-2 (March 1999): 44–69. http://dx.doi.org/10.1007/bf03322022.

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5

Yu, Xuehong, Minsoo Kim, Florian Herrault, Chang-Hyeon Ji, Jungkwung Kim, and Mark G. Allen. "Silicon-Embedding Approaches to 3-D Toroidal Inductor Fabrication." Journal of Microelectromechanical Systems 22, no. 3 (June 2013): 580–88. http://dx.doi.org/10.1109/jmems.2012.2233718.

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6

Strapasson, João Eloir, Sueli Irene Rodrigues Costa, and Marcelo Muniz. "A Note on Quadrangular Embedding of Abelian Cayley Graphs." TEMA (São Carlos) 17, no. 3 (December 20, 2016): 331. http://dx.doi.org/10.5540/tema.2016.017.03.0331.

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Анотація:

The genus graphs have been studied by many authors, but just a few results concerning in special cases: Planar, Toroidal, Complete, Bipartite and Cartesian Product of Bipartite. We present here a general lower bound for the genus of a abelian Cayley graph and construct a family of circulant graphs which reach this bound.

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7

Huang, Yan Tang, Ling Ou, and Yu Huang. "Generation of Multi-Atom W States in Microtoroidal Cavity-Atom System." Advanced Materials Research 571 (September 2012): 195–99. http://dx.doi.org/10.4028/www.scientific.net/amr.571.195.

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We proposed a scheme for the generation of multi–atom W states with two-photon Jaynes-Cummings Model in ultrahigh-Q toroidal microcavities. We consider that the two modes, clockwise (CW) and counterclockwise (CCW) modes inside the microtoroidal resonator, can be produced by embedding Bragg grating in the microtoroidal.

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8

Möller, Martin, and Don Zagier. "Modular embeddings of Teichmüller curves." Compositio Mathematica 152, no. 11 (September 21, 2016): 2269–349. http://dx.doi.org/10.1112/s0010437x16007636.

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Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related either to triangle groups or to Teichmüller curves. In Part I of this paper we study the arithmetic properties of the modular embedding and develop from scratch a theory of twisted modular forms for Fuchsian groups with a modular embedding, proving dimension formulas, coefficient growth estimates and differential equations. In Part II we provide a modular proof for an Apéry-like integrality statement for solutions of Picard–Fuchs equations. We illustrate the theory on a worked example, giving explicit Fourier expansions of twisted modular forms and the equation of a Teichmüller curve in a Hilbert modular surface. In Part III we show that genus two Teichmüller curves are cut out in Hilbert modular surfaces by a product of theta derivatives. We rederive most of the known properties of those Teichmüller curves from this viewpoint, without using the theory of flat surfaces. As a consequence we give the modular embeddings for all genus two Teichmüller curves and prove that the Fourier developments of their twisted modular forms are algebraic up to one transcendental scaling constant. Moreover, we prove that Bainbridge’s compactification of Hilbert modular surfaces is toroidal. The strategy to compactify can be expressed using continued fractions and resembles Hirzebruch’s in form, but every detail is different.

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9

Loyola, Mark, Ma Louise Antonette De Las Peñas, Grace Estrada, and Eko Santoso. "Symmetry Groups Associated with Tilings of a Flat Torus." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C1428. http://dx.doi.org/10.1107/s2053273314085714.

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A flat torus E^2/Λ is the quotient of the Euclidean plane E^2 with a full rank lattice Λ generated by two linearly independent vectors v_1 and v_2. A motif-transitive tiling T of the plane whose symmetry group G contains translations with vectors v_1 and v_2 induces a tiling T^* of the flat torus. Using a sequence of injective maps, we realize T^* as a tiling T-of a round torus (the surface of a doughnut) in the Euclidean space E^3. This realization is obtained by embedding T^* into the Clifford torus S^1 × S^1 ⊆ E^4 and then stereographically projecting its image to E^3. We then associate two groups of isometries with the tiling T^* – the symmetry group G^* of T^* itself and the symmetry group G-of its Euclidean realization T-. This work provides a method to compute for G^* and G-using results from the theory of space forms, abstract polytopes, and transformation geometry. Furthermore, we present results on the color symmetry properties of the toroidal tiling T^* in relation with the color symmetry properties of the planar tiling T. As an application, we construct toroidal polyhedra from T-and use these geometric structures to model carbon nanotori and their structural analogs.

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10

Al-Betar, Mohammed Azmi, Ahamad Tajudin Khader, Mohammed A. Awadallah, Mahmmoud Hafsaldin Alawan, and Belal Zaqaibeh. "Cellular Harmony Search for Optimization Problems." Journal of Applied Mathematics 2013 (2013): 1–20. http://dx.doi.org/10.1155/2013/139464.

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Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors. The memory consideration and population update are modified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS.

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11

Fulek, Radoslav, and Csaba D. Tóth. "Atomic Embeddability, Clustered Planarity, and Thickenability." Journal of the ACM 69, no. 2 (April 30, 2022): 1–34. http://dx.doi.org/10.1145/3502264.

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We study the atomic embeddability testing problem, which is a common generalization of clustered planarity ( c-planarity , for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity. C-planarity was introduced in 1995 by Feng, Cohen, and Eades as a variant of graph planarity, in which the vertex set of the input graph is endowed with a hierarchical clustering and we seek an embedding (crossing free drawing) of the graph in the plane that respects the clustering in a certain natural sense. Until now, it has been an open problem whether c-planarity can be tested efficiently. The thickenability problem for simplicial complexes emerged in the topology of manifolds in the 1960s. A 2-dimensional simplicial complex is thickenable if it embeds in some orientable 3-dimensional manifold. Recently, Carmesin announced that thickenability can be tested in polynomial time. Our algorithm for atomic embeddability combines ideas from Carmesin’s work with algorithmic tools previously developed for weak embeddability testing. We express our results purely in terms of graphs on surfaces, and rely on the machinery of topological graph theory. Finally, we give a polynomial-time reduction from atomic embeddability to thickenability thereby showing that both problems are polynomially equivalent, and show that a slight generalization of atomic embeddability to the setting in which clusters are toroidal graphs is NP-complete.

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12

Ambro, Florin. "Cyclic covers and toroidal embeddings." European Journal of Mathematics 2, no. 1 (November 18, 2015): 9–44. http://dx.doi.org/10.1007/s40879-015-0084-y.

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13

Ellingham, M. N., and Xiaoya Zha. "Separating Cycles in Doubly Toroidal Embeddings." Graphs and Combinatorics 19, no. 2 (June 2003): 161–75. http://dx.doi.org/10.1007/s00373-002-0491-y.

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14

Teicher, Mina. "On toroidal embeddings of 3-folds." Israel Journal of Mathematics 57, no. 1 (February 1987): 49–67. http://dx.doi.org/10.1007/bf02769460.

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15

Robertson, Neil, Xiaoya Zha, and Yue Zhao. "On the flexibility of toroidal embeddings." Journal of Combinatorial Theory, Series B 98, no. 1 (January 2008): 43–61. http://dx.doi.org/10.1016/j.jctb.2007.03.006.

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16

Gross, Andreas. "Intersection theory on tropicalizations of toroidal embeddings." Proceedings of the London Mathematical Society 116, no. 6 (January 31, 2018): 1365–405. http://dx.doi.org/10.1112/plms.12112.

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17

Stephens, D. Christopher, and Xiaoya Zha. "Spanning subsets of toroidal and Klein bottle embeddings." Electronic Notes in Discrete Mathematics 31 (August 2008): 241–42. http://dx.doi.org/10.1016/j.endm.2008.06.048.

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18

Barthel, Senja, and Dorothy Buck. "Toroidal embeddings of abstractly planar graphs are knotted or linked." Journal of Mathematical Chemistry 53, no. 8 (May 31, 2015): 1772–90. http://dx.doi.org/10.1007/s10910-015-0519-1.

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19

Castle, T., Myfanwy E. Evans, and S. T. Hyde. "All toroidal embeddings of polyhedral graphs in 3-space are chiral." New Journal of Chemistry 33, no. 10 (2009): 2107. http://dx.doi.org/10.1039/b907338h.

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20

Zha, Xiaoya. "The closed 2-cell embeddings of 2-connected doubly toroidal graphs." Discrete Mathematics 145, no. 1-3 (October 1995): 259–71. http://dx.doi.org/10.1016/0012-365x(94)00040-p.

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21

Barthel, Senja, and Dorothy Buck. "Erratum to: Toroidal embeddings of abstractly planar graphs are knotted or linked." Journal of Mathematical Chemistry 55, no. 9 (August 8, 2017): 1887. http://dx.doi.org/10.1007/s10910-017-0780-6.

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22

Burban, Igor, and Olivier Schiffmann. "The composition Hall algebra of a weighted projective line." Journal für die reine und angewandte Mathematik (Crelles Journal) 2013, no. 679 (June 2013): 75–124. http://dx.doi.org/10.1515/crelle.2012.023.

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Анотація:

Abstract In this article, we deal with properties of the reduced Drinfeld double of the composition subalgebra of the Hall algebra of the category of coherent sheaves on a weighted projective line. This study is motivated by applications in the theory of quantized enveloping algebras of some Lie algebras. We obtain a new realization of the quantized enveloping algebras of affine Lie algebras of simply-laced types as well as some new embeddings between them. Moreover, our approach allows to derive new results on the structure of the quantized enveloping algebras of the toroidal algebras of types D4(1, 1), E6(1, 1), E7(1, 1) and E8(1, 1). In particular, our method leads to a construction of a modular action and allows to define a PBW-type basis for that classes of algebras.

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23

Maggioni, Francesca, and Renzo L. Ricca. "On the groundstate energy of tight knots." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2109 (June 24, 2009): 2761–83. http://dx.doi.org/10.1098/rspa.2008.0536.

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New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field. Standard minimization of the magnetic energy is carried out under the usual assumptions of volume- and flux-preserving flow, with the additional constraints that the tube cross section remains circular and that the knot length (ropelength) is independent from internal field twist (framing). Under these constraints the minimum energy is determined analytically by a new, exact expression, function of ropelength and framing. Groundstate energy levels of tight knots are determined from ropelength data obtained by the SONO tightening algorithm. Results for torus knots are compared with previous work, and the groundstate energy spectrum of the first prime knots — up to 10 crossings — is presented and analysed in detail. These results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration.

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24

Faraggi, Alon E. "Spinor-Vector Duality and the Swampland." Universe 8, no. 8 (August 18, 2022): 426. http://dx.doi.org/10.3390/universe8080426.

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The Swampland Program aims to address the question, “when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?”, and can be regarded as a bottom-up approach for investigations of quantum gravity. An alternative top-down approach aims to explore the imprints and the constraints imposed by string-theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli and provide a probe to constrain and explore the moduli spaces of (2, 0) string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications have yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. T-duality is another important property of string theory and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality and the related equivalence postulate of quantum mechanics provide the background independent overarching principles underlying quantum gravity.

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25

Botero, Ana María, and José Ignacio Burgos Gil. "Toroidal b-divisors and Monge–Ampère measures." Mathematische Zeitschrift, June 24, 2021. http://dx.doi.org/10.1007/s00209-021-02789-5.

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AbstractWe generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of nef b-divisors on complete varieties which are toroidal with respect to a snc divisor. As a key ingredient we show the existence of a limit measure, supported on a balanced rational conical polyhedral space attached to the toroidal embedding, which arises as a limit of discrete measures defined via tropical intersection theory on the polyhedral space. We prove that the intersection theory of nef Cartier b-divisors can be extended continuously to nef toroidal Weil b-divisors and that their degree can be computed as an integral with respect to this limit measure. As an application, we show that a Hilbert–Samuel type formula holds for big and nef toroidal Weil b-divisors.

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26

Nagasaki, Koichi. "D5-brane on topological black holes." Progress of Theoretical and Experimental Physics, January 2, 2021. http://dx.doi.org/10.1093/ptep/ptaa189.

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Abstract Our interest is to find the difference of the behavior between black holes with three different topologies. These black holes have spherical, hyperbolic and toroidal structures. We study in this paper the behavior of a probe D5-branes in this nontrivial black hole spacetime. We would like to find the solution what describe the embedding of a probe D5-brane. This system realizes an “interface” solution, a kind of non-local operators, on the boundary gauge theories. These operators are important to deepen understanding of AdS/CFT correspondence.

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27

Ishiguro, Keiya, Tatsuo Kobayashi, and Hajime Otsuka. "Hierarchical structure of physical Yukawa couplings from matter field Kähler metric." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)064.

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Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

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28

Ishiguro, Keiya, Tatsuo Kobayashi, and Hajime Otsuka. "Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries." Journal of High Energy Physics 2022, no. 1 (January 2022). http://dx.doi.org/10.1007/jhep01(2022)020.

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Abstract We examine a common origin of four-dimensional flavor, CP, and U(1)R symmetries in the context of heterotic string theory with standard embedding. We find that flavor and U(1)R symmetries are unified into the Sp(2h + 2, ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP CP symmetry, they are enhanced to GSp(2h + 2, ℂ) ≃ Sp(2h + 2, ℂ) ⋊ $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP generalized symplectic modular symmetry. We exemplify the S3, S4, T′, S9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ2, S4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

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29

Anglés-Castillo, Andreu, Manel Perucho, José María Martí, and Robert A. Laing. "On the deceleration of Fanaroff-Riley Class I jets: mass loading of magnetized jets by stellar winds." Monthly Notices of the Royal Astronomical Society, October 23, 2020. http://dx.doi.org/10.1093/mnras/staa3291.

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Abstract In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma from stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from 10−14 to 10−9 M⊙ yr−1. The spatial jet evolution covers ∼500 pc from jet injection in the grid at 10 pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that toroidal magnetic fields can prevent fast jet expansion and the subsequent embedding of further stars via magnetic tension. In this sense, magnetic fields avoid a runaway deceleration process. Furthermore, when the mass-load is large enough to increase the jet density and produce fast, differential jet expansion, the conversion of magnetic energy flux into kinetic energy flux (i.e., magnetic acceleration), helps to delay the deceleration process with respect to non-magnetised jets. We conclude that the typical stellar population in elliptical galaxies cannot explain jet deceleration in classical FRI radio galaxies. However, we observe a significant change in the jet composition, thermodynamical parameters and energy dissipation along its evolution, even for moderate values of the mass-load.

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30

Conder, Marston, and Ricardo Grande. "On Embeddings of Circulant Graphs." Electronic Journal of Combinatorics 22, no. 2 (May 22, 2015). http://dx.doi.org/10.37236/4013.

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Анотація:

A circulant of order $n$ is a Cayley graph for the cyclic group $\mathbb{Z}_n$, and as such, admits a transitive action of $\mathbb{Z}_n$ on its vertices. This paper concerns 2-cell embeddings of connected circulants on closed orientable surfaces. Embeddings on the sphere (the planar case) were classified by Heuberger (2003), and by a theorem of Thomassen (1991), there are only finitely many vertex-transitive graphs with minimum genus $g$, for any given integer $g \ge 3$. Here we completely determine all connected circulants with minimum genus 1 or 2; this corrects and extends an attempted classification of all toroidal circulants by Costa, Strapasson, Alves and Carlos (2010).

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