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Journal articles on the topic 'Topological structures'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ota, Yasutomo, Kenta Takata, Tomoki Ozawa, et al. "Active topological photonics." Nanophotonics 9, no. 3 (2020): 547–67. http://dx.doi.org/10.1515/nanoph-2019-0376.

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AbstractTopological photonics emerged as a novel route to engineer the flow of light. Topologically protected photonic edge modes, which are supported at the perimeters of topologically nontrivial insulating bulk structures, are of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there has been a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolutionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of rema

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2

Zhong, Jinzhan, and Qiwen Zhan. "Structured Optical Toroidal Vortices with Rotational Symmetry." Photonics 12, no. 3 (2025): 288. https://doi.org/10.3390/photonics12030288.

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Toroidal vortices, as intriguing topological structures, play a fundamental role across a wide range of physical fields. In this study, we theoretically propose a family of structured optical toroidal vortices as generalized forms of toroidal vortices in paraxial continuous wave beams. These structured optical toroidal vortices exhibit unique rotational symmetry while preserving the topological properties of standard toroidal vortices. The three-dimensional topological structures demonstrate l-fold rotational symmetry, which is closely related to the topological charges. Structured toroidal vo

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3

Tholen, Walter. "Ordered topological structures." Topology and its Applications 156, no. 12 (2009): 2148–57. http://dx.doi.org/10.1016/j.topol.2009.03.038.

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4

Yeh, Jia Yi. "The Design and Analysis of Topological Phononic Crystals with Cavity." Key Engineering Materials 963 (October 13, 2023): 47–52. http://dx.doi.org/10.4028/p-fo9zp7.

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The topological phononic crystal is composed of two topologically distinct structures. The topological phononic crystal resonant cavity based are proposed and the acoustic wave propagate characteristics are also presented. The topological cavity with defects will change the resonance frequency and quality factor is also discussed. The advantages of the topological cavity are the better quality factors and the concentrated sound pressure larger than general defect cavity.

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5

Demirci, Mustafa. "Three topological structures of smooth topological spaces." Fuzzy Sets and Systems 101, no. 1 (1999): 185–90. http://dx.doi.org/10.1016/s0165-0114(97)00117-6.

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6

Atanassov, Krassimir. "Intuitionistic Fuzzy Modal Multi-Topological Structures and Intuitionistic Fuzzy Multi-Modal Multi-Topological Structures." Mathematics 12, no. 3 (2024): 361. http://dx.doi.org/10.3390/math12030361.

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On the basis of K. Kuratowski’s definitions of a topological structure with a closure or interior operator, the concept of a modal topological structure (MTS) with one of these operators was introduced by the author. This new structure was illustrated with examples with intuitionistic fuzzy topological operators from both examples, and for this reason, these structures were named intuitionistic fuzzy MTSs (IFMTSs). In a series of papers, the author introduced some modifications and extensions to the IFMTSs, e.g., intuitionistic fuzzy temporal topological structures, intuitionistic fuzzy level

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7

Guo, Yuning, Matheus Rosa, and Massimo Ruzzene. "Symmetry-enforced gapless surface states in three-dimensional acoustic gyroid structures." Journal of the Acoustical Society of America 151, no. 4 (2022): A97. http://dx.doi.org/10.1121/10.0010772.

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The discovery of topological gapless phases challenges the perception that topological features necessarily require a bandgap, expanding the understanding of topological phases of matter in various realms including electric, photonic, and phononic systems. The progress on 3D topological gapless states in elastic and acoustic systems is still in its early stages of formulation and design. We here investigate 3D acoustic gyroid crystals supporting symmetry-enforced gapless surface states in minimal surface-based structures. The inherent chirality and morphology of gyroid surfaces enable the impl

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8

Pilozzi, Laura, and Claudio Conti. "Anisotropic circular topological structures." Optical Materials Express 11, no. 2 (2021): 425. http://dx.doi.org/10.1364/ome.412528.

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9

Hughes, C. Bruce. "Controlled homotopy topological structures." Pacific Journal of Mathematics 133, no. 1 (1988): 69–97. http://dx.doi.org/10.2140/pjm.1988.133.69.

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10

Agarwal, Ravi P., Yeol Je Cho, and Reza Saadati. "On Random Topological Structures." Abstract and Applied Analysis 2011 (2011): 1–41. http://dx.doi.org/10.1155/2011/762361.

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We present some topics about random spaces. The main purpose of this paper is to study topological structure of random normed spaces and random functional analysis. These subjects are important to the study of nonlinear analysis in random normed spaces.

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11

Rota, Gian-Carlo. "Theory of topological structures." Advances in Mathematics 73, no. 2 (1989): 263. http://dx.doi.org/10.1016/0001-8708(89)90072-8.

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12

Gutiérrez García, J., T. Kubiak, and A. P. Šostak. "Ideal-valued topological structures." Fuzzy Sets and Systems 161, no. 18 (2010): 2380–88. http://dx.doi.org/10.1016/j.fss.2010.03.007.

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13

Sagave, Steffen. "Logarithmic structures on topological." Geometry & Topology 18, no. 1 (2014): 447–90. http://dx.doi.org/10.2140/gt.2014.18.447.

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14

Tsai, Ya-Wen, Yao-Ting Wang, Pi-Gang Luan, and Ta-Jen Yen. "Topological Phase Transition in a One-Dimensional Elastic String System." Crystals 9, no. 6 (2019): 313. http://dx.doi.org/10.3390/cryst9060313.

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We show that topological interface mode can emerge in a one-dimensional elastic string system which consists of two periodic strings with different band topologies. To verify their topological features, Zak-phase of each band is calculated and reveals the condition of topological phase transition accordingly. Apart from that, the transmittance spectrum illustrates that topological interface mode arises when two topologically distinct structures are connected. The vibration profile further exhibits the non-trivial interface mode in the domain wall between two periodic string composites.

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15

Lee, Jeong Gon, Pyung Ki Lim, and Kul Hur. "Some Topological Structures of Ordinary Smooth Topological Spaces." Journal of Korean Institute of Intelligent Systems 22, no. 6 (2012): 799–805. http://dx.doi.org/10.5391/jkiis.2012.22.6.799.

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16

Li, Hang, Ruizhe Yao, Bowen Zheng, et al. "Electrically Tunable and Reconfigurable Topological Edge State Laser." Optics 3, no. 2 (2022): 107–16. http://dx.doi.org/10.3390/opt3020013.

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Incorporating active components in photonic structures with a topological configuration has been shown to achieve lasing at topological edge states. Here, we report an electrically tunable topological edge-state laser in a one-dimensional complex Su–Schrieffer–Heeger chain. The proposed design is realized in an electrically injected Fabry–Perot (FP) laser chain. The lasing in topologically induced edge states is experimentally observed and a selective enhancement is realized by introducing a topological defect in the center. This work presents a versatile platform to investigate novel concepts

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17

Atanassov, Krassimir. "On Intuitionistic Fuzzy Temporal Topological Structures." Axioms 12, no. 2 (2023): 182. http://dx.doi.org/10.3390/axioms12020182.

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In the present paper, four different intuitionistic fuzzy temporal topological structures are introduced, and some of their properties are discussed. These topological structures are based on the intuitionistic fuzzy topological operators and on the temporal intuitionistic fuzzy topological operators, which exist in intuitionistic fuzzy sets theory. The new structures are direct extensions of the IFTSs and will be the basis for introducing of a new type of topological structures.

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18

P., Gnanachandra, and Muneesh kumar A. "Soft Structures of Monoids and Fields." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 4 (2020): 502–5. https://doi.org/10.35940/ijeat.C5767.049420.

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The ultimate purpose of this article is to introduce and examine some new kind of algebraic structures such as Soft topological fields, Soft topological groups and Soft monoids with illustrating counter examples. Also we established that every Soft field over a topological field is a Soft topological field and we have given an example GF(16), the finite field of 16 elements which is a soft topological field

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19

Atanassov, Krassimir. "Intuitionistic fuzzy bimodal topological structures." Notes on Intuitionistic Fuzzy Sets 29, no. 2 (2023): 133–43. http://dx.doi.org/10.7546/nifs.2023.29.2.133-143.

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Two new intuitionistic fuzzy operators from a modal type are defined. Some properties of these operators are studied. Based on them, four new intuitionistic fuzzy modal topological structures are introduced and after this, four intuitionistic fuzzy bimodal topological structures are constructed. All they are examples of modal and bimodal topological structures.

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20

Moshahary, Jwngsar. "Topological Structures on Fuzzy Multisets." International Journal of Scientific Research and Management (IJSRM) 5, no. 7 (2017): 6461–65. http://dx.doi.org/10.18535/ijsrm/v5i7.81.

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In this paper the concept of fuzzy topological space extended into fuzzy multiset topological space, closed fuzzy multiset, open fuzzy multisets, interior fuzzy multisets, closure of fuzzy multisets and their various properties discuss. Further, we extended the continuous functions to fuzzy multiset continuous function and also discussed subspace of fuzzy multiset topological space

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21

Atanassov, Krassimir. "Remark on Intuitionistic Fuzzy Temporal Modal Topological Structures." Axioms 13, no. 4 (2024): 256. http://dx.doi.org/10.3390/axioms13040256.

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In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy temporal modal topological structures. These structures are based on intuitionistic fuzzy topological, temporal and modal operators. They are extensions of the temporal topological structures as well as of the modal topological structures.

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22

Stoltenberg-Hansen, V., and J. V. Tucker. "Complete local rings as domains." Journal of Symbolic Logic 53, no. 2 (1988): 603–24. http://dx.doi.org/10.1017/s0022481200028498.

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Contents: Introduction. §1: Computable rings and modules. §2: Ideal membership relation. §3: Effective structured domains. §4: Completion of a local ring as a domain. §5: The recursive completion. Epilogue. References.Introduction. Completion is an important general mathematical device. Often, but not always, a completion takes the following form. Let A be a topological algebraic structure whose topology is derived from a metric. For A, a topological algebra Â and an embedding i: A → Â are constructed such that Â is a complete metric space in which A is densely embedded by i. The long list of

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23

Keerthana, D., and V. Visalakshi. "Isotropy group on some topological transformation group structures." Matematychni Studii 62, no. 1 (2024): 93–101. http://dx.doi.org/10.30970/ms.62.1.93-101.

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This paper explores the topological properties of irresolute topological groups, their quotient maps, and the role of topology in normal subgroups. It provides a detailed analysis\linebreak using examples and counterexamples. The study focuses on the essential features of irresolute topological groups and their quotient groups, for understanding the topological aspects of isotropy groups. For a trans\-for\-ma\-tion group $(\mathsf{H}, \mathsf{Y}, \psi)$ and a point $y \in \mathsf{Y},$ the set \centerline{$\mathsf{H}_{y} = \{h \in \mathsf{H} \colon hy = y\}$} \noi consisting of elements of $\ma

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24

Gao, Jingxiang, Ming Zhang, Xiefei Cheng, Xingcheng Tang, and Runjia Guo. "Observation of Multiple Topological edge States in Square-Root electric circuits." Academic Journal of Science and Technology 10, no. 1 (2024): 330–34. http://dx.doi.org/10.54097/srync083.

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Square-root topological states are new topological phases, whose intriguing topological properties are inherited from the parent lattice Hamiltonian. Because of the square-root procedure, the bulk gap of the parent Hamiltonian is doubled. In this letter, we report the observation of the square-root topological insulators (SRTIs) in topological LC circuits, whose squared Hamiltonian includes a Su-Schrieffer-Heeger (SSH) model, a well-known example of topological insulators (TI). The multiple localized edge states falling in different bandgaps are observed with characteristic phase structures, i

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25

Kirsch, Marco S., Yiqi Zhang, Mark Kremer, et al. "Nonlinear second-order photonic topological insulators." Nature Physics 17, no. 9 (2021): 995–1000. http://dx.doi.org/10.1038/s41567-021-01275-3.

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AbstractHigher-order topological insulators are a novel topological phase beyond the framework of conventional bulk–boundary correspondence1,2. In these peculiar systems, the topologically non-trivial boundary modes are characterized by a co-dimension of at least two3,4. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems5,6, the flourishing field of experimental higher-order topological insulator research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity

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26

Urban, Mur, and Ravnik Miha. "Numerical modeling of optical modes in topological soft matter." Optics Express 30, no. 9 (2022): 14393——14407. https://doi.org/10.1364/OE.454980.

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Vector and vortex laser beams are desired in many applications and are usually created by manipulating the laser output or by inserting optical components in the laser cavity. Distinctly, inserting liquid crystals into the laser cavity allows for extensive control over the emitted light due to their high susceptibility to external fields and birefringent nature. In this work we demonstrate diverse optical modes for lasing as enabled and stablised by topological birefringent soft matter structures using numerical modelling. We show diverse structuring of light—with different 3D inten

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27

CHU, Zheng-Qing, Muhammad Kamran SIDDIQUI, Muhammad Faisal NADEEM, and Muhammad NAEEM. "Topological properties of chemical structures." Revue Roumaine de Chimie 65, no. 5 (2020): 411–23. http://dx.doi.org/10.33224/rrch.2020.65.5.01.

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28

Voskoglou, Michael Gr. "Topological Spaces on Fuzzy Structures." WSEAS TRANSACTIONS ON MATHEMATICS 21 (September 1, 2022): 624–28. http://dx.doi.org/10.37394/23206.2022.21.72.

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Apart from their applications to almost all sectors of the human activity, fuzzy mathematics is also importantly developed on a theoretical basis providing useful links even to classical branches of pure mathematics, like Algebra, Analysis, Geometry, Topology, etc. The present paper comes across the steps that enabled the extension of the concept of topological space, the most general category of mathematical spaces, to fuzzy structures. Fuzzy and soft topological spaces are introduced in particular, the fundamental concepts of limits, continuity, compactness and Hausdorff space are defined on

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29

Hernández-Montes, E., R. Jurado-Piña, and E. Bayo. "Topological Mapping for Tension Structures." Journal of Structural Engineering 132, no. 6 (2006): 970–77. http://dx.doi.org/10.1061/(asce)0733-9445(2006)132:6(970).

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30

Seidel, Jan. "Nanoelectronics based on topological structures." Nature Materials 18, no. 3 (2019): 188–90. http://dx.doi.org/10.1038/s41563-019-0301-z.

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31

Qin, Jing, and Christian M. Reidys. "On Topological RNA Interaction Structures." Journal of Computational Biology 20, no. 7 (2013): 495–513. http://dx.doi.org/10.1089/cmb.2012.0282.

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32

Goddard, P., and P. Mansfield. "Topological structures in field theories." Reports on Progress in Physics 49, no. 7 (1986): 725–81. http://dx.doi.org/10.1088/0034-4885/49/7/001.

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33

Segal, G. "Topological structures in string theory." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359, no. 1784 (2001): 1389–98. http://dx.doi.org/10.1098/rsta.2001.0841.

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34

El-Bably, Mostafa K., and Kamel K. Fleifel. "Some Topological Structures by Relations." Journal of Computational and Theoretical Nanoscience 14, no. 8 (2017): 4104–13. http://dx.doi.org/10.1166/jctn.2017.6793.

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35

Caer, G. Le. "Topological models of cellular structures." Journal of Physics A: Mathematical and General 24, no. 6 (1991): 1307–17. http://dx.doi.org/10.1088/0305-4470/24/6/022.

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36

Abbas, S. E., and A. A. Abd-Allah. "Stratified double L-topological structures." Mathematical and Computer Modelling 54, no. 1-2 (2011): 423–39. http://dx.doi.org/10.1016/j.mcm.2011.02.032.

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37

Zsoldos, I., P. Szendro, L. Watson, and A. Szasz. "Topological correlation in amorphous structures." Computational Materials Science 20, no. 1 (2001): 28–36. http://dx.doi.org/10.1016/s0927-0256(00)00120-8.

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38

Li, Thomas J. X., and Christian M. Reidys. "The topological filtration of -structures." Mathematical Biosciences 241, no. 1 (2013): 24–33. http://dx.doi.org/10.1016/j.mbs.2012.09.006.

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39

Huang, Fenix W. D., and Christian M. Reidys. "Shapes of topological RNA structures." Mathematical Biosciences 270 (December 2015): 57–65. http://dx.doi.org/10.1016/j.mbs.2015.10.004.

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40

Bucknum, Michael J., and Eduardo A. Castro. "On topological form in structures." Journal of Mathematical Chemistry 39, no. 1 (2005): 33–46. http://dx.doi.org/10.1007/s10910-005-9002-8.

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41

Bucknum, Michael J., and Eduardo A. Castro. "On topological form in structures." Journal of Mathematical Chemistry 40, no. 4 (2006): 327–40. http://dx.doi.org/10.1007/s10910-006-9160-3.

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42

Jurado-Piña, Rafael, Luisa María Gil-Martín, and Enrique Hernández-Montes. "Topological mesh for shell structures." Applied Mathematical Modelling 33, no. 2 (2009): 948–58. http://dx.doi.org/10.1016/j.apm.2007.12.018.

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43

Santocanale, Luigi. "Topological Properties of Event Structures." Electronic Notes in Theoretical Computer Science 230 (March 2009): 149–60. http://dx.doi.org/10.1016/j.entcs.2009.02.023.

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44

Bon, Michael, Graziano Vernizzi, Henri Orland, and A. Zee. "Topological Classification of RNA Structures." Journal of Molecular Biology 379, no. 4 (2008): 900–911. http://dx.doi.org/10.1016/j.jmb.2008.04.033.

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45

Li, Thomas J. X., and Christian M. Reidys. "Statistics of topological RNA structures." Journal of Mathematical Biology 74, no. 7 (2016): 1793–821. http://dx.doi.org/10.1007/s00285-016-1078-1.

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46

Rohm, Ryan. "Topological defects and differential structures." Annals of Physics 189, no. 1 (1989): 223–39. http://dx.doi.org/10.1016/0003-4916(89)90085-7.

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47

Kaveh, A. "Topological properties of skeletal structures." Computers & Structures 29, no. 3 (1988): 403–11. http://dx.doi.org/10.1016/0045-7949(88)90393-8.

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48

László, István, André Rassat, P. W. Fowler, and Ante Graovac. "Topological coordinates for toroidal structures." Chemical Physics Letters 342, no. 3-4 (2001): 369–74. http://dx.doi.org/10.1016/s0009-2614(01)00609-1.

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49

Hernández-Arzusa, Julio, and Salvador Hernández. "Reflections in topological algebraic structures." Topology and its Applications 281 (August 2020): 107204. http://dx.doi.org/10.1016/j.topol.2020.107204.

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50

Ovid'ko, I. A. "Topological charges of dissipative structures." Soviet Physics Journal 31, no. 4 (1988): 334–37. http://dx.doi.org/10.1007/bf00892648.

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