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Статті в журналах з теми "Hierarchy structure"

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Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Hawthorne, F. C. "The structure hierarchy hypothesis." Mineralogical Magazine 78, no. 4 (August 2014): 957–1027. http://dx.doi.org/10.1180/minmag.2014.078.4.13.

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AbstractThe structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerization of coordination polyhedra of higher bond valence. A mathematical hierarchy is an ordered set of elements where the ordering reflects a natural hierarchical relation between (or arrangement of) the elements. Here, I review the structure hierarchies for the borate, uranyl oxide, phosphate, sulfate, beryllate and oxide-centred Cu, Pb and Hg minerals (plus synthetics where appropriate). Structure hierarchies have two functions: (1) they serve to organize our knowledge of minerals (crystal structures) in a coherent manner; (2) if the basis of the classification involves factors that are related to the mechanistic details of the stability and behaviour of minerals, then the physical, chemical and paragenetic characteristics of minerals should arise as natural consequences of their crystal structures and the interaction of those structures with the environment in which they occur. We may justify the structure hierarchy hypothesis by considering a hypothetical structure-building process whereby higher bond-valence polyhedra polymerize to form the structural unit. The clusters constituting the FBBs (fundamental building blocks) may polymerize to form the following types of structural unit: (1) isolated polyhedra; (2) clusters; (3) chains and ribbons; (4) sheets; and (5) frameworks. The major advantage of this approach to structure hierarchy is the fact that the hypothetical structure-building process outlined above resembles (our ideas of) crystallization from an aqueous solution, whereby complexes in aqueous and hydrothermal solutions condense to form crystal structures, or fragments of linked polyhedra in a magma condense to form a crystal. Although our knowledge of these processes is rather vague from a mechanistic perspective, the foundations of the structure hypothesis give us a framework within which to think about the processes of crystallization and dissolution.

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2

Chase, Ivan D. "Explanations of hierarchy structure." Animal Behaviour 34, no. 4 (August 1986): 1265–67. http://dx.doi.org/10.1016/s0003-3472(86)80188-9.

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3

Camussi, R., and R. Benzi. "Hierarchy of transverse structure functions." Physics of Fluids 9, no. 2 (February 1997): 257–59. http://dx.doi.org/10.1063/1.869144.

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4

Dibben, Nicola. "The Cognitive Reality of Hierarchic Structure in Tonal and Atonal Music." Music Perception 12, no. 1 (1994): 1–25. http://dx.doi.org/10.2307/40285753.

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Three experiments that form an empirical basis for discussing the cognitive reality of hierarchic structure in music are reported. The first experiment showed evidence of listeners' ability to match a performed reduction of an extract of tonal music to the piece of music from which it was derived. A second experiment showed that this choice of reduction could not be attributed to the relative " coherence" of reductions. These two experiments provide evidence for the internal representation of tonal music in terms of a hierarchy of events such as that proposed by Lerdahl and Jackendoff ( 1983). In a third experiment using atonal music, subjects were less successful in choosing as the best reduction that which resembled the extract at higher levels of the structural hierarchy. Thus there is no evidence for the perception of a hierarchy of events in atonal music of the sort proposed by Lerdahl (1989). This empirical work therefore suggests that whereas the tonal system allows events within a tonal work to be heard within a strict hierarchy, no such hierarchy exists for atonal music. This finding has two main implications. First, a new conception of the term "prolongation" is needed if it is to apply to atonal music. The lack of a pitch hierarchy means that atonal events are unable to "stand for" other events in the way that tonal events are, and it is this action of standing for that allows prolongation to occur. Second, if as this research suggests, atonal music is not perceived in terms of a hierarchic structure, then another approach may be to investigate associational properties of the music and the role that these play in the formation of a structural representation.

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5

DEPIREUX, DIDIER A. "A NOTE ON THE KP HIERARCHY." Modern Physics Letters A 07, no. 20 (June 28, 1992): 1825–33. http://dx.doi.org/10.1142/s0217732392001531.

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Given the two boson representation of the conformal algebra Ŵ∞, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system.

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6

Hughes, Holly L. "Metropolitan Structure and the Suburban Hierarchy." American Sociological Review 58, no. 3 (June 1993): 417. http://dx.doi.org/10.2307/2095909.

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7

Berezovsky, Igor N., Vladimir A. Namiot, Vladimir G. Tumanyan, and Natalia G. Esipova. "Towards hierarchy of protein domain structure." Biochemical Society Transactions 28, no. 5 (October 1, 2000): A457. http://dx.doi.org/10.1042/bst028a457c.

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8

Sawyer, Linda C. "Structure hierarchy in liquid crystalline polymers." Proceedings, annual meeting, Electron Microscopy Society of America 50, no. 2 (August 1992): 1030–31. http://dx.doi.org/10.1017/s0424820100129784.

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Structure models have been developed for the liquid crystalline polymers (LCPs), showing the existence of fibrillar hierarchies for both the lyotropic aramids and the thermotropic aromatic copolyesters. Hierarchies of structure have also been observed for biological materials. The nature of the smallest nanostructure that aggregates, typically microfibrils, and their interaction, are important in understanding the behavior of the material. This paper discusses the first application of scanning tunneling microscopy (STM) and field emission scanning electron microscopy (FESEM) to image the microfibrils in LCPs, in the 1-10 nm size range, resulting in a new LCP structural model.The structure model proposed earlier, was based on the study of Vectra® thermotropic LCP moldings and extrudates, and Vectran® and Kevlar® fibers. The model resulted from characterization by light microscopy, and transmission and scanning electron microscopy. Recent studies of similar fibers by STM and low voltage FESEM has provided additional insights. Details of single microfibrils and their aggregation into fibrils and macrofibrils was shown.

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9

Puhalla, Dennis M. "Perceiving hierarchy through intrinsic color structure." Visual Communication 7, no. 2 (May 2008): 199–228. http://dx.doi.org/10.1177/1470357208088759.

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10

Baertsch, Karen, and Stuart Davis. "split margin approach to syllable structure." ZAS Papers in Linguistics 32 (January 1, 2003): 1–14. http://dx.doi.org/10.21248/zaspil.32.2003.183.

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In this paper we focus on the similarities tying together the second segment of an onset cluster and a singleton coda segment. We offer a proposal based on Baertsch (2002) accounting for this similarity and show how it captures a number of observations which have defied previous explanation. In accounting for the similarity of patterning between the second member of an onset and a coda consonant, we propose to augment Prince & Smolensky's (P&S, 1993/2002) Margin Hierarchy so as to distinguish between structural positions that prefer low sonority and those that prefer high sonority. P&S's Margin Hierarchy, which gives preference to segments of low sonority, applies to singleton onsets; this is our M1 hierarchy. Our proposed M2 hierarchy applies both to the second member of an onset and to a singleton coda. The M2 hierarchy differs from the M1 hierarchy in giving preference to consonants of high sonority. Splitting the Margin Hierarchy into the M1 and M2 hierarchies allows us to explain typological, phonotactic, and acquisitional observations that have defied previous explanation. In Section 2 of this paper, we briefly provide background on the links that tie together the second member of an onset and a singleton coda. In Section 3, we review P&S's Margin Hierarchy, showing that it becomes problematic when extended to coda consonants. We then offer our proposal for a split margin hierarchy. Section 4 extends the split margin approach to complex onsets. We then show how it is able to account for various typological, phonotactic, and acquisitional observations. In Section 5, we will conclude the paper by briefly sketching how the split margin approach enables us to analyze syllable contact phenomena without requiring a specific syllable contact constraint (or additional hierarchy) or reference to an external sonority scale.

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11

Kim, Hyunsik, and Nicholas R. Eaton. "A Hierarchical Integration of Person-Centered Comorbidity Models: Structure, Stability, and Transition Over Time." Clinical Psychological Science 5, no. 4 (May 31, 2017): 595–612. http://dx.doi.org/10.1177/2167702617704018.

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Person-centered analyses of mental disorder comorbidity typically identify a single optimal latent group structure. We took an alternate approach, modeling every estimable comorbidity class model in a nationally representative sample ( N = 34,653) and integrating them into a single overarching hierarchy, providing a full multilevel accounting of various person-centered comorbidity structures. We then investigated the structural stability of this hierarchy across two waves of data collection, and the stability of, and transition between, comorbidity classes over time using latent transition analysis. Findings suggested that comorbidity classes were structured into an interpretable hierarchy. Evidence for robust structural stability of the hierarchy over time was found, regardless of assessment time points and diagnostic time frames used. Latent transition analysis provided evidence for both continuity and change of comorbidity group membership. We discuss how person- and variable-centered models provide complementary perspectives toward empirically supported classification.

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12

Hawthorne, Frank C., and Sasha Herwig. "A Structure Hierarchy for the Aluminofluoride Minerals." Canadian Mineralogist 59, no. 1 (January 1, 2021): 211–41. http://dx.doi.org/10.3749/canmin.2000047.

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ABSTRACT The structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerization of coordination polyhedra of higher bond-valence, and such hierarchies are useful in understanding the general compositional, structural, and paragenetic variations within the structural group of interest. Here we develop a structure hierarchy for the aluminofluoride minerals based on the polymerization of the dominant (AlΦ6) octahedra and their linkage with other strongly bonded complex anionic groups. The minerals are divided first into the following categories: (1) simple aluminofluorides and (2) compound aluminofluorides containing other oxyanions. The minerals are then ordered according to the polymerization of the constituent polyhedra into a coherent structural hierarchy. The chemical composition and crystal-chemical details of the ions of the interstitial complex are a collective function of the Lewis acidity of the interstitial cations; the presence of interstitial anions, both simple [F–, (OH)–] and complex [(SO4)2–]; self-polymerization of the (AlF6)3– octahedra; and polymerization with both Mg(F,OH)6 octahedra and other complex anions: (SO4)2–, (PO4)3–, (CO3)2–.

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13

GOHARA, KAZUTOSHI, and ARATA OKUYAMA. "FRACTAL TRANSITION: HIERARCHICAL STRUCTURE AND NOISE EFFECT." Fractals 07, no. 03 (September 1999): 313–26. http://dx.doi.org/10.1142/s0218348x99000311.

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A Sierpinski gasket with continuous trajectories is presented as an example of the fractal transition that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs. Using this example, we investigate the fractal transition from two points of views, i.e. a hierarchical structure and a noise effect. Depending on internal and external parameters, the structure can be geometrically classified as one of three types, i.e. totally disconnected, just-touching, and overlapping. For the totally disconnected structure, continuous trajectories and their starting points can be characterized by a definite hierarchical tree structure. Even for the just-touching and overlapping structure, a similar hierarchy exists. White noise contaminating the external inputs breaks the hierarchy. In particular, small clustered structures are sensitive to the noise. In such a case, the difference between trajectories and starting points is remarkable in the hierarchy.

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14

DEVILLERS, OLIVIER. "THE DELAUNAY HIERARCHY." International Journal of Foundations of Computer Science 13, no. 02 (April 2002): 163–80. http://dx.doi.org/10.1142/s0129054102001035.

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We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the level below. Point location is done by walking in a triangulation to determine the nearest neighbor of the query at that level, then the walk restarts from the neighbor at the level below. Using a small subset (3%) to sample a level allows a small memory occupation; the walk and the use of the nearest neighbor to change levels quickly locate the query.

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15

Lee, Eucman MAN, Jeho Lee, and Ji-Hwan Lee. "Regularity in Structure and Dynamics of Hierarchy." Academy of Management Proceedings 2016, no. 1 (January 2016): 15285. http://dx.doi.org/10.5465/ambpp.2016.15285abstract.

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16

Zhukhovitskiy, Aleksandr V., Julia Zhao, Mingjiang Zhong, Eric G. Keeler, Eric A. Alt, Paul Teichen, Robert G. Griffin, Michael J. A. Hore, Adam P. Willard, and Jeremiah A. Johnson. "Polymer Structure Dependent Hierarchy in PolyMOC Gels." Macromolecules 49, no. 18 (September 6, 2016): 6896–902. http://dx.doi.org/10.1021/acs.macromol.6b01607.

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17

REISER, MARK, and KARL F. SCHUESSLER. "A Hierarchy for Some Latent Structure Models." Sociological Methods & Research 19, no. 4 (May 1991): 419–65. http://dx.doi.org/10.1177/0049124191019004001.

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18

Yu, Feng. "Bi‐Hamiltonian structure of super KP hierarchy." Journal of Mathematical Physics 33, no. 9 (September 1992): 3180–89. http://dx.doi.org/10.1063/1.529536.

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19

Ma, Yixuan, Xuedong Gao, and Shujuan Gu. "Subject Hierarchy Structure Modeling in Data Warehouse." International Journal of Database Theory and Application 8, no. 4 (August 30, 2015): 256–72. http://dx.doi.org/10.14257/ijdta.2015.8.4.26.

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20

Chor, Benny, Mihály Geréb-Graus, and Eyal Kushilevitz. "On the structure of the privacy hierarchy." Journal of Cryptology 7, no. 1 (December 1994): 53–60. http://dx.doi.org/10.1007/bf00195209.

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21

Balluffi, R. W., and G. B. Olson. "On the hierarchy of interfacial dislocation structure." Metallurgical Transactions A 16, no. 4 (April 1985): 529–41. http://dx.doi.org/10.1007/bf02814227.

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22

Zhang, Y., and H. Tam. "(1+1)-dimensional m-cKdV, g-cKdV integrable systems, and (2+1)-dimensional m-cKdV hierarchy." Canadian Journal of Physics 86, no. 12 (December 1, 2008): 1367–80. http://dx.doi.org/10.1139/p08-098.

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A few isospectral problems are introduced by referring to that of the cKdV equation hierarchy, for which two types of integrable systems called the (1 + 1)-dimensional m-cKdV hierarchy and the g-cKdV hierarchy are generated, respectively, whose Hamiltonian structures are also discussed by employing a linear functional and the quadratic-form identity. The corresponding expanding integrable models of the (1 + 1)-dimensional m-cKdV hierarchy and g-cKdV hierarchy are obtained. The Hamiltonian structure of the latter one is given by the variational identity, proposed by Ma Wen-Xiu as well. Finally, we use a Lax pair from the self-dual Yang–Mills equations to deduce a higher dimensional m-cKdV hierarchy of evolution equations and its Hamiltonian structure. Furthermore, its expanding integrable model is produced by the use of a enlarged Lie algebra.PACS Nos.: 02.30, 03.40.K

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23

FIGUEROA-O'FARRILL, JOSÉ M., EDUARDO RAMOS, and JAVIER MAS. "INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKDV HIERARCHIES." Reviews in Mathematical Physics 03, no. 04 (December 1991): 479–501. http://dx.doi.org/10.1142/s0129055x91000175.

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We study reductions of the even order SKP hierarchy. We prove that these systems are integrable and bihamiltonian. We derive an infinite set of independent polynomial conservation laws, prove their nontriviality, and derive Lenard relations between them. A further reduction of the simplest such hierarchy is identified with the supersymmetric KdV hierarchy of Manin and Radul. We prove that it inherits all the bihamiltonian and integrability properties from the unreduced hierarchy.

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24

Willer Gold, Jana, Boban Arsenijević, Mia Batinić, Michael Becker, Nermina Čordalija, Marijana Kresić, Nedžad Leko, et al. "When linearity prevails over hierarchy in syntax." Proceedings of the National Academy of Sciences 115, no. 3 (December 29, 2017): 495–500. http://dx.doi.org/10.1073/pnas.1712729115.

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Hierarchical structure has been cherished as a grammatical universal. We use experimental methods to show where linear order is also a relevant syntactic relation. An identical methodology and design were used across six research sites on South Slavic languages. Experimental results show that in certain configurations, grammatical production can in fact favor linear order over hierarchical structure. However, these findings are limited to coordinate structures and distinct from the kind of production errors found with comparable configurations such as “attraction” errors. The results demonstrate that agreement morphology may be computed in a series of steps, one of which is partly independent from syntactic hierarchy.

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25

Caro, Juergen. "Hierarchy in inorganic membranes." Chemical Society Reviews 45, no. 12 (2016): 3468–78. http://dx.doi.org/10.1039/c5cs00597c.

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26

Chen, Xiao Yun, and Jin Hua Chen. "Class Hierarchical Structure-Based Text Classification." Advanced Materials Research 255-260 (May 2011): 2233–37. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2233.

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There is a problem that the difficulty in text classification will increase when the number of classes increases, to which hierarchical structure is a viable solution. Well, a document’s hierarchical structure is usually maintained only by hand, which require substantial manpower to find the correct position of a document in the class hierarchy or to reconstruct the hierarchy. Constructing the hierarchical structure automatically by clustering the training samples can effectively reduce the cost of manual maintenance, and at the same time, it can avoid the conflict between the prior knowledge and the statistical properties of the sample set caused by artificial maintenance of the hierarchy.

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27

Hu, Dyi-Chung, and James Ho. "Methods to Reduce the Hierarchy of Interconnections in Electronic System." International Symposium on Microelectronics 2020, no. 1 (September 1, 2020): 000156–59. http://dx.doi.org/10.4071/2380-4505-2020.1.000156.

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Abstract In the era of AI, 5G, big data, and autonomous driving, those applications all require a high bandwidth low latency data computing. Traditional electronic packaging structures are classified into many levels and each level are connected by solders or cables. These many levels of structures cause system performance degradation. Hence structure solutions of 2.5D, 2.1D, 2.3D and 2.0D with multi-chip packaging are needed for high performance computing system. Currently 2.5D is the HPC standard structure, however the cost and size limitation of 2.5D drive users to seek alternative solutions. The structure of 2.0D, 2.1D and 2.3D offer less solder and TXVs are emerging as contenders to fill the requirement of large substrate size and fine line requirements in the future. Among them 2.0D structure shows great potential. Three 2.0D test vehicles have been built to evaluate fine pitch assembly, reliability and structure enhancement. The results show 2.0D structure has great potential to be a HPC solution of the near future.

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28

Zhang, Yufeng, and Honwah Tam. "New integrable couplings and Hamiltonian structure of the KN hierarchy and the DLW hierarchy." Communications in Nonlinear Science and Numerical Simulation 13, no. 3 (June 2008): 524–33. http://dx.doi.org/10.1016/j.cnsns.2006.06.003.

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29

Fan, Jie, Na Zhu, Li-li Wang, Zhi Liu, Chang-Yuan Wang, and Yong Liu. "Influence of Hierarchic Structure on the Moisture Permeability of Biomimic Woven Fabric Using Fractal Derivative Method." Advances in Mathematical Physics 2015 (2015): 1–4. http://dx.doi.org/10.1155/2015/817437.

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The relationship between the unique internal structure of biomimic woven fabric and its moisture management property is investigated using fractal derivative method. The biomimic fabric exhibits a fractal hierarchic inner structure, and its fractal hierarchy can be further extended by fleece finishing treatment on both surfaces of the fabric. Fractal derivative analysis indicates that the fuzzy biomimic fabric with a higher hierarchic construction after fleece finishing performs better in moisture permeability, and the result was proved by experimental tests.

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30

ARATYN, HENRIK, and KLAUS BERING. "COMPATIBLE POISSON STRUCTURES OF TODA TYPE DISCRETE HIERARCHY." International Journal of Modern Physics A 20, no. 07 (March 20, 2005): 1367–88. http://dx.doi.org/10.1142/s0217751x05021087.

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An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and nonlocal families of R-matrix solutions to the modified Yang–Baxter equation. The three R-theoretic Poisson structures and the Suris quadratic bracket are derived. The resulting family of bi-Poisson structures include a seminal discrete bi-Poisson structure of Kupershmidt at a special value.

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31

BRUNELLI, J. C. "HAMILTONIAN STRUCTURES FOR THE GENERALIZED DISPERSIONLESS KdV HIERARCHY." Reviews in Mathematical Physics 08, no. 08 (November 1996): 1041–53. http://dx.doi.org/10.1142/s0129055x96000378.

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We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so-called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.

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32

Wei, Ke. "Analyzing Hierarchy Spatial Structure of Chinese Ancient Town." Advanced Materials Research 250-253 (May 2011): 2704–7. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2704.

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Village as the basic prototype, most of the Chinese ancient towns have formed distinctive spatial structure in the joint action of multiple factors. Space of Chinese ancient town embodies hierarchy structure from large to small in the process of formation and development. The space system of geography, town, environment, architecture, livingmaterial produce hierarchy structure, the higher level including the lower level, the lower level reflecting the higher level, and forming system of compound spatial structure in Chinese ancient towns in the end.

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33

Sheline, Raymond K. "Hierarchy of Spectroscopies and the Structure of Matter." Journal of Physical Chemistry 99, no. 19 (May 1995): 7211–17. http://dx.doi.org/10.1021/j100019a001.

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34

HAYASHI, Yuji, Tomoko MATSUMOTO, and Hirotsugu WAKE. "Hierarchy Structure and Database Concept for Sailing Directions." Journal of Japan Institute of Navigation 103 (2000): 9–15. http://dx.doi.org/10.9749/jin.103.9.

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35

Raikov, Alexander N. "Organizational Structure Optimization with the Questions-Criteria Hierarchy." IFAC-PapersOnLine 49, no. 12 (2016): 1532–37. http://dx.doi.org/10.1016/j.ifacol.2016.07.797.

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36

Hawthorne, Frank C., Yulia A. Uvarova, and Elena Sokolova. "A structure hierarchy for silicate minerals: sheet silicates." Mineralogical Magazine 83, no. 1 (November 9, 2018): 3–55. http://dx.doi.org/10.1180/mgm.2018.152.

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Анотація:

AbstractThe structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerisation of coordination polyhedra of higher bond-valence. A hierarchical structural classification is developed for sheet-silicate minerals based on the connectedness of the two-dimensional polymerisations of (TO4) tetrahedra, where T = Si4+ plus As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Two-dimensional nets and oikodoméic operations are used to generate the silicate (sensu lato) structural units of single-layer, double-layer and higher-layer sheet-silicate minerals, and the interstitial complexes (cation identity, coordination number and ligancy, and the types and amounts of interstitial (H2O) groups) are recorded. Key aspects of the silicate structural unit include: (1) the type of plane net on which the sheet (or parent sheet) is based; (2) the u (up) and d (down) directions of the constituent tetrahedra relative to the plane of the sheet; (3) the planar or folded nature of the sheet; (4) the layer multiplicity of the sheet (single, double or higher); and (5) the details of the oikodoméic operations for multiple-layer sheets. Simple 3-connected plane nets (such as 63, 4.82 and 4.6.12) have the stoichiometry (T2O5)n (Si:O = 1:2.5) and are the basis of most of the common rock-forming sheet-silicate minerals as well as many less-common species. Oikodoméic operations, e.g. insertion of 2- or 4-connected vertices into 3-connected plane nets, formation of double-layer sheet-structures by (topological) reflection or rotation operations, affect the connectedness of the resulting sheets and lead to both positive and negative deviations from Si:O = 1:2.5 stoichiometry. Following description of the structural units in all sheet-silicate minerals, the minerals are arranged into decreasing Si:O ratio from 3.0 to 2.0, an arrangement that reflects their increasing structural connectivity. Considering the silicate component of minerals, the range of composition of the sheet silicates completely overlaps the compositional ranges of framework silicates and most of the chain-ribbon-tube silicates.

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37

Hawbani, Ammar, Xingfu Wang, Saleem Karmoshi, Lin Wang, and Naji Husaini. "Sensors Grouping Hierarchy Structure for Wireless Sensor Network." International Journal of Distributed Sensor Networks 11, no. 8 (January 2015): 650519. http://dx.doi.org/10.1155/2015/650519.

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Scotti, Marco, Cristina Bondavalli, Antonio Bodini, and Stefano Allesina. "Using trophic hierarchy to understand food web structure." Oikos 118, no. 11 (November 2009): 1695–702. http://dx.doi.org/10.1111/j.1600-0706.2009.17073.x.

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39

Yao, Yuqin, and Yunbo Zeng. "Coupled Short Pulse Hierarchy and Its Hamiltonian Structure." Journal of the Physical Society of Japan 80, no. 6 (June 15, 2011): 064004. http://dx.doi.org/10.1143/jpsj.80.064004.

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40

Mazzocco, Marta, and Man Yue Mo. "The Hamiltonian structure of the second Painlevé hierarchy." Nonlinearity 20, no. 12 (November 15, 2007): 2845–82. http://dx.doi.org/10.1088/0951-7715/20/12/006.

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41

VELDMAN, WIM. "THE FINE STRUCTURE OF THE INTUITIONISTIC BOREL HIERARCHY." Review of Symbolic Logic 2, no. 1 (March 2009): 30–101. http://dx.doi.org/10.1017/s1755020309090121.

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In intuitionistic analysis, a subset of a Polish space like ℝ or ${\cal N}$ is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a positively Borel set is not always positively Borel itself (see Veldman, 2008a). The main result of Veldman (2008a) is that, assuming Brouwer's Continuity Principle and an Axiom of Countable Choice, one may prove that the hierarchy formed by the positively Borel sets is genuinely growing: every level of the hierarchy contains sets that do not occur at any lower level. The purpose of the present paper is a different one: we want to explore the truly remarkable fine structure of the hierarchy. Brouwer's Continuity Principle again is our main tool. A second axiom proposed by Brouwer, his Thesis on Bars is also used, but only incidentally.

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42

Helminck, G. F. "The Strict AKNS Hierarchy: Its Structure and Solutions." Advances in Mathematical Physics 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/3649205.

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We discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space ofsl2than that in the AKNS case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy.

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43

김홍주. "National-Space Hierarchy Structure of Creative Knowledge Production." Korea Spatial Planning Review 53, no. ll (June 2007): 3–20. http://dx.doi.org/10.15793/kspr.2007.53..001.

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44

Hanink, James G. "A Theory of Basic Goods: Structure and Hierarchy." Thomist: A Speculative Quarterly Review 52, no. 2 (1988): 221–45. http://dx.doi.org/10.1353/tho.1988.0047.

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45

Tao, Si-Xing, Tie-Cheng Xia, and Hui Shi. "Super-KN Hierarchy and Its Super-Hamiltonian Structure." Communications in Theoretical Physics 55, no. 3 (March 2011): 391–95. http://dx.doi.org/10.1088/0253-6102/55/3/03.

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46

Dai, Cong, Dongmei Li, Hui Han, Qichen Han, and Jiajia Hou. "Concept Similarity Measure with Hierarchy Structure and Information." International Journal of Hybrid Information Technology 8, no. 8 (August 31, 2015): 303–14. http://dx.doi.org/10.14257/ijhit.2015.8.8.31.

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47

Kamrani, Ali K., Hamid R. Parsaei, Kamran K. Kamrani, and Julius P. Wong. "A computer hierarchy structure for electric power utility." Computers & Industrial Engineering 21, no. 1-4 (January 1991): 507–11. http://dx.doi.org/10.1016/0360-8352(91)90143-t.

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48

Saxena, Rakhi, Sharanjit Kaur, and Vasudha Bhatnagar. "Social centrality using network hierarchy and community structure." Data Mining and Knowledge Discovery 32, no. 5 (July 13, 2018): 1421–43. http://dx.doi.org/10.1007/s10618-018-0582-x.

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49

Fairlie, D. B., and I. A. B. Strachan. "The Hamiltonian structure of the dispersionless Toda hierarchy." Physica D: Nonlinear Phenomena 90, no. 1-2 (January 1996): 1–8. http://dx.doi.org/10.1016/0167-2789(95)00229-4.

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50

Li, Shuangxing, Si-Qi Liu, Haonan Qu, and Youjin Zhang. "Tri-Hamiltonian structure of the Ablowitz–Ladik hierarchy." Physica D: Nonlinear Phenomena 433 (May 2022): 133180. http://dx.doi.org/10.1016/j.physd.2022.133180.

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