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Journal articles on the topic 'Dualitie'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Clark, David M., and Brian A. Davey. "The quest for strong dualities." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 58, no. 2 (April 1995): 248–80. http://dx.doi.org/10.1017/s1446788700038283.

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AbstractWe give a revised and updated exposition of the theory of full dualities initiated by Clark, Davey, Krauss and Werner, introducing the (stronger) notion of a strong duality. All known full dualities turn out to be strong. A series of theorems which provide necessary and sufficient conditions for a strong duality to exist is proved. All full dualities in the literature can be obtained from these results and many new strong dualities can be derived. In particular, we show that within congruence distributive varieties every duality can be upgraded to a strong duality. Amongst the new strong dualities are the dualities of Davey, Priestley and Werner for the varieties of pseudocomplemented distributive lattices which are either strong as they stand or can easily be made strong by the addition of partial operations to the dual structures.

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2

MONJARDET, BERNARD. "SOME ORDER DUALITIES IN LOGIC, GAMES AND CHOICES." International Game Theory Review 09, no. 01 (March 2007): 1–12. http://dx.doi.org/10.1142/s0219198907001242.

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We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally, we present two "concrete" dualities occuring in social choice and in choice functions theories.

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3

KRAUSE, AXEL. "ON THE FLATTENING OF NEGATIVE CURVATURE VIA T-DUALITY WITH A NON-CONSTANT B-FIELD." Modern Physics Letters A 18, no. 36 (November 30, 2003): 2571–79. http://dx.doi.org/10.1142/s0217732303012349.

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In an earlier paper, Alvarez, Alvarez-Gaumé, Barbón and Lozano pointed out, that the only way to "flatten" negative curvature by means of a T-duality is by introducing an appropriate, non-constant NS–NS two-form B. In this paper, we are investigating this further and ask, whether it is possible to T-dualize AdS d space to flat space with some suitably chosen B. To answer this question, we derive a relationship between the original curvature tensor and the one of the T-dualized metric involving the B-field. It turns out that there is one component which is independent of B. By inspection of this component, we show that it is not possible to dualize AdS d to flat space irrespective of the choice of B. Finally, we examine the extension of AdS to an AdS 5 × S5 geometry and propose a chain of S- and T-dualities together with an SL (2, ℤ) coordinate transformation, leading to a dual D9-brane geometry.

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4

Nakata, Yosuke, Yoshiro Urade, and Toshihiro Nakanishi. "Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials." Symmetry 11, no. 11 (October 28, 2019): 1336. http://dx.doi.org/10.3390/sym11111336.

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In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, electromagnetic, and Babinet dualities. These dualities have been developed individually in different research fields and frequency regimes, leading to a lack of unified perspective. In this paper, we establish a unified view of these dualities in electromagnetic systems. The underlying geometrical structures behind the dualities are elucidated by using concepts from algebraic topology and differential geometry. Moreover, we show that seemingly disparate phenomena, such as frequency-independent effective response, zero backscattering, and critical response, can be considered to be emergent phenomena of self-duality.

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5

LEE, TAEJIN. "STRING THEORY AND DUALITIES IN THE QUANTUM DISSIPATIVE HOFSTADTER SYSTEM." International Journal of Modern Physics A 24, no. 32 (December 30, 2009): 6141–56. http://dx.doi.org/10.1142/s0217751x09047582.

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We study the dualities of the quantum dissipative Hofstadter system which describes particles moving in two dimensions, subject to a uniform magnetic field, a periodic potential and a dissipative force. Using the string theory formulation, we show that the system has two kinds of dualities. The duality, previously known as the exact duality in the literature is shown to correspond to a subgroup of the T-dual symmetry group unbroken by the periodic boundary potential in string theory. The other duality is a particle–kink duality in the noncommutative open string theory which is a generalized Schmid duality in the presence of the uniform magnetic field. The kinks of the dissipative Hofstadter model are found to be noncommutative objects. The particle–kink duality, which is called previously the approximate duality, is shown to be also exact. In contrast to the previous derivation, which is based on the Coulomb gas expansion of the partition function and asserts that the duality holds only approximately in the regime of strong magnetic field, the string theory formulation proves that duality holds always exactly in the off-critical regions where the periodic potential becomes strong, regardless of the strength of the magnetic field. The dualities of the DHM may also be useful for studying the rolling tachyon in string theory in the presence of the Neveu–Schwarz (NS) B-field, since both DHM and rolling tachyon in the presence of NS B-field are described by the same action.

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6

Jelly, Jelly. "DUALITAS STIGMATISASI JANDA: REALITAS MASYARAKAT MINANGKABAU YANG MENDUA." Handep: Jurnal Sejarah dan Budaya 2, no. 1 (January 23, 2019): 39–58. http://dx.doi.org/10.33652/handep.v2i1.24.

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Tulisan ini bertujuan untuk mengungkap salah satu wujud dari dualisme yang merupakan fakta dalam sistem sosial masyarakat Minangkabau. Dualisme yang mulanya diistilahkan Saanin pada 1989 sebagai gambaran upaya masyarakat Minangkabau untuk menyeimbangkan agama dan adat ternyata muncul dalam sikap dualitas masyarakat ketika menghadapi berbagai situasi dan kondisi. Pada tulisan ini, peneliti mencoba melihat sikap dualitas masyarakat Minangkabau melalui stigmatisasi terhadap janda. Pandangan dan sikap yang mendua ini nampak dari stigma-stigma yang dibangun terhadap janda. Contohnya, masyarakat menganggap bahwa janda indak pandai balaki, tetapi disisi lain ia dianggap kancang ka laki-laki. Alat yang digunakan untuk menganalisis data adalah konsep dualitas. Melalui analisis dualisme terhadap stigma mengenai janda, peneliti menemukan bahwa masyarakat Minangkabau menerapkan sistem dualitas dalam kehidupannya.

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7

Ruis, A. R. "Pomegranate and the Mediation of Balance in Early Medicine." Gastronomica 15, no. 1 (2015): 22–33. http://dx.doi.org/10.1525/gfc.2015.15.1.22.

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Different elements of the pomegranate, both tree and fruit, had a wide range of uses in premodern therapeutics. Pomegranate also had a rich symbolic role in the art, literature, and religion of numerous cultures. In nearly every part of the globe where the pomegranate grew, it came to represent fundamental dualities: life and death, inside and out, many and one. The medicinal purposes for which healers recommended pomegranate at times reflected broader symbolic associations, and those associations are an important part of the therapeutic tradition. The dualistic symbolism that attended the pomegranate in various cultural traditions synergized with dualistic medical concepts, reinforcing the therapeutic power of pomegranate in otherwise diverse contexts. Reflecting this duality, pomegranate was both an astringent and a laxative, an emmenagogue and an antimenorrhagic, an expectorant and an antiemetic, a pyrogen and a febrifuge, a restorative and a soporific. In both literary and medical traditions, the pomegranate mediated transitions—or maintained balance—between opposing states. This essay provides an overview of the rich and sundry uses of pomegranate in premodern therapeutics, revealing how cultural associations both reflected and informed medical practices.

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8

SEN, ASHOKE. "ORBIFOLDS OF M-THEORY AND STRING THEORY." Modern Physics Letters A 11, no. 16 (May 30, 1996): 1339–47. http://dx.doi.org/10.1142/s021773239600134x.

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It is shown that many of the conjectured dualities involving orbifold compactification of M-theory follow from the known dualities involving M-theory and string theory in 10 dimensions, and the ansatz that orbifolding procedure commutes with the duality transformation. This ansatz also leads to a new duality conjecture, namely that M-theory compactified on T8/Z2 is dual to type I string theory on T7. In this case the “twisted sector states” in M-theory live on 16 membranes transverse to the internal manifold.

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9

HOOKER, JOHN, GREGER OTTOSSON, ERLENDER S. THORSTEINSSON, and HAK-JIN KIM. "A scheme for unifying optimization and constraint satisfaction methods." Knowledge Engineering Review 15, no. 1 (March 2000): 11–30. http://dx.doi.org/10.1017/s0269888900001077.

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Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities: the duality of search and inference, and the duality of strengthening and relaxation. Optimization as well as constraint satisfaction methods can be seen as exploiting these dualities in their respective ways. Our proposal is that rather than employ either type of method exclusively, one can focus on how these dualities can be exploited in a given problem class. The resulting algorithm is likely to contain elements from both optimization and constraint satisfaction, and perhaps new methods that belong to neither.

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10

Winter, David J. "Dualities and the duality density theorems." manuscripta mathematica 130, no. 2 (June 11, 2009): 201–23. http://dx.doi.org/10.1007/s00229-009-0285-0.

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11

LOZANO, Y. "DUALITY AND CANONICAL TRANSFORMATIONS." Modern Physics Letters A 11, no. 37 (December 7, 1996): 2893–914. http://dx.doi.org/10.1142/s0217732396002873.

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We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider Abelian and non-Abelian T-dualities in closed and open string theories as well as S-duality in Abelian and non-Abelian nonsupersymmetric gauge theories.

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12

DAVEY, BRIAN A., JANE G. PITKETHLY, and ROSS WILLARD. "THE LATTICE OF ALTER EGOS." International Journal of Algebra and Computation 22, no. 01 (February 2012): 1250007. http://dx.doi.org/10.1142/s021819671100673x.

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We introduce a new Galois connection for partial operations on a finite set, which induces a natural quasi-order on the collection of all partial algebras on this set. The quasi-order is compatible with the basic concepts of natural duality theory, and we use it to turn the set of all alter egos of a given finite algebra into a doubly algebraic lattice. The Galois connection provides a framework for us to develop further the theory of natural dualities for partial algebras. The development unifies several fundamental concepts from duality theory and reveals a new understanding of full dualities, particularly at the finite level.

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13

GOHM, ROLF, and MICHAEL SKEIDE. "CONSTRUCTING EXTENSIONS OF CP-MAPS VIA TENSOR DILATIONS WITH THE HELP OF VON NEUMANN MODULES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 02 (June 2005): 291–305. http://dx.doi.org/10.1142/s0219025705001986.

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We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We point out that this duality is part of a far reaching duality between a von Neumann bimodule and its commutant in which other dualities, known and new, also find their natural common place.

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14

Jensen, Kristan, and Andreas Karch. "ABJM mirrors and a duality of dualities." Journal of High Energy Physics 2009, no. 09 (September 1, 2009): 004. http://dx.doi.org/10.1088/1126-6708/2009/09/004.

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15

de Haro, Sebastian. "Dualities and emergent gravity: Gauge/gravity duality." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59 (August 2017): 109–25. http://dx.doi.org/10.1016/j.shpsb.2015.08.004.

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16

Gitin, Andrey Valerievich. "A Simple Proof of Damien’s Theorem and Duality in Theory of the Zero-Distance Phase Front." International Journal of Antennas and Propagation 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/478580.

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Duality plays the main role in all mathematical theories. In wave optics based on the concept of “the zero-distance phase front,” duality takes the form of Damien’s theorem and the mirror symmetry between the conic refracting surfaces with the plane zero-distance phase front and the plane refracting surfaces with the conic zero-distance phase front. A systematic study of these dualities has been performed.

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17

MUĆKA, A., and A. B. ROMANOWSKA. "DUALITY FOR QUASIPOLYTOPES." Journal of the Australian Mathematical Society 101, no. 1 (February 26, 2016): 95–117. http://dx.doi.org/10.1017/s1446788715000683.

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In an earlier paper, Romanowska, Ślusarski and Smith described a duality between the category of polytopes (finitely generated real convex sets considered as barycentric algebras) and a certain category of intersections of hypercubes, considered as barycentric algebras with additional constant operations. The present paper provides an extension of this duality to a much more general class of so-called quasipolytopes, that is, convex sets with polytopes as closures. The dual spaces of quasipolytopes are Płonka sums of open polytopes, which are considered as barycentric algebras with some additional operations. In constructing this duality, we use several known and new dualities: the Hofmann–Mislove–Stralka duality for semilattices; the Romanowska–Ślusarski–Smith duality for polytopes; a new duality for open polytopes; and a new duality for injective Płonka sums of polytopes.

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18

BETANCOURT, M., and A. KHOUDEIR. "TOPOLOGICAL MASS IN SEVEN DIMENSIONS AND DUALITIES IN FOUR DIMENSIONS." Modern Physics Letters A 20, no. 21 (July 10, 2005): 1619–25. http://dx.doi.org/10.1142/s0217732305016749.

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The massive topologically and self-dual theories in seven dimensions are considered. The local duality between these theories is established and the dimensional reduction leads to different dualities for massive antisymmetric fields in four dimensions.

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19

JOHANSEN, SARAH M. "DUALIZABILITY OF GRAPHS." Journal of the Australian Mathematical Society 89, no. 3 (December 2010): 377–92. http://dx.doi.org/10.1017/s1446788711001029.

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AbstractWe investigate natural dualities for classes of simple graphs. For example, we give a natural duality for the class consisting of all n-colourable graphs and show that, for all n≥3, there is no natural duality for the class consisting of all freely n-colourable graphs. We also prove that there exist arbitrarily long finite chains of 3-colourable graphs that alternate between being dualizable and nondualizable.

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20

Cabrer, Leonardo M., and Hilary A. Priestley. "Sugihara algebras and Sugihara monoids: Multisorted dualities." Mathematica Slovaca 70, no. 1 (February 25, 2020): 5–28. http://dx.doi.org/10.1515/ms-2017-0327.

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AbstractThe authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by Cabrer et al., give access to a viable method for studying admissible rules within relevance logic, specifically for extensions of the deductive system R-mingle.This paper builds on the work already done on the theory of natural dualities for Sugihara algebras. Its purpose is to provide an integrated suite of multisorted duality theorems of a uniform type, encompassing finitely generated quasivarieties and varieties of both Sugihara algebras and Sugihara monoids, and embracing both the odd and the even cases. The overarching theoretical framework of multisorted duality theory developed here leads on to amenable representations of free algebras. More widely, it provides a springboard to further applications.

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21

Balmer, Paul, Ivo Dell’Ambrogio, and Beren Sanders. "Grothendieck–Neeman duality and the Wirthmüller isomorphism." Compositio Mathematica 152, no. 8 (May 23, 2016): 1740–76. http://dx.doi.org/10.1112/s0010437x16007375.

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We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated tensor-triangulated categories, which leads to a surprising trichotomy: there exist either exactly three adjoints, exactly five, or infinitely many. We highlight the importance of so-called relative dualizing objects and explain how they give rise to dualities on canonical subcategories. This yields a duality theory rich enough to capture the main features of Grothendieck duality in algebraic geometry, of generalized Pontryagin–Matlis duality à la Dwyer–Greenless–Iyengar in the theory of ring spectra, and of Brown–Comenetz duality à la Neeman in stable homotopy theory.

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22

Davey, Brian A., and Miroslav Haviar. "Applications of Priestley duality in transferring optimal dualities." Studia Logica 78, no. 1-2 (November 2004): 213–36. http://dx.doi.org/10.1007/s11225-005-3236-0.

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23

Penot, Jean-Paul. "Are dualities appropriate for duality theories in optimization?" Journal of Global Optimization 47, no. 3 (October 28, 2009): 503–25. http://dx.doi.org/10.1007/s10898-009-9478-z.

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24

Klusoň, Josef. "Canonical description of T-duality for fundamental string and D1-brane and double Wick rotation." International Journal of Modern Physics A 31, no. 07 (March 2, 2016): 1650022. http://dx.doi.org/10.1142/s0217751x16500226.

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We study T-duality transformations in canonical formalism for Nambu–Goto action. Then we investigate the relation between worldsheet double Wick rotation and sequence of target space T-dualities and Wick rotation in case of fundamental string and D1-brane.

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25

SATO, HITOSHI. "ON THE POINCARÉ POLYNOMIALS FOR LANDAU-GINZBURG ORBIFOLDS." Modern Physics Letters A 09, no. 10 (March 28, 1994): 885–93. http://dx.doi.org/10.1142/s0217732394000708.

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We construct the Poincaré polynomials for Landau-Ginzburg orbifolds with projection operators. Using them we show that special types of dualities including Poincaré duality are realized under certain conditions. When Calabi-Yau interpretation exists, two simple formulas for Hodge numbers h2,1 and h1,1 are obtained.

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26

Gregori, Verónica. "Discrete duality for De Morgan Algebras with operators." Asian-European Journal of Mathematics 12, no. 01 (February 2019): 1950010. http://dx.doi.org/10.1142/s1793557119500104.

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A discrete duality is a relationship between classes of algebras and classes of relational systems (frames). In this paper, discrete dualities are presented for De Morgan algebras with various kind of unary operators. To do this, we will extend the discrete duality given in [W. Dzik, E. Orłowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162–176], for De Morgan algebras.

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27

Crépeau, Robert R. "Les Kaingang dans le contexte des études gé et bororo." Anthropologie et Sociétés 21, no. 2-3 (September 10, 2003): 45–66. http://dx.doi.org/10.7202/015484ar.

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Résumé RÉSUMÉ Les Kaingang dans le contexte des études gé et bororo Les études portant sur les Gé et les Bororo du Brésil sont exemplaires de la rencontre de plusieurs approches se déployant sur une scène régionale et nationale et prenant appui sur : 1- une identité linguistique : l'appartenance au tronc linguistique macro-gé et 2- une organisation sociale dualiste d'une grande complexité. La nature de l'organisation dualiste est au centre des travaux des Gé-ologues depuis les années 1930. Plusieurs approches concurrentes ont tenté de comprendre les interrelations complexes existant entre l'idéologie dualiste telle que conçue par les sociétés elles-mêmes et l'hétérogénéité de leurs pratiques concrètes qui ne se limitent que rarement à un schème duel. À partir du cas des Kaingang du sud du Brésil, ce texte insiste sur une approche contextuelle qui tient compte du dualisme gé et du fait que les Kaingang se conçoivent à la fois et sans contradiction comme monade, dyade et polyade. Mots clés : Crépeau, dualisme, mythologie, système symbolique, identité, parenté, espace social, Autochtones, Gé, Kaingang, Brésil

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28

Frandsen, Ann-Christine, and Elton G. McGoun. "To Be Human Is To Account?" Accounting and the Public Interest 10, no. 1 (January 1, 2010): 1–12. http://dx.doi.org/10.2308/api.2010.10.1.1.

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ABSTRACT: Humans have a proclivity for creating good-evil dualities. If accounting is fundamentally naming and counting and if these good-evil dualities are examples of naming (the two parts of the duality) and counting (one part counts more on a goodness scale than the other part), then this proclivity for creating good-evil dualities represents a proclivity for the practice of accounting. Through a chain of translations as described by Bruno Latour, the practice of accounting subsequently reproduces itself and infuses itself into more and more areas of daily life (Latour 1987, 1998). The consequence of these assumptions would be that accounting is an inherent characteristic of our humanity, and the expansion of accounting would be inevitable. To be human would be to account, and humanity would evolve to do more accounting. But is it?

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29

SARAMAGO, M. J., and H. A. PRIESTLEY. "OPTIMAL NATURAL DUALITIES: THE STRUCTURE OF FAILSETS." International Journal of Algebra and Computation 12, no. 03 (June 2002): 407–36. http://dx.doi.org/10.1142/s0218196702000791.

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B. A. Davey and H. A. Priestley have investigated the optimality of dualities on a quasivariety [Formula: see text], where [Formula: see text] is a finite algebra. Relative to a given set Ω of relations yielding a duality, they characterized the optimal dualities as the dualities determined by the transversals of a certain family of subsets of Ω. However the structure of these subsets — known as globally minimal failsets — remained to be understood. This paper gives a complete description of the globally minimal failsets which do not contain partial endomorphisms, and an algorithmic method to determine them. These results are applied, by way of illustration, to the variety of de Morgan algebras and to two further varieties, one of them an Ockham algebra variety and the other a variety of Heyting algebras. All the globally minimal failsets are determined in each case.

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30

GAONA, ALEJANDRO, and J. ANTONIO GARCÍA. "FIRST-ORDER ACTIONS AND DUALITY." International Journal of Modern Physics A 22, no. 04 (February 10, 2007): 851–67. http://dx.doi.org/10.1142/s0217751x07034386.

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We consider some aspects of classical S-duality transformations in first-order actions taking into account the general covariance of the Dirac algorithm and the transformation properties of the Dirac bracket. By classical S-duality transformations we mean a field redefinition that interchanges the equations of motion and its associated Bianchi identities. By working from a first-order variational principle and performing the corresponding Dirac analysis we find that the standard electromagnetic duality can be reformulated as a canonical local transformation. The reduction from this phase space to the original phase space variables coincides with the well-known result about duality as a canonical nonlocal transformation. We have also applied our ideas to the bosonic string. These dualities are not canonical transformations for the Dirac bracket and relate actions with different kinetic terms in the reduced space.

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31

Malek, Emanuel. "U-duality in three and four dimensions." International Journal of Modern Physics A 32, no. 27 (September 30, 2017): 1750169. http://dx.doi.org/10.1142/s0217751x1750169x.

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Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of 11-dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the [Formula: see text] and [Formula: see text] U-duality groups reduce to the [Formula: see text] and [Formula: see text] T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group [Formula: see text].

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32

Musaev, Edvard T. "On the Non-Abelian U-Duality of 11D Backgrounds." Universe 8, no. 5 (May 9, 2022): 276. http://dx.doi.org/10.3390/universe8050276.

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In this work, we generalise the procedure of the non-abelian T-duality based on a B-shift and a sequence of formal abelian T-dualities in non-isometric directions to 11-dimensional backgrounds. This consists of a C-shift followed by either a formal (abelian) U-duality transformation or taking an IIB section. By construction, this is a solution generating transformation. We investigate the restrictions and applicability of the procedure and find that it can provide supergravity solutions for the SL(5) exceptional Drinfeld algebra only when the isometry algebra of the sigma-model target space decomposes into a direct sum. This is consistent with examples known in the literature.

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33

BHATTACHARYYA, RAJSEKHAR, and DEBASHIS GANGOPADHYAY. "DUALITY IN EQUATIONS OF MOTION FROM SPACE–TIME DEPENDENT LAGRANGIANS." Modern Physics Letters A 15, no. 14 (May 10, 2000): 901–11. http://dx.doi.org/10.1142/s0217732300000906.

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Starting from Lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit space–time dependence of the Lagrangian. Poincaré invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both Abelian and non-Abelian dualities. We illustrate how (a) Dirac string solution, (b) Dirac quantization condition, (c) 't Hooft–Polyakov monopole solutions and (d) a procedure emerges for obtaining new classical solutions of Yang–Mills (YM) theory. Moreover, these results occur in a way that is strongly reminiscent of the holographic principle.

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34

PETERSSON, HENRIK. "GENERALIZED ANALYTIC FUNCTIONS ON THE COUNTABLE PRODUCT AND DIRECT SUM OF THE COMPLEX NUMBERS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 04 (December 2001): 559–67. http://dx.doi.org/10.1142/s0219025701000590.

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A classical result states that, in n variables, the space of the entire functionals can be identified with the space of exponential type functions via the Fourier–Borel transform. Thus, in this way the spaces of the entire and exponential type functions can be put in duality, the Martineau duality. We give a proof that the entire functionals, on the countable direct product and direct sum of the field of complex numbers, can be identified with exponential type functions in the same way. In other words, we show that the infinite dimensional Fourier–Borel transform defines Martineau dualities analogous to the finite dimensional case.

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35

Kaloper, Nemanja. "Hidden finite symmetries in string theory and duality of dualities." Physics Letters B 366, no. 1-4 (January 1996): 124–30. http://dx.doi.org/10.1016/0370-2693(95)01370-9.

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ABRAMO, L. R., L. BRENIG, E. GUNZIG, and ALBERTO SAA. "A NOTE ON DUALITIES IN EINSTEIN'S GRAVITY IN THE PRESENCE OF A NON-MINIMALLY COUPLED SCALAR FIELD." Modern Physics Letters A 18, no. 15 (May 20, 2003): 1043–51. http://dx.doi.org/10.1142/s0217732303010958.

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We show that the action of Einstein's gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the effective couplings of the theory are scaled uniformly. In the simplest case, this class of dualities reduces to the S-duality of low-energy effective action of string theory.

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Rastier, François. "Langage et pensée : dualisme cognitif ou dualité sémiotique ?" Intellectica. Revue de l'Association pour la Recherche Cognitive 56, no. 2 (2011): 29–79. http://dx.doi.org/10.3406/intel.2011.1147.

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IGUCHI, KAZUMOTO, and KAZUHIKO AOMOTO. "QUASI-MODULAR SYMMETRY AND QUASI-HYPERGEOMETRIC FUNCTIONS IN QUANTUM STATISTICAL MECHANICS OF FRACTIONAL EXCLUSION STATISTICS." Modern Physics Letters B 13, no. 29n30 (December 30, 1999): 1039–46. http://dx.doi.org/10.1142/s0217984999001287.

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We investigate a novel symmetry in dualities of Wu's equation: wg(1+w)1-g=eβ(ε-μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β=1/k B T, ∊ the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1-g form a novel quasi-modular group of order six for Wu's equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.

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MACKENZIE, K. C. H. "ON SYMPLECTIC DOUBLE GROUPOIDS AND THE DUALITY OF POISSON GROUPOIDS." International Journal of Mathematics 10, no. 04 (June 1999): 435–56. http://dx.doi.org/10.1142/s0129167x99000185.

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We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result outlined by Weinstein in 1988, that the side groupoids of a general symplectic double groupoid are Poisson groupoids in duality. Further, we prove that any double Lie groupoid gives rise to a pair of Poisson groupoids (and thus of Lie bialgebroids) in duality. To handle the structures involved effectively we extend to this context the dualities and canonical isomorphisms for tangent and cotangent structures of the author and Ping Xu.

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Biloslavo, Roberto, David Alex Edgar, and Roland Rusjan. "Strategic Dualities and Business Model Innovation within SMEs." Journal of East European Management Studies 27, no. 3 (2022): 462–86. http://dx.doi.org/10.5771/0949-6181-2022-3-462.

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Applying a business model approach, this paper explores how SMEs perceive, understand and deal with the range of strategic dualities that they face and how this may impact their business model innovation. Qualitative research was conducted using a sample of eight SMEs with the results analysed using content analysis. The findings suggest that SMEs address strategic dualities along four dimensions: degree of globalization (local vs. global), type of offering (individual experience vs. mass product), time orientation (short-term survival vs. long-term orientation), and modernity orientation (tradition vs. modern). It appears to be that SMEs do not recognize these dualities directly but are continuously trying to cope with the tensions they create, and that the whole process is biased by a strong link of SMEs to the local environment (i.e. terroir) that prevents radical innovation of business models. These findings are significant as they cast new insights into the strategic duality faced by SMEs and start to untangle the complex relationships between elements of the business model and SMEs’ local environments.

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Valcke, Louis. "Le monisme épistémologique de la science contemporaine." Articles 1, no. 2 (January 24, 2007): 3–13. http://dx.doi.org/10.7202/203010ar.

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Résumé L'auteur part du postulat d'objectivité de la méthode scientifique dans son affirmation d'une distinction radicale entre le sujet qui observe et l'objet observé. Il montre en quoi ce dualisme du sujet et de l'objet a été remis en question dans la physique quantique de Heisenberg et dans la psychologie behavioriste de Watson. Cependant, l'auteur soutient que le dépassement de ce dualisme cartésien par le monisme objectiviste (Monod) ou par le monisme subjectiviste (Eddington) est impossible pour la raison très simple que le monisme est impensable. De fait, le monisme a été pensé, mais dans un langage dualiste.

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HUSAIN, VIQAR. "NAKED SINGULARITIES AND THE WILSON LOOP." Modern Physics Letters A 17, no. 15n17 (June 7, 2002): 955–65. http://dx.doi.org/10.1142/s021773230200693x.

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We give observations about dualities where one of the dual theories is geometric. These are illustrated with a duality between the simple harmonic oscillator and a topological field theory. We then discuss the Wilson loop in the context of the AdS/CFT duality. We show that the Wilson loop calculation for certain asymptotically AdS scalar field space–times with naked singularities gives results qualitatively similar to that for the AdS black hole. In particular, it is apparent that (dimensional) metric parameters in the singular space–times permit a "thermal screening" interpretation for the uark potential in the boundary theory, just like black hole mass. This suggests that the Wilson loop calculation merely captures metric parameter information rather than true horizon information.

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Nian, Jun. "Note on nonlinear Schrödinger equation, KdV equation and 2D topological Yang–Mills–Higgs theory." International Journal of Modern Physics A 34, no. 15 (May 30, 2019): 1950074. http://dx.doi.org/10.1142/s0217751x1950074x.

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In this paper, we discuss the relation between the [Formula: see text]D nonlinear Schrödinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schrödinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe ansatz equations of the spin-[Formula: see text] [Formula: see text] chain and the [Formula: see text] chain in the continuum limit, respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schrödinger equation, the KdV equation and the 2D [Formula: see text] topological Yang–Mills–Higgs theory.

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Khunjua, Tamaz G., Konstantin G. Klimenko, and Roman N. Zhokhov. "Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities." Particles 3, no. 1 (January 19, 2020): 62–79. http://dx.doi.org/10.3390/particles3010006.

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Recently it has been found that quantum chromodynamics (QCD) phase diagram possesses a duality between chiral symmetry breaking and pion condensation. For the first time this was revealed in the QCD motivated toy model. Then it was demonstrated in effective models as well and new additional dualities being found. We briefly recap the main features of this story and then discuss its applications as a tool to explore the QCD phase structure. The most appealing application is the possibility of getting the results on the QCD phase diagram at large baryon density. Taking the idea from large 1 / N c universalities it was argued that the scenario of circumventing the sign problem with the help of dualities seems plausible. It is also discussed that there is a persistent problem about whether there should be catalysis or anti-catalysis of chiral symmetry breaking by chiral imbalance. One can probably say that the issue is settled after lattice results (first principle approach), where the catalysis was observed. But they used an unphysically large pion mass so it is still interesting to get additional indications that this is the case. It is shown just by the duality property that there exists catalysis of chiral symmetry breaking. So, having in mind our results and the earlier lattice simulations, one can probably claim that this issue is settled. It is demonstrated that the duality can be used to obtain new results. As an example, it is showcased how the phase structure of dense quark matter with chiral imbalance (with possibility of inhomogeneous phases) can be obtained from the knowledge of a QCD phase diagram with isopin asymmetry.

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Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (July 5, 2021): 542–63. http://dx.doi.org/10.15864/jmscm.2408.

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The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.

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Dimov, G., E. Ivanova-Dimova, and W. Tholen. "Extensions of dualities and a new approach to the Fedorchuk duality." Topology and its Applications 281 (August 2020): 107207. http://dx.doi.org/10.1016/j.topol.2020.107207.

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47

Xue, Weimin. "Characterizations of injective cogenerators and morita duality via equivalences and dualities." Journal of Pure and Applied Algebra 102, no. 1 (July 1995): 103–7. http://dx.doi.org/10.1016/0022-4049(95)00078-b.

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SHEIKH-JABBARI, M. M. "NONCOMMUTATIVE OPEN STRING THEORIES AND THEIR DUALITIES." Modern Physics Letters A 16, no. 04n06 (February 28, 2001): 349–59. http://dx.doi.org/10.1142/s0217732301003450.

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The recently found noncritical open string theories is reviewed. These open strings, noncommutative open string theories (NCOS), arise as consistent quantum theories describing the low energy theory of D-branes in a background electric B-field in the critical limit. Focusing on the D3-brane case, we construct the most general (3+1) NCOS, which is described by four parameters. We study S- and T-dualities of these theories and argue the existence of a U-duality group.

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Klimčík, Ctirad. "Brief lectures on duality, integrability and deformations." Reviews in Mathematical Physics 33, no. 06 (June 23, 2021): 2130004. http://dx.doi.org/10.1142/s0129055x21300041.

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We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in [Formula: see text] and in [Formula: see text] dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on the Ruijsenaars duality of finite many-body integrable models, we review the concept of the integrability and, in particular, of the Lax integrability and we analyze the basic examples of the Yang–Baxter deformations of nonlinear [Formula: see text]-models. The central mathematical structure which we describe in detail is the [Formula: see text]-model which is the dynamical system exhibiting all those three phenomena simultaneously. The last part of the paper contains original results, in particular, a formulation of sufficient conditions for strong integrability of non-degenerate [Formula: see text]-models.

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CHATRABHUTI, AUTTAKIT. "TARGET SPACE DUALITY AND MODULI STABILIZATION IN STRING GAS COSMOLOGY." International Journal of Modern Physics A 22, no. 01 (January 10, 2007): 165–79. http://dx.doi.org/10.1142/s0217751x07034143.

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Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

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