scholarly journals EQUIVARIANT ANDERSON DUALITY AND MACKEY FUNCTOR DUALITY

2015 ◽  
Vol 58 (3) ◽  
pp. 649-676 ◽  
Author(s):  
NICOLAS RICKA
Keyword(s):  
Exact Sequence ◽  
Equivariant Cohomology ◽  
The Self ◽  
Cohomology Groups ◽  
Mackey Functor ◽  
Self Duality ◽  
K Theory ◽  
Made In

AbstractWe show that the$\mathbb{Z}$/2-equivariantnth integral MoravaK-theory with reality is self-dual with respect to equivariant Anderson duality. In particular, there is a universal coefficients exact sequence in integral Morava K-theory with reality, and we recover the self-duality of the spectrumKOas a corollary. The study of$\mathbb{Z}$/2-equivariant Anderson duality made in this paper gives a nice interpretation of some symmetries ofRO($\mathbb{Z}$/2)-graded (i.e. bigraded) equivariant cohomology groups in terms of Mackey functor duality.

scholarly journals Higher rank FZZ-dualities

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Thomas Creutzig ◽  
Yasuaki Hikida
Keyword(s):  
Field Theory ◽  
Reduction Method ◽  
Operator Algebras ◽  
The Self ◽  
Liouville Theory ◽  
Conformal Field ◽  
Self Duality ◽  
Higher Rank ◽  
Corner Vertex ◽  
Liouville Field Theory

Abstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ sl 2 / u 1 coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ sl 2 Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ sl N + 1 / sl N × u 1 and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ sl N + 1 N structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ sl N and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y0,N,N+1[ψ] and YN,0,N+1[ψ−1].

scholarly journals Approaching the self-dual point of the sinh-Gordon model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert Konik ◽  
Márton Lájer ◽  
Giuseppe Mussardo
Keyword(s):  
Small Volume ◽  
Zero Mode ◽  
Form Factors ◽  
Lagrangian Formulation ◽  
The Self ◽  
Quantum Mechanical ◽  
Exact Form ◽  
Coupling Constant ◽  
Self Duality ◽  
Hyperbolic Cosine

Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

A SUFFICIENT AND NECESSARY CONDITION FOR CREDIBILITY MEASURES

2006 ◽  
Vol 14 (05) ◽  
pp. 527-535 ◽  
Author(s):  
XIANG LI ◽  
BAODING LIU
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Extension Theorem ◽  
The Self ◽  
Necessary Condition ◽  
Self Duality ◽  
Duality Property ◽  
Sufficient And Necessary Condition

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

scholarly journals A new description of equivariant cohomology for totally disconnected groups

2008 ◽  
Vol 1 (3) ◽  
pp. 431-472 ◽  
Author(s):  
Christian Voigt
Keyword(s):  
Equivariant Cohomology ◽  
Simplicial Complexes ◽  
Cyclic Homology ◽  
Cohomology Theory ◽  
Cohomology Groups ◽  
Natural Class ◽  
New Approach ◽  
Totally Disconnected

AbstractWe consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as well as a computation of equivariant periodic cyclic homology for a natural class of examples. In addition we discuss the relation between cosheaf homology and equivariant Bredon homology. Since the theory of Baum and Schneider generalizes cosheaf homology we finally see that all these approaches to equivariant cohomology for totally disconnected groups are closely related.

scholarly journals I. Note on an extension of the comparison of magnetic disturbances with magnetic effects inferred from observed terrestrial galvanic currents; and discussion of the magnetic effects inferred from galvanic currents on days of tranquil magnetism

1870 ◽  
Vol 18 (114-122) ◽  
pp. 183-185
Keyword(s):  
Magnetic Force ◽  
The Self ◽  
Instrumental Error ◽  
Magnetic Disturbance ◽  
Magnetic Effects ◽  
Royal Observatory ◽  
Moderate Disturbance ◽  
Magnetic Disturbances ◽  
Made In

The author, after referring to his paper in the Philosophical Transactions for 1868 on the comparison of Magnetic Disturbances inferred from Galvanic Currents recorded by the Self-registering Galvanometers of the Royal Observatory of Greenwich with the Magnetic Disturbances registered by the Magnetometers, on 17 days, states that he had now undertaken the examination of the whole of the Galvanic Currents recorded during the establishment of the Croydon and Dartford wires (from 1865 April 1 to 1867 October 24). The days of observation were divided into three groups,—No. I containing days of considerable magnetic disturbance, and therein including not only the 17 days above mentioned, but also 36 additional days, No. 2 containing days of moderate disturbance, of which no further use was made, and No. 3 containing the days of tranquil magnetism. The comparisons of the additional 36 disturbed days were made in the same manner as those of the preceding 17 days, and the inferences were the same. The results were shown in the same manner, by comparison of curves, which were exhibited to the Society. The points most worthy of notice are, that the general agreement of the strong irregularities, Galvanic and Magnetic, is very close, that the galvanic irregularities usually precede the magnetic, in time, and that the northerly magnetic force appears to be increased. The author remarks that no records appeared open to doubt as regards instrumental error, except those of western declination; and to remove this he had compared the Greenwich Curves with the Kew Curves, and had found them absolutely identical.

Touching Brains in the Neuronovel

2018 ◽  
Author(s):  
Jason Tougaw
Keyword(s):  
The Self ◽  
Contemporary Fiction ◽  
Explanatory Gap ◽  
The Relationship ◽  
The Explanatory Gap ◽  
Considerable Detail ◽  
Made In ◽  
Literary Phenomenon

In contemporary fiction, the appearance of a physical brain leads swiftly to explicit focus on questions that proliferate from the explanatory gap. Writers don’t use the term, but they explore and contextualize its implications in considerable detail. In this chapter, Tougaw examine the portrayal of those three pounds of intricately designed flesh in five novels: Thomas Harris’s Hannibal (1999), Ian McEwan’s Saturday (2006), Siri Hustvedt’s The Sorrows of an American (2009), John Wray’s Lowboy (2010), and Maud Casey’s The Man Who Walked Away (2014). These novels are representative of a common literary phenomenon: the dramatization of a fantasy whereby touching brains may reveal the stuff of which self is made. In each of these novels, the representation of physical brains provokes questions about the relationship between physiology and the self that become central to narrative closure.

scholarly journals Multivariate Self-Dual Morphological Operators Based on Extremum Constraint

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Tao Lei ◽  
Yi Wang ◽  
Weiwei Luo
Keyword(s):  
Noise Removal ◽  
Complete Characterization ◽  
The Self ◽  
Experimental Results ◽  
Watershed Transformation ◽  
Morphological Operators ◽  
Self Duality ◽  
Multichannel Images ◽  
Duality Property ◽  
Image Details

Self-dual morphological operators (SDMO) do not rely on whether one starts the sequence with erosion or dilation; they treat the image foreground and background identically. However, it is difficult to extend SDMO to multichannel images. Based on the self-duality property of traditional morphological operators and the theory of extremum constraint, this paper gives a complete characterization for the construction of multivariate SDMO. We introduce a pair of symmetric vector orderings (SVO) to construct multivariate dual morphological operators. Furthermore, utilizing extremum constraint to optimize multivariate morphological operators, we construct multivariate SDMO. Finally, we illustrate the importance and effectiveness of the multivariate SDMO by applications of noise removal and segmentation performance. The experimental results show that the proposed multivariate SDMO achieves better results, and they suppress noises more efficiently without losing image details compared with other filtering methods. Moreover, the proposed multivariate SDMO is also shown to have the best segmentation performance after the filtered images via watershed transformation.

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