Lattice realizations of unitary minimal modular invariant partition functions [PDF]
, 1995 The conformal spectra of the critical dilute A-D-E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A-D-E classification of unitary minimal modular ...
D.L. O'Brien +3 more
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Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields
Journal of High Energy Physics, 2018 We study the entanglement entropy and the modular Hamiltonian of slightly excited states reduced to a ball shaped region in generic conformal field theories.
Gábor Sárosi, Tomonori Ugajin
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Modular properties of massive scalar partition functions [PDF]
Journal of High Energy PhysicsWe compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form ℝ d−q × 𝕋 q+1 and show that they possess an SL(q + 1, ℤ) symmetry.
Ankit Aggarwal, Glenn Barnich
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Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions
Mathematical and Computational Applications, 2021 In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO ...
Ahmad Taher Azar +2 more
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Class fields generated by coordinates of elliptic curves
Open Mathematics, 2022 Let KK be an imaginary quadratic field different from Q(−1){\mathbb{Q}}\left(\sqrt{-1}) and Q(−3){\mathbb{Q}}\left(\sqrt{-3}). For a nontrivial integral ideal m{\mathfrak{m}} of KK, let Km{K}_{{\mathfrak{m}}} be the ray class field modulo m{\mathfrak{m}}.
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
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Synergistic Structure in the Speed Dependent Modulation of Muscle Activity in Human Walking. [PDF]
PLoS ONE, 2016 Recently, a modular organisation has been proposed to simplify control of the large number of muscles involved in human walking. Although previous research indicates that a single set of modular activation patterns can account for muscle activity at ...
Tom J W Buurke +3 more
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On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds [PDF]
Royal Society Open Science, 2015 In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds.
Kathrin Bringmann +2 more
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On some extensions of Gauss’ work and applications
Open Mathematics, 2020 Let K be an imaginary quadratic field of discriminant dK{d}_{K} with ring of integers OK{{\mathcal{O}}}_{K}, and let τK{\tau }_{K} be an element of the complex upper half plane so that OK=[τK,1]{{\mathcal{O}}}_{K}={[}{\tau }_{K},1].
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
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Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms
Journal of High Energy Physics, 2022 We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of)
Daniele Dorigoni +2 more
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Three dimensional pure gravity and generalized Hecke operators
Journal of High Energy Physics, 2020 In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into ...
M. Ashrafi
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