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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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Communications in Number Theory and Physics, 2017 In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II ...
d'Hoker, Eric +3 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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Transactions of the American Mathematical Society, 1994 A new family of symmetric functions is considered. These functions are analogous to the classical Schur functions, but depend on an integer modulus p ⩾ 2 p \geqslant 2 , as well as on a partition λ \lambda .
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Tetrahedral modular graph functions
Journal of High Energy Physics, 2017 The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams.
Axel Kleinschmidt, Valentin Verschinin
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