Chirogenesis in Supramolecular Systems on the Basis of Porphyrinoids

Abstract

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Chirogenesis in Supramolecular Systems on the Basis of Porphyrinoids † by Victor Borovkov Department of Chemistry and Biotechnology, Tallinn University of Technology, Academia tee 15, 12616 Tallinn, Estonia † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 83; https://doi.org/10.3390/proceedings2010083 Published: 5 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Noether’s theorem provides a systematic method to obtain conservation laws (conserved integrals) for differential equations but it requires an equation to have a variational (Lagrangian) formulation. In a series of publications [1,2,3,4,5,6], a generalization of Noether’s theorem has been developed using the concept of adjoint-symmetries. This generalization applies to all differential equations, without requiring that a variational formulation exists, and is algorithmic in the same sense as Lie’s method for finding symmetries of differential equations. The main steps in the generalization will be outlined and examples of finding conservation laws for non-variational differential equations will be illustrated. ReferencesBluman, G.; Anco, S.C. Symmetry and Integration Methods for Differential Equations. In Applied Mathematical Sciences Series; Springer: Berlin/Heidelberg, Germany, 2002; Volume 154. [Google Scholar]Bluman, G.; Cheviakov, A.F.; Anco, S.C. Applications of Symmetry Methods to Partial Differential Equations. In Applied Mathematical Sciences Series; Springer: Berlin/Heidelberg, Germany, 2009; Volume 168. [Google Scholar]Anco, S.C. Generalization of Noether’s theorem in modern form to non-variational partial differential equations. arXiv 2017, arXiv:mathph/1605.08734. [Google Scholar]Anco, S.C.; Kara, A. Symmetry invariance of conservation laws. arXiv 2017, arXiv:1510.09154 math-ph. [Google Scholar]Anco, S.C. On the incompleteness of Ibragimov’s conservation law theorem and its equivalence to a standard formula using symmetries and adjoint-symmetries. Symmetry 2017, 9, 33. [Google Scholar] [CrossRef]Anco, S.C. Symmetry properties of conservation laws. Int. J. Mod. Phys. B 2016, 30, 1640004. [Google Scholar] [CrossRef]Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Borovkov, V. Chirogenesis in Supramolecular Systems on the Basis of Porphyrinoids. Proceedings 2018, 2, 83. https://doi.org/10.3390/proceedings2010083 AMA Style Borovkov V. Chirogenesis in Supramolecular Systems on the Basis of Porphyrinoids. Proceedings. 2018; 2(1):83. https://doi.org/10.3390/proceedings2010083 Chicago/Turabian Style Borovkov, Victor. 2018. "Chirogenesis in Supramolecular Systems on the Basis of Porphyrinoids" Proceedings 2, no. 1: 83. https://doi.org/10.3390/proceedings2010083 Find Other Styles Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here. Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.