| 1. |
- Euler, Marianna, 1961-, et al.
(author)
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Aufgaben, Theorie und Lösungen zur Linearen Algebra, Teil 1 : Der Euklidische Raum
- 2017
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Book (peer-reviewed)abstract
- Dieses Buch ist der erste Teil einer dreiteiligen Serie mit dem Titel Aufgaben, Theorieund L¨osungen zur Linearen Algebra. Dieser erste Teil behandelt Vektoren des euklidischen Raumes sowie Matrizen, Matrixalgebra und Systeme von linearen Gleichungen. Wir l¨osen lineare System mit Hilfe des Gaußschen Eliminationsverfahrens und auf anderem Wege und untersuchen die Eigenschaften dieser Systeme in Bezug auf Vektoren und Matrizen. Dar¨uber hinaus betrachten wir lineare Abbildungen und berechnendie Standardmatrizen dieser Abbildungen.
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| 2. |
- Euler, Marianna, 1961-, et al.
(author)
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Multipotentializations and nonlocal symmetries: Kupershmidt, Kaup-Kupershmidt and Sawada-Kotera equations
- 2017
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In: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 24:3, s. 303-314
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Journal article (other academic/artistic)abstract
- In this letter we report a new invariant for the Sawada-Kotera equation that is obtained by a systematic potentialization of the Kupershmidt equation. We show that this result can be derived from nonlocal symmetriesand that, conversely, a previously known invariant of the Kaup-Kupershmidt equation can be recovered using potentializations.
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| 3. |
- Euler, Marianna, 1961-, et al.
(author)
-
On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative
- 2019
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In: Studies in applied mathematics (Cambridge). - : John Wiley & Sons. - 0022-2526 .- 1467-9590. ; 143:2, s. 139-156
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Journal article (peer-reviewed)abstract
- We consider symmetry‐integrable evolution equations in 1 + 1 dimensions of order 3 and order 5. We show that there exist only three equations in this class that are invariant under the Möbius transformation, and we name those Schwarzian equations. We report an interesting relation between the recursion operators of the Schwarzian equations and the corresponding adjoint operators that generate hierarchies of Schwarzian systems in terms of the Schwarzian derivative. This indicates a deep relation between the Schwarzian equations and the Schwarzian derivative. A classification of the fully nonlinear third‐order Schwarzian equations is also reported.
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| 4. |
- Euler, Marianna, 1961-, et al.
(author)
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On nonlocal symmetries generated by recursion operators: Second-order evolution equations
- 2017
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In: Discrete and Continuous Dynamical Systems. - : American Institute of Mathematical Sciences. - 1078-0947 .- 1553-5231. ; 37:8, s. 4239-4247
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Journal article (peer-reviewed)abstract
- We introduce a new type of recursion operator to generate a class of nonlocal symmetries for second-order evolution equations in 1+1 dimensions, namely those evolution equations which allow the complete integration of their stationary equations. We show that this class of evolution equations is C-integrable (linearizable by a point transformation). We also discuss some applications.
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| 5. |
- Euler, Marianna, et al.
(author)
-
Problemas, Teoria y Soluciones en Algebra Lineal : Parte 1 Espacio Euclideo
- 2016. - 1
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Book (peer-reviewed)abstract
- This book is the first part of a three-part series titled Problems, Theory and Solutions in Linear Algebra. This first part contains over 100 solved problems and 100 exercises on vectors, matrices, linear systems, as well as linear transformations in Euclidean space. It is intended as a supplement to a textbook in Linear Algebra and the aim of the series it to provide the student with a well-structured and carefully selected set of solved problems as well as a thorough revision of the material taught in a course on this subject for undergraduate engineering and science students.
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| 6. |
- Euler, Marianna, et al.
(author)
-
Problems, Theory and Solutions in Linear Algebra : Part 1: Euclidean Space
- 2015. - 2
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Book (peer-reviewed)abstract
- This book is the first part of a three-part series titled Problems, Theory and Solutions in Linear Algebra. This first part contains over 100 solved problems and 100 exercises on vectors, matrices, linear systems, as well as linear transformations in Euclidean space. It is intended as a supplement to a textbook in Linear Algebra and the aim of the series it to provide the student with a well-structured and carefully selected set of solved problems as well as a thorough revision of the material taught in a course on this subject for undergraduate engineering and science students.
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| 7. |
- Euler, Marianna, 1961-, et al.
(author)
-
Théorie et Problémes Résolus d'Algèbre Linéaire : Volume 1 Espaces Euclidiens
- 2017. - 1
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Book (peer-reviewed)abstract
- Ce livre est le premier d'une série de trois ouvrages intitulés Théorie et Problèmes Résolus d'algèbre linéaire. Cette première partie contient plus de 100 problèmes résolus et plus de 100 exercices sur les vecteurs en espaces euclidiens, les matrices, les systèmes linéaires ainsi que les applications linéaires entre espaces euclidiens. Le but de cette série est de fournir aux étudiants de filières scientifiques et techniques un ensemble structuré de problèmes soigneusement choisis ainsi qu'une opportunité d'approfondir leurs connaissances acquises en cours d'algèbre linéaire.
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| 8. |
- Euler, Norbert, 1964-, et al.
(author)
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Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
- 2018. - 1
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In: Nonlinear Systems and Their Remarkable Mathematical Structures. - Boca Raton, USA : CRC Press. - 9781138601000 - 9780429470462 ; , s. 317-351
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Book chapter (peer-reviewed)abstract
- The term multipotentialisation of evolution equations in 1+1 dimensions refers to the process of potentialising a given evolution equation, followed by at least one further potentialisation of the resulting potential equation. For certain equations this process can be applied several times to result in a finite chain of potential equations, where each equation in the chain is a potential equation of the previous equation. By a potentialisation of an equation with dependent variable u to an equation with dependent variable v, we mean a differential substitution v_x=\Phi^t, where \Phi^t is a conserved current of the equation in u. The process of multipotentialisation may lead to interesting nonlocal transformations between the equations. Remarkably, this can, in some cases, result in nonlocal invariance transformations for the equations, which then serve as iteration formulas by which solutions can be generated for all the equations in the chain.In the current paper we give a comprehensive introduction to this subject and report new nonlocal invariance transformations that result from the multipotentialisation of the Kupershmidt equation and its higher-order hierarchies. The recursion operators that define the hierarchies are given explicitly.
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