@misc{Reich1980,
  author    = {Reich, Sebastian},
  title     = {Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-47290},
  year      = {1980},
  abstract  = {In diesem Beitrag wird der Zusammenhang zwischen Algebrodifferentialgleichungen (ADGL) und Vektorfeldern auf Mannigfaltigkeiten untersucht. Dazu wird zun{\"a}chst der Begriff der regul{\"a}ren ADGL eingef{\"u}hrt, wobei unter eirter regul{\"a}ren ADGL eine ADGL verstanden wird, deren L{\"o}sungsmenge identisch mit der L{\"o}sungsmenge eines Vektorfeldes ist. Ausgehend von bekannten Aussagen {\"u}ber die L{\"o}sungsmenge eines Vektorfeldes werden analoge Aussagen f{\"u}r die L{\"o}sungsmenge einer regul{\"a}ren ADGL abgeleitet. Es wird eine Reduktionsmethode angegeben, die auf ein Kriterium f{\"u}r die Begularit{\"a}t einer ADGL und auf die Definition des Index einer nichtlinearen ADGL f{\"u}hrt. Außerdem wird gezeigt, daß beliebige Vektorfelder durch regul{\"a}re ADGL so realisiert werden k{\"o}nnen, daß die L{\"o}sungsmenge des Vektorfeldes mit der der realisierenden ADGL identisch ist. Abschließend werden die f{\"u}r autonome ADGL gewonnenen Aussagen auf den Fall der nichtautonomen ADGL {\"u}bertragen.},
  language  = {de}
}
@misc{Reich1990,
  author    = {Reich, Sebastian},
  title     = {On a geometrical interpretation of differential-algebraic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46683},
  year      = {1990},
  abstract  = {The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena.},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Congruences on maximal partial clones and strong regular varieties generated by preprimal partial algebras II},
  year      = {1991},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Strong regular varieties of partial algebras I},
  year      = {1991},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Minimal algebras and category equivalences},
  year      = {1991},
  language  = {en}
}
@misc{Quaisser1991,
  author    = {Quaisser, Erhard},
  title     = {Erd{\"o}s, P., Geombinatorics, 1 (1991), 3, S. 4},
  year      = {1991},
  language  = {de}
}
@misc{Reich1991,
  author    = {Reich, Sebastian},
  title     = {On an existence and uniqueness theory for nonlinear differential-algebraic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46706},
  year      = {1991},
  abstract  = {An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example.},
  language  = {en}
}
@misc{Reich1992,
  author    = {Reich, Sebastian},
  title     = {Differential-algebraic equations and applications in circuit theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46646},
  year      = {1992},
  abstract  = {Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples.},
  language  = {en}
}
@phdthesis{Lueders1992,
  author    = {L{\"u}ders, Otfried},
  title     = {{\"A}quivalenzen und Dualit{\"a}ten von Variet{\"a}ten und Quasivariet{\"a}ten die von endlichen Algebren erzeugt werden},
  pages     = {111, II Bl. : Ill.},
  year      = {1992},
  language  = {de}
}
@misc{Quaisser1992,
  author    = {Quaisser, Erhard},
  title     = {Woodall, D., Geombinatorics, 1 (1992), 4, S. 18 - 20},
  year      = {1992},
  language  = {de}
}
@misc{Quaisser1992,
  author    = {Quaisser, Erhard},
  title     = {Zeitler, H., Mathematische Semesterberichte, 39 (1992), S. 163 - 183},
  year      = {1992},
  language  = {de}
}
@book{SchmidtWang1992,
  author    = {Schmidt, Hans-J{\"u}rgen and Wang, Anzhong},
  title     = {Plane domain walls when coupled with the Brans-Dicke scalar field},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 06},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {27 S.},
  year      = {1992},
  language  = {en}
}
@book{Kasper1992,
  author    = {Kasper, Uwe},
  title     = {On the phenomenological description of particle and entropy creation},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 07},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {10 S.},
  year      = {1992},
  language  = {en}
}
@book{Waltz1992,
  author    = {Waltz, Christine},
  title     = {Interpolation von holomorphen Typen},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 01},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {23 Bl.},
  year      = {1992},
  language  = {de}
}
@article{Braunss1992,
  author    = {Braunß, Hans-Andreas},
  title     = {On holomorphic mappings of Schatten class type},
  year      = {1992},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 17},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {14 Bl.},
  year      = {1992},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 18},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {17 Bl.},
  year      = {1992},
  language  = {en}
}
@book{Schmidt1992,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {On inflation within closed Fiedmann universe models},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 02},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {9 Bl.},
  year      = {1992},
  language  = {en}
}
@book{Schmidt1992,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Scale-invariant gravity in two dimensions II},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 03},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {[3] Bl.},
  year      = {1992},
  language  = {en}
}
@article{AmendolaBattagliaMayerCapozzielloetal.1992,
  author    = {Amendola, Luca and Battaglia Mayer, Alexandra and Capozziello, Salvatore and Gottl{\"o}ber, Stefan and M{\"u}ller, Volker and Occhionero, Franco and Schmidt, Hans-J{\"u}rgen},
  title     = {Generalized sixth-order gravity and inflation},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 04},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {7 S.},
  year      = {1992},
  language  = {en}
}