@phdthesis{Hommel,
  author    = {Hommel, Angela},
  title     = {Diskret holomorphe Funktionen und deren Bedeutung bei der L{\"o}sung von Differenzengleichungen},
  doi       = {10.25643/bauhaus-universitaet.3784},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180827-37846},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Auf der Grundlage diskreter Cauchy-Riemann Operatoren werden diskret holomorphe Funktionen definiert und detailliert studiert. Darauf aufbauend wird die L{\"o}sung von Differenzengleichungen mit Hilfe der diskret holomorphen Funktionen beschrieben.},
  subject      = {Differenzengleichung},
  language  = {de}
}
@phdthesis{Legatiuk,
  author    = {Legatiuk, Anastasiia},
  title     = {Discrete potential and function theories on a rectangular lattice and their applications},
  doi       = {10.25643/bauhaus-universitaet.4865},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221220-48654},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The growing complexity of modern engineering problems necessitates development of advanced numerical methods. In particular, methods working directly with discrete structures, and thus, representing exactly some important properties of the solution on a lattice and not just approximating the continuous properties, become more and more popular nowadays. Among others, discrete potential theory and discrete function theory provide a variety of methods, which are discrete counterparts of the classical continuous methods for solving boundary value problems. A lot of results related to the discrete potential and function theories have been presented in recent years. However, these results are related to the discrete theories constructed on square lattices, and, thus, limiting their practical applicability and potentially leading to higher computational costs while discretising realistic domains. This thesis presents an extension of the discrete potential theory and discrete function theory to rectangular lattices. As usual in the discrete theories, construction of discrete operators is strongly influenced by a definition of discrete geometric setting. For providing consistent constructions throughout the whole thesis, a detailed discussion on the discrete geometric setting is presented in the beginning. After that, the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, which is the core of the discrete potential theory, its numerical analysis, and practical calculations are presented. By using the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, the discrete potential theory is then constructed for interior and exterior settings. Several discrete interior and exterior boundary value problems are then solved. Moreover, discrete transmission problems are introduced and several numerical examples of these problems are discussed. Finally, a discrete fundamental solution of the discrete Cauchy-Riemann operator on a rectangular lattice is constructed, and basics of the discrete function theory on a rectangular lattice are provided. This work indicates that the discrete theories provide solution methods with very good numerical properties to tackle various boundary value problems, as well as transmission problems coupling interior and exterior problems. The results presented in this thesis provide a basis for further development of discrete theories on irregular lattices.},
  subject      = {Diskrete Funktionentheorie},
  language  = {en}
}
@article{Legatiuk,
  author    = {Legatiuk, Dmitrii},
  title     = {Mathematical Modelling by Help of Category Theory: Models and Relations between Them},
  series = {mathematics},
  volume    = {2021},
  journal   = {mathematics},
  number    = {volume 9, issue 16, article 1946},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/math9161946},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210817-44844},
  pages     = {17},
  abstract  = {The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computationbased, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios.},
  subject      = {Kategorientheorie},
  language  = {en}
}
@phdthesis{Nguyen,
  author    = {Nguyen, Manh Hung},
  title     = {µ-Hyperholomorphic Function Theory in R³: Geometric Mapping Properties and Applications},
  doi       = {10.25643/bauhaus-universitaet.2447},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150817-24477},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {155},
  abstract  = {This thesis applies the theory of \psi-hyperholomorphic functions dened in R^3 with values in the set of paravectors, which is identified with the Eucledian space R^3, to tackle some problems in theory and practice: geometric mapping properties, additive decompositions of harmonic functions and applications in the theory of linear elasticity.},
  subject      = {Mathematik},
  language  = {en}
}
@masterthesis{Nguyen,
  type      = {Bachelor Thesis},
  author    = {Nguyen, Thai Cuong},
  title     = {Fl{\"a}chen zweiter Ordnung - D{\"a}cher m{\"u}ssen nicht eben sein},
  doi       = {10.25643/bauhaus-universitaet.3749},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20181024-37496},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {47},
  abstract  = {In dieser Arbeit geht es um die Quadriken in der Ebene und im Raum. Dabei werden die Transformation in die Normalform und die Klassifikation untersucht. Aus den geometrischen Eigenschaften werden einige Anwendungsbeispiele der Quadriken in der Technik und dem allt{\"a}glichen Leben vorgestellt.},
  subject      = {Quadrik},
  language  = {de}
}