@inproceedings{MalonekFalcaoCruz,
  author    = {Malonek, Helmuth Robert and Falc{\~a}o, M. Irene and Cruz, Carla},
  title     = {TOTALLY REGULAR VARIABLES AND APPELL SEQUENCES IN HYPERCOMPLEX FUNCTION THEORY},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2775},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27751},
  pages     = {5},
  abstract  = {The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. G{\"u}rlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{JaouadiLahmer,
  author    = {Jaouadi, Zouhour and Lahmer, Tom},
  title     = {Topology optimization of structures subjected to multiple load cases by introducing the Epsilon constraint method},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2804},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28042},
  pages     = {7},
  abstract  = {A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{HommelGuerlebeck,
  author    = {Hommel, Angela and G{\"u}rlebeck, Klaus},
  title     = {THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2801},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28010},
  pages     = {6},
  abstract  = {It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Vasileva,
  author    = {Vasileva, Iuliia},
  title     = {THE PROBLEM OF PARTIAL REINFORCING AN INTERFACE CRACK EDGE BY A RIGID PATCH PLATE UNDER IN-PLANE AND ANTIPLANE LOADS},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2824},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28242},
  pages     = {5},
  abstract  = {The stress state of a piecewise-homogeneous elastic body, which has a semi-infinite crack along the interface, under in-plane and antiplane loads is considered. One of the crack edges is reinforced by a rigid patch plate on a finite interval adjacent to the crack tip. The crack edges are loaded with specified stresses. The body is stretched at infinity by specified stresses. External forces with a given principal vector and moment act on the patch plate. The problem reduces to a Riemann-Hilbert boundary-value matrix problem with a piecewise-constant coefficient for two complex potentials in the plane case and for one in the antiplane case. The complex potentials are found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the ends of the patch plate, one of which is also simultaneously the crack tip, is investigated. Stress intensity factors near the singular points are determined.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{LegatiukBockGuerlebeck,
  author    = {Legatiuk, Dmitrii and Bock, Sebastian and G{\"u}rlebeck, Klaus},
  title     = {THE PROBLEM OF COUPLING BETWEEN ANALYTICAL SOLUTION AND FINITE ELEMENT METHOD},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2773},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27730},
  pages     = {11},
  abstract  = {This paper is focused on the first numerical tests for coupling between analytical solution and finite element method on the example of one problem of fracture mechanics. The calculations were done according to ideas proposed in [1]. The analytical solutions are constructed by using an orthogonal basis of holomorphic and anti-holomorphic functions. For coupling with finite element method the special elements are constructed by using the trigonometric interpolation theorem.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{KulchytskyyHorokhovGubanovetal.,
  author    = {Kulchytskyy, Artem and Horokhov, Yevgen and Gubanov, Vadim and Golikov, Alexandr},
  title     = {THE INFLUENCE OF THE LOCAL CONCAVITY ON THE FUNCTIONING OF BEARING SHELL OF HIGH-RISE CONSTRUCTION},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2770},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27701},
  pages     = {10},
  abstract  = {Areas with various defects and damages, which reduce carrying capacity, were examined in a study of metal chimneys. In this work, the influence of the local dimples on the function of metal chimneys was considered. Modeling tasks were completed in the software packages LIRA and ANSYS. Parameters were identified, which characterize the local dimples, and a numerical study of the influence of local dimples on the stress-strain state of shells of metal chimneys was conducted. A distribution field of circular and meridional tension was analyzed in a researched area. Zones of influence of dimples on the bearing cover of metal chimneys were investigated. The bearing capacities of high-rise structures with various dimple geometries and various cover parameters were determined with respect to specified areas of the trunk. Dependent relationships are represented graphically for the decrease in bearing capacity of a cover with respect to dimples. Diameter and thickness of covers of metal chimneys were constructed according to the resulting data.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Musial,
  author    = {Musial, Michal},
  title     = {THE INFLUENCE OF CRACKS AND OVERESTIMATION ERRORS ON THE DEFLECTION OF THE REINFORCED CONCRETE BEAMS IN THE RIGID FINITE ELEMENT METHOD},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2814},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28142},
  pages     = {6},
  abstract  = {This article presents the Rigid Finite Element Method in the calculation of reinforced concrete beam deflection with cracks. Initially, this method was used in the shipbuilding industry. Later, it was adapted in the homogeneous calculations of the bar structures. In this method, rigid mass discs serve as an element model. In the flat layout, three generalized coordinates (two translational and one rotational) correspond to each disc. These discs are connected by elastic ties. The genuine idea is to take into account a discrete crack in the Rigid Finite Element Method. It consists in the suitable reduction of the rigidity in rotational ties located in the spots, where cracks occurred. The susceptibility of this tie results from the flexural deformability of the element and the occurrence of the crack. As part of the numerical analyses, the influence of cracks on the total deflection of beams was determined. Furthermore, the results of the calculations were compared to the results of the experiment. Overestimations of the calculated deflections against the measured deflections were found. The article specifies the size of the overestimation and describes its causes.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{GrobConstalesKrausshar,
  author    = {Grob, Dennis and Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {THE HYPERCOMPLEX SZEG{\"O} KERNEL METHOD FOR 3D MAPPING PROBLEMS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2846},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28464},
  pages     = {7},
  abstract  = {In this paper we present rudiments of a higher dimensional analogue of the Szeg{\"o} kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{LavickaDelangheSoucek,
  author    = {Lavicka, Roman and Delanghe, Richard and Soucek, Vladimir},
  title     = {THE HOWE DUALITY FOR HODGE SYSTEMS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2866},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28669},
  pages     = {11},
  abstract  = {In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{DeSchepperBrackxSommen,
  author    = {De Schepper, Nele and Brackx, Fred and Sommen, Frank},
  title     = {THE FOURIER-BESSEL TRANSFORM},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2838},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28387},
  pages     = {18},
  abstract  = {In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform.},
  subject      = {Angewandte Informatik},
  language  = {en}
}