@inproceedings{ConstalesKrausshar,
  author    = {Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2863},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28639},
  pages     = {10},
  abstract  = {In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{DeAguinaga,
  author    = {De Aguinaga, Jos{\´e} Guillermo},
  title     = {INFLUENCE OF DIFFERENT DATA TYPES FOR THE ESTIMATION OF HYDROMECHANICAL PARAMETERS FOR A WATER RETAINING DAM USING SYNTHETIC DATA},
  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.2760},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170306-27607},
  pages     = {12},
  abstract  = {The present research analyses the error on prediction obtained under different data availability scenarios to determine which measurements contribute to an improvement of model prognosis and which not. A fully coupled 2D hydromechanical model of a water retaining dam is taken as an example. Here, the mean effective stress in the porous skeleton is reduced due to an increase in pore water pressure under drawdown conditions. Relevant model parameters are ranked by scaled sensitivities, Particle Swarm Optimization is applied to determine the optimal parameter values and model validation is performed to determine the magnitude of error forecast. We compare the predictions of the optimized models with results from a forward run of the reference model to obtain actual prediction errors. The analyses presented here were performed to 31 data sets of 100 observations of varying data types. Calibrating with multiple information types instead of only one sort, brings better calibration results and improvement in model prognosis. However, when using several types of information the number of observations have to be increased to be able to cover a representative part of the model domain; otherwise a compromise between data availability and domain coverage prove best. Which type of information for calibration contributes to the best prognoses, could not be determined in advance. For the error in model prognosis does not depends on the error in calibration, but on the parameter error, which unfortunately can not be determined in reality since we do not know its real value. Excellent calibration fits with parameters' values near the limits of reasonable physical values, provided the highest prognosis errors. While models which included excess pore pressure values for calibration provided the best prognosis, independent of the calibration fit.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{DeBieSommen,
  author    = {De Bie, Hendrik and Sommen, Frank},
  title     = {VECTOR AND BIVECTOR FOURIER TRANSFORMS IN CLIFFORD ANALYSIS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2837},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28371},
  pages     = {11},
  abstract  = {In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms.},
  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}
}
@inproceedings{DeebZabel,
  author    = {Deeb, Maher and Zabel, Volkmar},
  title     = {THE APPLICATION OF POD CURVES TO DAMAGE DETECTION BASED ON PARTIAL MODELS- A NUMERICAL AND EXPERIMENTAL STUDY},
  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.2761},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170306-27615},
  pages     = {18},
  abstract  = {Non-destructive techniques for damage detection became the focus of engineering interests in the last few years. However, applying these techniques to large complex structures like civil engineering buildings still has some limitations since these types of structures are unique and the methodologies often need a large number of specimens for reliable results. For this reason, cost and time can greatly influence the final results. Model Assisted Probability Of Detection (MAPOD) has taken its place among the ranks of damage identification techniques, especially with advances in computer capacity and modeling tools. Nevertheless, the essential condition for a successful MAPOD is having a reliable model in advance. This condition is opening the door for model assessment and model quality problems. In this work, an approach is proposed that uses Partial Models (PM) to compute the Probability Of damage Detection (POD). A simply supported beam, that can be structurally modified and tested under laboratory conditions, is taken as an example. The study includes both experimental and numerical investigations, the application of vibration-based damage detection approaches and a comparison of the results obtained based on tests and simulations. Eventually, a proposal for a methodology to assess the reliability and the robustness of the models is given.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{DjordjevicPetkovicZivkovic,
  author    = {Djordjevic, Djordje and Petkovic, Dusan and Zivkovic, Darko},
  title     = {THE APPLICATION OF INTERVAL CALCULUS TO ESTIMATION OF PLATE DEFLECTION BY SOLVING POISSON'S PARTIAL DIFFERENTIAL EQUATION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2839},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28397},
  pages     = {12},
  abstract  = {This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{EbertBernsteinCerejeirasetal.,
  author    = {Ebert, Svend and Bernstein, Swanhild and Cerejeiras, Paula and K{\"a}hler, Uwe},
  title     = {NONZONAL WAVELETS ON S^N},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2840},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28406},
  pages     = {18},
  abstract  = {In the present article we will construct wavelets on an arbitrary dimensional sphere S^n due the approach of approximate Identities. There are two equivalently approaches to wavelets. The group theoretical approach formulates a square integrability condition for a group acting via unitary, irreducible representation on the sphere. The connection to the group theoretical approach will be sketched. The concept of approximate identities uses the same constructions in the background, here we select an appropriate section of dilations and translations in the group acting on the sphere in two steps. At First we will formulate dilations in terms of approximate identities and than we call in translations on the sphere as rotations. This leads to the construction of an orthogonal polynomial system in L²(SO(n+1)). That approach is convenient to construct concrete wavelets, since the appropriate kernels can be constructed form the heat kernel leading to the approximate Identity of Gauss-Weierstra\ss. We will work out conditions to functions forming a family of wavelets, subsequently we formulate how we can construct zonal wavelets from a approximate Identity and the relation to admissibility of nonzonal wavelets. Eventually we will give an example of a nonzonal Wavelet on \$S^n\$, which we obtain from the approximate identity of Gauss-Weierstraß.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{EckardtKoenke,
  author    = {Eckardt, Stefan and K{\"o}nke, Carsten},
  title     = {ENERGY RELEASE CONTROL FOR NONLINEAR MESOSCALE SIMULATIONS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2841},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28414},
  pages     = {5},
  abstract  = {In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Eriksson,
  author    = {Eriksson, Sirkka-Liisa},
  title     = {MEAN VALUE PROPERTIES FOR THE WEINSTEIN EQUATION AND MODIFIED DIRAC OPERATORS},
  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.2762},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27621},
  pages     = {16},
  abstract  = {We study the Weinstein equation u on the upper half space R3+. The Weinstein equation is connected to the axially symmetric potentials. We compute solutions of the Weinstein equation depending on the hyperbolic distance and x2. These results imply the explicit mean value properties. We also compute the fundamental solution. The main tools are the hyperbolic metric and its invariance properties.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{FerreiraVieira,
  author    = {Ferreira, Milton dos Santos and Vieira, Nelson},
  title     = {EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS},
  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.2796},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27968},
  pages     = {6},
  abstract  = {Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developedin [3]. We compute the fundamental solution for the three-parameter fractional Laplace operator Δ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to [3] where it is also presented an operational approach based on the two Laplace transform.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{FlaigApel,
  author    = {Flaig, Thomas and Apel, Thomas},
  title     = {SIMULATION AND MATHEMATICAL OPTIMIZATION OF THE HYDRATION OF CONCRETE FOR AVOIDING THERMAL CRACKS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2842},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28424},
  pages     = {15},
  abstract  = {After mixing of concrete, the hardening starts by an exothermic chemical reaction known as hydration. As the reaction rate depends on the temperature the time in the description of the hydration is replaced by the maturity which is defined as an integral over a certain function depending on the temperature. The temperature distribution is governed by the heat equation with a right hand side depending on the maturity and the temperature itself. We compare of the performance of different time integration schemes of higher order with an automatic time step control. The simulation of the heat distribution is of importance as the development of mechanical properties is driven by the hydration. During this process it is possible that the tensile stresses exceed the tensile strength and cracks occur. The goal is to produce cheap concrete without cracks. Simple crack-criterions use only temperature differences, more involved ones are based on thermal stresses. If the criterion predicts cracks some changes in the input data are needed. This can be interpreted as optimization. The final goal will be to adopt model based optimization (in contrast to simulation based optimization) to the problem of the hydration of young concrete and the avoidance of cracks. The first step is the simulation of the hydration, which we focus in this paper.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Franssens,
  author    = {Franssens, Ghislain R.},
  title     = {INTRODUCTION TO CLIFFORD ANALYSIS OVER PSEUDO-EUCLIDEAN SPACE},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2843},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28433},
  pages     = {16},
  abstract  = {An introduction is given to Clifford Analysis over pseudo-Euclidean space of arbitrary signature, called for short Ultrahyperbolic Clifford Analysis (UCA). UCA is regarded as a function theory of Clifford-valued functions, satisfying a first order partial differential equation involving a vector-valued differential operator, called a Dirac operator. The formulation of UCA presented here pays special attention to its geometrical setting. This permits to identify tensors which qualify as geometrically invariant Dirac operators and to take a position on the naturalness of contravariant and covariant versions of such a theory. In addition, a formal method is described to construct the general solution to the aforementioned equation in the context of covariant UCA.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{FroebelFirmenichKoch,
  author    = {Fr{\"o}bel, Toni and Firmenich, Berthold and Koch, Christian},
  title     = {COUPLING PATTERNS IN CIVIL ENGINEERING APPLICATIONS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2844},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28443},
  pages     = {15},
  abstract  = {Buildings can be divided into various types and described by a huge number of parameters. Within the life cycle of a building, especially during the design and construction phases, a lot of engineers with different points of view, proprietary applications and data formats are involved. The collaboration of all participating engineers is characterised by a high amount of communication. Due to these aspects, a homogeneous building model for all engineers is not feasible. The status quo of civil engineering is the segmentation of the complete model into partial models. Currently, the interdependencies of these partial models are not in the focus of available engineering solutions. This paper addresses the problem of coupling partial models in civil engineering. According to the state-of-the-art, applications and partial models are formulated by the object-oriented method. Although this method solves basic communication problems like subclass coupling directly it was found that many relevant coupling problems remain to be solved. Therefore, it is necessary to analyse and classify the relevant coupling types in building modelling. Coupling in computer science refers to the relationship between modules and their mutual interaction and can be divided into different coupling types. The coupling types differ on the degree by which the coupled modules rely upon each other. This is exemplified by a general reference example from civil engineering. A uniform formulation of coupling patterns is described analogously to design patterns, which are a common methodology in software engineering. Design patterns are templates for describing a general reusable solution to a commonly occurring problem. A template is independent of the programming language and the operating system. These coupling patterns are selected according to the specific problems of building modelling. A specific meta-model for coupling problems in civil engineering is introduced. In our meta-model the coupling patterns are a semantic description of a specific coupling design.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{GhorashiRabczukRodenasGarciaetal.,
  author    = {Ghorashi, Seyed Shahram and Rabczuk, Timon and R{\´o}denas Garc{\´i}a, Juan Jos{\´e} and Lahmer, Tom},
  title     = {T-SPLINE BASED XIGA FOR ADAPTIVE MODELING OF CRACKED BODIES},
  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.2763},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27637},
  pages     = {13},
  abstract  = {Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{GokceBrowneGokceetal.,
  author    = {Gokce, Hasan Ufuk and Browne, Donal and Gokce, Kamil Umut and Menzel, Karsten},
  title     = {IMPROVING ENERGY EFFICIENT OPERATION OF BUILDINGS WITH WIRELESS IT 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.2845},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28453},
  pages     = {19},
  abstract  = {Reducing energy consumption is one of the major challenges for present day and will continue for future generations. The emerging EU directives relating to energy (EU EPBD and the EU Directive on Emissions Trading) now place demands on building owners to rate the energy performance of their buildings for efficient energy management. Moreover European Legislation (Directive 2006/32/EC) requires Facility Managers to reduce building energy consumption and operational costs. Currently sophisticated building services systems are available integrating off-the-shelf building management components. However this ad-hoc combination presents many difficulties to building owners in the management and upgrade of these systems. This paper addresses the need for integration concepts, holistic monitoring and analysis methodologies, life-cycle oriented decision support and sophisticated control strategies through the seamless integration of people, ICT-devices and computational resources via introducing the newly developed integrated system architecture. The first concept was applied to a residential building and the results were elaborated to improve current building conditions.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{GonzalezCalvet,
  author    = {Gonzalez Calvet, Ramon},
  title     = {NEW FOUNDATIONS FOR GEOMETRIC ALGEBRA},
  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.2764},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27644},
  pages     = {12},
  abstract  = {New foundations for geometric algebra are proposed based upon the existing isomorphisms between geometric and matrix algebras. Each geometric algebra always has a faithful real matrix representation with a periodicity of 8. On the other hand, each matrix algebra is always embedded in a geometric algebra of a convenient dimension. The geometric product is also isomorphic to the matrix product, and many vector transformations such as rotations, axial symmetries and Lorentz transformations can be written in a form isomorphic to a similarity transformation of matrices. We collect the idea that Dirac applied to develop the relativistic electron equation when he took a basis of matrices for the geometric algebra instead of a basis of geometric vectors. Of course, this way of understanding the geometric algebra requires new definitions: the geometric vector space is defined as the algebraic subspace that generates the rest of the matrix algebra by addition and multiplication; isometries are simply defined as the similarity transformations of matrices as shown above, and finally the norm of any element of the geometric algebra is defined as the nth root of the determinant of its representative matrix of order n×n. The main idea of this proposal is an arithmetic point of view consisting of reversing the roles of matrix and geometric algebras in the sense that geometric algebra is a way of accessing, working and understanding the most fundamental conception of matrix algebra as the algebra of transformations of multilinear quantities.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Grigor'ev,
  author    = {Grigor'ev, Yuri},
  title     = {REGULAR QUATERNIONIC FUNCTIONS AND THEIR APPLICATIONS},
  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.2798},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27988},
  pages     = {6},
  abstract  = {The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given.},
  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}
}
@techreport{GrossBeckmann2008,
  author    = {Gross, Tom and Beckmann, Christoph},
  title     = {CoLocScribe: A Media Space for Information Disclosure in Storytelling},
  doi       = {10.25643/bauhaus-universitaet.1361},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20081103-14361},
  year      = {2008},
  abstract  = {Digital storytelling of remote social interaction, where the situation of a remote group distributed over two locations is captured and a story is generated for later retrieval, can provide valuable insight into the structure and processes in a group. Yet, capturing these situations is a challenge—both from a technical perspective, and from a social perspective. In this paper we present CoLocScribe: a concept and prototype of an advanced media space featuring ubiquitous computing technology for capturing remote social interaction as well as a study of its use providing valuable feedback for the captured persons as well as input for the authors.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@techreport{GrossEglaMarquardt2006,
  author    = {Gross, Tom and Egla, Tareg and Marquardt, Nicolai},
  title     = {Sens-ation: A Service-Oriented Platform for Developing Sensor-Based Infrastructures},
  doi       = {10.25643/bauhaus-universitaet.744},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-7447},
  year      = {2006},
  abstract  = {In today's information society the vast technical progress and the sinking cost of information and communication technology provide new opportunities for information supply, and new technical support for communication and cooperation over distance. These trends also entail challenges such as supplying information that is adequate for a particular person in a specific situation as well as managing communication among geographically distributed parties efficiently. Context-aware systems that use sensors in order to analyse their environment and to adapt their behaviour. Yet, adequate tools for developing sensor-based infrastructures are missing. We have designed and developed Sens-ation, an open and generic service-oriented platform, which provides powerful, yet easy-to-use, tools to software developers who want to develop context-aware, sensor-based infrastructures. The service-oriented paradigm of Sens-ation enables standardised communication within individual infrastructures, between infrastructures and their sensors, but also among distributed infrastructures. On a whole, Sens-ation facilitates the development allowing developers to concentrate on the semantics of their infrastructures, and to develop innovative concepts and implementations of context-aware systems.},
  subject      = {Angewandte Informatik},
  language  = {en}
}