@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{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{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{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{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{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{GutierrezSRamirezRodriguezetal.,
  author    = {Gutierrez S, Andrei and Ramirez, Marco P. and Rodriguez, Octavio and Sanchez N., V.D.},
  title     = {ON THE SOLUTIONS OF ELECTRICAL IMPEDANCE EQUATION: A PSEUDOANALYTIC APPROACH FOR SEPARABLE-VARIABLES CONDUCTIVITY FUNCTION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2847},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28478},
  pages     = {11},
  abstract  = {Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.},
  subject      = {Angewandte Informatik},
  language  = {en}
}