@inproceedings{LopesRodriguesVilaReal,
  author    = {Lopes, Nuno and Rodrigues, Daniela and Vila Real, Paulo},
  title     = {ANALYSIS OF STEEL STRUCTURAL MEMBERS IN FIRE WITH SLENDER CROSS-SECTIONS THROUGH BEAM FINITE ELEMENTS APPLYING AN EFFECTIVE CONSTITUTIVE LAW},
  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.2811},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28116},
  pages     = {6},
  abstract  = {Steel profiles with slender cross-sections are characterized by their high susceptibility to instability phenomena, especially local buckling, which are intensified under fire conditions. This work presents a study on numerical modelling of the behaviour of steel structural elements in case of fire with slender cross-sections. To accurately carry out these analyses it is necessary to take into account those local instability modes, which normally is only possible with shell finite elements. However, aiming at the development of more expeditious methods, particularly important for analysing complete structures in case of fire, recent studies have proposed the use of beam finite elements considering the presence of local buckling through the implementation of a new effective steel constitutive law. The objective of this work is to develop a study to validate this methodology using the program SAFIR. Comparisons are made between the results obtained applying the referred new methodology and finite element analyses using shell elements. The studies were made to laterally restrained beams, unrestrained beams, axially compressed columns and columns subjected to bending plus compression.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Rodrigues,
  author    = {Rodrigues, M. Manuela},
  title     = {OPERATIONAL PROPERTIES OF THE LAGUERRE TRANSFORM},
  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.2818},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28186},
  pages     = {5},
  abstract  = {The Laguerre polynomials appear naturally in many branches of pure and applied mathematics and mathematical physics. Debnath introduced the Laguerre transform and derived some of its properties. He also discussed the applications in study of heat conduction and to the oscillations of a very long and heavy chain with variable tension. An explicit boundedness for some class of Laguerre integral transforms will be present.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Karaki,
  author    = {Karaki, Ghada},
  title     = {SELECTION AND SCALING OF GROUND MOTION RECORDS FOR SEISMIC ANALYSIS USING AN OPTIMIZATION ALGORITHM},
  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.2805},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28058},
  pages     = {7},
  abstract  = {The nonlinear time history analysis and seismic performance based methods require a set of scaled ground motions. The conventional procedure of ground motion selection is based on matching the motion properties, e.g. magnitude, amplitude, fault distance, and fault mechanism. The seismic target spectrum is only used in the scaling process following the random selection process. Therefore, the aim of the paper is to present a procedure to select a sets of ground motions from a built database of ground motions. The selection procedure is based on running an optimization problem using Dijkstra's algorithm to match the selected set of ground motions to a target response spectrum. The selection and scaling procedure of optimized sets of ground motions is presented by examining the analyses of nonlinear single degree of freedom systems.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{KrausshardeAlmeida,
  author    = {Kraußhar, Rolf S{\"o}ren and de Almeida, Regina},
  title     = {FUNDAMENTALS OF A WIMAN VALIRON THEORY FOR POLYMONOGENIC FUNCTIONS},
  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.2810},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28100},
  pages     = {6},
  abstract  = {In this paper we present some rudiments of a generalized Wiman-Valiron theory in the context of polymonogenic functions. In particular, we analyze the relations between different notions of growth orders and the Taylor coefficients. Our main intention is to look for generalizations of the Lindel¨of-Pringsheim theorem. In contrast to the classical holomorphic and the monogenic setting we only obtain inequality relations in the polymonogenic setting. This is due to the fact that the Almansi-Fischer decomposition of a polymonogenic function consists of different monogenic component functions where each of them can have a totally different kind of asymptotic growth behavior.},
  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{MiroHartmannSchanzetal.,
  author    = {Miro, Shorash and Hartmann, Dietrich and Schanz, Tom and Zarev, Veselin},
  title     = {SYSTEM IDENTIFICATION METHODS FOR GROUND MODELS IN MECHANIZED TUNNELING},
  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.2777},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27771},
  pages     = {13},
  abstract  = {Due to the complex interactions between the ground, the driving machine, the lining tube and the built environment, the accurate assignment of in-situ system parameters for numerical simulation in mechanized tunneling is always subject to tremendous difficulties. However, the more accurate these parameters are, the more applicable the responses gained from computations will be. In particular, if the entire length of the tunnel lining is examined, then, the appropriate selection of various kinds of ground parameters is accountable for the success of a tunnel project and, more importantly, will prevent potential casualties. In this context, methods of system identification for the adaptation of numerical simulation of ground models are presented. Hereby, both deterministic and probabilistic approaches are considered for typical scenarios representing notable variations or changes in the ground model.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Schmeikal,
  author    = {Schmeikal, Bernd Anton},
  title     = {BAUHAUS ISOMETRY AND FIELDS},
  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.2785},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27859},
  pages     = {9},
  abstract  = {While integration increases by networking, segregation strides ahead too. Most of us fixate our mind on special topics. Yet we are relying on our intuition too. We are sometimes waiting for the inflow of new ideas or valuable information that we hold in high esteem, although we are not entirely conscious of its origin. We may even say the most precious intuitions are rooting in deep subconscious, collective layers of the mind. Take as a simple example the emergence of orientation in paleolithic events and its relation to the dihedral symmetry of the compass. Consider also the extension of this algebraic matter into the operational structures of the mind on the one hand and into the algebra of geometry, Clifford algebra as we use to call it today, on the other. Culture and mind, and even the individual act of creation may be connected with transient events that are subconscious and inaccessible to cognition in principle. Other events causative for our work may be merely invisible too us, though in principle they should turn out attainable. In this case we are just ignorant of the whole creative process. Sometimes we begin to use unusual tools or turn into handicraft enthusiasts. Then our small institutes turn into workshops and factories. All this is indeed joining with the Bauhaus and its spirit. We shall go together into this, and we shall present a record of this session.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{CastilloPerezCedilloDiazKravchenkoetal.,
  author    = {Castillo-P{\´e}rez, Ra{\´u}l and Cedillo - D{\´i}az, A. del C. and Kravchenko, Vladislav and Oviedo - Galdeano, H.},
  title     = {COMPUTATION OF THE REFLECTANCE AND TRANSMITTANCE FOR AN INHOMOGENEOUS LAYERED MEDIUM WITH TURNING POINT S USING THE WKB AND SPPS METHODS},
  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.2759},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170306-27598},
  pages     = {16},
  abstract  = {Electromagnetic wave propagation is currently present in the vast majority of situations which occur in veryday life, whether in mobile communications, DTV, satellite tracking, broadcasting, etc. Because of this the study of increasingly complex means of propagation of lectromagnetic waves has become necessary in order to optimize resources and increase the capabilities of the devices as required by the growing demand for such services. Within the electromagnetic wave propagation different parameters are considered that characterize it under various circumstances and of particular importance are the reflectance and transmittance. There are several methods or the analysis of the reflectance and transmittance such as the method of approximation by boundary condition, the plane wave expansion method (PWE), etc., but this work focuses on the WKB and SPPS methods. The implementation of the WKB method is relatively simple but is found to be relatively efficient only when working at high frequencies. The SPPS method (Spectral Parameter Powers Series) based on the theory of pseudoanalytic functions, is used to solve this problem through a new representation for solutions of Sturm Liouville equations and has recently proven to be a powerful tool to solve different boundary value and eigenvalue problems. Moreover, it has a very suitable structure for numerical implementation, which in this case took place in the Matlab software for the valuation of both conventional and turning points profiles. The comparison between the two methods allows us to obtain valuable information about their perfor mance which is useful for determining the validity and propriety of their application for solving problems where these parameters are calculated in real life applications.},
  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{LiuLeimbachHartmann,
  author    = {Liu, Xiangqin and Leimbach, Robert and Hartmann, Dietrich},
  title     = {SYSTEM IDENTIFICATION OF A WIND TURBINE STRUCTURE USING ROBUST MODEL UPDATING STRATEGY},
  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.2774},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27744},
  pages     = {11},
  abstract  = {This paper presents a robust model updating strategy for system identification of wind turbines. To control the updating parameters and to avoid ill-conditioning, the global sensitivity analysis using the elementary effects method is conducted. The formulation of the objective function is based on M¨uller-Slany's strategy for multi-criteria functions. As a simulationbased optimization, a simulation adapter is developed to interface the simulation software ANSYS and the locally developed optimization software MOPACK. Model updating is firstly tested on the beam model of the rotor blade. The defect between the numerical model and the reference has been markedly reduced by the process of model updating. The effect of model updating becomes more pronounced in the comparison of the measured and the numerical properties of the wind turbine model. The deviations of the frequencies of the updated model are rather small. The complete comparison including the free vibration modes by the modal assurance criteria shows the excellent coincidence of the modal parameters of the updated model with the ones from the measurements. By successful implementation of the model validation via model updating, the applicability and effectiveness of the solution concept has been demonstrated.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{MusialUbyszUlatowski,
  author    = {Musial, Michal and Ubysz, Andrzej and Ulatowski, Piotr},
  title     = {MODEL DESCRIBING STATIC AND DYNAMIC DISPLACEMENTS OF SILOS WALL DURING THE FLOW OF LOOSE MATERIAL},
  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.2789},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27896},
  pages     = {16},
  abstract  = {Correct evaluation of wall displacements is a key matter when designing silos. This issue is important from both the standpoint of design engineer (load-bearing capacity of structures) and end-consumer (durability of structures). Commonplace methods of silo design mainly focus on satisfying limit states of load-bearing capacity. Current standards fail to specify methods of dynamic displacements analysis. Measurements of stressacting on silo walls prove that the actual stress is sum of static and dynamic stresses. Janssen came up with differential equation describing state of static equilibrium in cross-section of a silo. By solving the equation static stress of granular solid on silo walls can be determined. Equations of motion were determined from equilibrium equations of feature objects. General solution, describing dynamic stresses was presented as parametric model. This paper presents particular integrals of differential equation, which enable analysing displacements and vibrations for different rigidities of silo walls, types of granular solid and its flow rate.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Karaki,
  author    = {Karaki, Ghada},
  title     = {DEPENDENCY OF THE INFLUENCE OF INPUT PARAMETERS OF BVI MODELS ON THE INITIAL EXCITATIONS AND SPEED RANGES},
  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.2767},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27675},
  pages     = {13},
  abstract  = {Bridge vibration due to traffic loading has been subject of extensive research in the last decades. Such studies are concerned with deriving solutions for the bridge-vehicle interaction (BVI) and analyzing the dynamic responses considering randomness of the coupled model's (BVI) input parameters and randomness of road unevenness. This study goes further to examine the effects of such randomness of input parameters and processes on the variance of dynamic responses in quantitative measures. The input parameters examined in the sensitivity analysis are, stiffness and damping of vehicle's suspension system, axle spacing, and stiffness and damping of bridge. This study also examines the effects of the initial excitation of a vehicle on the influences of the considered input parameters. Variance based sensitivity analysis is often applied to deterministic models. However, the models for the dynamic problem is a stochastic one due to the simulations of the random processes. Thus, a setting using a joint meta-model; one for the mean response and other for the dispersion of the response is developed. The joint model is developed within the framework of Generalized Linear Models (GLM). An enhancement of the GLM procedure is suggested and tested; this enhancement incorporates Moving Least Squares (MLS) approximation algorithms in the fitting of the mean component of the joint model. The sensitivity analysis is then performed on the joint-model developed for the dynamic responses caused by BVI.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{MoraisGeorgiev,
  author    = {Morais, Joao and Georgiev, Svetlin},
  title     = {COMPLETE ORTHOGONAL SYSTEMS OF 3D SPHEROIDAL MONOGENICS},
  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.2778},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27785},
  pages     = {14},
  abstract  = {In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil Th{\´e}odoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szeg{\"o} kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szeg{\"o} kernel function over 3D prolate spheroids.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{MusialKamińskiUbysz,
  author    = {Musial, Michal and Kamiński, Mieczysław and Ubysz, Andrzej},
  title     = {DISCRETE CRACK MODEL OF BORCZ FOR CALCULATING THE DEFLECTIONS OF BENDING REINFORCED CONCRETE BEAM},
  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.2790},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27907},
  pages     = {11},
  abstract  = {In the design of the reinforced concrete beams loaded by the bending moment, it is assumed that the structure can be used at a level of load, that there are local discontinuities - cracks. Designing the element demands checking two limit states of construction, load capacity and usability. Limit states usability include also the deflection of the element. Deflections in the reinforced concrete beams with cracks are based on actual rigidity of the element. After cracking there is a local change in rigidity of the beam. The rigidity is variable in the element's length and due to the heterogeneous structure of concrete, it is not possible to clearly describe those changes. Most standards of testing methods tend to simplify the calculations and take the average value of the beam's rigidity on its entire length. The rigidity depends on the level of the maximal load of the beam. Experimental researches verify the value by inserting the coefficients into the formulas used in the theory of elasticity. The researches describe the changes in rigidity in the beam's length more precisely. The authors take into consideration the change of rigidity, depending on the level of maximum load (continuum models), or localize the changes in rigidity in the area of the cracks (discrete models). This paper presents one of the discrete models. It is distinguished by the fact that the left side of the differential equation, that depends on the rigidity, is constant, and all effects associated with the scratches are taken as the external load and placed on the right side of the equation. This allows to generalize the description. The paper presents a particular integral of the differential equation, which allow analyzing the displacement and vibration for different rigidity of the silo's walls, the flow rate and type of the flowing material.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{MusialUbysz,
  author    = {Musial, Michal and Ubysz, Andrzej},
  title     = {ROTATIONAL DUCTILITY OF CRACK IN STATIC AND DYNAMIC CALCULATIONS OF REINFORCED CONCRETE BAR STRUCTURES},
  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.2781},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27813},
  pages     = {9},
  abstract  = {In this paper experimental studies and numerical analysis carried out on reinforced concrete beam are partially reported. They aimed to apply the rigid finite element method to calculations for reinforced concrete beams using discrete crack model. Hence rotational ductility resulting from crack occurrence had to be determined. A relationship for calculating it in static equilibrium was proposed. Laboratory experiments proved that dynamic ductility is considerably smaller. Therefore scaling of the empirical parameter was carried out. Consequently a formula for its value depending on reinforcement ratio was obtained.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Simsek,
  author    = {Simsek, Yilmaz},
  title     = {ON INTERPOLATION FUNCTION OF THE BERNSTEIN POLYNOMIALS},
  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.2786},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27867},
  pages     = {8},
  abstract  = {The Bernstein polynomials are used for important applications in many branches of Mathematics and the other sciences, for instance, approximation theory, probability theory, statistic theory, num- ber theory, the solution of the di\ierential equations, numerical analysis, constructing Bezier curves, q-calculus, operator theory and applications in computer graphics. The Bernstein polynomials are used to construct Bezier curves. Bezier was an engineer with the Renault car company and set out in the early 1960's to develop a curve formulation which would lend itself to shape design. Engineers may …nd it most understandable to think of Bezier curves in terms of the center of mass of a set of point masses. Therefore, in this paper, we study on generating functions and functional equations for these polynomials. By applying these functions, we investigate interpolation function and many properties of these polynomials.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{SuzukiLawrynowiczNounoetal.,
  author    = {Suzuki, Osamu and Lawrynowicz, Julian and Nouno, Kiyoharu and Nagayama, Daiki},
  title     = {BINARY AND TERNARY CLIFFORD ANALYSIS ON NONION ALGEBRA AND SU(3)},
  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.2788},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27880},
  pages     = {12},
  abstract  = {A concept of non-commutative Galois extension is introduced and binary and ternary extensions are chosen. Non-commutative Galois extensions of Nonion algebra and su(3) are constructed. Then ternary and binary Clifford analysis are introduced for non-commutative Galois extensions and the corresponding Dirac operators are associated.},
  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{Hitzer,
  author    = {Hitzer, Eckhard},
  title     = {THE CLIFFORD FOURIER TRANSFORM IN REAL CLIFFORD ALGEBRAS},
  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.2765},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27652},
  pages     = {11},
  abstract  = {We briefly review and use the recent comprehensive research on the manifolds of square roots of -1 in real Clifford geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the complex imaginary unit j is replaced by a square root of -1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs, which replaced the complex imaginary unit j only by blades (usually pseudoscalars) squaring to -1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w -shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Krausshar,
  author    = {Kraußhar, Rolf S{\"o}ren},
  title     = {SOME HARMONIC ANALYSIS ON M{\"O}BIUS STRIP DOMAINS AND THE KLEIN BOTTLE IN Rn},
  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.2769},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27692},
  pages     = {10},
  abstract  = {The aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional M{\"o}bius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds.},
  subject      = {Angewandte Informatik},
  language  = {en}
}