Publications

2024

  • S. Kraußhar, A. Legatiuk, D. Legatiuk, Hardy spaces of monogenic and discrete monogenic functions revisited on octonionic half-space, under review.
  • D. Luckey, D. Legatiuk, Meta-metamodelling in Automation Construction by Help of Abstract Mathematics, under review.
  • S. Kraußhar, A. Legatiuk, D. Legatiuk, Application of the Weyl calculus perspective on discrete octonionic analysis in bounded domains, under review.
  • K. Gürlebeck, A. Legatiuk, Discrete Borel-Pompeiu and Cauchy formulae on a rectangular lattice for bounded domains in $\mathbb{R}^{2}$, Research Perspectives: Ghent Analysis and PDE Center, Springer.
  • R.S. Kraußhar, A. Legatiuk, D. Legatiuk, The discrete octonionic Stokes’ formula revisited, Research Perspectives: Ghent Analysis and PDE Center, Springer.
  • R.S. Kraußhar, D. Legatiuk, Cauchy formulae and Hardy spaces in discrete octonionic analysis, Complex Analysis and Operator Theory, 18:23.

  • D. Legatiuk, Mathematical modelling by help of category theory, Habilitation thesis, Bauhaus-Universität Weimar. DOI: 10.25643/dbt.62110

     

2023

  • R.S. Kraußhar, D. Legatiuk, Weyl calculus perspective on the discrete Stokes' formula in octonions, Lecture Notes in Computer Science, 14498.
  • P. Cerejeiras, U. Kähler, R.S. Kraußhar, Variational principles in quaternionic analysis with applications to the stationary MHD equations, under review.
  • F. Colombo, R.S. Kraußhar, I. Sabadini, Y. Simsek, On the generating functions and special functions associated with superoscillations, under review.
  • F. Colombo, R.S. Kraußhar, S. Pinton, I. Sabadini, Entire monogenic functions of given proximate order and continuous homomorphisms, under review.
  • F. Colombo, R.S. Kraußhar, I. Sabadini, Octonionic monogenic and slice monogenic Hardy and Bergman spaces, under review.
  • R.S. Kraußhar, A. Legatiuk, D. Legatiuk, Towards discrete octonionic analysis, In:
    V. Vasilyev (Ed.), Differential Equations, Mathematical Modeling and Computational Algorithms, Springer, 2023.
  • D. Legatiuk, D. Luckey, Formalising autonomous construction sites by help of abstract mathematics, Eng, 4(1), 799-815. Online available on: https://www.mdpi.com/2673-4117/4/1/48
  • R. Möller, P. Collignon, Towards a Philosophy of Algorithms as an Element of Mathematics Education. To appear in: Aparecida Viggiani Bicudo, Maria; Czarnocha, Bronislaw;  Rosa, Mauricio & Marciniak, Małgorzata (Eds.) (2023): Ongoing Advancements in Philosophy of Mathematics Education. Berlin, Heidelberg: Springer Nature.

2022

  • S. Bernstein, D. Legatiuk, Brownian motion, martingales and Itô formula in Clifford analysis, Advances in Applied Clifford Algebras, 32, Article number: 27.
  • F. Colombo, R.S. Kraußhar, I. Sabadini, Slice-monogenic theta series, Indiana University Journal of Mathematics, accepted for publication.
    Preprint available on: https://www.mate.polimi.it/collezioni-digitali-di-dipartimento
  • K. Gürlebeck, D. Legatiuk, K. Webber, Operator calculus approach to comparison of elasticity models for modelling of masonry structures, Mathematics, 10(10), 1670.
  • R.S. Kraußhar, The Cauchy transform and Kerzman-Stein Theory revisited in the octonionic monogenic setting, AIP Conference Proceedings.
  • R.S. Kraußhar, D. Legatiuk, B. Schneider, T. Truong, A Dynamic Derivative for Fuzzy-Valued Functions, AIP Conference Proceedings.
  • R.S. Kraußhar, A. Perotti, Eigenvalue problems for slice functions, Annali di Matematica Pura ed Applicata, 201, 2519–2548.
  • A. Legatiuk, Discrete potential and function theories on a rectangular lattice and their applications, PhD thesis, Bauhaus-Universität Weimar, 2022.
  • R. Möller, K. Eilerts, P. Collignon, S. Beyer, Zur aktuellen Bedeutung von Algorithmen im Mathematikunterricht - Perspektiven der Digitalisierung. In: Eilerts, Katja; Möller, Regina D. & Huhmann, Tobias (Hrsg.) Auf dem Weg zum Neuen - Mathematikunterricht 2.0. Berlin, Heidelberg: Springer, 2022.

2021

  • P. Cerejeiras, U. Kähler, A. Legatiuk, D. Legatiuk, Discrete Hardy spaces for bounded domains in $\mathbb{R}^{n}$, Complex Analysis and Operator Theory, 15(4).
  • D. Constales, R.S. Kraußhar, Octonionic Kerzman-Stein operators, Complex Analysis and Operator Theory, 15(6),  Paper No. 104.
  • H. Fritz, J. Peralta, D. Legatiuk, M. Steiner, K. Dragos, K. Smarsly, Fault diagnosis in structural health monitoring systems using signal processing and machine learning techniques, Structural health monitoring based on data science techniques, Springer.
  • K. Gürlebeck, A. Hommel, A. Legatiuk, Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, Mathematical Methods in the Applied Science, 1-23. DOI:  doi.org/10.1002/mma.7747
  • R.S. Kraußhar, Recent and new results on octonionic Bergman and Szegö kernels, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.7316
  • R.S. Kraußhar, Function Theories in Cayley-Dickson algebras and Number Theory, Milan Journal of Mathematics, 89(1).
  • D. Legatiuk, Mathematical modelling by help of category theory: models and relations between them, Mathematics, 9(16), 1946.
  • D. Legatiuk, D. Weisz-Patrault, Coupling of complex function theory and finite element method for crack propagation through energetic formulation: conformal mapping approach and reduction to a Riemann-Hilbert problem, Computational Methods and Function Theory, DOI: 10.1007/s40315-021-00403-7.
  • D. Luckey, H. Fritz, D. Legatiuk, J. Peralta, C. Walther, K. Smarsly, Explainable artificial intelligence to advance structural health monitoring,  Structural health monitoring based on data science techniques, Springer.

2020

  • F. Colombo, R.S. Kraußhar, I. Sabadini, Symmetries of slice monogenic functions, Journal of Non-Commutative Geometry, 14(3), 1075-1106.
  • K. Gürlebeck, A. Hommel, A. Legatiuk, Geometry discretisation algorithm for discrete potential and function theories, AIP Conference Proceedings 2293, 110001.
  • R.S. Kraußhar, Differential Topological Aspects in Octonionic Monogenic Function Theory, Advances in Applied Clifford Algebras, 30(4), Paper No. 51.
  • R.S. Kraußhar, Conformal Mappings Revisited in the Octonions and Clifford Algebras in Arbitrary Dimension, Advances in Applied Clifford Algebras, 30(3), Paper No. 36.
  • D. Legatiuk, K. Lossev, K. Smarsly, A. Volkov, Abstract life-cycle modeling of cyber-physical systems in civil engineering, Proceedings of European Conference on Product and Process Modelling (ECPPM), Moscow, Russia.
  • M. Theiler, S. Ibanez, D. Legatiuk, K. Smarsly, Metaization concepts for monitoring-related information, Advanced Engineering Informatics, 46, 101158.
  • D. Luckey, H. Fritz, D. Legatiuk, K. Dragos, K. Smarsly, Artificial intelligence techniques for smart city applications, Lecture Notes in Civil Engineering, 98, pp. 3-15.

2019

  • S. Bock, D. Legatiuk, Constructive orthonormalisation of monogenic polynomials on a finite cylinder, Topics in Clifford Analysis, Springer series "Trends in Mathematics", pp. 235-250.
  • P. Cerejeiras, U. Kähler, R.S. Kraußhar, Applications of parabolic Dirac operators to the instationary MHD equations on conformally flat manifolds, Topics in Clifford Analysis, Springer series "Trends in Mathematics", 173-190.
  • P. Cerejeiras, U. Kähler, A. Legatiuk, D. Legatiuk, Boundary values of discrete monogenic functions over bounded domains in $\mathbb{R}^{3}$, Operator Theory: Advances and Applications, Vol. 275, pp. 149-165.
  • P. Cerejeiras, U. Kähler, D. Legatiuk, Finite element exterior calculus with script geometry, AIP Conference Proceedings, 2116.
  • K. Diki, R.S. Kraußhar,  I. Sabadini, On the Bargmann-Fock-Fueter and Bergman Fueter integral transforms, Journal of Mathematical Physics, 60(8):083506.
  • M. Ferreira, R.S. Kraußhar, M.M. Rodrigues, N. Vieira, A higher dimensional fractional Borel-Pompeiu formula and a related hypercomplex fractional operator calculus, Mathematical Methods in the Applied Sciences, 42(10), 3633-3653.
  • Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, On quaternionic functions for the solution of an ill-posed Cauchy problem for a viscous fluid, AIP Conference Proceedings, 2116:1.
  • K. Gürlebeck, A. Hommel, A. Legatiuk, Numerical modelling of an induction heating problem, AIP Conference Proceedings 2116, 160002 (2019); doi: 10.1063/1.5114146.
  • K. Gürlebeck, D. Legatiuk, Quaternionic operator calculus for boundary value problems of micropolar elasticity, Topics in Clifford Analysis, Springer series "Trends in Mathematics", pp. 221-234.
  • K. Gürlebeck, D. Legatiuk, H. Nilsson, K. Smarsly, Conceptual modelling: towards detecting modelling errors in engineering applications, Mathematical Methods in the Applied Sciences, 43(3), pp. 1243-1252.
  • I. Kavrakov, D. Legatiuk, K. Gürlebeck, G. Morgenthal, A categorical perspective towards aerodynamic models for aeroelastic analyses of bridges, Royal Society Open Science, 6: 181848.
  • R.S. Kraußhar, Automorphic Forms and Dirac operators on Conformally Flat Manifolds, Topics in Clifford Analysis, Springer series "Trends in Mathematics", 331-345.
  • R. Möller, P. Collignon, On the Historical Development of Algorithms – Hidden in Technical Devices? Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. Available online
  • K. Smarsly, T. Fitz, D. Legatiuk, Metamodeling wireless communication in cyber-physical systems, The 26th International Workshop on Intelligent Computing in Engineering (EG-ICE)At: Leuven, Belgium.
  • M. Steiner, D. Legatiuk, K. Smarsly, A support vector regression-based approach towards decentralized fault diagnosis in wireless structural health monitoring systems, Proceedings of the 12th International Workshop on Structural Health Monitoring (IWSHM). Stanford, CA, USA, September 12, 2019.

2018

  • L. Abrahamczyk, Z. Jaouadi, U. Kähler, D. Legatiuk, Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten, Bautechnik, 95(7), pp. 485-493.
  • P. Cerejeiras, U. Kähler, R.S. Kraußhar, Some applications of parabolic Dirac operators to the instationary Navier-Stokes problem on conformally flat cylinders and tori in R3. Clifford Analysis and Related Topics CART 2014. Springer Proceedings in Mathematics & Statistics 260, 19-37.
  • P. Cerejeiras, U. Kähler, D. Legatiuk, Interpolation of monogenic functions by using reproducing kernel Hilbert spaces, Mathematical Methods in the Applied Sciences, 41(17), pp. 8100-8114.
  • R. De Almeida, R.S. Kraußhar, Wiman-Valiron theory for higher dimensional polynomial Cauchy-Riemann equations, Mathematical Methods in the Applied Sciences, 41(1), 15-27.
  • M. Ferreira, R.S. Kraußhar, M.M. Rodrigues, N. Vieira, Application of the hypercomplex fractional integro-differential operators to the fractional Stokes equation, AIP Conference Proceedings, 2116(1): 160004.
  • Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, Quaternionic formulation of a Cauchy problem for the Lamé equation, AIP Conference Proceedings, 1978 (1), 280007.
  • K. Gürlebeck, A. Hommel, A. Legatiuk, Methods of discrete potential theory for an induction heating problem, AIP Conference Proceeding 1978, 280003 (2018); doi: 10.1063/1.5043903.
  • A. Legatiuk, K. Gürlebeck, A. Hommel, The discrete Borel-Pompeiu formula on a rectangular lattice, Advances in Applied Clifford Algebras, 28(69), doi: 10.1007/s00006-018-0887-2
  • D. Legatiuk, K. Smarsly, An abstract approach towards modeling intelligent structural systems, Proceedings of the  European Workshop on Structural Health Monitoring Series (EWSHM). Manchester, UK, July, 2018.

2017

  • R. De Almeida, R.S. Kraußhar, On the growth type of entire solutions to higher dimensional polynomial Cauchy-Riemann equations, AIP Conference Proceedings.
  • Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, Interpolation problem for the solutions of linear elasticity equations based on monogenic functions, AIP Conference proceedings, 1907, 030054, 2017.
  • K. Gürlebeck, D. Hofmann, D. Legatiuk, Categorical approach to modelling and to coupling of models, Mathematical Methods in the Applied Sciences, 40(3), 523-534.
  • K. Gürlebeck, U. Kähler, D. Legatiuk, Error estimates for the coupling of analytical and numerical solutions, Complex Analysis and Operator Theory, 11(5), 1221-1240.
  • K. Gürlebeck, D. Legatiuk, Three-dimensional interpolation with monogenic polynomials, Complex Variables and Elliptic Equations, Vol. 62, pp. 1364-1373.
  • D. Legatiuk, K. Dragos, K. Smarsly,  Modeling and evaluation of cyber-physical systems in civil engineering, Proceedings in Applied Mathematics and Mechanics, 17 (1), pp. 807-808.
  • D. Legatiuk, H. Nilsson, Abstract modelling: towards a typed declarative language for the conceptual modelling phase, Proceedings of 8th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools, Munich, Germany, December 2017 (EOOLT 2017).
  • D. Legatiuk, M. Theiler, K. Dragos, K. Smarsly,  A categorical approach towards metamodeling cyber-physical systems, Proceedings of the 11th International Workshop on Structural Health Monitoring (IWSHM). Stanford, CA, USA, September 12, 2017.
  • R. Möller, P. Collignon, The Concept of Infinity – Different Meanings through the Centuries. CERME 10, Feb 2017, Dublin, Ireland. Available online

2016

  • P. Collignon, Teaching Applied Mathematics as a Bridge from Philosophy of Science to Philosophy of Mathematics Education. In: Ernest, Paul (Ed.): Philosophy of Mathematics Education Journal, 31, 2016. Available online
  • R. De Almeida, R.S. Kraußhar, Generalized growth orders for polymonogenic functions and related inequalities, Complex Analysis an Operator Theory, 10(2), 233-250.
  • L. Göbel, F. Mucha, Z. Jaouadi, I. Kavrakov, D. Legatiuk, L. Abrahamczyk, M. Kraus, K. Smarsly, Monitoring the structural response of reinforced concrete poles along high-speed railway tracks, Proceedings of the International RILEM Conference Materials, Systems and Structures in Civil Engineering, 2016.
  • K. Gürlebeck, D. Legatiuk, On some properties of pseudo-complex polynomials, Modern Trends in Hypercomplex Analysis, Birkhäuser, pp. 217-226.
  • R.S. Kraußhar, M. Rodrigues, N. Vieira, Maximum principle and parabolic inequalities for the regularized Schrödinger operator, Results in Mathematics, 69(1-2), 49-68.
  • R.S. Kraußhar, M. Rodrigues, N. Vieira, Time-dependent operators on some non-orientable projective orbifolds, Mathematical Methods in the Applied Sciences, 38(18), 5305-5319.
  • F. Scheiber, H.B. Motra, D. Legatiuk, F. Werner, Uncertainty-based evaluation and coupling of mathematical and physical models, Probabilistic Engineering Mechanics, 45, pp. 52-60.

2015

  • S. Bock, K. Gürlebeck, D. Legatiuk, H. M. Nguyen, $\psi$-Hyperholomorphic Functions and a Kolosov-Muskhelishvili Formula, Mathematical Methods in the Applied Sciences, 38(18), 5114-5123.
  • P. Collignon, Mathematisches Modellieren in ökonomischen Kontexten – (auch) ein wissenschaftstheoretisches Propädeutikum. In: Mathematikunterricht unter der Perspektive von Tradition, Moderne und Lehrerprofessionalität: Festschrift für Regina Dorothea Möller. Hildesheim: Franzbecker S. 140-147, 2015.
  • P. Collignon, Using Calculus in Economics: Learning from History in Teacher Education. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.1811-1816. Available online
  • R. De Almeida, R.S. Kraußhar, Basics on growth orders of polymonogenic functions, Complex Variables and Elliptic Equations, 60(11), 1480-1504.
  • R. De Almeida, R.S. Kraußhar, Fundamentals of a Wiman Valiron Theory for Polymonogenic Functions, Proceedings of 20th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2015, 20.-22. July 2015, Weimar [eds. K. Gürlebeck, T. Lahmer].
  • D. Grob, R.S. Kraußhar, A Selberg trace formula for hypercomplex analytic cusp forms, Journal of Number Theory, 148 , 398-428.
  • K. Gürlebeck, U. Kähler, D. Legatiuk, Interpolation problem arising in a coupling of finite element method with holomorphic basis functions, AIP Conference proceedings, 1648.
  • R.S. Kraußhar, Dirac and Laplace operators on some non-orientable conformally flat manifolds, Journal of Mathematical Analysis and its Applications, 427(2), 669-685.
  • R.S. Kraußhar, J. Tolksdorf, Applications of hypercomplex automorphic forms in Yang-Mills gauge theories, Complex Analysis and Operator theory, 9, 431-444.
  • D. Legatiuk, Evaluation of the coupling between an analytical and a numerical solution for boundary value problems with singularities. PhD Thesis, Weimar. ISBN: 978-3-95773-193-7.

2014 and earlier

  • H. Albuquerque, R.S. Kraußhar, Multiplicative invariant lattices in Rn obtained by twisting of group algebra and some explicit characterizations, Journal of Algebra, 319(3), 1116-1131, 2008.
  • S. Bernstein, S. Ebert, R.S. Kraußhar, On the diffusion equation and diffusion wavelets on flat cylinders and the n-torus, Mathematical Methods in the Applied Sciences, 34(4), 428-441, 2011.
  • S. Bernstein, S. Ebert, R.S. Kraußhar, Diffusion wavelets on conformally flat cylinders and tori, AIP Conference Proeedings, 1168(2), 773-776, 2009.
  • K. Bringmann, D. Constales, R.S. Kraußhar, Applications of hypercomplex Poincaré series to Bergman spaces, in: Proceedings of the International Conference on Numerical and Applied Mathematics ICNAAM 2004, 10.-14. September 2004, Chalkis, Greece, [eds. T.E. Simos, Ch. Tsitouras], Wiley VCH Weinheim 2004, 490-492. [mit D. Constales] [ISBN 3-527-40563-1]
  • S. Bock, K. Gürlebeck, D. Legatiuk, Convergence of the finite element method with holomorphic functions, AIP Conference proceedings, 1558, 513, 2013.
  • S. Bock, K. Gürlebeck, D. Legatiuk, On the continuous coupling between analytical and finite element solutions, Le Hung Son & Wolfgang Tutschke eds. Interactions between real and complex analysis, 3-19. Science and Technics Publishing House, Hanoi, 2012.
  • S. Bock, K. Gürlebeck, D. Legatiuk, On a special finite element based on holomorphic functions, AIP Conference proceedings, 1479, 308, 2012.
  • S. Bock, K. Gürlebeck, D. Legatiuk, The problem of coupling between analytical solution and finite element method, in: 19th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2012, 04.-06. Juli 2012, Weimar [eds. K. Gürlebeck, T. Lahmer, F. Werner].
  • E. Bulla, D. Constales, R.S. Kraußhar, J. Ryan, Dirac Type Operators for Arithmetic Subgroups of Generalized Modular Groups, Journal für die reine und angewandte Mathematik, 643, 1-19, 2010.
  • I. Cação, D. Constales, R.S. Kraußhar, Explicit representations of the regular solutions of the time-harmonic Maxwell equations combined with the radial symmetric Euler operator, Mathematical Methods in the Applied Sciences, 32(1), 1-11, 2009.
  • I. Cação, D. Constales, R.S. Kraußhar, A unified approach for the treatment of some higher dimensional Dirac type equations on spheres, Proceedings of the 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2009, 7.-9. Juli 2009, Weimar [eds. K. Gürlebeck, C. Könke]
  • I. Cação, D. Constales, R.S. Kraußhar, On rotationally symmetric Dirac equations and hypergeometric functions I, Archiv der Mathematik, 90(5),  440-449, 2008.
  • I. Cação, D. Constales, R.S. Kraußhar, On the role of hypergeometric functions in Dirac type equations, AIP Conference Proceedings, 936, 726-729, 2007.
  • I. Cação, D. Constales, R.S. Kraußhar, On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations, Archiv der Mathematik, 87(5), 468-477, 2006.
  • I. Cação, D. Constales, R.S. Kraußhar, Bessel functions and higher dimensional Diractype equations, in: 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2006, 12.-14. Juli 2006, Weimar [eds. K. Gürlebeck, C. Könke]
  • P. Collignon, Analysis und mathematisches Modellieren Normung oder Kreation? In: Matthias Ludwig, Matthias; Kleine, Michael (Hrsg.): Beiträge zum Mathematikunterricht 2012, 185-188.
  • P. Collignon, Zur Erweiterung der Perspektiven auf die Analysis in der Grund- und Regelschullehrerausbildung. In: Lindmeier, Andreas; Ufer, Stefan (Hrsg.):  Beiträge zum Mathematikunterricht 2010, 225-228.
  • P. Collignon, Didaktische Aspekte wirtschaftsmathematischer Ausbildung. In: Beiträge zum Mathematikunterricht 2007, 41. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 25.03. bis 30.03.2007 in Berlin, 757-760.
  • D. Constales, R. De Almeida, R.S. Kraußhar, The Fourier expansion of the hypermonogenic generalized trigonometric and elliptic functions, Journal of Number Theory, 133, 1991-2004, 2013.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Fundamentals of a generalized Wiman-Valiron theory for solutions to the Dirac-Hodge equation on upper half-space of Rn+1, Journal of Mathematical Analysis and Applications, 378, 238-251, 2011.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius, Mathematische Zeitschrift, 266, 665-881, 2010.
  • D. Constales, R. De Almeida, R.S. Kraußhar, On a generalization of Valiron´s inequality for k-hypermonogenic functions on upper half-space, AIP Conference Proceedings, 1281(3), 1464-1468, 2010.
  • D. Constales, R. De Almeida, R.S. Kraußhar, A Generalization of Wiman and Valiron's theory to the Clifford analysis setting, Cubo, 11(1), 1-20, 2009.
  • D. Constales, R. De Almeida, R.S. Kraußhar, On the growth behavior of hypermonogenic functions on upper half-space, AIP Conference Proceedings, 1168(2), 757-760, 2009.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Applications of the maximum term and the central index in the asymptotic growth analysis of entire solutions to higher dimensional polynomial Cauchy-Riemann equations, Complex Variables, 53(3), 195-213, 2008.
  • D. Constales, R. De Almeida, R.S. Kraußhar, On the growth type of entire monogenic functions, Archiv der Mathematik, 88(2), 153-163, 2007.
  • D. Constales, R. De Almeida, R.S. Kraußhar, On the relation between the growth and the Taylor coefficients of entire solutions to the higher dimensional Cauchy-Riemann system in Rn+1, Journal of Mathematical Analysis and Applications, 327(2), 763-775, 2007.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Growth orders of monogenic functions in the ball, AIP Conference Proceedings, 936, 730-733, 2007.
  • D. Constales, R. De Almeida, R.S. Kraußhar, On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy-Riemann equations, Mathematical Methods in the Applied Sciences, 29(14), 1663-1686, 2006.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Further results on the asymptotic growth of entire solutions of iterated Dirac equations in Rn, Mathematical Methods in the Applied Sciences, 29(5), 537-556, 2006.
  • D. Constales, R. De Almeida, R.S. Kraußhar, Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations I, in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005, 16.-20. September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005, 928-931. [ISBN 3-527-40652-2]
  • D. Constales, R. De Almeida, R.S. Kraußhar, Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations II, in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005, 16.-20. September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005 pp. 133-136 [ISBN 3-527-40652-2]
  • D. Constales, R. De Almeida, R.S. Kraußhar, Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations Part II, in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005, 16-20 September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005 pp.. 892-895 [ISBN 3-527-40652-2]
  • D. Constales, N. Faustino, R.S. Kraußhar, Fock spaces, Landau operators and the time-harmonic Maxwell equations, Journal of Physics A: Mathematical and Theoretical, 44, 135303, 2011.
  • D. Constales, D. Grob, R.S. Kraußhar, A new class of hypercomplex analytic cusp forms, Transactions of the AMS, 365(2), 811-835, 2013.
  • D. Constales, D. Grob, R.S. Kraußhar, On Dirichlet problems of polynomial Dirac equations with boundary conditions, Results in Mathematics, 64, 193-213, 2013.
  • D. Constales, D. Grob, R.S. Kraußhar, Explicit formulas for the Green's function and the Bergman kernel for monogenic functions in annular shaped domains in Rn+1, Results in Mathematics, 58, 173-179, 2010.
  • D. Constales, D. Grob, R.S. Kraußhar, On generalized Helmholtz type equations in concentric annular domains in R3, Mathematical Methods in the Applied Sciences, 33(4), 431-438, 2010.
  • D. Constales, D. Grob, R.S. Kraußhar, Constructing 3D mappings onto the unit sphere with the hypercomplex Szego kernel, Journal of Computational and Applied Mathematics, 233(11), 2884-2910, 2010.
  • D. Constales, D. Grob, R.S. Kraußhar, Reproducing kernel functions of solutions to polynomial Dirac equations in the annulus of the unit ball in Rn and applications to boundary value problems, Journal of Mathematical Analysis and Applications, 358(2), 281-293, 2009.
  • D. Constales, D. Grob, R.S. Kraußhar, The hypercomplex Szegö kernel method for 3D mapping problems, Proceedings of the 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2009, 7.-9. Juli 2009, Weimar [eds. K. Gürlebeck, C. Könke]
  • D. Constales, K. Gürlebeck, R.S. Kraußhar, W. Sprößig, Applications of quaternionic analysis in Engineering, in: 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2006, 12.-14. Juli 2006, Weimar, [eds. K. Gürlebeck, C. Könke]
  • D. Constales, R.S. Kraußhar, Multiperiodic eigensolutions to the Dirac operator and applications to the generalized Helmholtz equation on flat cylinders and on the n-torus, Mathematical Methods in the Applied Sciences, 32, 2050-2070, 2009.
  • D. Constales, R.S. Kraußhar, On the Klein-Gordon equation on the 3-torus, Proceedings of the 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2009, 7.-9. Juli 2009, Weimar [eds. K. Gürlebeck, C. Könke].
  • D. Constales, R.S. Kraußhar, On the Navier-Stokes equation with Free Convection in three dimensional unbounded triangular channels, Mathematical Methods in the Applied Sciences, 31(6), 735-751, 2008.
  • D. Constales, R.S. Kraußhar, On the Navier-Stokes equations with Free Convection in 3D triangular symmetric channels, AIP Conference Proceedings, 936, 623-626, 2007.
  • D. Constales, R.S. Kraußhar, Explicit solutions of the stationary Navier-Stokes equation in a class of reflection symmetric domains, in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2006, 15.-19. September 2006, Kreta, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2006
  • D. Constales, R.S. Kraußhar, Bergman Spaces of higher dimensional hyperbolic polyhedron type domains I, Mathematical Methods in the Applied Sciences, 29(1), 85-98, 2006.
  • D. Constales, R.S. Kraußhar, On the Navier-Stokes equation with Free Convection in strip domains and 3D triangular channels, in: 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2006, 12.-14. Juli 2006, Weimar, [eds. K. Gürlebeck, C. Könke]
  • D. Constales, R.S. Kraußhar, Hilbert Spaces of Solutions to Polynomial Dirac equations, Fourier Transforms and Reproducing Kernel Functions for Cylindrical Domains, Zeitschrift für Analysis und ihre Anwendungen, 24(3), 611-636, 2005.
  • D. Constales, R.S. Kraußhar, The Bergman Kernels for the half-ball and for fractional wedge-shaped domains in Clifford Analysis, Forum Mathematicum, 17(5), 809-821, 2005.
  • D. Constales, R.S. Kraußhar, Closed formulas for singly-periodic monogenic cotangent, cosecant and cosecant-squared functions in Clifford Analysis, Journal of the London Mathematical Society, 67(2), 401-416, 2003.
  • D. Constales, R.S. Kraußhar, Bergman Kernels for rectangular domains and Multiperiodic Functions in Clifford Analysis, Mathematical Methods in the Applied Sciences, 25(16-18), 1509-1526, 2002.
  • D. Constales, R.S. Kraußhar, Representation formulas for the general derivatives of the fundamental solution of the Cauchy-Riemann operator in Clifford Analysis and Applications, Zeitschrift für Analysis und ihre Anwendungen, 21(3), 579-597, 2002.
  • D. Constales, R.S. Kraußhar, Szegö and Polymonogenic Bergman Kernels for half-space and strip domains, and Single-periodic Functions in Clifford Analysis, Complex Variables, 47(4), 349-360, 2002.
  • D. Constales, R.S. Kraußhar, J. Ryan, Hyperbolic Dirac and Laplace Operators on examples of Hyperbolic spin manifolds, Houston Journal of Mathematics, 38(2), 405-420, 2012.
  • D. Constales, R.S. Kraußhar, J. Ryan, k-hypermonogenic automorphic forms, Journal of Number Theory, 126(2), 254-271, 2007.
  • R. De Almeida, R.S. Kraußhar, On the asymptotic growth of entire monogenic functions, Zeitschrift für Analysis und ihre Anwendungen, 24(4), 791-813, 2005.
  • R. Delanghe, R.S. Kraußhar, H.R. Malonek, Differentiability of functions with values in some real associative algebras: approaches to an old problem, Bulletin de la Société Royale des Sciences de Liège, 70(4-6), 231-249, 2001.
  • D. Grob, R.S. Kraußhar, The Szegö metric associated to Hardy spaces of Clifford algebra valued functions and some geometric properties, Complex Analysis and Operator Theory, 6(2), 491-513, 2012.
  • K. Gürlebeck, R.S. Kraußhar, S. Poedts, A quaternionic approach to treat the ideally stationary magnetohydrodynamic equations, AIP Conference Proceedings, 1168(2), 789-792, 2009.
  • K. Gürlebeck, D. Legatiuk, On the continuous coupling of finite elements with holomorphic basis functions, Hypercomplex Analysis: New perspectives and applications, Birkhäuser, Basel, 2014.
  • K. Gürlebeck, H.M. Nguyen, D. Legatiuk, An additive decomposition of harmonic functions in $\mathbb{R}^{3}$, Lecture Notes in Computer Science, 8579,  189-204, 2014.
  • T. Hempfling, R.S. Kraußhar, Order Theory for Isolated Points of Monogenic Functions, Archiv der Mathematik, 80, 406-423, 2003.
  • R.S. Kraußhar, Applications of the quaternionic calculus to the convective stationary MHD equations in Rn, Advances in Applied Clifford Algebras, 24(4),  1047-1058, 2014.
  • R.S. Kraußhar, The Klein-Gordon operator on Möbius strip domains and the Klein bottle in Rn, Mathematical Physics, Analysis and Geometry, 16, 363-379, 2013.
  • R.S. Kraußhar, The Helmholtz operator on higher dimensional Möbius strips, Advances in Applied Clifford Algebras, 22(3), 745-755, 2012.
  • R.S. Kraußhar, On the incompressible viscous MHD equations and explicit solution formulas for some three dimensional radially symmetric domains,  Hypercomplex Analysis and Applications, Springer series "Trends in Mathematics", Birkhäuser, 125-137, 2011.
  • R.S. Kraußhar, On the Klein-Gordon equation on some examples of conformally flat spin 3-manifolds, Recent advances in computational and applied Mathematics, Springer, 2011 .
  • R.S. Kraußhar, Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the n-Dimensional Hyperbolic Space, Bulletin of the Belgian Mathematical Society – Simon Stevin, 11(5), 759-774, 2004.
  • R.S. Kraußhar, Generalized Analytic Automorphic Forms in Hypercomplex Spaces, Frontiers in Mathematics, Birkhäuser, Basel, 2004.
  • R.S. Kraußhar, A Theory of Modular Forms in Clifford Analysis, their Applications and Perspectives, Advances in Analysis and Geometry New Developments Using Clifford Algebras, Springer series "Trends in Mathematics", Birkhäuser, 311-343, 2004.
  • R.S. Kraußhar, The Multiplication of the Clifford-analytic Eisenstein Series, Journal of Number Theory, 102, 353-382, 2003.
  • R.S. Kraußhar, Poincaré Series in Clifford Analysis, Clifford Algebras: Application to Mathematics, Physics, and Engineering, Progress in Mathematical Physics, Birkhäuser, 75-90, 2003.
  • R.S. Kraußhar, Monogenic Modular Forms in Two and Several Real and Complex Vector Variables, Computational Methods and Function Theory, 2(2), 299-318, 2002.
  • R.S. Kraußhar, Eisenstein Series in Complexified Clifford Analysis, Computational Methods and Function Theory, 2(1), 29-65, 2002.
  • R.S. Kraußhar, Automorphic forms in Clifford analysis, Complex Variables, 47(5), 417-440, 2002.
  • R.S. Kraußhar, On a new type of Eisenstein series in Clifford analysis, Zeitschrift für Analysis und ihre Anwendungen, 20(4), 1007-1029, 2001.
  • R.S. Kraußhar, Monogenic multiperiodic functions in Clifford analysis, Complex Variables, 46(4), 337-368, 2001.
  • R.S. Kraußhar, Generalizations of the Complex Analytic Trigonometric Functions to Clifford Analysis by Eisenstein Series, Functional-Analytic and complex methods, their interactions, and Applications to Partial Differential Equations, World Scientific, 438-456, 2001.
  • R.S. Kraußhar, Eisenstein Series in Clifford Analysis. Dissertation RWTH Aachen, Aachener Beiträge zur Mathematik (Band 28), Wissenschaftsverlag Mainz, Aachen, 2000.
  • R.S. Kraußhar, H.R. Malonek, A characterization of conformal mappings in R4 by a formal differentiability condition, Bulletin de la Société Royale des Sciences de Liège, 70(4-6), 231-249, 2001.
  • R.S. Kraußhar, J. Ryan, Some Conformally Flat Spin Manifolds, Dirac Operators and Automorphic Forms, Journal of Mathematical Analysis and Applications, 325(1), 359-376, 2007.
  • R.S. Kraußhar, J. Ryan, Clifford and Harmonic Analysis on Cylinders and Tori, Revista Matemática Iberoamericana, 21, 87-110, 2005.
  • R.S. Kraußhar, J. Ryan, Analysis of Dirac Operators on some Conformally Flat Manifolds, in 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2006, 12.-14. Juli 2006, Weimar [eds. K. Gürlebeck, C. Könke]
  • R.S. Kraußhar, M.M. Rodrigues, N. Vieira, Hodge type decomposition for time dependent first order parabolic operators with non-constant coefficients: the variable exponent case, Milan Journal of Mathematics, 82, 407-422, 2014.
  • R.S. Kraußhar, M.M. Rodrigues, N. Vieira, Hodge decomposition for some first order time dependent parabolic operators with non-constant coefficients, Annali di Matematica Pura ed Applicata, 193, 1807-1821, 2014.
  • R.S. Kraußhar, M.M. Rodrigues, N. Vieira, The Schrödinger semigroup on some flat and non flat manifolds, Complex Analysis and Operator Theory, 8(2), 461-484, 2014.
  • R.S. Kraußhar, J. Tolksdorf, Applications of hyper-complex analysis in Yang-Mills gauge theories, AIP Conference Proceedings, 936, 754-757, 2007.
  • R.S. Kraußhar, N. Vieira, The Schrödinger equation on cylinders and the n-torus, Journal of Evolution Equations, 11, 215-237, 2011.
  • R.S. Kraußhar, Q. Yuying, J. Ryan, Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in Rn arising from Special Arithmetic Groups of the Vahlen Group, Contemporary Mathematics, AMS, 370, 159-173, 2005.
  • D. Legatiuk, K. Gürlebeck, G. Morgenthal, Modelling of concrete hinges through coupling of analytical and finite element solutions, Bautechnik Sonderdruck, ISSN 0932-8351, A 1556, 2013.
  • D. Legatiuk, H.M. Nguyen, Improved convergence results for the finite element method with holomorphic functions, Advances in Applied Clifford Algebra, 24(4), pp. 1077-1092, 2014.
  • R. Möller, P. Collignon, Calculus and applications – Learning from history in teacher education. In Proceedings of CERME 8, Antalya, 2013. Available online
  • R. Möller, P. Collignon, Analysis unter einer postmodernen Perspektive. In: Greefrath, Gilbert; Käpnick, Friedhelm; Martin Stein, Martin: (Hrsg.): Beiträge zum Mathematikunterricht 2013, WTM-Verlag, Münster 2008, 664-667.
  • F. Scheiber, H.B. Motra, D. Legatiuk, F. Werner, Model coupling in structural engineering application, Proceedings of the International Probabilistic Workshop (IPW 2014), Weimar, 2014.