Dr. rer. nat. Sebastian Bock
Wissenschaftlicher Mitarbeiter
Coudraystraße 13B, Raum 202
99423 Weimar
E-Mail: sebastian.bock[at]uni-weimar.de
Telefon: +49 (0) 3643/58 42 83
Forschungsinteressen
- Komplexe und hyperkomplexe Analysis
- Approximations- und Interpolationstheorie
- Spezielle Funktionen
- Funktionentheoretische Methoden in der linear-elastischen Bruchmechanik
Publikationen
Buchkapitel
S. Bock, D. Legatiuk: Constructive orthonormalisation of monogenic polynomials on a finite cylinder, S. Bernstein (Ed.): Topics in Clifford Analysis, Trends in Mathematics, 2019.
S. Bock: On a hypercomplex version of the Kelvin solution in linear elasticity, P. Drygás, S. Rogosin (Eds.): Modern Problems in Applied Analysis, Trends in Mathematics, 2018.
Zeitschriftenbeiträge
C. Ding, S. Bock, K. Gürlebeck: Construction of Special Solutions for the Maxwell Equations, Advances in Applied Clifford Algebras 29(95), 2019.
S. Bock: A generalized monogenic exponential function in IH, Complex Variables and Elliptic Equations 64(11), 2019.
C. Ding, S. Bock, K. Gürlebeck: Special bases for solutions of a generalized Maxwell system in 3-dimensional space, Math Meth Appl Sci:1-19, 2018.
S. Bock: Special classes of monogenic functions in IH, Advances in Applied Clifford Algebras 28(56), 2018.
S. Bock: On a class of monogenic functions with (logarithmic) line singularities, Advances in Applied Clifford Algebras 28(6), 2018.
T. Lahmer, S. Bock, J. Hildebrand, K. Gürlebeck: Non-destructive identification of residual stresses in steel under thermal loadings, Inverse Problems in Science and Engineering 25(10), 2017.
S. Bock, T. Gebhardt, J. Hildebrand, W. Schwarz, A. Almamou, S. Herzog: Qualitätskontrolle von Ingenieurkonstruktionen durch terrestrisches Laserscanning, Allgemeine Vermessungs-Nachrichten avn 123(8-9):239-252, 2016.
S. Bock, K. Gürlebeck, D. Legatiuk and H. M. Nguyen: ψ-Hyperholomorphic Functions and a Kolosov-Muskhelishvili Formula, Mathematical Methods in the Applied Sciences 38(18):5114–5123, 2015.
D. Weisz-Patrault, S. Bock, K. Gürlebeck: Three-dimensional elasticity based on quaternion-valued potentials, International Journal of Solids and Structures 51(19-20):3422-3430, 2014.
S. Bock, T. Gebhardt, M. Kuhne: Entwicklung von faseroptischen Messsystemen, Allgemeine Vermessungs-Nachrichten avn 121(3):97-111, 2014.
S. Bock, T. Gebhardt, M. Kuhne, W. Schwarz: Ein faseroptischer Sensor zur zweiachsigen Neigungsmessung, Wissenschaftliche Berichte, Wissenschaftliche Zeitschrift der Hochschule Mittweida 4:23-26, 2014.
S. Bock: On Monogenic Series Expansions with Applications to Linear Elasticity, Advances in Applied Clifford Algebras 24(4):931-943, 2014.
K. Gürlebeck, M. N. Hung, S. Bock, J. Morais: On Orthogonal Monogenics in Oblate Spheroidal Domains and Recurrence Formulae, Integral Transforms And Special Functions 25(7):513-527, 2014.
S. Bock: On a three dimensional analogue to the holomorphic z-powers: power series and recurrence formulae, Complex Variables and Elliptic Equations 57(12):1349-1370, 2012.
S. Bock: On a three-dimensional analogue to the holomorphic z-powers: Laurent series expansions, Complex Variables and Elliptic Equations 57(12):1271-1287, 2012.
S. Bock, K. Gürlebeck, R. Lávicka, V. Soucek: Gelfand-Tsetlin bases for spherical monogenics in dimension 3, Revista Matemática Iberoamericana 28(4):1165-1192, 2012.
P. Stein, T. Lahmer, S. Bock: Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau, Bautechnik Sonderdruck 88(6):8-11, 2011.
S. Bock, K. Gürlebeck: On a generalized Appell system and monogenic power series, Mathematical Methods in the Applied Sciences 33(4):394-411, 2010.
S. Bock, K. Gürlebeck: On a polynomial basis generated from the generalized Kolosov-Muskhelishvili formulae, Advances in Applied Clifford Algebras 12(2):191-209, 2009.
S. Bock, K. Gürlebeck: On a spatial generalization of the Kolosov-Muskhelishvili formulae, Mathematical Methods in the Applied Sciences 32:223-240, 2009.
I. Cação, K. Gürlebeck, S. Bock: On Derivatives of Spherical Monogenics, Complex Variables and Elliptic Equations 51:847-869, 2006.
S. Bock, M. I. Falcão, K. Gürlebeck, H. Malonek: A 3-dimensional Bergman Kernel Method with Applications to Rectangular Domains, Computational and Applied Mathematics 189(1-2):67-79, 2006.
Konferenz- und Tagungsbeiträge
S. Bock: Rational monogenic functions in IH, J. Vigo-Aguiar (Ed.): Proceedings of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE, Rota/Cadiz (2018).
S. Bock: On generalized Kolosov-Muskhelishvili formulae for the finite cylinder, AIP Conference Proceedings 1978, 280002 (2018); https://doi.org/10.1063/1.5043902.
S. Bock: On monogenic functions with line singularities, J. Vigo-Aguiar (Ed.): Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE, Rota/Cadiz (2017).
T. Gebhardt, J. Hildebrand, W. Schwarz, S. Bock, S. Herzog, A. Almamou: Qualitätssicherung von Brückenbauwerken während der Fertigung und Montage sowie im Betrieb mit terrestrischem Laserscanning, Tagungsband zum 2. Brückenkolloquium: Beurteilung, Ertüchtigung und Instandsetzung von Brücken, Ostfildern/Stuttgart (21.-22. Juni 2016), S. 311-320.
S. Bock, K. Gürlebeck, D. Legatiuk: Convergence of the finite element method with holomorphic functions, International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, and Ch. Tsitouras (eds.), AIP Conference Proceedings, vol. 1558, 513 (2013).
S. Bock, K. Gürlebeck, D. Legatiuk: On the coupling between analytical and finite element solutions, (in) Interactions between real and complex analysis, (eds.) Le Hung Son and Wolfgang Tutschke, Science and Technics Publishing House, Hanoi 2012, pp. 3-19.
S. Bock, K. Gürlebeck, D. Legatiuk: On a special finite element based on holomorphic functions, International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, and Ch. Tsitouras (eds.), AIP Conference Proceedings, vol. 1479, 2012, pp. 765-768.
S. Bock, K. Gürlebeck: On an Orthonormal Basis of Solid Spherical Monogenics Recursively Generated by Anti-Holomorphic z-Powers, International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, and Ch. Tsitouras (eds.), AIP Conference Proceedings, vol. 1168, 2009, pp. 308-312.
S. Bock, K. Gürlebeck: On recurrence formulae of solid spherical monogenics, International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, and Ch. Tsitouras (eds.), AIP Conference Proceedings, vol. 1048, 2008, pp. 638-648.
S. Bock, K. Gürlebeck: On hypercomplex differential and primitivation operators with applications to representation formulae of linear elastostatics, International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, and Ch. Tsitouras (eds.), AIP Conference Proceedings 936:717-720, 2007.
S. Bock, K. Gürlebeck: A Coupled Ritz-Galerkin Approach using Holomorphic and Anti-Holomorphic Functions, Proceedings of the 17th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering (IKM), Weimar, 12.-14. Juli 2006.
I. Cação, K. Gürlebeck, S. Bock: Complete Orthonormal Systems of Spherical Monogenics-A Constructive Approach, (eds.) Le Hung Son, W. Tutschke, S. Jain, (in) Methods of Complex and Clifford Analysis (Proceedings of ICAM Hanoi 2004), SAS International Publications.
S. Bock: Ein Algorithmus zur Schnittpunktbestimmung von kubischen Beziér-Kurven, Forum Bauinformatik 2004, Technische Universität Braunschweig.
S. Bock, M. I. Falcão, K. Gürlebeck: Applications of Bergman Kernel Functions, Proceedings of the 16th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering (IKM), Weimar, 10.-12. Juni 2003.