Prof. Dr. rer. nat. habil. Detlef Hauke MacheWissenschaftsbereich Elektro-/Informationstechnik und Wirtschaftsingenieurwesen

nach Vereinbarung

Curriculum Vitae: That’s my scientific life so far …
from Wintersemester  

• 1981/82       I studied Mathematics, Sport, Philosophy and Computer Sciences at the University of Dortmund, where I finished
• 1988           my "Diplom" in Mathematics (& Computer Sciences); Diploma thesis in Applied Mathematics - Approximation Theory;
• 1988 - 1991 Research staff member ("wissenschaftl. Mitarbeiter") at the Department of Mathematics, Dortmund;
• 1991           Doctor's degree (Dr. rer. nat) in Mathematics;
• 1992 - 1998 Research Assistant at the Department of Mathematics, Dortmund;
• 1997           Habilitation (Dr. habil.) for qualifying as a university lecturer;
•                   Venia Legendi in Mathematics (University of Dortmund);
• 1997            Assistant Professor for Mathematics at the Institute of Applied Mathematics, Dortmund;
• 1998            Visiting Professor at the University of Witwatersrand, Center of Applicable Analysis, Johannesburg (South Africa);
• 1998 - 1999  Full University Professor for Applied Mathematics - Numerical Analysis (I took the function for the chair) at the University of Munich;
• 2000 - 2001 I took again the function for a chair for Applied Analysis (Numerical Mathematics) at the University of Duisburg.
• Since 2003  Professor at the TH Georg Agricola, University of Applied Sciences (Bochum) for Applied Mathematics (Constructive Approximation)

Lehr- und Arbeitsschwerpunkte / Teaching Areas

• Höhere Mathematik I & II / Mathematics I & II
• Angewandte Mathematik / Applied Mathematics
• Differentialgleichungen / (Partial) Differential Equations
• Numerische Mathematik / Numerical Analysis

Forschungsschwerpunkte / Research Areas:

• Constructive Approximation
• RBF-Netzworks
• Neural Networks and Fuzzy Logic
• Approximation by Quasi-Interpolation

Publications (selected since 1993)

I. Proceedings (Chief-Editor)

• Trends and Applications in Constructive Approximation, (edited by M.G. de Bruin,  D.H. Mache and J. Szabados), Int. Series of Numerical Mathematics Vol. 151, (ISBN 3-7643-7124-2), Birkhäuser Verlag Basel, Springer Science Group (2005).  

• Advanced Problems in Constructive Approximation, (edited by M.D. Buhmann and D.H. Mache), Int. Series of Numerical Mathematics Vol. 142, (ISBN 3-7643-6648-6) Birkhäuser Verlag Basel (2003).

• New Developments in Approximations Theory, (edited by M.D. Buhmann, M. Felten,  D.H. Mache & M.W. Müller), Int. Series of Numerical Mathematics Vol. 132, (ISBN 3-7643-6143-3) Birkhäuser Verlag Basel (1999).

• Approximation Theory, (edited by M. Felten,  D.H. Mache and M.W. Müller), Mathematical Research, Vol. 86 (ISBN 3-05-501673-4), Akademie Verlag Berlin (Wiley-Group) (1995).

II. Journal (Editor)  

• Journal General Mathematics (ISSN 1221 - 5023) · Electronic Edition  

III. Publications (selected since 1991)

• Some C_0 - Semigroups related to Polynomial Operators, (jointly with I. Rasa), in: Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 76(2005), pp. 459-467
•  Finding Relevant Input Arguments with Radial Basisfunction Networks (jointly with Meyer, J.),  in: Int. Series of Numerical Mathematics Vol. 151, Trends & Applications in Constructive Approximation, Birkhäuser Verlag (2005), 125  - 134.  
• (0,2) Pal-Type Interpolation : A General Method for Regularity, (jointly with M.G. de Bruin)  in: Int. Series of Numerical Mathematics Vol. 151, Trends & Applications in Constructive Approximation, Birkhäuser Verlag (2005), 61 - 70.  
• (0,2) Pal-Type Interpolation : A General Method , (jointly with M.G. de Bruin),in: Communications in the Analytic Theory of Continued Fractions, Vol. XII, Mesa State Colorado (2004), 111 – 112.
• Rekonstruktionsbasierte Selektion relevanter Einflussgrößen (jointly with Kiendl, H., Meyer, J., Schauten, D.), in: Computational Intelligence (Sonderforschungsbereich 531 „Design und Management komplexer technischer Prozesse & Systeme mit Methoden der Computational Intelligence“ ) ISSN 1433-3325   (2003)
• (0,1) Pal-Type Interpolation : A General Method for Regularity, (jointly with M.G. de Bruin), in: Communications in the Analytic Theory of Continued Fractions, Vol. XI, Mesa State Colorado (2003), 119 – 120.
• The Rate of Approximation by Interpolating the Endpoints, Technical Report (Institute Applied Mathematics), University Dortmund (2003).
• (0,1) Pal-Type Interpolation : A General Method for Regularity, (jointly with M.G. de Bruin), in: Int. Series of Numerical Mathematics Vol. 142, Advanced Problems in Constructive Approximation, Birkhäuser Verlag (2003), 21 - 26.
• On Approximation Methods by using Orthogonal Polynomial Expansions, (jointly with R. Lasser, J. Obermaier), in: Int. Series of Numerical Mathematics Vol. 142, Advanced Problems in Constructive Approximation, Birkhäuser Verlag (2003), 95 - 107.
• Generalized Methods using Integral Transforms and Convolution Structures with Orthogonal Polynomials, in: Journal Rendiconti del Circolo Matematicodi Palermo, Serie II, Suppl. 68 (2002), 625 -640.

• Approximation by Bernstein Quasi-Interpolants, (jointly with P. Mache); Primary publication: Technical Report Nr. 184 (Institute Applied Mathematics), University Dortmund (2000), in: Numerical Functional Analysis and Optimization Vol. 22 (1 & 2), (2001), 159 - 175.
• (C,1) Means of Orthonormal Expansions for Exponential Weights,  (jointly with D.S. Lubinsky); Primary publication in: Graduiertenkolleg Mathematik im Bereich ihrer Wechselwirkung mit der Physik, Mathematisches, Institut, Ludwig-Maximilians Universität München, (1998), in: Journal of Approximation Theory, Vol. 103, No.1, (2000), 151 - 182.
• Certain Results involving Gammaoperators, (jointly with A. Lupas, V. Maier, M.W. Müller); in:  Int. Series of Numerical Mathematics Vol. 132,  Birkhäuser Verlag Basel (1999), 199 - 214.
• On Approximation Properties of Stancu-Kantorovich Operators, (jointly with B. Della Vecchia); In: Revue d'Analyse Numerique et de Theorie de l' Approximation, Tome 27, No. 1 (1998), 71 - 80.
• Linear Combinations of Gammaoperators in $L_p$ - Spaces, (jointly with A. Lupas, V. Maier, M.W. Müller); in: Results in Mathematics 34 (1998), 156 - 168.
• Optimale Konvergenzordnung positiver Summationsverfahren der Durrmeyer Operatoren mit Jacobi - Gewichtungen; Habilitation thesis, Dortmund (1997).
• On Numerical Differentiation, (jointly with A. Lupas); in: Revue d' Analyse Numerique et de Theorie de l' Approximation, Tome 26, No. 1-2 (1997), 109 - 115.
• Approximation by $V_n$ - Operators, (jointly with A. Lupas); in: Facta Univ. Ser. Math. Inform. 12 (1997), 203 - 216.
• Summation of Durrmeyer Operators with Chebyshev Weights; in: Approximation and Optimization, Proceedings of the Int.Conf. on Approximation and Optimization - ICAOR, Cluj-Napoca Vol. I, (1996), 307 - 318.
• Estimations of Chebyshev Convolution Operators by an Algebraic Modulus of Smoothness, (jointly with M. Felten); in: Numerical Functional Analysis and Optimization Vol. 17 (5 & 6), (1996), 577 - 585.
• Characterization Theorems for the Approximation by a Family of Operators, (jointly with D.X. Zhou); in: Journal of Approximation Theory,  Vol. 84, No. 2, (1996), 145 - 161.
• The $\Theta$ -- Transformation of Certain Positive Linear Operators,  (jointly with A. Lupas); in: International Journal of Mathematics and Mathematical Sciences, Vol. 19, No. 4, (1996), 667 - 678.
• Weighted $L_p$ - Approximation of Derivatives by the Method of Gammaoperators, (jointly with A. Lupas, M.W. Müller); in: Results in Mathematics, Vol. 28, No. 3/4 (1995), 277 - 286.
• A Link between Bernstein Polynomials and Durrmeyer Polynomials with Jacobi Weights; in: Approximation Theory  VIII, Vol. 1, Approximation and Interpolation, Charles K. Chui and Larry L. Schumaker (eds.), World Scientific Publishing Co., (1995), 403 - 410.
• Generalization of Bernstein - Type Approximation Methods, (jointly with I. Gavrea); in: Approximation Theory, Proc. IDoMAT 95, Mathematical Research, Vol. 86, Akademie Verlag, Berlin, (1995), 115 - 126.
• Best Direct and Converse Results for Lagrange - Type Operators, (jointly with D.X. Zhou); in: Approximation Theory and its Applications, Vol. 11, No. 2, (1995), 76 - 93.
• Equivalence Theorem on Weighted Simultaneous $L_p$ -- Approximation by the Method of Kantorovic Operators; in: Journal of Approximation Theory, Vol. 78, No. 3, (1994), 321 - 350.
• A Method for Summability of Lagrange Interpolation; in: International Journal of Mathematics and Mathematical Sciences, Vol. 17, No. 1, (1994), 19 - 26.
• Approximation by Linear Positive Polynomial Operators with Saturation Order ${\cal O}(n^{-2})$; in:"Tiberiu Popoviciu " Seminaire Itinerant D'equations Fonctionnelles, Approximation et Convexite, Faculte de Mathematique, Universite Babes - Bolyai, Cluj - Napoca, Vol. 6, (1993), 115 - 122.
• New local error estimates for Meyer - König and Zeller Kantorovic-operators using maximal functions, (jointly with M.W. Müller); in: Mathematica (Cluj), Tome 34 (57), No. 2, (1992), 157 - 165.
• Gewichtete Simultanapproximation in der $L_p$ - Metrik durch das Verfahren der Kantorovic Operatoren, Dissertation, University of Dortmund (1991).