## Prof. Dr. rer. nat. habil. Detlef H. Mache

Wissenschaftsbereich 3

### Kontakt

Telefon: (0234) 968-3212

Telefax: (0234) 968-3346

E-Mail: Detlef.Mache(at) thga.de

Gebäude 7, Raum 124

### Sprechstunden

nach Vereinbarung

### Aufgabengebiete

Professor für Mathematik und Angewandte Mathematik / Applied Mathematics & Constructive Approximation

### Vita

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 Forschungsschwerpunkte

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

### Publikationen

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),

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).