Thomas Wolf

Professor of Mathematics

Headshot of Thomas Wolf, Brock University Professor of Mathematics

Office: Mackenzie Chown J413
905 688 5550 x3803
twolf@brocku.ca

Research Interests

My research interests include differential equations and integrability,
computer algebra, General Relativity, Combinatorial Game Theory,
Computer GO and aspects of Mathematics Education.

Work in computer algebra concerns algorithms to simplify and solve
overdetermined systems of equations (linear/non-linear), (algebraic/ordinary
differential (ODEs)/partial differential (PDEs)). These basic algorithms are
applied in higher level programs for the determination of symmetries,
conservation laws or other properties of differential equations. Applications
include the classification of integrable systems of evolutionary scalar PDEs,
vector PDEs, single and systems of supersymmetric evolutionary PDEs,
integrable quadratic Hamiltonians with higher degree first integrals
but also discrete integrable system from Discrete Differential Geometry.

An old hobby of mine concerns the computerization of the Asian game of Go. My
algorithms and programs specialized on life and death problems in Go. More
recent activities concern mathematical aspects of special classes of
situations, like semeai and seki.

Past and current initiatives towards youth outreach include organizing the BBB
(Brock Brain Benders) Club, the Brock Go Club and (externally) the Caribou
Math Contests.

Computer Algebra Programs

Computer Go

Youth Outreach

Publications and collections

View Recent Publications
View Recent Talks

Sorted by Subject

Sorted by Type

Computer Algebra + ODEs/PDEs

  • Hussin, V., Kiselev, A.V., Krutov, A.O., Wolf, T.: N=2 Supersymmetric a=4 – KdV Hierarchy Derived via Gardner’s Deformation of Kaup-Bousinesq Equation, preprint MPIM(Bonn), 22 pages, (2009).
  • Tsarev, S.P. and Wolf, T.: Hyperdeterminants as integrable discrete systems, J. Phys. A: Math. Theor., 42 (2009), doi: 10.1088/1751-8113/42/45/454023, 9 pages. also arXiv:0903.3864 (nlin.SI) dvi file, ps file,
  • Wolf, T.: On Solving Large Systems of Polynomial Equations Appearing in Discrete Differential Geometry, Programming and Computer Software, 34 (2008), no 2, p 75-83.
  • Anco, S., Bluman, G. and Wolf, T.: Invertible Mappings of Nonlinear PDEs through Admitted Conservation Laws, Acta Appl Math 2008, electronic publication: http://dx.doi.org/10.1007/s10440-008-9205-7
  • Wolf, T., Neun, W. and Tsarev, S.P.: About parallelizing the search for 3-dim. scalar discrete integrable equations, talk given at PASCO 2007, July 2007 London/Ontario,
  • Tsarev, S.P. and Wolf, T.: Classification of 3-dimensional integrable scalar discrete equations, preprint, 19 pages (2007) arXiv:0706.2464, Lett. in Math. Phys. (available at www.springerlink.com as DOI:10.1007/s11005-008-0230-2). dvi file, ps file,
  • Wolf, T., Neun, W.: About a Computer Algebra based online Mathtest, in Michael J Wester, Michel Beaudin (eds), “Computer Algebra in Education”, p. 1-6, ISBN-978-0-9754541-9-6, Aulonna Press 2008 (Proceedings of the session “Computer Algebra in Education” at the Int. Conf. on Applications of Computer Algebra (ACA’07)). dvi file, ps file,
  • Wolf, T.: The Parametric Solution of Underdetermined linear ODEs, preprint, 16 pages (2006). dvi file, ps file,
  • Kiselev, A. and Wolf, T.: Classification of integrable super-equations by the SsTools environment, Comp Phys Comm, Vol. 177, no. 3 (2007) p 315-328 (and on arXiv: nlin.SI/0609065). dvi file, ps file,
  • Wolf, T.: Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket, Gen. Relativ. Gravit. 38, no 6(2006) 1115-1127, DOI 10.1007/s10714-006-0293-2 (online jounal issue).
  • Kiselev, A. and Wolf, T.: Supersymmetric Representations and Integrable Super-Extensions of the Burgers and Bussinesq Equations, SIGMA, Vol. 2 (2006), Paper 030, 19 pages (arXiv math-ph/0511071). ps file,
  • Kiselev, A. and Wolf, T.: On weakly non-local, nilpotent, and super-recursion operators for N=1 homogeneous super-equations, Proc. Int. Workshop “Supersymmetries and Quantum Symmetries” (SQS’05), Dubna, July 24-31, 2005, JINR, p. 231-237. (arXiv nlin.SI/0511056) dvi file, ps file,
  • Sokolov, V.V. and Wolf, T.: Integrable quadratic Hamiltonians on so(4) and so(3,1), J. Phys. A: Math. Gen. 39 (2006) 1915-1926. (arXiv: nlin.SI/0405066)
  • Anco, S. and Wolf, T.: Erratum on `Some symmetry classifications of hyperbolic vector evolution equations’, JNMP, Volume 12, no 4 (2005), p 607-608. ps file
  • Tsuchida, T. and Wolf, T.: Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I, J. Phys. A: Math. Gen. 38 (2005) 7691-7733 and on arxiv as nlin.SI/0412003.
  • Anco, S. and Wolf, T.: Some symmetry classifications of hyperbolic vector evolution equations, nlin.SI/0412015 (2004), Journal of Nonl. Math. Physics, 12, Supplement 1 (2005), p 13 – 31. dvi file, ps file
  • Wolf, T.: Partial and Complete Linearization of PDEs Based on Conservation Laws, in: Trends in Mathematics: Differential Equations with Symbolic Computation, p. 291-306, Birkhäuser Verlag Basel/Switzerland, Ed. Dongming Wang, Zhiming Zheng (2005), also as preprint arXiv nlin.SI/0501034 (2004). dvi file, ps file
  • T. Wolf: Merging Solutions of Polynomial Algebraic Systems, preprint (2003), 5 pages. dvi file, ps file
  • T. Wolf, O.V. Efimovskaya: Classification of integrable quadratic Hamiltonians on e(3), Regular and Chaotic Dynamics, 8, no 2 (2003), p 155-162. (arxiv nlin.SI/0302001) dvi file, ps file
  • T. Wolf: Applications of CRACK in the Classification of Integrable Systems, CRM Proceedings and Lecture Notes, 37 (2004) pp. 283-300. dvi file, ps file
  • T. Wolf, The integration of systems of linear PDEs using conservation laws of syzygies, J. of Symb. Comp. 35, no 5 (2003) 499-526. dvi file, ps file
  • N. Euler, T. Wolf, P.G.L. Leach and M. Euler: Linearizable Third-Order ODEs and Generalised Sundman Transformations: The Case X”’=0, Acta Applicandae Mathematicae, 76, (2003) Issue 1, March, 89-115.
    dvi file, ps file
  • T. Wolf, Crack, LiePDE, ApplySym and ConLaw, section 4.3.5 and computer program on CD-ROM in: Grabmeier, J., Kaltofen, E. and Weispfenning, V. (Eds.): Computer Algebra Handbook, Springer (2002) pp. 465-468. dvi file, ps file
  • T. Wolf, Conservation Laws for Geodesic Motion in Curved Spaces and PDEs, section 3.1.5.1 in: Grabmeier, J., Kaltofen, E. and Weispfenning, V. (Eds.): Computer Algebra Handbook, Springer (2002) pp. 187-190. dvi file,ps file
  • T. Wolf, Size reduction and partial decoupling of systems of equations, J. Symb. Comp., 33 no 3 (2002) 367-383. dvi file, ps file
  • T. Wolf, A comparison of four approaches to the calculation of conservation laws, Euro. Jnl of Applied Mathematics 13 part 2 (2002) 129-152. dvi file, ps file
  • V.V. Sokolov and T. Wolf, Classification of integrable polynomial vector evolution equations, J. Phys. A: Math. Gen. 34 (2001) 11139-11148. dvi file, ps file
  • A. Triulzi and T. Wolf, Recognizing overdetermined subsystems of systems of equations, preprint, 6 pages (2000). ps file
  • T. Wolf, The Symbolic Integration of Exact PDEs, J. Symb. Comp. 30 (no. 5) (2000) 619-629. dvi file, ps file
  • T. Wolf, A. Brand, M. Mohammadzadeh, Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions, J. Symb. Comp., 27 (1999) 221-238. dvi file, ps file
  • V.V. Sokolov, T. Wolf, A symmetry test for quasilinear coupled systems, Inverse Problems 15 (1998) L5-L11. dvi file ps file
  • T. Wolf, A study of Genetic Algorithms solving a Combinatorial Puzzle. preprint (1997), 21 pages. ps file
  • T. Wolf, A. Brand, Examples of the investigation of differential equations with modularized programs, Mathl. Comput. Modelling 25 (1997), no 8/9, 133 – 139.
  • T. Wolf, A. Brand, Approaches to solving nonlinear ODEs, Mathematics and Computers in Simulation 42, (1996) 391-398.
  • T. Wolf, APPLYSYM – a package for the application of Lie-symmetries, software distributed together with the computer algebra system REDUCE, (1995).
  • T. Wolf, A. Brand, Investigating DEs with CRACK and Related Programs,SIGSAM Bulletin, Special Issue, (June 1995), p 1-8.
  • T. Wolf, Programs for Applying Symmetries of PDEs, ISSAC-95, 7-15, ACM Press, (1995).
  • T. Wolf, An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs, Proc.of Modern Group Analysis: advanced analytical and computational methods in mathematical physics, Catania, Italy Oct.1992, Kluwer Acad.Publ. (1993) 377-385.
  • T. Wolf, Solving overdetermined PDE-systems with CRACK, software included in the REDUCE network library, Aug.(1992)
  • T. Wolf, The Computer Algebra Package CRACK for investigating PDEs, with A Brand, in proceedings of ERCIM, Partial Diffential Equations and Group Theory, Bonn, (1992)
  • V. Sokolov, S. Svinolupov, T. Wolf, Linearizable evolutionary equations of second order, Physics Lett.A , 163, (1992), pp.415-418
  • H.J. Pohle, T. Wolf, Automatic Determination of Dynamical Symmetries of Ordinary Differential Equations, Computing 41, (1989) 297-307.
  • T. Wolf, A package for the analytic investigation and exact solution of differential equations, Proc. EUROCAL 87, Lect. Notes in Comp. Sci. 378, (1989) 479-91.
  • T. Wolf, Analytical decoupling, decision of compatibility and partial integration of systems of nonlinear ordinary and partial differential equations, Proc. EUROCAL 85, Lect. Notes of Comp. Sci. 204, (1985) 597-98.
  • T. Wolf, An analytic algorithm for decoupling and integrating systems of nonlinear partial differential equations, J. of Comp. Phys. 60, no. 3, (1985) 437-46.

General Relativity

  • Adel Bouchareb, Chiang-Mei Chen, Gérard Clément, Dmitri V. Gal’tsov, Nikolai G. Scherbluk, and Thomas Wolf: G2 generating technique for minimal D=5 supergravity and black rings, Phys. Rev. D 76, 104032 (2007) [arXiv:0708.2361 [hep-th]]. ps file
  • Adel Bouchareb, Chiang-Mei Chen, Gérard Clément, Dmitri V. Gal’tsov, Nikolai G. Scherbluk, and Thomas Wolf: Erratum: G2 generating technique for minimal D=5 supergravity and black rings, 1 page (2008). ps file
  • T. Wolf, Structural equations for Killing tensors of arbitrary rank Comp. Phys. Comm., 115 (1998) 316 – 329. dvi file
    ps file
  • T. Wolf, Killing Pairs in Flat Space, Gen Rel and Grav , 30 (1998) 123-129.
  • M. Mars, T. Wolf, G_2 Perfect-Fluid Cosmologies with a proper conformal Killing Vector, Class. Quantum Grav. 14 (1997) 2303-2330.
  • T. Wolf, The program CRACK for solving PDEs in General Relativity, in F.W. Hehl, R.A. Puntigam, and H. Ruder (Eds.): Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization Springer Verlag (1996), 241-258.
  • H. Stephani, T. Wolf, Spherically symmetric perfect fluids in shear-free motion – the symmetry approach, Class. Quantum Grav. 13 (1996) 1261 – 1271.
  • T. Wolf, G.Grebot, Automatic symmetry investigation of space-time metrics, Internat.J.of Modern Physics D. 3, No 1 (1994) 323-326.
  • T. Wolf, G. Neugebauer,About the non-existence of perfect fluid bodies with the Kerr metric outside , J.Class & Quantum Grav. 9, (1992) no.3 L37-L42
  • T. Wolf, About vacuum solutions of Einstein’s field equations with flat three-dimensional hypersurfaces, J. Math. Phys. 27, (1987) 2354-9.
  • T. Wolf, A class of perfect fluid metrics with flat three-dimensional hypersurfaces, J. Math. Phys. 27, (1987) 2340-53.
  • T. Wolf, A note on the equivalence of two vacuum solutions, Class. & Quantum Grav. 3, (1986)725.
  • H. Stephani, T. Wolf, Perfect fluid and vacuum solutions of Einstein’s field equations with flat 3-dim slices, in Galaxies, axisymmetric systems and relativity: essays presented to W. B. Bonnor on his 65th birthday, ed. by Malcolm MacCallum, CUP, (1985) 275-87.

Computer Go

 

  • T. Wolf: A Dynamical Systems Approach for Static Evaluation in Go, preprint, 8 pages, submitted to IEEE Transactions on Computational Intelligence and AI in Games (2010), ps file
  • T. Wolf: Positions in the game of Go as Complex Systems, Proceedings of 2009 IEEE Toronto International Conference (TIC-STH 2009) – Science and Technology for Humanity, IEEE, Toronto, pp. 222-229, ISBN 978-1-4244-3878-5. ps file
  • Book: Wolf, T., Mastering Ladders, Richmond, VA: Slate & Shell, 2008. ISBN 1-932001-40-9
  • T. Wolf: Two Applications of a Life & Death Problem Solver in Go, Journal of ÖGAI, Vol. 26 (2007), no. 2, 11-18 (special issue for the European Go Championship in Vienna 2007). ps file
  • T. Wolf and L. Shen: Checking Life & Death Problems in Go I: The Program ScanLD, ICGA Journal, vol. 30, no. 2, p67-74, and Proceedings of the Computer Games Workshop 2007 (CGW 2007), MICC Technical Report Series, ISSN 0922-8721, number 07-06 (2007), p71-80. (ps file)
    and available as presentation at that workshop in Amsterdam (15-17 June 2007):
  • L. Shen and T. Wolf, Checking Life & Death Problems in Go II: Results, preprint, 29 pages, May 2007. ps file
  • T. Wolf: Weiqi and Artificial Intelligence, in the journal “The World of Weiqi”, no 4, 2006, p63-64 (in Chinese).
  • T. Wolf: A library of eyes in Go, I: Life & death definition consistent with `bent-4′, preprint, 10 pages, accepted for publication in the proceedings of the International Workshop on Combinatorial Game theory at BIRS (Banff International Research Station), June 2005. ps file
  • T. Wolf, M. Pratola: A library of eyes in Go, II: Monolithic eyes, preprint, 16 pages, accepted for publication in the proceedings of the International Workshop on Combinatorial Game theory at BIRS (Banff International Research Station), June 2005. ps file
  • T. Wolf: A Visit to the Chinese Go Association, Canadian Go Gazette 2003-2004, 20-21.
  • M. Pratola and T. Wolf: Optimizing GoTools’ Search Heuristics using Genetic Algorithms, ICGA Journal 26 (2003), no 1, pp. 28-49. ps file
  • T. Wolf, Forward pruning and other heuristic search techniques in tsume go, Special issue of Information Sciences 122 (2000), no 1, pp. 59-76. ps file
  • T. Wolf: Heuristic search in the tsumego program GoTools, Proceedings of JCIS 98, Research Triangle Park, North Carolina, Oct 1998.
  • T. Wolf, The Diamond, British Go Journal, 108 (1997), 34-36.
  • T. Wolf, About computer go and the tsume go program GoTools, Special issue of BIT (ISBN 00110-2-57035) (1997) 139-149.
  • T. Wolf, About problems in generalizing a tsumego program to open positions, in Proceedings of the GPW’96 in Hakone/Japan, (Sep. 1996), 20-26.
  • T. Yoshikawa, K. Ishihara, T. Wolf, About a tsumego processor (in Japanese) Computer Today, 69, (1995) No 9, p 48-54.
  • T. Wolf, The program GoTools and its computer-generated tsume go database, Proceedings of the Game Programming Workshop in Japan’94, Hakone/Japan, (Oct. 1994) 84-96.
  • T. Wolf, Go und Künstliche Intelligenz (I), ‘Die Wurzel, Zeitschrift für Mathematik, 12/93, 270-276
  • T. Wolf, Quality improvements in tsume Go mass production, Proc.of the Second GO & Computer Science Workshop, Cannes, 1993, publ.by INRIA Sophia-Antipolis
  • T. Wolf, Generating tsume go problems with GoTools, in Proc.of the Fourth International Computer Olympidade, London, (1992)
  • T. Wolf, Tsume Go, with Risiko, in the Proc.of the First Go & Computer Sc.Workshop, Cannes, (1992), publ.by INRIA Sophia-Antipolis
  • T. Wolf, Tsume Go on a Computer, Proceedings of the ICOT-workshop, (Nov. 1991) in Tokyo.
  • T. Wolf, Investigating tsumego problems with “RisiKo”, in “Heuristic Programming in Artificial Intelligence 2” ed. D.N.L. Levy, D.F. Beal, Ellis Horwood Limited (1991), 153-160.

Preprints

 

  • Hussin, V., Kiselev, A.V., Krutov, A.O., Wolf, T.: N=2 Supersymmetric a=4 – KdV Hierarchy Derived via Gardner’s Deformation of Kaup-Bousinesq Equation, preprint MPIM(Bonn), 22 pages, (2009).
  • T. Wolf: A Dynamical Systems Approach for Static Evaluation in Go, preprint, 8 pages, submitted to IEEE Transactions on Computational Intelligence and AI in Games (2010), ps file
  • Adel Bouchareb, Chiang-Mei Chen, Gérard Clément, Dmitri V. Gal’tsov, Nikolai G. Scherbluk, and Thomas Wolf: Erratum: G2 generating technique for minimal D=5 supergravity and black rings, 1 page (2008). ps file
  • L. Shen and T. Wolf, Checking Life & Death Problems in Go II: Results, preprint, 29 pages, May 2007. ps file
  • T. Wolf: A library of eyes in Go, I: Life & death definition consistent with `bent-4′, preprint, 10 pages, accepted for publication in the proceedings of the International Workshop on Combinatorial Game theory at BIRS (Banff International Research Station), June 2005. ps file
  • T. Wolf, M. Pratola: A library of eyes in Go, II: Monolithic eyes, preprint, 16 pages, accepted for publication in the proceedings of the International Workshop on Combinatorial Game theory at BIRS (Banff International Research Station), June 2005. ps file
  • T. Wolf: Merging Solutions of Polynomial Algebraic Systems, preprint, 5 pages. dvi file, ps file
  • A. Triulzi and T. Wolf, Recognizing overdetermined subsystems of systems of equations, preprint, 6 pages (2000). ps file
  • T. Wolf, A study of Genetic Algorithms solving a Combinatorial Puzzle. preprint (1997), 21 pages. ps file,

Published papers

 

  1. Tsarev, S.P. and Wolf, T.: Hyperdeterminants as integrable discrete systems, J. Phys. A: Math. Theor., 42 (2009), doi: 10.1088/1751-8113/42/45/454023, 9 pages. also arXiv:0903.3864 (nlin.SI) dvi file, ps file
  2. T. Wolf: Positions in the game of Go as Complex Systems, Proceedings of 2009 IEEE Toronto International Conference (TIC-STH 2009) – Science and Technology for Humanity, IEEE, Toronto, pp. 222-229, ISBN 978-1-4244-3878-5. ps file
  3. Wolf, T., Neun, W.: About a Computer Algebra based online Mathtest, in Michael J Wester, Michel Beaudin (eds), “Computer Algebra in Education”, p. 1-6, ISBN-978-0-9754541-9-6, Aulonna Press 2008 (Proceedings of the session “Computer Algebra in Education” at the Int. Conf. on Applications of Computer Algebra (ACA’07)). dvi file, ps file
  4. Tsarev, S.P. and Wolf, T.: Classification of 3-dimensional integrable scalar discrete equations, 19 pages (2007) arXiv:0706.2464, Lett. in Math. Phys. (available at www.springerlink.com as DOI:10.1007/s11005-008-0230-2). dvi file, ps file
  5. Wolf, T.: On Solving Large Systems of Polynomial Equations Appearing in Discrete Differential Geometry, Programming and Computer Software, 34 (2008), no 2, p 75-83.
  6. Anco, S., Bluman, G. and Wolf, T.: Invertible Mappings of Nonlinear PDEs through Admitted Conservation Laws, Acta Appl Math 2008, electronic publication: http://dx.doi.org/10.1007/s10440-008-9205-7
  7. Adel Bouchareb, Chiang-Mei Chen, Gérard Clément, Dmitri V. Gal’tsov, Nikolai G. Scherbluk, and Thomas Wolf: G2 generating technique for minimal D=5 supergravity and black rings, Phys. Rev. D 76, 104032 (2007) [arXiv:0708.2361 [hep-th]]. ps file
  8. T. Wolf and L. Shen: Checking Life & Death Problems in Go I: The Program ScanLD, ICGA Journal, vol. 30 (2007), no. 2, p67-74. ps file
  9. T. Wolf: Two Applications of a Life & Death Problem Solver in Go, Journal of ÖGAI, Vol. 26 (2007), no. 2, 11-18 (special issue for the European Go Championship in Vienna 2007). ps file
  10. Kiselev, A. and Wolf, T.: Classification of integrable super-equations by the SsTools environment, Comp Phys Comm, Vol. 177, no. 3 (2007) p 315-328 (and on arXiv: nlin.SI/0609065). dvi file, ps file
  11. Wolf, T.: Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket, Gen. Relativ. Gravit. 38, no 6(2006) 1115-1127, DOI 10.1007/s10714-006-0293-2 (online jounal issue).
  12. Kiselev, A. and Wolf, T.: Supersymmetric Representations and Integrable Super-Extensions of the Burgers and Bussinesq Equations, SIGMA, Vol. 2 (2006), Paper 030, 19 pages (arXiv math-ph/0511071). ps file
  13. Sokolov, V.V. and Wolf, T.: Integrable quadratic Hamiltonians on so(4) and so(3,1), J. Phys. A: Math. Gen. 39 (2006) 1915-1926. (arXiv: nlin.SI/0405066)
  14. Anco, S. and Wolf, T.: Erratum on `Some symmetry classifications of hyperbolic vector evolution equations’, nlin.SI/0412015, JNMP, Volume 12, no 4 (2005), p 607-608.
  15. Wolf, T.: Partial and Complete Linearization of PDEs Based on Conservation Laws, in: Trends in Mathematics: Differential Equations with Symbolic Computation, p. 291-306, Birkhäuser Verlag Basel/Switzerland, Ed. Dongming Wang, Zhiming Zheng (2005), also as preprint arXiv nlin.SI/0501034 (2004). dvi file, ps file
  16. T. Tsuchida and T. Wolf: Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I, J. Phys. A: Math. Gen. 38 (2005) 7691-7733 and on arxiv as nlin.SI/0412003.
  17. Anco, S. and Wolf, T.: Some symmetry classifications of hyperbolic vector evolution equations, nlin.SI/0412015 (2004), Journal of Nonl. Math. Physics, 12, Supplement 1 (2005), p 13 – 31. dvi file, ps file
  18. T. Wolf: Applications of CRACK in the Classification of Integrable Systems, CRM Proceedings and Lecture Notes, 37 (2004) pp. 283-300. dvi file, ps file
  19. T. Wolf, O.V. Efimovskaya: Classification of integrable quadratic Hamiltonians on e(3), Regular and Chaotic Dynamics, 8, no 2 (2003), p 155-162. dvi file, ps file
  20. M. Pratola and T. Wolf: Optimizing GoTools’ Search Heuristics using Genetic Algorithms, ICGA Journal 26 (2003), no 1, pp. 28-49. ps file
  21. T. Wolf, The integration of systems of linear PDEs using conservation laws of syzygies, J. of Symb. Comp. 35, no 5 (2003) 499-526. dvi file, ps file
  22. N. Euler, T. Wolf, P.G.L. Leach and M. Euler: Linearizable Third-Order ODEs and Generalised Sundman Transformations: The Case X”’=0, Acta Applicandae Mathematicae, 76, (2003) Issue 1, March, 89-115.
    dvi file, ps file
  23. T. Wolf, A comparison of four approaches to the calculation of conservation laws, Euro. Jnl of Applied Mathematics 13 part 2 (2002) 129-152. dvi file, ps file
  24. T. Wolf, Size reduction and partial decoupling of systems of equations, J. Symb. Comp., 33 (no. 3) (2002) 367-383. dvi file, ps file
  25. V.V. Sokolov and T. Wolf, Classification of integrable polynomial vector evolution equations, J. Phys. A: Math. Gen. 34 (2001) 11139-11148. dvi file, ps file
  26. T. Wolf, The Symbolic Integration of Exact PDEs, J. Symb. Comp. 30 (no. 5) (2000) 619-629. dvi file, ps file
  27. T. Wolf, Forward pruning and other heuristic search techniques in tsume go, Information Sciences 122 (no. 1) (2000) pp. 59-76. ps file
  28. T. Wolf, A. Brand, M. Mohammadzadeh, Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions, J. Symb. Comp., 27 (1999) 221-238. dvi file, ps file
  29. V.V. Sokolov, T. Wolf, A symmetry test for quasilinear coupled systems, Inverse Problems 15 (1998) L5-L11. dvi file ps file
  30. T. Wolf, Structural equations for Killing tensors of arbitrary rank Comp. Phys. Comm., 115 (1998) 316 – 329. dvi file
    ps file
  31. T. Wolf, Killing Pairs in Flat Space, Gen Rel and Grav , 30 (1998) 123-129.
  32. M. Mars, T. Wolf, G_2 Perfect-Fluid Cosmologies with a proper conformal Killing Vector, Class. Quantum Grav. 14 (1997) 2303-2330.
  33. T. Wolf, A. Brand, Examples of the investigation of differential equations with modularized programs, Mathl. Comput. Modelling 25 (1997), no 8/9, 133 – 139.
  34. T. Wolf, About computer go and the tsume go program GoTools, Special issue of BIT (ISBN 00110-2-57035) (1997) 139-149.
  35. H. Stephani & T. Wolf, Spherically symmetric perfect fluids in shear-free motion – the symmetry approach, Class. Quantum Grav. 13 (1996) 1261 – 1271.
  36. T. Wolf, A. Brand, Approaches to solving nonlinear ODEs, Mathematics and Computers in Simulation 42, (1996) 391-398.
  37. T. Wolf, G.Grebot, Automatic symmetry investigation of space-time metrics, Internat.J.of Modern Physics D. 3, No 1 (1994) 323-326.
  38. T. Wolf, G. Neugebauer,About the non-existence of perfect fluid bodies with the Kerr metric outside , J.Class & Quantum Grav. 9, (1992) no.3 L37-L42
  39. V. Sokolov, S. Svinolupov, T. Wolf, Linearizable evolutionary equations of second order, Physics Lett.A , 163, (1992), pp.415-418
  40. H.J. Pohle, T. Wolf, Automatic Determination of Dynamical Symmetries of Ordinary Differential Equations, Computing 41, (1989) 297-307.
  41. T. Wolf, A class of perfect fluid metrics with flat three-dimensional hypersurfaces, J. Math. Phys. 27, (1987) 2340-53.
  42. T. Wolf, About vacuum solutions of Einstein’s field equations with flat three-dimensional hypersurfaces, J. Math. Phys. 27, (1987) 2354-9.
  43. T. Wolf, A note on the equivalence of two vacuum solutions, Class. & Quantum Grav. 3, (1986)725.
  44. T. Wolf, An analytic algorithm for decoupling and integrating systems of nonlinear partial differential equations, J. of Comp. Phys. 60, no. 3, (1985) 437-46.

In conference proceedings

  1. T. Wolf and L. Shen: Checking Life & Death Problems in Go I: The Program ScanLD, Proceedings of the Computer Games Workshop 2007 (CGW 2007), MICC Technical Report Series, ISSN 0922-8721, number 07-06 (2007), p71-80. ps file
  2. Kiselev, A. and Wolf, T.: On weakly non-local, nilpotent, and super-recursion operators for N=1 homogeneous super-equations, Proc. Int. Workshop “Supersymmetries and Quantum Symmetries” (SQS’05), Dubna, July 24-31, 2005. JINR, p. 231-237. (arXiv nlin.SI/0511056) dvi file, ps file,
  3. T. Tsuchida and T. Wolf: Classification of integrable coupled systems with one scalar and one vector unknown (in Japanese), in RIMS Kokyuroku, ISSN 0034-5318, No. 1302 (2003) pp. 68-90 (Proceedings of the conference “New Developments in the Research of Integrable Systems — Continuous, Discrete, Ultra-discrete”, July 31-August 2, 2002, RIMS, Kyoto Univ.).
  4. T. Wolf: Heuristic search in the tsumego program GoTools, Proceedings of JCIS 98, Research Triangle Park, North Carolina, Oct 1998.
  5. T. Wolf, About problems in generalizing a tsumego program to open positions, in Proceedings of the GPW’96 in Hakone/Japan, (Sep. 1996), 20-26.
  6. T. Wolf, Programs for Applying Symmetries of PDEs, ISSAC-95, 7-15, ACM Press, (1995).
  7. T. Wolf, The program GoTools and its computer-generated tsume go database, Proceedings of the Game Programming Workshop in Japan’94, Hakone/Japan, (Oct. 1994) 84-96.
  8. T. Wolf, A. Brand, Heuristics for Solving Overdetermined Systems of Partial Differential Equations, in Artificial Intelligence in Mathematics ed. by J.H.Johnson, S.McKee & A.Vella, The Institute of Mathematics and its Applications, Oxford University Press, (1994) 225-232.
  9. T. Wolf, An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs, Proc.of Modern Group Analysis: advanced analytical and computational methods in mathematical physics, Catania, Italy Oct.1992, Kluwer Acad.Publ. (1993) 377-385.
  10. T. Wolf, Quality improvements in tsume Go mass production, Proc.of the Second GO & Computer Science Workshop, Cannes, 1993, publ.by INRIA Sophia-Antipolis
  11. T. Wolf, Generating tsume go problems with GoTools, in Proc.of the Fourth International Computer Olympidade, London, (1992)
  12. T. Wolf, The Computer Algebra Package CRACK for investigating PDEs, with A Brand, in proceedings of ERCIM, Partial Diffential Equations and Group Theory, Bonn, (1992)
  13. T. Wolf, Tsume Go, with Risiko, in the Proc.of the First Go & Computer Sc.Workshop, Cannes, (1992), publ.by INRIA Sophia-Antipolis
  14. T. Wolf, Tsume Go on a Computer, Proceedings of the ICOT-workshop, (Nov. 1991) in Tokyo.
  15. T. Wolf, Investigating tsumego problems with “RisiKo”, in “Heuristic Programming in Artificial Intelligence 2” ed. D.N.L. Levy, D.F. Beal, Ellis Horwood Limited (1991), 153-160.
  16. T. Wolf, A package for the analytic investigation and exact solution of differential equations, Proc. EUROCAL 87, Lect. Notes in Comp. Sci. 378, (1989) 479-91.
  17. T. Wolf, Analytical decoupling, decision of compatibility and partial integration of systems of nonlinear ordinary and partial differential equations, Proc. EUROCAL 85, Lect. Notes of Comp. Sci. 204, (1985) 597-98.

Other publications

 

  1. Book: T. Wolf, Mastering Ladders, Richmond, VA: Slate & Shell, 2008. ISBN 1-932001-40-9
  2. Wolf, T., Neun, W. and Tsarev, S.P.: About parallelizing the search for 3-dim. scalar discrete integrable equations, talk given at PASCO 2007, July 2007 London/Ontario, pdf file
  3. T. Wolf: Weiqi and Artificial Intelligence, in the journal “The World of Weiqi”, no 4, 2006, p63-64 (in Chinese).
  4. T. Wolf: A Visit to the Chinese Go Association, Canadian Go Gazette 2003-2004, 20-21.
  5. T. Wolf, Crack, LiePDE, ApplySym and ConLaw, section 4.3.5 and computer program on CD-ROM in: Grabmeier, J., Kaltofen, E. and Weispfenning, V. (Eds.): Computer Algebra Handbook, Springer (2002) pp. 465-468. dvi file, ps file
  6. T. Wolf, Conservation Laws for Geodesic Motion in Curved Spaces and PDEs, section 3.1.5.1 in: Grabmeier, J., Kaltofen, E. and Weispfenning, V. (Eds.): Computer Algebra Handbook, Springer (2002) pp. 187-190. dvi file,ps file
  7. T. Wolf, The Diamond, British Go Journal, 108 (1997), 34-36.
  8. T. Wolf, The program CRACK for solving PDEs in General Relativity, in F.W. Hehl, R.A. Puntigam, and H. Ruder (Eds.): Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization Springer Verlag (1996), 241-258.
  9. T. Yoshikawa, K. Ishihara, T. Wolf, About a tsumego processor (in Japanese) Computer Today, 69, (1995) No 9, p 48-54.
  10. T. Wolf, A. Brand, Investigating DEs with CRACK and Related Programs,SIGSAM Bulletin, Special Issue, (June 1995), p 1-8.
  11. T. Wolf, APPLYSYM – a package for the application of Lie-symmetries, software distributed together with the computer algebra system REDUCE, (1995).
  12. T. Wolf, Solving overdetermined PDE-systems with CRACK, software included in the REDUCE network library, Aug.(1992)
  13. T. Wolf, Go und Künstliche Intelligenz (I), ‘Die Wurzel, Zeitschrift für Mathematik, 12/93, 270-276
  14. H. Stephani, T. Wolf, Perfect fluid and vacuum solutions of Einstein’s field equations with flat 3-dim slices, in Galaxies, axisymmetric systems and relativity: essays presented to W. B. Bonnor on his 65th birthday, ed. by Malcolm MacCallum, CUP, (1985) 275-87.