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| Perturbation Theory in Differential Homological Algebra I, with V.K.A.M. Gugenheim, IL. J. Math., 33 (1989), 566-582. pdf | Keywords: distinguished resolution;
twisting cochains; free resolutions over the group ring of
two-stage nilpotent groups; homological perturbation;
differential tor
Classification: *55U99 Applied homological algebra and category theory 55T20 Eilenberg-Moore spectral sequences 57T10 Homology and cohomology of Lie groups 55R20 Spectral sequences and homology of fiber spaces 55P62 Rational homotopy theory 57T35 Appl. of Eilenberg-Moore spectral sequences |
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| Perturbation Theory in Differential Homological Algebra II, with V.K.A.M. Gugenheim and Jim Stasheff, IL. J. Math., 35 (1991), 359-373. pdf | Keywords: homological perturbation theory;
twisting cochain; differential Tor; differential complexes
representing a given chain homotopy type; coalgebra; SDR-data;
coalgebra homotopy; coderivation; tensor coalgebra; bar
construction differential; perturbation lemma
Classification: *55U15 Chain complexes 57T30 Bar and cobar constructions 18G35 Chain complexes (homological algebra) 18G15 Ext and Tor, generalizations |
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| A Fixed Point Approach to Homological Perturbation Theory, with Don Barnes, Proc. AMS, 112 (1991), 881-892. pdf | Keywords: homological perturbation;
SDR-data; chain homotopy; perturbation algebra
Classification: *55U15 Chain complexes 18G35 Chain complexes (homological algebra) |
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| Resolutions via homological perturbation, J. Symbolic Comput. 12 (1991), 71--87. pdf | Keywords: resolutions; homological
perturbation theory
Classification: *55-04 Machine computation, programs (algebraic topology) 68W30 Symbolic computation and algebraic computation 55U99 Applied homological algebra and category theory |
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| Homological Perturbation Theory Hochschild Homology and Formal Groups, Cont. Math., 189 (1992), Amer. Math. Soc. pdf | Keywords: filtered algebra; graded
algebra; resolutions; enveloping algebra; homological
perturbation; differential homological algebra; augmented
algebra; chain complex; contraction; reduced bar construction;
Hochschild cohomology; cohomology of finitely generated torsion
free nilpotent groups; formal groups
Classification: *16W50 Graded associative rings and modules 18G35 Chain complexes (homological algebra) 55U15 Chain complexes 16E40 Homology and cohomology theories for assoc. rings 14L05 Formal groups 57T30 Bar and cobar constructions 16W60 Filtrations and valuations, etc. (assoc. rings and algebras) 20J05 Homological methods in group theory 18G10 Resolutions (homological algebra) |
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| Resolutions which Split off of the Bar Construction, J. Pure and Appl. Alg., 84 (1993) 311-329. pdf | Keywords: distinguished resolution;
twisting cochains; free resolutions over the group ring of
two-stage nilpotent groups; homological perturbation;
differential tor
Classification: *55U99 Applied homological algebra and category theory 55T20 Eilenberg-Moore spectral sequences 57T10 Homology and cohomology of Lie groups 55R20 Spectral sequences and homology of fiber spaces 55P62 Rational homotopy theory 57T35 Appl. of Eilenberg-Moore spectral sequences |
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| Algebraic Aspects of the Quantum Yang-Baxter Equation, with David Radford, Journal of Algebra, 154 (1993), 228-288. pdf | Keywords: quantum deformations;
bialgebras; Hopf algebras; left quantum Yang-Baxter
$H$-modules; graded Yang-Baxter equation; comodule algebra;
quantum plane
Classification: *17B37 Quantum groups and related deformations 16W30 Hopf algebras (assoc. rings and algebras) |
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| Construction of Quantum Groups and the Yang-Baxter Equation with Spectral Parameter, with Paolo Cotta-Ramusino and Maurizio Rinaldi, in Symmetries in Science VI, editor B. Gruber, Plenum Press, New York (1993). pdf | Keywords: quantum groups; Yang-Baxter
equation with spectral parameter
Classification: *17B37 Quantum groups and related deformations 81R50 Quantum groups and related algebraic methods in quantum theory |
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| Object-Oriented Mathematical Programming and Symbolic/Numeric Interface, with Richard Luczak, 3rd International Conf. on Expert Systems for Numerical Computing, May, 1993, in MATCOM 981, Mathematics and Computers in Simulation 36 (1994), no. 4-6, 493-503, Elsevier Science B.V, The Netherlands. pdf | Keywords: Finite element method; FEM; NAG
library; AXIOM; mathemtical programming
Classification: *90 Operations research, mathematical programming 90-04 Explicit machine computation and programs (not the theory of computation or programming) |
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| On the Quantum Yang-Baxter Equation with Spectral Parameter I, Lond. Maths. Soc. Proc., 68 (1994), 31-50. pdf | Keywords: coalgebra; tensor product;
quantum Yang-Baxter solutions; spectral parameter
Classification: *17B37 Quantum groups and related deformations 16W30 Hopf algebras (assoc. rings and algebras) 81R50 Quantum groups and related algebraic methods in quantum theory 81-08 Computational methods (quantum theory) 82B23 Exactly solvable models |
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| Next generation computer algebra systems AXIOM and the Scratchpad concept: Applications to research in algebra, Gyllenberg, Mats (ed.) et al., Analysis, algebra, and computers in mathematical research. Proceedings of the 21st Nordic congress of mathematicians, Lulea Univ. of Technology, Sweden, 1992. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 156, 201-222 (1994). pdf | Keywords: Ext; Tor; bar construction;
perturbation lemma; Scratchpad; symbolic exponents; symbolic
limits; AXIOM; computer algebra; parameterized types; generic
operators; domains
Classification: *18-04 Machine computation, programs (category theory) 68W30 Symbolic computation and algebraic computation 20-04 Machine computation, programs (group theory) 18G15 Ext and Tor, generalizations 18G35 Chain complexes (homological algebra) 55U15 Chain complexes 20J05 Homological methods in group theory 16E40 Homology and cohomology theories for assoc. rings |
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| The Cohomology Ring of the Free Loop Space of a Wedge of Spheres and Cyclic Homology, with Clas Löfwall, CR Acad. Sci., Paris, 320 (1995), 1237-1242. pdf | Keywords: wedge product of two 3-spheres;
free loop space; Poincare series
Classification: *57T25 Homology and cohomology of H-spaces 19D55 K-theory and homology 55P35 Loop spaces |
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| Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach, with David E. Radford, Mathematics and its Applications Series, no. 423, Springer (1997), xx+293pp. Springer online listing | Keywords: Faddeev-Reshetikhin-Takhtadzhan
constructions; quantum Yang-Baxter equations; quantum groups;
coalgebras; bialgebras; Hopf algebras; comodules; quantum
universal enveloping algebras; quantum function algebras;
quasitriangular Hopf algebras; Drinfeld doubles;
coquasitriangular bialgebras
Classification: *16W30 Hopf algebras (assoc. rings and algebras) 17B37 Quantum groups and related deformations 17-02 Research monographs (nonassoc. rings and algebras) 16-02 Research monographs (assoc. rings and algebras) 81R50 Quantum groups and related algebraic methods in quantum theory 81-02 Research monographs (quantum theory) |
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| Solutions to the Quantum Yang-Baxter Equation Having Certain Bialgebras as Their Reduced FRT Construction, with David E. Radford, IL. J. Math., 42 (1998), 630-654. pdf | Keywords: Faddeev-Reshetikhin-Takhtadzhan
constructions; quantum Yang-Baxter equations; quantum groups;
coalgebras; bialgebras; Hopf algebras; comodules;
Classification: *16W30 Hopf algebras (assoc. rings and algebras) 17B37 Quantum groups and related deformations 81R50 Quantum groups and related algebraic methods in quantum theory |
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| Entry on Homological Perturbation Theory in the Encyclopaedia of Mathematics, Supplement II, Kluwer Academic Press, (2000). pdf | Keywords: SDR, Strong Deformation
Retraction, chain complex, perturbation lemma, transference
problem, generalized Gugenheim-Munkholm formula, tensor trick;
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| Transferring Algebra Structures Up to Homology Equivalence, with Leif Johansson, Scand. Math., 89 (2001), no. 2, 181--200. pdf | Keywords: A-infinity algebra; SDR; perturbation lemma; Gugenheim-Munkholm formula; deRham theory; shm-map; Massey product; |
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| Computing Resolutions Over Finite p-Groups, with Johannes Grabmeier, Algebraic Combinatorics and Applications, A. Betten, A. Kohnert, R. Laue, and A. Wassermann (Eds), Springer-Verlag, Heidelberg, (2001). pdf | Keywords: p-groups; resolution; chain complex; perturbation lemma; SDR; Hadamard code; cocycle; |
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| On Constructing Resolutions Over the Polynomial Algebra, with Leif Johansson and Emil Sköldberg, Special Issue of Homology, Homotopy and Applications in honor of Jan-Erik's Roos' 65th birthday, Homology, Homotopy and Applications, vol. 4, no. 2, pp. 315-336, (2002) pdf | Keywords: Homological Perturbation,
Resolution, Splitting Homotopy, Polynomial Ring, Gröbner Basis,
Normal Form
Classification: *55U15 Chain complexes 57T30 Bar and cobar constructions 18G35 Chain complexes (homological algebra) *55-04 Machine computation, programs (algebraic topology) 68W30 Symbolic computation and algebraic computation |
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| Differential Equations, Spencer Cohomology, and Computing Resolutions, with Werner M. Seiler, Georgian Math. J., vol. 9, No. 4, 2002, 723-772. pdf | Keywords: partial differential equations,
Spencer cohomology, formal theory, homological resolutions,
symbolic computation
Classification: 35A10 Cauchy-Kovalevskaya theorems 35N05, 35N10 Overdetermined systems 35A25 Other special methods 57T30 Bar and cobar constructions 18G35 Chain complexes (homological algebra) 18G10 Resolutions 18G15 Ext and Tor 18G60 Other (co) homology theories 78-04 Explicit machine computation and programs 68W30 Symbolic computation and algebraic computation |
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| A New Finite Difference Method for the Helmholtz Equation Using Symbolic Computation, with Richard Luczak and John W. Nehrbass, International Journal of Computational Engineering Science, Mar 2003, Vol. 4 Issue 1, p121-144. pdf | Keywords: finite difference method,
Helmholtz equation, symbolic computation, refined mesh,
interpolation
Classification: 78M20 Finite difference methods 78-04 Explicit machine computation and programs 68W30 Symbolic computation and algebraic computation |
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| Decision trees for binary classification variables grow equally with the Gini impurity measure and Pearsons chi-square test, with Johannes Grabmeier, Int. J. Business Intelligence and Data Mining, to appear in Vol. 2, No. 2, 2007 | Keywords: decision tree; Ginis impurity measure; Pearsons chi-square test; entropy; binary classification; contingency matrix; power series expansion of entropy; symmetric polynomial; purity measure. |
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| Some Notes on Symbolic Computation Ongoing thoughts (1999 -- 2011). | Keywords: computer algebra; symbolic computation; Baker-Cambell-Housdorff formula; Lie algebra; Steenrod algebra; normal form; rewrite rule;homology decomposition; SDR; finite difference method; Helmholtz equation |