Ian Anderson Ph.D.

Publications | Book Chapters

• Anderson, I.M, (1976). The Uniqueness of the Neutrino Energy-Momentum Tensor and the Einstein- Weyl Equations: Topics in Differential Geometry. Academic Press

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Journal Articles

Academic Journal

• Fels, M.E, Anderson, I.M, (2015). Backlund Transformations for Darboux Integrable Systems: Examples and Applications. Journal of Geometry and Physics, 102, 1-31. doi: doi:10.1016/j.geomphys.2015.12.005
• Fels, M.E, Anderson, I.M, (2014). Backlund Transformations for Darboux Integrable Differential Systems: General Theory. Selecta Mathematica, New Series
• Anderson, I.M, Torre, C.G, (2013). GR 20 Workshop, Warsaw, July 2013.
• Anderson, I.M, Torre, C.G, (2013). Lessons from GR 20 Workshop, Warsaw, July 2013.
• Fels, M.E, Anderson, I.M, (2013). The Cauchy Problem for Darboux Integrable Systems and non-linear D'Alembert Formulas. Symmetry, Integrability and Geometry: Methods and Applications, 9:17, 1-22.
• Torre, C.G, Anderson, I.M, (2012). New symbolic tools for differential geometry, gravitation, and field theory. Journal of Mathematical Physics, 53, 013511 (12 pages).
• Torre, C.G, Anderson, I.M, (2011). New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory. preprint
• Anderson, I.M, Fels, M.E, Vassiliou, P., (2009). Superposition Formulas for Darboux Integrable Exterior Differential Systems. Advances in Mathematics, 221:6, 1910-1963.
• Anderson, I.M, Fels, M.E, (2005). Exterior Differential Systems with Symmetry. Acta Applicandae Mathematicae, 87, 3-31.
• Anderson, I.M, Fels, M.E, (2002). Transverse Group Actions on Bundles. Topology and its Applications, 123:3, 443-459.
• Anderson, I.M, Fels, M., Torre, C., (2001). Group invariant solutions in mathematical physics and differential geometry. Contemporary Mathematics, 285
• Anderson, I.M, Fels, M.E, Torre, C.G, (2000). Group invariant solutions without transversality. Comm. Math. Phys., 212:3, 653-686.
• Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Department of Mathematics Utah State University Logan, Utah 84322.
• Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Symmetry Reduction Without Transversality. arXiv preprint math-ph/9910015
• Anderson, I.M, Juras, M., (1997). Generalized Laplace Invariants and the Method of Darboux. Duke J. Math., 89, 351-375.
• Fels, M.E, Anderson, I.M, (1997). Symmetry reduction of variational bicomplexes and the principle of sym- metric criticality. Amer. Jour. Math., 119:3, 609-670.
• Anderson, I.M, Kamran, N., (1997). The Variational Bicomplex for Second Order Partial Differential Equa- tions in the Plane. Duke J. Math, 87, 265-319.
• Anderson, I.M, Torre, C., (1996). Asymptotic Conservation Laws in Classical Field Theory. Phys. Rev. Lett., 77, 4109-4133.
• Anderson, I.M, Torre, C.G, (1996). Asymptotic conservation laws in classical field theory. Physical review letters, 77:20, 4109.
• Anderson, I.M, Torre, C.G, (1996). Classification of local generalized symmetries for the vacuum Einstein equations. Communications in mathematical physics, 176:3, 479–539.
• Anderson, I.M, Torre, C.G, Fredenhagen, K., Jörß, M., Guhr, T., Bogomolny, E., Leyvraz, F., Schmit, C., Jakšic, V., Pillet, C., others, , (1996). Miscellaneous front pages, Comm. Math. Phys., Volume 176, Number 3 (1996).
• Anderson, I.M, Pohjanpelto, J., (1996). Symmetries, Conservation Laws, and Variational Principles for Vector Field Theories. Proc. Camb. Phil. Soc., 120, 369-384.
• Anderson, I.M, Torre, C., (1996). The Classification of Local Generalized Symmetries for the Einstein Equations. Comm. Math. Physics, 176, 479-539.
• Anderson, I.M, Pohjanpelto, J., (1995). Variational Principles for Differential Equations with Symmetries and Conservation Laws II: Polynomial Equations. Mathematische Annalen, 301, 627-653.
• Anderson, I.M, Torre, C.G, (1994). Classification of generalized symmetries for the vacuum Einstein equations. arXiv preprint gr-qc/9404030
• Anderson, I.M, Pohjanpelto, J., (1994). Variational Principles for Differential Equations with Symmetries and Conservation Laws I: Second Order Scalar Equations. Mathematische Annalen, 299, 191-222.
• Anderson, I.M, Kamran, N., Olver, P., (1993). Internal, External and Generalized Symmetries. Advances in Mathematics, 100, 53-100.
• Anderson, I.M, Torre, C., (1993). Symmetries of the Einstein Equations. Physical Rev. Let- ters, 70, 3525-3529.
• Torre, C.G, Anderson, I.M, (1993). Symmetries of the Einstein equations. arXiv preprint gr-qc/9302033
• Anderson, I.M, Thompson, G., (1992). The Inverse Problem in the Calculus of Variations for Ordinary Differen- tial Equations. Memoirs of the AMS, 473
• Anderson, I.M, (1988). Aspects of the Inverse Problem to the Calculus of Variations. Archivum Mathematicum (Brno), 24, 329-370.
• Anderson, I.M, Arms, J., (1986). Perturbations of Conservation Laws in Field Theories. Annals of Physics, 167, 354-689.
• Anderson, I.M, Bezdek, J., (1985). An Application of the c-Varieties Clustering Algorithm to Polygonal Curve Fitting. IEEE Trans SMC, 15, doi: 637-641
• Anderson, I.M, (1985). Determinantal Ideals and the Capelli Identities. Linear Algebra and its Applications, 69, 269-277.
• Anderson, I.M, Bezdek, J., (1984). Curvature and Tangential Deflections of Discrete Arcs. IEEE Trans. PAMI, 6, 27-40.
• Anderson, I.M, (1984). Natural Variational Principles on Riemannian Structures. Annals ofMath- ematics, 120, 329-370.
• Anderson, I.M, Duchamp, T., (1984). Variational Principles for Second-Order Quasi-Linear Scalar Equations. J. Diff. Equations, 51, 1-47.
• Anderson, I.M, (1981). The Principle of Minimal Gravitational Coupling. Arch. RationalMech. Anal., 75, 349-372.
• Anderson, I.M, Duchamp, T., (1980). On the Existence of Global Variational Principles. Amer. J. Math., 102, 781-868.
• Anderson, I.M, (1979). On the Characterization of Energy-Momentum Tensors. General Relativ- ity and Gravitation, 10, 461-465.
• Anderson, I.M, (1978). On the Structure of Divergence-Free Tensors. J. Math. Phys, 19, 2570-2575.
• Anderson, I.M, (1978). Tensorial Euler-Lagrange Expressions and Conservation Laws. Aequa- tiones Mathematicae, 17, 255-291.
• Anderson, I.M, Lovelock, D., (1976). A Characterization of the Einstein Tensor in Terms of Spinors. J. Math. Phys., 17, 1001-1003.
• Anderson, I.M, (1974). The Neutrino Energy-Momentum Tensor and the Weyl Equations in Curved Space-Time. General Relativity and Gravitation, 6, 621-642.
• Anderson, I.M, Leistner, T., Nurowski, P., Explicit Ambient Metrics and Holonomy. Journal of Differential Geometry

In-House Journal

Professional Journal

• Anderson, I.M, Pohjanpelto, J., (2012). Variational principles for natural divergence-free tensors in metric field theories. Journal of Geometry and Physics , 62, 2376--2388.
• Anderson, I.M, Kruglikov, B., (2011). Rank 2 distributions of Monge equations: Symmetries, equivalences, extensions. Advances in Mathematics, 228, 1435-1465.

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | MultiMedia

Software

• Torre, C.G, Anderson, I.M, (2016). DifferentialGeometry - third USU release (beta). *
• Torre, C.G, Anderson, I.M, (2015). DifferentialGeometry - second USU release. *
• Torre, C.G, Anderson, I.M, (2015). DGApplications, Version 2. *
• Torre, C.G, Anderson, I.M, (2015). DifferentialGeometry - first USU release. *
• Anderson, I.M, Torre, C.G, (2013). DIfferentialGeometry software in Maple 17. Maplesoft *
• Torre, C.G, Anderson, I.M, (2012). DifferentialGeometry software in Maple 16. Maplesoft

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Technical Reports

Research Reports

• Torre, C.G, Anderson, I.M, (2011). New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory. arXiv.org *

Other Reports

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Other

Other

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.