Works (34)
Updated: September 1st, 2023 05:00
2023 article
Invariants: Computation and Applications
PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC & ALGEBRAIC COMPUTATION, ISSAC 2023, pp. 40–49.
author keywords: group actions; algebraic and differential invariants; moving frames; equivalence; signatures
Sources: ORCID, Web Of Science
Added: July 6, 2023
2021 journal article
Non-congruent non-degenerate curves with identical signatures
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 63(5), 601–625.
author keywords: Closed curves; Euclidean transformations; Signature curves; Signature graphs (quivers); Object recognition
arxiv.org (repository)
Sources: ORCID, Web Of Science
Added: February 10, 2021
2021 article
Non-congruent non-degenerate curves with identical signatures (Feb, 1007/s10851-020-01015-x, 2021)
JOURNAL OF MATHEMATICAL IMAGING AND VISION, Vol. 63, pp. 776–776.
Sources: ORCID, Web Of Science
Added: April 8, 2021
2020 journal article
A mixed boundary value problem for u(xy) = f (x , y, u, u(x), u(y))
JOURNAL OF DIFFERENTIAL EQUATIONS, 268(12), 7535–7560.
author keywords: Second order hyperbolic partial differential equations; Mixed problems; Non-uniqueness
Sources: Web Of Science, ORCID
Added: April 6, 2020
2020 journal article
Differential Signatures of Algebraic Curves
SIAM Journal on Applied Algebra and Geometry.
author keywords: algebraic curves; projective action; affine action; Euclidean action; equivalence classes of curves; differential invariants; classifying invariants; signatures; Fermat curves
Source: ORCID
Added: March 11, 2020
2019 journal article
Jacobians with prescribed eigenvectors
Differential Geometry and Its Applications, 65, 108–146.
Sources: Web Of Science, Crossref, ORCID
Added: July 1, 2019
2018 journal article
A Generalization of an Integrability Theorem of Darboux
The Journal of Geometric Analysis, 29(4), 3470–3493.
author keywords: Overdetermined systems of PDEs; Integrability theorems; Systems of first order PDEs; Local existence; Picard iteration
Sources: ORCID, Crossref
Added: July 20, 2019
2017 journal article
Algorithm for computing mu-bases of univariate polynomials
JOURNAL OF SYMBOLIC COMPUTATION, 80, 844–874.
author keywords: mu-basis; Syzygy module; Polynomial vectors; Rational curves
Sources: Web Of Science, ORCID
Added: August 6, 2018
2017 article
Degree-optimal moving frames for rational curves
(2017, March 8).
Source: ORCID
Added: September 16, 2020
2017 article
On Two Theorems of Darboux
(2017, September 21).
Source: ORCID
Added: September 16, 2020
2015 journal article
Invariants of objects and their images under surjective maps
Lobachevskii Journal of Mathematics, 36(3), 260–285.
author keywords: invariant; surjective map; curve; centro-affine; affine; projective actions; image processing
Sources: Crossref, ORCID
Added: July 20, 2019
2013 journal article
Object-Image Correspondence for Algebraic Curves under Projections
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 9.
author keywords: central and parallel projections; finite and affine cameras; camera decomposition; curves; classifying differential invariants; projective and affine transformations; signatures; machine vision
Sources: Web Of Science, ORCID
Added: August 6, 2018
2012 journal article
Extensions for Systems of Conservation Laws
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 37(6), 1096–1140.
author keywords: Eigenvector fields; Entropies; Extensions; Frame bundles; Hessian metric; Hyperbolic systems of conservation laws; Integrability; Rich systems
Sources: Web Of Science, ORCID
Added: August 6, 2018
2012 conference paper
Object-image correspondence for curves under central and parallel projections
Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12, 373–382.
Event: the 2012 symposuim
Sources: Crossref, ORCID
Added: July 20, 2019
2010 journal article
Classification of Curves in 2D and 3D via Affine Integral Signatures
ACTA APPLICANDAE MATHEMATICAE, 109(3), 903–937.
author keywords: Euclidean and affine transformations; Equivalence problem for curves; Integral invariants; Signatures; Image recognition
Sources: Web Of Science, ORCID
Added: August 6, 2018
2010 journal article
SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(2), 211–254.
author keywords: Hyperbolic systems of conservation laws; eigenvector fields; eigenvalues; rich systems; Frobenius, Darboux and Cartan-Kahler integrability theorems; connections on frame bundles
Sources: Web Of Science, ORCID
Added: August 6, 2018
2009 other
Construction of conservative systems
Sources: Crossref, ORCID
Added: July 20, 2019
2007 conference paper
3D Face Recognition using Euclidean Integral Invariants Signature
2007 IEEE/SP 14th Workshop on Statistical Signal Processing, 156–160.
Event: 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Sources: Crossref, ORCID
Added: July 20, 2019
2007 conference paper
3D Mixed Invariant and its Application on Object Classification
2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07, 1.
Event: 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing
Sources: Crossref, ORCID
Added: July 20, 2019
2007 conference paper
College geometry students' uses of technology in the process of constructing arguments
In T. Lamberg (Ed.), Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 1153–1160).
Ed(s): T. Lamberg
Source: NC State University Libraries
Added: July 28, 2019
2007 conference paper
Integral invariants for 3D curves: an inductive approach
In C. W. Chen, D. Schonfeld, & J. Luo (Eds.), Visual Communications and Image Processing 2007 (Vol. 6508).
Ed(s): C. Chen, D. Schonfeld & J. Luo
Event: Electronic Imaging 2007
author keywords: 3D affine and Euclidean transformations; integral affine invariants; moving frames; object classification
Sources: Crossref, ORCID
Added: July 20, 2019
2007 article
Rational invariants of a group action. Construction and rewriting
JOURNAL OF SYMBOLIC COMPUTATION, Vol. 42, pp. 203–217.
author keywords: rational invariants; algebraic group actions; cross-section; Grobner basis; differential invariants; moving frame
Sources: Web Of Science, ORCID
Added: August 6, 2018
2007 journal article
Smooth and algebraic invariants of a group action. Local and global constructions.
Foundations of Computational Math., 7(4), 345–383.
Source: NC State University Libraries
Added: July 28, 2019
2007 journal article
Smooth and algebraic invariants of a group action: Local and global constructions
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 7(4), 455–493.
author keywords: rational and algebraic invariants; smooth and differential invariants; algebraic and Lie group actions; cross-section; moving frame method; Grobner basis
Sources: Web Of Science, ORCID
Added: August 6, 2018
2007 conference paper
The effects of a dynamic program for geometry on college students' understandings of properties of quadrilaterals in the Poincare Disk model
Proceedings of the 9th International Conference on Mathematics Education in a Global Community, 613–618.
Source: NC State University Libraries
Added: July 10, 2019
2005 conference paper
3D object representation with topo-geometric shape models
Proceedings of European Signal Processing Conference (EUSIPCO), 2386–2389. http://www.scopus.com/inward/record.url?eid=2-s2.0-84863687976&partnerID=MN8TOARS
Sources: NC State University Libraries, ORCID
Added: July 10, 2019
2005 conference paper
Rotation invariant topology coding of 2D and 3D objects using Morse theory
IEEE International Conference on Image Processing 2005, 3, 796–799.
Event: rnational Conference on Image Processing
Sources: Crossref, ORCID
Added: July 20, 2019
2003 journal article
Invariant Euler-Lagrange equations and the invariant variational bicomplex
Acta Applicandae Mathematicae, 76(2), 137–193.
author keywords: calculus of variations; Lie group; moving frame; differential invariant; Euler-Lagrange equation; variational bicomplex
Sources: ORCID, NC State University Libraries
Added: July 28, 2019
2003 journal article
Two Algorithms for a Moving Frame Construction
Canadian Journal of Mathematics, 55(2), 266–291.
Sources: Crossref, ORCID
Added: July 20, 2019
2002 conference paper
Computation of canonical forms for ternary cubics
Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02, 151–160.
Event: the 2002 international symposium
Sources: Crossref, ORCID
Added: July 28, 2019
2001 other
Inductive construction of moving frames
Sources: Crossref, ORCID
Added: July 28, 2019
2001 other
The invariant variational bicomplex
Sources: Crossref, ORCID
Added: July 28, 2019
2000 thesis
Inductive approach to Cartan's moving frame method with applications to classical invariant theory
https://www-proquest-com.prox.lib.ncsu.edu/docview/304612470/fulltextPDF/23BAF25E0A874972PQ/8?accountid=12725
Source: ORCID
Added: September 15, 2020
2000 journal article
Symmetries of Polynomials
Journal of Symbolic Computation, 29(4-5), 485–514.
Sources: Crossref, ORCID
Added: July 28, 2019
Employment
Updated: September 15th, 2020 16:26
2003 - present
North Carolina State University Raleigh, North Carolina, US
Professor
Mathematics
2000 - 2003
Yale University New Haven, Connecticut, US
Gibbs Instructor
Mathematics
Education
Updated: September 15th, 2020 16:35
1994 - 2000
University of Minnesota Minneapolis, Minnesota, US
Ph.D.
Mathematics
1986 - 1993
Gubkin Russian State University of Oil and Gas Moscow, RU
diploma (equivalent of MS)
Applied Mathematics
Funding History
Funding history based on the linked ORCID record. Updated: September 15th, 2020 14:29
grant
September 1, 2013 - August 31, 2017
AF: Small: Quantifier elimination by group analysis
Directorate for Computer & Information Science & Engineering
grant
July 1, 2013 - June 30, 2017
Collaborative Research: Fundamental challenges in nonlinear hyperbolic PDEs
Directorate for Mathematical & Physical Sciences
grant
September 15, 2007 - August 31, 2010
Symbolic Group-Invariant Computation
Directorate for Computer & Information Science & Engineering
grant
September 15, 2007 - August 31, 2015
Noyce Mathematics Education Teaching Scholars at NC State University
Directorate for Education & Human Resources
grant
September 15, 2005 - August 31, 2009
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS): Parallel Computer Algebra
Directorate for Mathematical & Physical Sciences
