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

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

Kogan, I. (2017, March 8).

Source: ORCID

Added: September 16, 2020

2017 article

On Two Theorems of Darboux

Kogan, I. (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: NC State University Libraries, ORCID

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

2003 - present

2000 - 2003

1994 - 2000

1986 - 1993

Funding history based on the linked ORCID record.

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