Here is a list of all my publications, published, accepted and submitted. I list only research in preparation if its close to being finished.

Last updated 1 May, 2008

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Discrepancy, Numerical analysis, Differential Geometry, Approximation theory, Combinatorial/graph designs

Books

  • [1] "Linear independent vectors and applications", in preparation with G. Michalski and A. Sills (Georgia Southern).

    Papers

  • [1] S.B. Damelin and D.S. Lubinsky, Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erd\H{o}s weights, Canad. Math. J., (40)(1996), pp 710--736.
  • [2] S.B. Damelin and D.S. Lubinsky, Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erd\H{o}s weights II, Canad. Math. J., (40) (1996), pp 737--757.
  • [3] S.B. Damelin, Converse and smoothness theorems for Erdos weights in L_p, J. Approx. Theory., Volume 93, (3)(1998), pp 349-398.
  • [4] S.B. Damelin and D.S. Lubinsky, Jackson theorems for Erdos weights in L_p, J. Approx. Theory., Volume 94, (3) (1998), pp 333-382.
  • [5] S.B. Damelin, The Lebesgue constant of Lagrange interpolation for Erdos weights, J. Approx. Theory., Volume 94, 2, (1998), pp 235-262.
  • [6] S.B. Damelin, Smoothness theorems for Erdos Weights II, J. Approx. Theory., Volume 97, (1999), pp 220-239.
  • [7] S.B. Damelin, The weighted Lebesgue constant of Lagrange interpolation for exponential weights on [-1,1], Acta-Mathematica (Hungarica)., 81(3) (1998), pp 211-228.
  • [8] S.B. Damelin and K. Diethelm, Interpolatory Product quadratures for Cauchy principal value integrals with Freud weights, Numer. Math. 83 (1999), pp. 87-105.
  • [9] S.B. Damelin, A characterisation of smoothness for Freud weights, Journal of Computational and Applied mathematics., 99(1998), pp 463-473.
  • [10] S.B. Damelin, Smoothness theorems for generalized symmetric Pollakzek weights on [-1,1], Journal of Computational and Applied mathematics., 101 (1999), pp 87-103.
  • [11] S.B. Damelin, Marchaud inequalities for a class of Erd\H{o}s weights, Approximation Theory VIII-Vol I (1995)., Approximation and Interpolation, Chui et al, pp 169--175.
  • [12] S.B. Damelin, Lagrange interpolation for non Szeg\"o weights on [-1,1], in the Proceedings of the International Workshop on Approximation Theory and Numerical Analysis., Dedicated to Prof. M. R. Occorsio.
  • [13] S.B. Damelin, Weighted approximation for Erdos weights, Diss. Math., Vol 1 (1996), pp 163--171.
  • [14] S.B. Damelin, H.S Jung and K.H Kwon, Necessary conditions for mean convergence of Lagrange interpolation for exponential weights, Journal of Computational and Applied Mathematics, Volume 132(2)(2001), pp 357-369.
  • [15] S.B. Damelin and K. Diethelm, Boundedness and uniform approximation of the weighted Hilbert transform on the real line, Numer. Funct. Anal. and Optimiz., 22(1 and 2) (2001), pp 13-54.
  • [16] S.B. Damelin, H.S. Jung and K.H. Kwon, On mean convergence of Hermite-Fej\'er and Hermite interpolation for Erd\H{o}s weights on the real line, Journal of Computational and Applied Math, Volume 137 (2001), pp 71-76.
  • [17] S.B. Damelin, H.S. Jung and K.H. Kwon, A note on mean convergence of Lagrange interpolation in Lp, Journal of Computational and Applied mathematics, 133 (1-2) (2001), pp 277-282.
  • [18] S.B. Damelin, H.S. Jung and K.H. Kwon, Mean convergence of Hermite-Fej\'er and Hermite interpolation of higher order for Freud weights, Journal of Approximation Theory, 113 (2001), pp 21-58.
  • [19] S.B. Damelin, H.S. Jung and K.H. Kwon, Converse quadrature sum estimates for weights on the real line, Analysis, 22(2002), pp 33-55.
  • [20] S.B. Damelin, The Hilbert transform and orthonormal expansions for exponential weights, Approximation Theory X: Abstract and Classical Analysis, Chui, Schumaker and Stoekler (eds), Vanderbilt Univ. Press (2002), pp 117-135.
  • [21] S.B. Damelin, Marcinkiewicz-Zygmund inequalities and the Numerical approximation of singular integrals for exponential weights: Methods, Results and Open Problems, some new, some old; Journal of Complexity, 19(2003), pp 406-415.
  • [22] S.B. Damelin, H.S. Jung and K.H. Kwon, Mean convergence of extended Lagrange interpolation for exponential weights, Acta Applicandae Mathematicae, 76(2003), pp 17-36.
  • [23] S.B. Damelin, Pointwise bounds of orthogonal expansions on the real line via weighted Hilbert Transforms, Advances in Computational Mathematics (2006), pp 1-21.
  • [24] S.B. Damelin and H.S. Jung, Pointwise convergence of derivatives of weighted Lagrange interpolation polynomials, Journal of Computational and Applied Mathematics, Volume 173, (2)(2005), pp 303-319
  • [25] S.B. Damelin and K. Diethelm, Numerical solution of Fredholm integral equations on the line, Journal of Integral equations and Applications, Volume 13(3), 2004, pp 273-292
  • [26] S.B. Damelin and K. Diethelm, Weighted polynomial approximation and Hilbert Transforms: Their connections to the numerical solution of singular integral equations, Proceedings of Dynamic Systems & Applications, Volume 4 (2004), pp 20-26 Ed. G. S. Ladde, N.G. Medhin. M. Sambandham
  • [27] S.B. Damelin and P. Grabner, Numerical integration, energy and asymptotic equidistribution on the sphere, Journal of Complexity, 19(2003), pp 231-246. (Postscript) Corrigendum, Journal of Complexity, (20)(2004), pp 883-884.
  • [28] S.B. Damelin, J. Levesley and X. Sun, Energy estimates and the Weyl criterion on compact homogeneous manifolds, Algorithms for Approximation, A. Iske and J. Levesley (eds.), Springer-Verlag, Heidelberg, pp 359-368.
  • [29] S. B. Damelin, J. Leversley and D. Ragozin, Koksma-Hlawka inequalities in Euclidean space via Balayage, submitted.
  • [30] B. Bajnok, S.B. Damelin, J. Li and G. Mullen, A constructive method of scattering points on d dimensional spheres using finite fields, Computing (Springer), 68 (2002), pp 97-109.
  • [31] S.B. Damelin, G. Michalski, G. Mullen and D.Stone, On the number of linearly independent binary vectors of fixed length with applications to the existence of completely orthogonal structures, Monatsh Math, (1)(2003), pp 1-12.
  • [32] S. B. Damelin, G. Michalski and G. Mullen, The cardinality of sets of $k$ independent vectors over finite fields, Monatsh.Math, 150(2007), pp 289-295.
  • [33] S. B. Damelin, J. Levesley, D. Ragozin and X. Sun, Energies, Group Invariant Kernels and Numerical Integration on Compact Manifolds, submitted.
  • [34] S. B. Damelin, F.Hickernell, D. Ragozin and X. Zeng, On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space, submitted.
  • [35] S. B. Damelin, A Walk through Energy, Discrepancy, Numerical Integration and Group Invariant Measures on Measurable Subsets of Euclidean Space, accepted, numerical algorithms
  • [36] S. B. Damelin, J. Leversley, D. Ragozin and X. Sun, A descrepancy theorem for 2 point homogeneous spaces, submitted.

    Harmonic analysis, Minimal energy configurations (which occur for example in crystal structure), Orthogonal Polynomials, Random Matrices.

    Books

  • [1] Hilbert Space, Boundary Value Problems and Orthogonal Polynomials by A. Krall, 2002. (Editor).
  • [2] (with W. Xu-Ma (University of South Florida)): "Topics in Integrable Systems, Special Functions, Orthogonal Polynomials and Random Matrices", Journal of Computational and Applied Mathematics, Special Volume, 202, (1), May 2007, pp 1-154.

    Papers

  • [1] S.B. Damelin, Asymptotics of recurrence coefficients for orthonormal polynomials on the line-Magnus's method revisited, Mathematics of Computation, 73(2004), pp 191-209.
  • [2] S.B. Damelin and A. Kuijlaars, The support of the extremal measure for monomial external fields on $[ -1,1]$., Trans.Amer.Math. Soc. 351 (1999), 4561-4584.
  • [3] S.B. Damelin, P. Dragnev and A. Kuijlaars, The support of the equilibrium measure for a class of external fields on a finite interval, Pacific Journal of Mathematics, Volume 199 (2)(2001), pp 303-321.
  • [4] S.B. Damelin, The distribution of general interpolation arrays for exponential weights, Electronic Transactions of Numerical Analysis, Volume 12, 2002, pp 12-20.
  • [5] S.B. Damelin, Weighted polynomial approximation on discrete sets, Monatshefte fur Mathematik, (138)(2)(2003), pp 111-131.
  • [6] S.B. Damelin, On the maximum modulus of weighted polynomials in the plane, a theorem of Rakhmanov, Mhaskar and Saff revisited, Journal of Computational and Applied Mathematics, vol. 155 (2003), pp 455-459.
  • [7] S. B. Damelin and V. Maymeskul, On Point Energies, Separation Radius and Mesh Norm for $s$-Extremal Configurations on Compact Sets in $R^n$, Journal of Complexity, Volume 21(6), pp 845-863.
  • [8] D. Benko, S. B. Damelin and P. Dragnev, On the support of the equilibrium measure for arcs of the unit circle and real intervals, Electronic Transactions on Numerical Analysis, (25)(2006), pp 27-40
  • [9] S. B. Damelin and V. Maymeskul, Minimal Discrete Energy Problems and Numerical Integration on Compact Sets in Euclidean Spaces, Algorithms for Approximation, A. Iske and J. Levesley (eds.), Springer-Verlag, Heidelberg, pp 369-378.
  • [10] S. B. Damelin, Advances on regularity and dislocation properties of energy minimizing configurations, discrepancy, manifold learning and their applications, submitted.
  • [11] S. B Damelin and V. Maymeskul, On dislocation and mesh norm of s extremal configurations, to appear Acta Math (Hung)
  • [12] D. Benko, S. B. Damelin and P. Dragnev, On supports of equlibrium measures with concave signed equilibria and the Iterated Balayage Algorithm, manuscript

    Computer Vision, Imaging, Recognition/Feature Extraction Problems, Signal Processing, Computational intelligence, Inverse problems.

    The work below can be found on the comprehensive webpage

    Cyber which covers most of my ongoing work in these areas.

    Books

  • [1] "Topics in Applied Mathematics, Computer Vision, Imaging and Wavelets", in preparation with W. Miller (U Minnesota). [Please note the link to this will be active when the book is complete]

    Papers

  • [1] D. Greenblatt and S.B. Damelin, Laminar boundary layers subject to high frequency travelling--wave fluctuations, AJAA Journal., Vol. 31, {\bf 5} (1993), pp 957--959.
  • [2] L. H. Damelin, S. Volles, J. M. Whitcutt, S. B. Damelin, J. J. Alexander, Hormesis: A stress response in cells exposed to low levels of heavy metals, Human and Experimental Toxicology, Volume 19 (2000), pp 420-430.
  • [3] Y. Ma, S. B. Damelin, O. Masoud and N. Papanikolopoulos, Activity Recognition via Classification Constrained Diffusion Maps, ISCV (International Symposium on Computer Vision), 2006, pp 1-8.
  • [4] S. B. Damelin and A. J. Devaney, Local Paley Wiener theorems for analytic functions on the unit sphere, Inverse Problems, (23)(2007), pp 1-12.
  • [5] S. B. Damelin, On Bounds for Diffusion, Discrepancy and Fill Distance Metrics, Principal Manfolds, Springer Verlag 2007, Editor, A. Gorban
  • [6] S. B. Damelin and A. J Devaney, Local Paley Wiener theorems, to appear in Proceedings of Inverse Problems Symposium, East Lansing, Michigan, 11-12 June 2007.
  • [7] J. H Ann, P. Bigeleisen and S. B. Damelin, Image segmentation of nerves by ultrasound using modified Mumford-Shah and prior information methods, submitted.
  • [8] Rui Xu, Steven Damelin, and Donald C. Wunsch II, "Applications of diffusion maps in gene expression data-based cancer diagnosis analysis," In Proceedings of the 29th Annual International Conference of IEEE Engineering in Medicine and Biology Society, Lyon, France, pp. 4613-4616, August, 2007.
  • [9] Rui Xu, Steven Damelin, B. Nadler, and Donald C. Wunsch II, Clustering of high-dimensional gene expression data with feature filtering methods and diffusion maps, Proceedings of the International Conference on Biomedical Engineering and Informatics, Sanya, China, May, 2008.
  • [10] R. Xu, S. B. Damelin and D. Wunsch, Clustering of Cancer Tissues using Diffusion Maps and Fuzzy ART with Gene Expression Data, submitted.
  • [11] Kerry-Anne Cawse, Steven Damelin, Richard McIntyre, Michael Mitchley, Louis du Plessis and Michael Sears, An Investigation of data compression for Hyperspectral core image data, submitted for publication.
  • [12] G. Sundaramoorthi, A. Yezzi, Francisco Fedele, Steven Damelin, Anuradha Godavarty, BEM based Fluorescense optical tomography via Sobolev active contours for Breast Cancer Diagnostic Imaging, in preperation.