Department of Mathematical Sciences
Georgia Southern University
Statesboro, GA 30460-8093
USA
E-mails:
smngai@geoergiasouthern.edu
My main research interests are fractal geometry
and the theory of multifractal measures.
I am also interested in their interactions with
the theories of wavelets, self-affine tilings,
and fractal differential equations.
Publications and Preprints
-
Laplace
operators related to self-similar measures on Rd (with J. Hu and K.-S.
Lau), J. Funct. Anal. 239 (2006), 542 - 565.
-
Vertices
of self-similar tiles (with D.-W. Deng), Illinois J. Math. 49
(2005), no. 3, 857 - 872.
-
Reptiles
with holes (with F. Jordan), Proc. Edinb. Math. Soc. (2) 48
(2005),
issue 03, 651 - 671.
-
Self-similar
measures associated with IFS with non-uniform contraction ratios (with
Y. Wang), Asian J. Math. 9 (2005), no. 2, 227 - 244.
-
Topology
of connected self-similar tiles in the plane with disconnected interiors
(with T.-M. Tang), Topology Appl. 150 (2005), no.
1-3, 139 - 155.
-
A
technique in the topology of connected self-similar tiles (with T.-M.
Tang), Fractals 12, no. 4 (2004), 389 - 403.
-
Graph-directed
iterated function systems with overlaps (with Manav. Das), Indiana
Univ. Math. J. 59 (2004), no. 1, 109-134.
-
Fractal
Laplacians on the unit interval (with Erik J. Bird and Alexander Teplyaev),
Ann.
Sci. Math. Quebec 27 (2003), no. 2, 135-168.
-
Dimensions
of the boundaries of self-similar sets (with K.-S. Lau), Experiment.
Math. 12 (2003), 13-26.
-
The Heighway
dragon revisited (with Nhu Nguyen), Discrete Comput. Geom. 29
(2003),
603-623.
-
Hausdorff
dimension of self-similar sets with overlaps (with Y. Wang), J.
London Math. Soc. (2)
63 (2001), no. 3, 655-672.
-
Iterated
function systems with overlaps and self-similar measures (with
K.-S. Lau and H. Rao),
J. London Math. Soc. (2) 63 (2001), no. 1, 99-116.
-
Multifractal measures and a weak separation condition (with K.-S.
Lau), Adv. Math. 141 (1999), 45-96.
-
Lq-spectrum of Bernoulli convolutions associated with
P.V. numbers (with K.-S. Lau), Osaka J. Math. 36 (1999),
993 -1010.
-
Lq-spectrum of the Bernoulli convolution associated with the
golden ratio (with K.-S. Lau),
Studia Math. 131 (1998), 225-251.
-
Multifractal decomposition for a family of overlapping self-similar
measures, Fractal frontiers
(Denver, CO, 1997), 151--161, World Sci. Publishing, River Edge, NJ,
1997.
-
A dimension result arising from the Lq-spectrum of a measure,
Proc.
Amer. Math. Soc. 125 (1997), 2943-2951.
Selected Presentations
-
Multifractal structure of noncompactly supported measures, Special
Session on Fractals and Tilings, 21st Summer Conference on Topology
and its Applications, Georgia Southern Univ. Statesboro, GA, July 2006.
-
On a class of Laplacians defined by fractal measures. Conference
on Differential & Difference Equations and Applications. Florida Institute
of Technology, Melbourne, FL. August 2005.
-
Fractal Laplace operators on bounded open subsets of Euclidean spaces.
2nd
Conference on Analysis and Probability on Fractals, Cornell University,
Ithaca, NY, May -- June 2005.
-
Fractal Laplace operators on open subsets of Rd. International
Conference on Applicable Harmonic Analysis, Hangzhou, China, May 2005.
-
Iterated function systems of generalized finite type. The Third
International Congress of Chinese Mathematicians (ICCM 2004), December,
2004.
-
A generalized finite type condition for iterated function systems,
2004 AMS Central Sectional Meeting, Northwestern University, Evanston,
IL, October 23, 2004.
-
Topological structure of connected self-similar tiles in the plane,
Department of Mathematics, the Chinese University of Hong Kong, June 26,
2003.
-
Hausdorff dimension of the boundaries of a class
of self-similar sets, International
Conference on Fractal Geometry & Stochastics III, Friedrichroda, Germany,
March 20, 2003.
-
Topological structure of reptiles and self-affine tiles, AMS Southeasten
Sectional Meeting, University of Central Florida, Orlando, FL, November
10, 2002.
-
Fractal Laplacians on an interval, Conference
on Analysis and Probability on Fractals, Cornell University, Ithaca, N.Y.,
June 16, 2002.
-
Fractal Fourier Series, Department of Mathematics,
The Chinese University of Hong Kong, May 15, 2002.
-
Eigenvalues and eigenfunctions of a class of fractal
Laplacians on the unit interval, Special Session on Dynamic Equations
on Time Scales, AMS-MAA Joint Meeting, Atlanta, Georgia, March 10, 2002.
-
Hausdorff dimension of boundaries of self-similar
sets, Department of Mathematics, The Chinese University of Hong
Kong, December 22, 2001.
-
Graph-directed iterated function systems with
overlaps, Special Session on Fractals of the American Mathematical
Society Meeting, Columbus, OH, September 22, 2001.
-
Self-similar measures associated to iterated
function systems with different contraction ratios, Department of Mathematics,
The Chinese University of Hong Kong, June 23, 2001.
-
Hausdorff dimension of graph self-similar sets
with overlaps, Department of Mathematics, The Chinese University of
Hong Kong, June 9, 2001.
-
Self-similar measures and dilation equations,
Colloquium,
Department of Mathematics, University of Louisville, November 10, 2000.
-
Fractal measures and dilation equations,
Georgia Institute of Technology, March 15, 2000.
-
Laplacians on fractals I, II, III, lecture series given at the Chinese
University of Hong Kong, August 9-11, 1999.
-
Absolute Continuity of Self-Similar Measures, Young Analysts Meeting
of the Southeast, Furman University, Greenville, SC, July 6-10, 1999.
-
Hausdorff Dimension of Overlapping Self-Similar Sets, Southeastern
Analysis Meeting, Vanderbilt Univ., Nashville, TN, May 20-23, 1999.
-
Dilation equations and iterated function systems with overlaps,
Minisymposium on ``Wavelets and Their Applications", SIAM Annual Meeting,
Atlanta, GA, May 9-15, 1999.
-
Hausdorff dimension of overlapping self-similar fractals,
Georgia Institute of Technology, January 13, 1999.
-
Second-order self-similar identities, AMS special session meeting
on Fractal Geometry and Related Topics, Louisville, KY, March 20-21, 1998.
-
Self-similarity in fractals, wavelets and tilings, Cornell University,
March 1998.
-
Multifractal formalism for overlapping self-similar measures, Cornell
University, February 1998.
-
Some Applications of the Renewal Theorem in Fractal Geometry, Conference
on Dynamical Systems and Fractal Geometry, ZhongshanUniv., Dec 23-26, 1997.
-
Using Mathematical Softwares in Education and Research, South China
Normal Univ., Dec 22, 1997.
-
Dilation equations with scaling factor equal to the golden ratio,
Workshop on Wavelets and Their Applications, Hong Kong, May5 - 9, 1997.
-
Multifractal decomposition for a family of overlapping self-similar
measures,
Fractal 97 --- The 4-th International Multidisciplinary Working Conference
on Fractals, Denver Colorado, USA, April 8 - 11 1997.
-
Multifractal decomposition for certain iterated function systems with
overlaps, Hong Kong Polytechnic University, Dec 1996.
-
Multifractal decomposition for certain overlapping self-similar measures,
Zhongshan Univ., China, and Guangdong Univ. of Technology, China, Nov 1996.
-
A dimension result arising from the $L^q$-spectrum of a measure,
The South China Normal University, May 1996.
-
Multifractal formalism and a dimension formula, Workshop on
nonlinear dynamics, chaos and complexity, Hong Kong Baptist Univ.,
March 1996.
-
Iterated function systems and multifractal decomposition, Hong Kong
University of Science and Technology, April 1995.
-
L^q-dimension of the Bernoulli convolution associated with the P.V.
numbers, Conference in Wavelets and Fractals, University of
Pittsburgh, May 1994.
My
Mathematical Geneology
(Last updated: October 2, 2005.)
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Web Author: Sze-man Ngai