Projects per year
Personal profile
About
Dr. Ngai received his B.Sc. from University of Hong Kong, and his M.A. and Ph.D. from University of Pittsburgh. After receiving his Ph.D., he has held research and teaching positions at The Chinese University of Hong Kong, Cornell University, and Georgia Institute of Technology. He joined the Department of Mathematical Sciences of Georgia Southern University in 2000. His main research areas are fractal geometry and the theory of fractal measures. Because of the underlying self-similarity, he is also interested in the theories of wavelets, self-affine tiles, fractal differential equations, and Markov chains and boundary theory on fractals.
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Related documents
Education/Academic qualification
Ph.D. in Mathematics, University of Pittsburgh
… → 1995
M.A. in Mathematics, University of Pittsburgh
… → 1989
B.S. in Mathematics/Physics, University of Hong Kong
… → 1987
Keywords
- Q Science (General)
Disciplines
- Other Mathematics
Research Interests
- Fractal Partial Differential Equations
- Fractal Sets
- Fractal Measures
- Self-affine Tiles
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Collaborations and top research areas from the last five years
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Projects/Grants
- 2 Finished
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Induced Dirichlet forms on Self-similar sets
Feng, D.-J. D. (PI), Lau, K.-S. (CoPI) & Ngai, S.-M. (CoPI)
01/1/16 → 12/31/19
Project: Research
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Boundary Theory and Analysis on Fractals
Lau, K.-S. (PI) & Ngai, S.-M. (CoPI)
01/1/10 → 12/31/13
Project: Research
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Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds
Ngai, S. M. & Xu, Y., May 2023, In: Nonlinear Analysis, Theory, Methods and Applications. 230, 113226.Research output: Contribution to journal › Article › peer-review
1 Scopus citations -
Green's Function of a Subgraph of a Complete Graph
Lin, Y., Ngai, S. M. & Yau, S. T., Jun 1 2023, In: International Mathematics Research Notices. 2023, 13, p. 11145-11171 27 p.Research output: Contribution to journal › Article › peer-review
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Lq-SPECTRUM OF A CLASS OF SELF-SIMILAR MEASURES∗
Ngai, S. M. & Zhao, W. Q., 2023, In: Asian Journal of Mathematics. 27, 6, p. 867-892 26 p.Research output: Contribution to journal › Article › peer-review
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Schrödinger equations defined by a class of self-similar measures
Ngai, S. M. & Tang, W., 2023, In: Journal of Fractal Geometry. 10, 3-4, p. 209-241 33 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Self-Affine Tiles Generated by a Finite Number of Matrices
Deng, G., Liu, C. & Ngai, S. M., Oct 2023, In: Discrete and Computational Geometry. 70, 3, p. 620-644 25 p.Research output: Contribution to journal › Article › peer-review