倪思敏 - 北京雁栖湖应用数学研究院

办公室: A15-203

邮箱: ngai@bimsa.cn

研究方向: 分形几何

个人简介

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, Georgia Institute of Technology, and Georgia Southern University. He joined Beijing Institute of Mathematical Sciences and Applications as a professor in 2024. His main research areas are fractal geometry and the theory of fractal measures. He is also interested in the theories of wavelets, self-affine tiles, fractal differential equations, and spectral graph theory.

教育经历

1988 - 1995 University of Pittsburgh Mathematics Ph.D (Supervisor: Ka-Sing Lau)
1988 - 1989 University of Pittsburgh Mathematics Master
1984 - 1987 University of Hong Kong Mathematics/Physics

工作经历

2016 - 2017 Harvard University Visiting Scholar
2011 - 2024 Hunan Normal University Adjunct Professor
2011 - 2024 Georgia Southern University, USA Professor
2008 - 2009 Chinese University of Hong Kong Visiting Scholar
2006 - 2011 Georgia Southern University Associate Professor
2000 - 2006 Georgia Southern University Assistant Professor
1998 - 2000 Georgia Institute of Technology Visiting Assistant Professor
1998 - 1998 Cornell University Visiting Assistant Professor
1996 - 1997 Chinese University of Hong Kong Postdoctoral Fellow
1995 - 1995 Chinese University of Hong Kong Instructor

出版物

[1] Sze-Man Ngai and Wen-Quan Zhao, Lq-spectrum of a class of self-similar measures, Asian J. Math., 27(6), 867-892 (2023)
[2] Sze-Man Ngai and Wei Tang, Schrodinger equations defined by a class of self-similar measures, J. Fractal Geom., 10(2023), 3/4, 209-241
[3] Guotai Deng, Chuntai Liu, and Sze-Man Ngai, Self-affine tiles generated by a finite number of matrices, Discrete Comput. Geom., 70(2023), 602-644
[4] Yong Lin, Sze-Man Ngai, and Shing-Tung Yau, Green's function of a subgraph of a complete graph, Int. Math. Res. Not. IMRN, 2023(2023), 13, 11145-11171
[5] Sze-Man Ngai and Yangyang Xu, Separation conditions for iterated function systems with overlaps on Riemannian manifolds, J. Geom. Anal. , 33(2023), 262
[6] Sze-Man Ngai and Yangyang Xu, Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds, Nonlinear Anal., 230(2023), 113226
[7] Sze-Man Ngai, Wei Tang, Anh Tran, and Shuai Yuan, Orthogonal polynomials de ned by self-similar measures with overlaps, Exp. Math, 31(2022), 3, 1026-1038
[8] Guotai Deng, Chuntai Liu, and Sze-Man Ngai, A class of self-affine tiles in Rd that are d-dimensional tame balls, Adv. Math., 410(2022), 108716
[9] Da-Wen Deng, Yulan Huang, and Sze-Man Ngai, Continuous maps that preserve Hausdor measure, J. Math. Anal. Appl. , 516(2022), 126485
[10] Wei Tang and Sze-Man Ngai, Heat equations defined by self-similar measures with overlaps, Fractals , 30(3), 2250073 (2022)
[11] Y. Lin, S.-M. Ngai, and S.-T. Yau, Heat kernels on forms defined on a subgraph of a complete graph, Math. Ann., 380, 1891-1931 (2021)
[12] D.-W. Deng and S.-M. Ngai, Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces, Proc. Roy. Soc. Edinburgh Sect. A, 151, 842-861 (2021)
[13] S.-M. Ngai and Y. Xie, Spectral asymptotics of Laplacians associated with a class of higherdimensional graph-directed self-similar measures, Nonlinearity, 34, 5375{5398. (2021)
[14] C.-Y. Chu and S.-M. Ngai, Dimensions in in nite iterated function systems consisting of bi-Lipschitz mappings, Dyn. Syst., 549-583 (2020)
[15] S.-M. Ngai, W. Tang, and Y. Xie, Wave propagation speed on fractals, J. Fourier Anal. Appl., 26(31) (2020)
[16] Q. Gu, J. Hu and S.-M. Ngai, , Geometry of self-similar measures on intervals with overlaps and applications to sub-Gaussian heat kernel estimates, Commun. Pure Appl. Anal., 19, 641-676 (2020)
[17] G. Deng, C. Liu, and S.-M. Ngai, Topological properties of a class of higher-dimensional self-affine tiles, Canad. Math. Bull., 62, 727--740 (2019)
[18] S.-M. Ngai and Y. Xie, $L^q$-spectrum of self-similar measures with overlaps in the absence of second-order identities, J. Aust. Math. Soc., 106, 56-103 (2019)
[19] S.-M. Ngai and W. Tang, Eigenvalue asymptotics and Bohr's formula for fractal Schr"odinger operators, Pacific J. Math., 300, 83-119 (2019)
[20] S.-M. Ngai, W. Tang, and Y. Xie, Spectral asymptotics of one-dimensional fractal Laplacians in the absence of second-order identities, Discrete Contin. Dyn. Syst., 38, 1849-1887 (2018)
[21] G. Deng, C. Liu, and S.-M. Ngai, Topological properties of a class of self-affine tiles in ${\mathbb R}^3$, Trans. Amer. Math. Soc., 370, 1321-1350 (2018)
[22] G. Deng and S.-M. Ngai, Differentiability of $L^q$-spectrum and multifractal decomposition by using infinite graph-directed IFSs, Adv. Math., 311, 190-237 (2017)
[23] S.-M. Ngai and J.-X. Tong, Infinite iterated function systems with overlaps, Ergodic Theory Dynam. Systems, 36, 890-907 (2016)
[24] G. Deng, C. Liu and S.-M. Ngai, Dimensions of the boundary of a graph-directed self-similar set with overlaps, Houston J. Math., 42, 179-210 (2016)
[25] J. Liu, S.-M. Ngai, and J. Tao, Connectedness of a class of two-dimensional self-affine tiles associated with triangular matrices, J. Math. Anal. Appl., 435, 1499-1513 (2016)
[26] J. F.-C. Chan, S.-M. Ngai, and A. Teplyaev, One-dimensional wave equations defined by fractal Laplacians, J. Anal. Math., 127, 219--246 (2015)
[27] D.-W. Deng and S.-M. Ngai, Eigenvalue estimates for Laplacians on measure spaces, J. Funct. Anal., 268, 2231-2260 (2015)
[28] D.-W. Deng and S.-M. Ngai, Fractal tiles and quasidisks, Math. Z., 279, 359-387 (2015)
[29] K.-S. Lau and S.-M. Ngai, Boundary theory on the Hata tree, Nonlinear Anal., 95, 292-307 (2014)
[30] Q.-R. Deng and S.-M. Ngai, Dimensions of fractals generated by bi-Lipschitz maps, Abstr. Appl. Anal. (2014)
[31] SM Ngai, MK Zhang, WQ Zhao, Nodal sets and continuity of eigenfunctions of Krein-Feller operators, Electronic Journal of Differential Equations, 2025(1), 12-25 (2025)
[32] SM Ngai, L Ouyang, Hodge Theorem for Krein-Feller operators on compact Riemannian manifolds, arXiv (2024)
[33] SM Ngai, L Ouyang, Differential equations defined by Kre\u {\i} n-Feller operators on Riemannian manifolds, arXiv (2024)
[34] SM Ngai, WQ Zhao, Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds, arXiv (2024)
[35] Y Lin, SM Ngai, ST Yau, Green’s Function of a Subgraph of a Complete Graph, International Mathematics Research Notices, 2023(13), 11145-11171 (2023)
[36] SM Ngai, L Ouyang, Krein-Feller operators on Riemannian manifolds and a compact embedding theorem, arXiv (2023)
[37] SM Ngai, Y Xu, Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds, Nonlinear Analysis, 230, 113226 (2023)
[38] G Deng, C Liu, SM Ngai, A class of self-affine tiles in Rd that are d-dimensional tame balls, Advances in Mathematics, 410, 108716 (2022)
[39] SM Ngai, Y Xie, Spectral asymptotics of Laplacians associated with a class of higher-dimensional graph-directed self-similar measures, Nonlinearity, 34(8), 5375 (2021)
[40] CY Chu, SM Ngai, Dimensions in infinite iterated function systems consisting of bi-Lipschitz mappings, Dynamical Systems, 35(4), 549-583 (2020)
[41] SM Ngai, Y Xie, Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps (2020)
[42] Q Gu, J Hu, SM Ngai, Geometry of self-similar measures on intervals with overlaps and applications to sub-Gaussian heat kernel estimates., Communications on Pure & Applied Analysis, 19(2) (2020)
[43] Q Gu, J Hu, SM Ngai, Two-sided sub-Gaussian estimates of heat kernels on intervals for self-similar measures with overlaps, Commun. Pure Appl. Anal, 19, 641-676 (2020)
[44] SM Ngai, Y Xie, -SPECTRUM OF SELF-SIMILAR MEASURES WITH OVERLAPS IN THE ABSENCE OF SECOND-ORDER IDENTITIES, Journal of the Australian Mathematical Society, 106(1), 56-103 (2019)
[45] SM Ngai, W Tang, Eigenvalue asymptotics and Bohr’s formula for fractal Schrödinger operators, Pacific Journal of Mathematics, 300(1), 83-119 (2019)
[46] G Deng, C Liu, SM Ngai, Topological properties of a class of self-affine tiles in ℝ³, Transactions of the American Mathematical Society, 370(2), 1321-1350 (2018)
[47] G Deng, SM Ngai, Differentiability of Lq-spectrum and multifractal decomposition by using infinite graph-directed IFSs, Advances in Mathematics, 311, 190-237 (2017)
[48] QR Deng, SM Ngai, Dimensions of Fractals Generated by Bi‐Lipschitz Maps, Abstract and Applied Analysis, 2014(1), 549741 (2014)
[49] QR Deng, KS Lau, SM Ngai, Separation conditions for iterated function systems with overlaps, Fractal geometry and dynamical systems in pure and applied mathematics. I (2013)
[50] DW Deng, T Jiang, SM Ngai, Structure of planar integral self‐affine tilings, Mathematische Nachrichten, 285(4), 447-475 (2012)
[51] KS Lau, SM Ngai, Martin boundary and exit space on the Sierpinski gasket, Science China Mathematics, 55, 475-494 (2012)
[52] SM Ngai, Singularity and L2-dimension of self-similar measures, Chaos, Solitons & Fractals, 45(3), 256-265 (2012)
[53] SM Ngai, Spectral asymptotics of Laplacians associated with one-dimensional iterated function systems with overlaps, Canadian Journal of Mathematics, 63(3), 648-688 (2011)
[54] QR Deng, SM Ngai, Conformal iterated function systems with overlaps, Dynamical Systems, 26(1), 103-123 (2011)
[55] J Chen, SM Ngai, Eigenvalues and eigenfunctions of one-dimensional fractal Laplacians defined by iterated function systems with overlaps, Journal of mathematical analysis and applications, 364(1), 222-241 (2010)
[56] SM Ngai, F Wang, X Dong, Graph-directed iterated function systems satisfying the generalized finite type condition, Nonlinearity, 23(9), 2333 (2010)
[57] KS Lau, SM Ngai, XY Wang, Separation conditions for conformal iterated function systems, Monatshefte für Mathematik, 156(4), 325-355 (2009)
[58] QR Deng, SM Ngai, Multifractal formalism for self-affine measures with overlaps, Archiv der Mathematik, 92, 614-625 (2009)
[59] SM Ngai, Multifractal structure of non-compactly supported infinite measures, Fractals, 16(3), 209-226 (2008)
[60] KS Lau, SM Ngai, A generalized finite type condition for iterated function systems, Advances in Mathematics, 208(2), 647-671 (2007)
[61] J Hu, KS Lau, SM Ngai, Laplace operators related to self-similar measures on Rd, Journal of Functional Analysis, 239(2), 542-565 (2006)
[62] DW Deng, SM Ngai, Vertices of self-similar tiles, Illinois Journal of Mathematics, 49(3), 857-872 (2005)
[63] SM Ngai, Y Wang, Self-similar measures associated to {IFS} with non-uniform contraction ratios (2005)
[64] SM Ngai, TM Tang, Topology of connected self-similar tiles in the plane with disconnected interiors, Topology and its Applications, 150(1-3), 139-155 (2005)
[65] F Jordan, SM Ngai, Reptiles with holes, Proceedings of the Edinburgh Mathematical Society, 48(3), 651-671 (2005)
[66] SM Ngai, TM Tang, A technique in the topology of connected self-similar tiles, Fractals, 12(4), 389-403 (2004)
[67] M Das, SM Ngai, Graph-directed iterated function systems with overlaps, Indiana University mathematics journal, 109-134 (2004)
[68] KS Lau, SM Ngai, Dimensions of the boundaries of self-similar sets, Experimental Mathematics, 12(1), 13-26 (2003)
[69] SM Ngai, N Nguyen, The Heighway dragon revisited, Discrete & Computational Geometry, 29, 603-623 (2003)
[70] EJ Bird, SM Ngai, A Teplyaev, Fractal Laplacians on the unit interval, Ann. Sci. Math. Québec, 27(2), 135-168 (2003)
[71] KS Lau, SM Ngai, H Rao, Iterated function systems with overlaps and self-similar measures, Journal of the London Mathematical Society, 63(1), 99-116 (2001)
[72] SM Ngai, Y Wang, Hausdorff dimension of self‐similar sets with overlaps, Journal of the London Mathematical Society, 63(3), 655-672 (2001)
[73] KS Lau, SM Ngai, Second-order self-similar identities and multifractal decompositions, Indiana University Mathematics Journal, 925-972 (2000)
[74] AH Fan, KS Lau, SM Ngai, Iterated function systems with overlaps, Asian Journal of Mathematics, 4, 527-552 (2000)
[75] KS Lau, SM Ngai, Multifractal measures and a weak separation condition, Advances in mathematics, 141(1), 45-96 (1999)
[76] N Sze-Man, L Ka-Sing, L^ q-spectrum of Bernoulli convolutions associated with PV numbers, Osaka Journal of Mathematics, 36(4), 993-1010 (1999)
[77] KS Lau, SM Ngai, $L\sp q$-spectrum of Bernoulli convolutions associated with P. V. numbers (1999)
[78] SM Ngai, VF Sirvent, JJP Veerman, Y Wang, On 2-reptiles in the plane (1999)
[79] KS Lau, SM Ngai, Lq-spectrum of the Bernoulli convolution associated with the golden ratio, Studia Math, 131(3), 225-251 (1998)
[80] SM Ngai, A dimension result arising from the 𝐿^{𝑞}-spectrum of a measure, Proceedings of the American Mathematical Society, 125(10), 2943-2951 (1997)
[81] SM Ngai, MM Novak, TG Dewey, Multifractal decomposition for a family of overlapping self-similar measures, Fractal Frontiers, 151-161 (1997)

更新时间: 2025-08-12 16:00:07