BIMSA > 倪思敏
研究员 倪思敏

团队: 分析和几何

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 Lei Ouyang, Differential equations defined by Krein-Feller operators on Riemannian manifolds, Chaos, Solitons and Fractals, 204(117773) (2026)
  • [2] Sze-Man Ngai and Wen-Quan Zhao, Lq-spectrum of a class of self-similar measures, Asian J. Math., 27(6), 867-892 (2023)
  • [3] 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
  • [4] 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
  • [5] 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
  • [6] Sze-Man Ngai and Yangyang Xu, Separation conditions for iterated function systems with overlaps on Riemannian manifolds, J. Geom. Anal. , 33(2023), 262
  • [7] 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
  • [8] 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
  • [9] 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
  • [10] Da-Wen Deng, Yulan Huang, and Sze-Man Ngai, Continuous maps that preserve Hausdor measure, J. Math. Anal. Appl. , 516(2022), 126485
  • [11] Wei Tang and Sze-Man Ngai, Heat equations defined by self-similar measures with overlaps, Fractals , 30(3), 2250073 (2022)
  • [12] 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)
  • [13] 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)
  • [14] 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)
  • [15] C.-Y. Chu and S.-M. Ngai, Dimensions in in nite iterated function systems consisting of bi-Lipschitz mappings, Dyn. Syst., 549-583 (2020)
  • [16] S.-M. Ngai, W. Tang, and Y. Xie, Wave propagation speed on fractals, J. Fourier Anal. Appl., 26(31) (2020)
  • [17] 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)
  • [18] 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)
  • [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 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)
  • [21] 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)
  • [22] 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)
  • [23] 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)
  • [24] S.-M. Ngai and J.-X. Tong, Infinite iterated function systems with overlaps, Ergodic Theory Dynam. Systems, 36, 890-907 (2016)
  • [25] 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)
  • [26] 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)
  • [27] 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)
  • [28] D.-W. Deng and S.-M. Ngai, Eigenvalue estimates for Laplacians on measure spaces, J. Funct. Anal., 268, 2231-2260 (2015)
  • [29] D.-W. Deng and S.-M. Ngai, Fractal tiles and quasidisks, Math. Z., 279, 359-387 (2015)
  • [30] Q.-R. Deng and S.-M. Ngai, Dimensions of fractals generated by bi-Lipschitz maps, Abstr. Appl. Anal. (2014)
  • [31] K.-S. Lau and S.-M. Ngai, Boundary theory on the Hata tree, Nonlinear Anal., 95, 292-307 (2014)
  • [32] SM Ngai, L Ouyang, Spectral properties of Krein-Feller operators defined by measures without compact support, 2026 Spring Southeastern Sectional Meeting (2026)
  • [33] 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)
  • [34] J Liu, SM Ngai, L Ouyang, Iterated relation systems on Riemannian manifolds, Fractal and Fractional, 9(10), 637 (2025)
  • [35] SM Ngai, SH Zhou, Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets, arXiv, 2508.12319 (2025)
  • [36] SM Ngai, WQ Zhao, Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds, arXiv (2024)
  • [37] SM Ngai, L Ouyang, Krein-Feller operators on Riemannian manifolds: Compactness of embedding and Hodge’s theorem, 2024 Fall Southeastern Sectional Meeting (2024)
  • [38] SM Ngai, Y Xu, Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds, Nonlinear Analysis, 230, 113226 (2023)
  • [39] 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)
  • [40] SM Ngai, WQ Zhao, $ L^ q $ -spectrum of a class of self-similar measures, Asian Journal of Mathematics, 27(6), 867-892 (2023)
  • [41] 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)
  • [42] DW Deng, Y Huang, SM Ngai, Continuous maps that preserve Hausdorff measure, Journal of Mathematical Analysis and Applications, 516(1), 126485 (2022)
  • [43] SM Ngai, W Tang, A Tran, S Yuan, Orthogonal Polynomials Defined by Self-Similar Measures with Overlaps, Experimental mathematics, 31(3), 1026-1038 (2022)
  • [44] SM Ngai, L Ouyang, Laplacians on Riemannian and pseudo-Riemannian manifolds defined by fractal measures and Hodge’s theorem for functions, 2022 Spring Western Sectional Meeting (2022)
  • [45] 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)
  • [46] SM Ngai, Y Xie, Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps (2020)
  • [47] 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)
  • [48] 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)
  • [49] CY Chu, SM Ngai, Dimensions in infinite iterated function systems consisting of bi-Lipschitz mappings, Dynamical Systems, 35(4), 549-583 (2020)
  • [50] SM Ngai, Measures Essentially of Finite Type and Spectral Asymptotics of Fractal Laplacians, Analysis, Probability and Mathematical Physics on Fractals, 337-362 (2020)
  • [51] 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)
  • [52] SM Ngai, W Tang, Eigenvalue asymptotics and Bohr’s formula for fractal Schrödinger operators, Pacific Journal of Mathematics, 300(1), 83-119 (2019)
  • [53] SM Ngai, Spectral Asymptotics of Laplacians Defined by Fractal Measures and Some Applications (2019)
  • [54] 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)
  • [55] S NGAI, Y XIE, SPECTRAL ASYMPTOTICS OF ONE-DIMENSIONAL GRAPH-DIRECTED SELF-SIMILAR MEASURES WITH OVERLAPS (2018)
  • [56] WEI TANG, S NGAI, HEAT EQUATIONS DEFINED BY A CLASS OF FRACTAL MEASURES (2018)
  • [57] G Deng, SM Ngai, Differentiability of Lq-spectrum and multifractal decomposition by using infinite graph-directed IFSs, Advances in Mathematics, 311, 190-237 (2017)
  • [58] SM Ngai, Spectral Asymptotics of Fractal Laplace and Schrödinger Operators (2017)
  • [59] SM Ngai, Spectral Dimension of a Class of One-Dimensional Fractal Laplacians (2017)
  • [60] SM Ngai, Spectral Asymptotics of Some One-Dimensional Fractal Laplacians (2017)
  • [61] SM Ngai, Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians (2017)
  • [62] SM Ngai, The Multifractal Formalism and Spectral Asymptotics of Self-Similar Measures With Overlaps (2016)
  • [63] SM Ngai, Topological Properties of a Class of Three Dimensional Self-Affine Tiles, Part I: Connectedness (2015)
  • [64] SM Ngai, Topological Properties of a Class of Three Dimensional Self-Affine Tiles, Part II: Homeomorphism to a Round 3-Ball (2015)
  • [65] SM Ngai, Topological Properties of a Class of Self-Affine Tiles in (2015)
  • [66] SM Ngai, Lq-Spectrum and Multifractal Formalism of a Class of Self-Similar Measures of General Finite Type (2015)
  • [67] QR Deng, SM Ngai, Dimensions of Fractals Generated by Bi‐Lipschitz Maps, Abstract and Applied Analysis, 2014(1), 549741 (2014)
  • [68] SM Ngai, Eigenvalue Estimates of Laplacians defined by fractal measures (2014)
  • [69] 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)
  • [70] KS Lau, SM Ngai, Martin boundary and exit space on the Sierpinski gasket, Science China Mathematics, 55, 475-494 (2012)
  • [71] DW Deng, T Jiang, SM Ngai, Structure of planar integral self‐affine tilings, Mathematische Nachrichten, 285(4), 447-475 (2012)
  • [72] SM Ngai, Singularity and L2-dimension of self-similar measures, Chaos, Solitons & Fractals, 45(3), 256-265 (2012)
  • [73] SM Ngai, Spectral asymptotics of Laplacians associated with one-dimensional iterated function systems with overlaps, Canadian Journal of Mathematics, 63(3), 648-688 (2011)
  • [74] QR Deng, SM Ngai, Conformal iterated function systems with overlaps, Dynamical Systems, 26(1), 103-123 (2011)
  • [75] SM Ngai, Boundary Theory on the Sierpinski Gasket and Hata Tree (2011)
  • [76] 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)
  • [77] SM Ngai, F Wang, X Dong, Graph-directed iterated function systems satisfying the generalized finite type condition, Nonlinearity, 23(9), 2333 (2010)
  • [78] SM Ngai, J Chan, J Chen, J Hu, KS Lau, Fractal Differential Equations Defined by Iterated Function Systems with Overlaps (2010)
  • [79] KS Lau, SM Ngai, XY Wang, Separation conditions for conformal iterated function systems, Monatshefte für Mathematik, 156(4), 325-355 (2009)
  • [80] QR Deng, SM Ngai, Multifractal formalism for self-affine measures with overlaps, Archiv der Mathematik, 92, 614-625 (2009)
  • [81] SM Ngai, Multifractal structure of non-compactly supported infinite measures, Fractals, 16(3), 209-226 (2008)
  • [82] SM Ngai, Analysis on Fractals Defined by Iterated Function Systems with Overlaps (2008)
  • [83] SM Ngai, Fractal Laplacians Defined by Iterated Function Systems With Overlaps and Their Spectral Asymptotics (2008)
  • [84] KS Lau, SM Ngai, A generalized finite type condition for iterated function systems, Advances in Mathematics, 208(2), 647-671 (2007)
  • [85] J Hu, KS Lau, SM Ngai, Laplace operators related to self-similar measures on Rd, Journal of Functional Analysis, 239(2), 542-565 (2006)
  • [86] SM Ngai, Multifractal Structure of Noncompactly Supported Measures (2006)
  • [87] SM Ngai, Spectral Dimension of Fractal Laplacians Defined by Iterated Function Systems With Overlaps (2006)
  • [88] 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)
  • [89] SM Ngai, Y Wang, Self-similar measures associated to {IFS} with non-uniform contraction ratios (2005)
  • [90] DW Deng, SM Ngai, Vertices of self-similar tiles, Illinois Journal of Mathematics, 49(3), 857-872 (2005)
  • [91] F Jordan, SM Ngai, Reptiles with holes, Proceedings of the Edinburgh Mathematical Society, 48(3), 651-671 (2005)
  • [92] SM Ngai, On a Class of Laplacians Defined by Fractal Measures (2005)
  • [93] SM Ngai, Fractal Laplace Operators on Open Subsets of (2005)
  • [94] SM Ngai, Fractal Laplace Operators on Bounded Open Subsets of Euclidean Spaces (2005)
  • [95] M Das, SM Ngai, Graph-directed iterated function systems with overlaps, Indiana University mathematics journal, 109-134 (2004)
  • [96] SM Ngai, TM Tang, A technique in the topology of connected self-similar tiles, Fractals, 12(4), 389-403 (2004)
  • [97] KS Lau, SM Ngai, Iterated Function Systems of Generalized Finite Type (2004)
  • [98] EJ Bird, SM Ngai, A Teplyaev, Fractal Laplacians on the unit interval, Ann. Sci. Math. Québec, 27(2), 135-168 (2003)
  • [99] SM Ngai, N Nguyen, The Heighway dragon revisited, Discrete & Computational Geometry, 29, 603-623 (2003)
  • [100] KS Lau, SM Ngai, Dimensions of the boundaries of self-similar sets, Experimental Mathematics, 12(1), 13-26 (2003)
  • [101] SM Ngai, Hausdorff Dimension of the Boundaries of a Class of Self-Similar Sets (2003)
  • [102] SM Ngai, Eigenvalues and Eigenfunctions of a Class of Fractal Laplacians on the Unit Interval (2002)
  • [103] SM Ngai, Fractal Laplacians on an Interval (2002)
  • [104] SM Ngai, N Nguyen, TM Tang, Topological Structure of Reptiles and Self-Affine Tiles (2002)
  • [105] SM Ngai, Y Wang, Hausdorff dimension of self‐similar sets with overlaps, Journal of the London Mathematical Society, 63(3), 655-672 (2001)
  • [106] 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)
  • [107] KS Lau, SM Ngai, Second-order self-similar identities and multifractal decompositions, Indiana University Mathematics Journal, 925-972 (2000)
  • [108] AH Fan, KS Lau, SM Ngai, Iterated function systems with overlaps, Asian Journal of Mathematics, 4, 527-552 (2000)
  • [109] KS Lau, SM Ngai, Multifractal measures and a weak separation condition, Advances in mathematics, 141(1), 45-96 (1999)
  • [110] KS Lau, SM Ngai, $L\sp q$-spectrum of Bernoulli convolutions associated with P. V. numbers (1999)
  • [111] SM Ngai, VF Sirvent, JJP Veerman, Y Wang, On 2-reptiles in the plane (1999)
  • [112] 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)
  • [113] KS Lau, SM Ngai, Multifractal measures and a weak separation condition (vol 141, pg 45, 1999), ADVANCES IN MATHEMATICS, 143(2), 376-376 (1999)
  • [114] SM Ngai, KS Lau, L^ q-spectrum of Bernoulli convolutions, Osaka Journal of Mathematics, 36(4), 993-1010 (1999)
  • [115] HJ Baues, H Derksen, O Foda, AS Kechris, T Kerler, KS Lau, B Leclerc, ..., Article ID aima. 1998.1805, available online at http: ТТwww. idealibrary. com on, Advances in Mathematics, 141, 418 (1999)
  • [116] KS Lau, SM Ngai, L9-SPECTRUM OF BERNOULLI CONVOLUTIONS ASSOCIATED WITH PV NURHEERS, Osaka J. Math, 36, 993-1010 (1999)
  • [117] KS Lau, SM Ngai, Lq-spectrum of the Bernoulli convolution associated with the golden ratio, Studia Math, 131(3), 225-251 (1998)
  • [118] 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)
  • [119] SM Ngai, MM Novak, TG Dewey, Multifractal decomposition for a family of overlapping self-similar measures, Fractal Frontiers, 151-161 (1997)
  • [120] S NGAI, Shatin, NT, Hong Kong We discuss two methods for computing the multifractal dimension spectrum of a self, Fractal Frontiers: Fractals In The Natural And Applied Sciences, 151 (1997)
  • [121] SM Ngai, Multifractal measures and dimension spectra, University of Pittsburgh (1995)

 

更新时间: 2026-03-26 22:53:23