Publications of Stephen Yau

Stephen S. T. Yau and HuaiQing Zuo.  On variance of exponents for isolated surface singularities with modality $łeqslant2$.  Sci. China Math., 57(1):31--41, 2014. MR3146513
Chenglong Yu, Rong Lucy He and Stephen S.-T. Yau.  Viral genome phylogeny based on Lempel-Ziv complexity and Hausdorff distance.  J. Theoret. Biol., 348:12--20, 2014. MR3178820
Changchuan Yin, Ying Chen and Stephen S.-T. Yau.  A measure of DNA sequence similarity by Fourier transform with applications on hierarchical clustering.  J. Theoret. Biol., 359:18--28, 2014. MR3248415
Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau and Huaiqing Zuo.  On a number-theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman--de Bruijn function.  J. Eur. Math. Soc. (JEMS), 16(9):1937--1966, 2014. MR3273313
Stephen S. T. Yau and Linda Zhao.  Sharp polynomial estimate of integral points in right-angled simplices.  J. Number Theory, 133(2):398--425, 2013. MR2994364
Yang Jiao, Stephen Yau and Wen-Lin Chiou.  Mitter conjecture and structure theorem for six-dimensional estimation algebras.  Internat. J. Control, 86(1):146--158, 2013. MR3006313
Stephen Yau and Huaiqing Zuo.  Characterization of isolated complete intersection singularities with $\mathbb C^*$-action of dimension $n\geq 2$ by means of geometric genus and irregularity.  Comm. Anal. Geom., 21(3):509--526, 2013. MR3078945
Xue Luo and Stephen S.-T. Yau.  Hermite spectral method to 1-D forward Kolmogorov equation and its application to nonlinear filtering problems.  IEEE Trans. Automat. Control, 58(10):2495--2507, 2013. MR3106057
Xue Luo and Stephen S.-T. Yau.  Complete real time solution of the general nonlinear filtering problem without memory.  IEEE Trans. Automat. Control, 58(10):2563--2578, 2013. MR3106062
Yu-Chao Tu, Stephen S.-T. Yau and Huaiqing Zuo.  Nonconstant CR morphisms between compact strongly pseudoconvex CR manifolds and étale covering between resolutions of isolated singularities.  J. Differential Geom., 95(2):337--354, 2013. MR3128987
Stephen S.-T. Yau and Fei Ye.  Several splitting criteria for vector bundles and reflexive sheaves.  Pacific J. Math., 266(2):449--456, 2013. MR3130631
Xue Luo and Stephen S.-T. Yau.  Hermite spectral method with hyperbolic cross approximations to high-dimensional parabolic PDEs.  SIAM J. Numer. Anal., 51(6):3186--3212, 2013. MR3131484
Rong Du and Stephen Yau.  Kohn-Rossi cohomology and its application to the complex Plateau problem, III.  J. Differential Geom., 90(2):251--266, 2012. MR2899875
Bruce M. Bennett, Hing Sun Luk and Stephen S.-T. Yau.  Codes from infinitely near points.  Asian J. Math., 16(1):89--101, 2012. MR2904913
Rong Du and Stephen Yau.  New invariants for complex manifolds, singularities, and CR manifolds with applications.  In Fifth International Congress of Chinese Mathematicians. Part 1, 2, pages 431--445.  Amer. Math. Soc., Providence, RI, 2012. MR2908085
Lu Zheng, Yingwei Yao, Mo Deng and Stephen S. T. Yau.  Decentralized detection in \it ad hoc sensor networks with low data rate inter sensor communication.  IEEE Trans. Inform. Theory, 58(5):3215--3224, 2012. MR2952541
Stephen S.-T. Yau and Huaiqing Zuo.  Lower estimate of Milnor number and characterization of isolated homogeneous hypersurface singularities.  Pacific J. Math., 260(1):245--255, 2012. MR3001794
Stephen S.-T. Yau.  Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds.  J. Eur. Math. Soc. (JEMS), 13(1):175--184, 2011. MR2735079
Chenglong Yu, Mo Deng and Stephen S.-T. Yau.  DNA sequence comparison by a novel probabilistic method.  Inform. Sci., 181(8):1484--1492, 2011. MR2770365
Stephen S.-T. Yau, Linda Zhao and Huaiqing Zuo.  Biggest sharp polynomial estimate of integral points in right-angled simplices.  In Topology of algebraic varieties and singularities, pages 433--467.  Amer. Math. Soc., Providence, RI, 2011. MR2777834
Sheng-Li Tan, Stephen S.-T. Yau and Fei Ye.  A note on the topology of the complements of fiber-type line arrangements in $\mathbb C\mathbb P^2$.  Pacific J. Math., 251(1):207--218, 2011. MR2794621
Irene Chen, Ke-Pao Lin, Stephen Yau and Huaiqing Zuo.  Coordinate-free characterization of homogeneous polynomials with isolated singularities.  Comm. Anal. Geom., 19(4):661--704, 2011. MR2880212
Rong Du, Hing Sun Luk and Stephen Yau.  New invariants for complex manifolds and isolated singularities.  Comm. Anal. Geom., 19(5):991--1021, 2011. MR2886715
Bo Zhao, Victor Duan and Stephen S.-T. Yau.  A novel clustering method via nucleotide-based Fourier power spectrum analysis.  J. Theoret. Biol., 279:83--89, 2011. MR2975026
Shan Yu Ji, Stephen S. T. Yau and Cheng Zhan.  Spherical extension property no longer true for domains in algebraic variety with isolated singularity.  Sci. China Math., 53(2):257--260, 2010. MR2606844
Rong Du and Stephen S. T. Yau.  The second pluri-genus of smoothable Gorenstein surface singularities.  Sci. China Math., 53(3):635--639, 2010. MR2608320
Der-Chen Chang and Stephen S.-T. Yau.  Geometric analysis on a family of pseudoconvex hypersurfaces.  In Recent advances in geometric analysis, pages 61--99.  Int. Press, Somerville, MA, 2010. MR2648939
Fabrizio Catanese, John Coates, Christopher Hacon, Jun Li, Shigeru Mukai, Wilfried Schmid, Christophe Soulé, Stephen S.-T. Yau and Shouwu Zhang.  In memoriam: Eckart Viehweg.  J. Algebraic Geom., 19(4):599--601, 2010. MR2669726
Rong Du and Stephen Yau.  Local holomorphic de Rham cohomology.  Comm. Anal. Geom., 18(2):365--374, 2010. MR2672237
Salah Baouendi, Yum-Tong Siu and Stephen S.-T. Yau.  Preface [Special issue: In honor of Joseph J. Kohn, Part 1 of 2].  Pure Appl. Math. Q., 6(3, Special Issue: In honor of Joseph J. Kohn. Part 1):1--2, 2010. MR2677305
Shengli Tan, Stephen S.-T. Yau and Huaiqing Zuo.  łojasiewicz inequality for weighted homogeneous polynomial with isolated singularity.  Proc. Amer. Math. Soc., 138(11):3975--3984, 2010. MR2679619
Bozenna Pasik-Duncan, Jie Huang, Hua Wang, Keyong Li, Wing-Shing Wong and S.-T. Yau.  Preface: Dedicated to John Baillieul on the occasion of his 65th birthday.  Commun. Inf. Syst., 10(4):2, 2010. MR2737876
Ovidiu Calin, Der-Chen Chang and Stephen S. T. Yau.  Nonholonomic systems and sub-Riemannian geometry.  Commun. Inf. Syst., 10(4):293--316, 2010. MR2737881
Rong Du, Yun Gao and Stephen S. Yau.  Explicit construction of moduli space of bounded complete Reinhardt domains in $\mathbb C^n$.  Comm. Anal. Geom., 18(3):601--626, 2010. MR2747440
Shanyu Ji Stephen Yau and Cheng Zhan.  Spherical extension property no longer true for domains in algebraic variety with isolated singularity.  Science in China Mathematics, 53(2):257-260, 2010.
Stephen Yau, Kareem Carr, Eleanor Murray, Ebeneger Armah and Rong He.  A rapid method for characterization of protein relatedness using feature vectors.  PLoS One, 18, 2010.
Huaiqing Zuo Stephen Yau, Shangli Tan.  Lojasiewicz inequality for weighted homogeneous polynomial with isolated singularities.  Proceding of AMS, 12, 2010.
Stephen Yau and Fei Ye.  Rigidity of differential structure for a new class of arrangements in $CP^4$.  2010.
Stephen Yau, Lu Zheng, Yingwei Yao and Mo Deng.  Decentralized detection in ad hoc sensor network with how data rate inter sensor communication.  2010.
Huaiqing Zuo Stephen Yau, Xue Luo.  A sharp estimate of dickman-de bruijin function and a sharp polynomial estimate of positive integral points in 4-dimensional tetrahedron.  2010.
Rong Du Stephen Yau.  The second pluri-genus of smoothable gorenstein surface singularities.  2010.
Der-Chen Chang Stephen Yau, Ovidiu Calin.  Non-holonomic systems and subriemannian geometry.  2010.
Fan Chung, Yi-Jing Xu and Stephen S.-T. Yau.  Classification of weighted dual graphs with only complete intersection singularities structures.  Trans. Amer. Math. Soc., 361(7):3535--3596, 2009. MR2491891
Stephen S.-T. Yau and Huaiqing Zuo.  Notes on classification of toric surface codes of dimension 5.  Appl. Algebra Engrg. Comm. Comput., 20(2):175--185, 2009. MR2511885
Stephen T. Yau and Letian Zhang.  On formulas for Dedekind sums and the number of lattice points in tetrahedra.  J. Number Theory, 129(8):1931--1955, 2009. MR2522715
Rong Du and Stephen Yau.  Higher order Bergman functions and explicit construction of moduli space for complete Reinhardt domains.  J. Differential Geom., 82(3):567--610, 2009. MR2534988
Chung-Lin Hsu, Wei Liang Kuo, Stephen S.-T. Yau and Yung Yu.  Automorphism groups of the extended quadratic residue codes over $Z_{16}$ and $Z_{32}$.  Rocky Mountain J. Math., 39(6):1947--1991, 2009. MR2575889
Stephen S.-T. Yau and Fei Ye.  Diffeomorphic types of complements of nice point arrangements in $CP^1$.  Sci. China Ser. A, 52(12):2774--2791, 2009. MR2577190
Stephen S.-T. Yau, Yung Yu and HuaiQing Zuo.  Classification of gradient space of dimension 8 by a reducible ${\rm sl(2,C)}$ action.  Sci. China Ser. A, 52(12):2792--2828, 2009. MR2577191
Ming-chang Kang, Ji-ping Zhang, Jian-yi Shi, Yung Yu and Stephen S. T. Yau.  Some primitive linear groups of prime degree.  J. Math. Soc. Japan, 61(4):1013--1070, 2009. MR2588503
Stephen Yau, Chung-Lin Hsu, Wei-Liang Kuo and Yung Yu.  Automorphism groups of the extended quadratic residue codes over $z_16$ and $z_32$.  Rocky Mountain Journal of Mathematics , 39(6):1947-1991, 2009.
Fan Chung Graham, Xu Y.-J. and Stephen Yau.  Classification of weight dual graphs admitting only complete intersection singularities structures.  Trans. Amer Math, 361:3535-3596, 2009.
Stephen Yau and Fei Ye .  Rigidity of differential structure for a new class of arrangements in cp4.  34pp.  2009.
Rong Du and S. T. Stephen Yau.  Higher order bergman functions and explicit construction of moduli space for complete reinhardt domains .  Journal of Differential Geometry, 82:567-610, 2009. 55pp. 
S. T. Stephen Yau and Junfeng Ding .  TCOM, an innovative data structure for mining association rule among infrequent items.  Computers and Mathematics with Applications, 57:290-301, 2009. 32pp. 
Der-Chen Chang and S.T. Stephen Yau.  Geometric analysis on a family of pseudoconvex hypersurfaces.  Recent Advanced in Geometric Analysis, 61-99, 2009. 34pp. 
Stephen Yau and Fei Ye.  Diffeomorphic types of complements of nice arrangements in $\mathbbCP^l$.  Science in China, Series A: Mathematics, 52:2774-2791, 2009.
J.-P. Zhang M.-C. Kang, J.-Y. Shi and Stephen S.-T Yau Y. Yu.  Some primitive linear groups of prime degree.  Journal of Mathematical Society of Japan., 61:1013-1070, 2009.
Stephen S.-T Yau Ling Zhou.  Efficient association rule and quantitative association rule mining among infrequent items.  Rare Association Rule Mining and Knowledge Discovery: Technology for Infrequent and Critical Event Detection, a special edition of the ”Advances in Data Warehousing and Mining Series”, 62, 2009.
Stephen S.-T Yau Huaiqing Zuo.  Notes on classification of toric surface codes of dimension 5.  Applicable Algebra in Engineering, Communication and Computing, 14pp, 2009.
Stephen S.-T Yau Peng He.  A risk-neutral stochastic at-the-money implied volatility.  In Proceedings of the 5th international financial conference, pages 5pp.  2009.
Stephen S.-T Yau.  New algorithms in real time solution of the nonlinear filtering problem.  Communication in Information and Systems, 8(3):303-332, 2009.
Stephen S.-T Yau, Yung Yu and Huaiqing Zuo.  Classification of gradient space of dimension 8 with a reducible sl(2,c) action.  Science in China, Series A: Mathematics, 44p, 2009.
Stephen S.-T Yau and Linda Zhao.  New sharp polynomial estimate of integral points in right-angled simplices.  2009.
Rong Du and Stephen S.-T Yau.  New cr invariants and its application to the complex plateau problem.  2009.
Stephen S.-T Yau Chenglong Yu.  A novel construction of genome space with biological geometry.  2009.
Stephen S.-T Yau, Mo Deng and Lu Zheng.  Classification of intron-containing and intronless genes based on z curve and cumulative distance matrix.  2009.
Stephen S.-T Yau Linda Zhao.  Sharp polynomial estimate of integral points in right-angled simplices.  2009.
Stephen Yau and Fei Ye .  On the topology of the complements of fiber-type line arrangements in cp2,.  2009.
Rong Du and Stephen S.-T Yau Yun Gao.  Explicit construction of moduli space of bounded complete Reinhardt domains in $\mathbb C^n$ .  2009.
Stephen S.-T Yau Der-Chen Chang.  Schrodinger equation with quartic potential and nonlinear filtering problem.  In Ieee 48th cdc and 28th chinese control conference, shanghai prc, pages 8089-8094.  2009.
Stephen S.-T Yau and Rong Du.  Local holomorphic de rham cohomology.  2009.
Stephen S.-T Yau and Letian Zhang.  On the formulas of dedekind sums and the lattice points of integral tetrahedrons.  To appear Journal of Number Theory.  2009.
Stephen Yau.  New invariants for complex manifolds and isolated singularities.  2009.
Rong Du Stephen Yau.  New invariants for complex manifolds and isolated singularities.  2009.
Huaiqing Zuo Stephen Yau, Linda Zhao.  Biggest sharp polynomial estimate of integral points in right-angled simplices.  2009.
Shing-Tung Yau and Stephen S.-T. Yau.  Real time solution of the nonlinear filtering problem without memory. II.  SIAM J. Control Optim., 47(1):163--195, 2008. MR2373467
ShaoBo Wang and Stephen S.-T. Yau.  The diffeomorphic types of the complements of arrangements in $\mathbb C\mathbb P^ 3$. II.  Sci. China Ser. A, 51(4):785--802, 2008. MR2395423
Stephen S.-T. Yau.  CR equivalence problem of strongly pseudoconvex CR manifolds.  In Third International Congress of Chinese Mathematicians. Part 1, 2, pages 197--207.  Amer. Math. Soc., Providence, RI, 2008. MR2409633
Xianyang Jiang, Dominique Lavenier and Stephen S.-T. Yau.  Coding region prediction based on a universal DNA sequence representation method.  J. Comput. Biol., 15(10):1237--1256, 2008. MR2461974
Wen-Lin Chiou, Woei-Ren Chiueh and Stephen S.-T. Yau.  Mitter conjecture for low dimensional estimation algebras in non-linear filtering.  Internat. J. Control, 81(11):1793--1805, 2008. MR2462575
Stephen S. T. Yau.  New algorithms in real time solution of the nonlinear filtering problem.  Commun. Inf. Syst., 8(3):303--332, 2008. MR2495878
Stephen Yau, Ling Zhou and Qing-long Zhang.  A fast algorithm for mining association rules with bounded lenth among infrequent items.  30pp.  2008.
Bruce Bennett, Hing Sun Luk and Stephen Yau.  Codes from infinitely near points.  16pp.  2008.
Stephen Yau and Ning Jin.  Hausdorff dimension of three families of fractals and a conjecture on falconer's problem.  19pp.  2008.
Dongmin Cai and Stephen Yau.  Information-based projection method for categorical attributes.  26pp.  2008.
Changlin Yan and Stephen Yau.  New suboptimal filter for polynomial filtering problem.  20pp.  2008.
Stephen Yau and Ning Jin.  New techniques in fractal geometry: matrix of sets of mappings and vectors of compact sets.  66pp.  2008.
Stephen Yau and Jiuhong Tang.  Pricing high water mark exotic options with management free.  44pp.  2008.
M.-C. Kang, J.-Y. Shi, Stephen Zhang, J.-P.Yau and Y. and Yu.  Some primitive linear croups of prime degree.  53pp.  2008.
Stephen Yau and Peng He.  Volatility forecasting from implied volatility: evidence from stock market.  20pp.  2008.
Changlin Yan and Stephen Yau.  Real time solution of nonlinear filtering problem without memory III : extended yau's algorithm.  26pp.  2008.
S. T. Yau and Stephen S.T. Yau.  Real time solution of nonlinear filtering problem without memory II.  SIAM J. Control and Optimization, Vol 47(No1):163-195, 2008.
Stephen S. T. Yau.  Three methods in solving nonlinear filtering problem.  In Proceedings of the 4th international congress of chinese mathematics, hangzhou 2007, december 17-22, volume III of, pages 160-197.  2008.
Chaoxiao Lu and Stephen S. T. Yau.  Pricing stock options in mergers and acquisitions with jump-diffusion model.  American Control conference, Seattle, Washington, June 11-13, 1008-1012.  2008.
Xiangyang Jiang and Stephen Yau.  Bioinformation oriented algorithms and dedicated architecture.  18pp.  2008.
Eb Armah, Kareem Carr and Stephen Yau.  Quantifying relationships in protein sequences.  18pp.  2008.
Changchuan Yin and Stephen Yau.  Numerical representation of DNA sequences based on genetic code.  In Computational intelligence in bioinformatics and computational biology, pages 223-227.  2008. 4pp. 
Peng He and Stephen Yau.  Evolution of smile surfaces and applications in pricing exotic derivatives.  22pp.  2008.
N. Jin and Stephen Yau.  New method in nonlinear filtering.  5pp.  2008.
X.J. Wang, Jie Huang and Stephen Yau.  Linear tracking-differentiator.  10pp.  2008.
W.S. Wong C.W. Sung and Stephen Yau.  System theoretical aspects of the power control problem.  10pp.  2008.
Stephen Yau.  Kohn-Rossi cohomology for CR-manifolds of low codimension in $c^n$.  2008.
Stephen S.-T Yau, Chenglong Yu and Rong He.  A protein map and its application.  DNA and Cell Biology, 27:241-250, 2008.
M Kashiwara, S. Mori, S Mukai, K. Saito, S.-T. Yau and B. Teissier, editors.  Special issue dedicated to professor heisuke hironaka on the occasian of his 77th birthday, may, volume 44 of.  2008.
Xianyang Jiang and Stephen S.-T Yau.  A novel analysis model for dna sequences.  In Proceeding of international conference on biomedical engineering and informatics, may 27-30, sanya, hainan, pages 24-28.  2008. May 27-30 Sanya Hainan. 
S.T. Yau Stephen S.-T Yau.  Real time solution of duncan-mortensen-zakai equation without memory.  In 47th ieee cdc, pages 5086- 5091.  2008.
Stephen S.-T Yau.  Rigidity of cr-morphisms between compact strongly pseudoconvex cr manifolds.  Journal of European Mathematical Society, 12, 2008.
Xuejun Wang and Stephen Yau.  On the GLY Conjecture of upper estimate of positive integral points in real right-angled simplices.  J. Number Theory, 122(1):184--210, 2007. MR2287119
D. Yoo, S. S.-T. Yau and Z. Gao.  Optimal fast tracking observer bandwidth of the linear extended state observer.  Internat. J. Control, 80(1):102--111, 2007. MR2287163
Ovidiu Calin, Der-Chen Chang and Stephen S.-T. Yau.  Periodic solutions for a family of Euler-Lagrange systems.  Asian J. Math., 11(1):69--87, 2007. MR2304582
Shaobo Wang and Stephen S.-T. Yau.  The diffeomorphic types of the complements of arrangements in ${\bf C}{\rm P}^ 3$. I. Point arrangements.  J. Math. Soc. Japan, 59(2):423--447, 2007. MR2325692
Lixing Jia, Hing Sun Luk and Stephen S.-T. Yau.  From CR geometry to algebraic geometry and combinatorial geometry.  In Proceedings of the International Conference on Complex Geometry and Related Fields, volume 39 of AMS/IP Stud. Adv. Math., pages 109--124.  Amer. Math. Soc., Providence, RI, 2007. MR2338622
Zhijie Chen, Sheng-Li Tan, Jianpan Wang and Stephen S.-T. Yau, editors.  Proceedings of the International Conference on Complex Geometry and Related Fields, volume 39 of AMS/IP Studies in Advanced Mathematics.  American Mathematical Society, Providence, RI, 2007. MR2341396
Stephen S. T. Yau, Ruxu Du and Lixing Jia.  Special solutions to some Kolmogorov equations arising from cubic sensor problems.  Commun. Inf. Syst., 7(2):195--206, 2007. MR2344197
Hing Sun Luk and Stephen S.-T. Yau.  Kohn-Rossi cohomology and its application to the complex Plateau problem. II.  J. Differential Geom., 77(1):135--148, 2007. MR2344356
Ling Zhou and Stephen Yau.  Efficient association rule mining among both frequent and infrequent items.  Comput. Math. Appl., 54(6):737--749, 2007. MR2348260
Changchuan Yin and Stephen S.-T. Yau.  Prediction of protein coding regions by the 3-base periodicity analysis of a DNA sequence.  J. Theoret. Biol., 247(4):687--694, 2007. MR2479617
Yen-Tai Lai and Stephen Yau.  Circuit design for yau filter.  International Journal of Electronic, 94:137--156, 2007.
Peng He and Stephen Yau.  Forecasting stock market volatility using implied volatility.  Proceedings of the 2007 American Control Conference at New York City, 1823-1828, 2007.
Changchuan Yin and Stephen Yau.  Prediction of protein coding region by the 3-base periodicity analysis of a DNA sequence.  Journal of Theoretical Biology, 185-212, 2007.
Libin Liu, Yee-Kin Ho and Stephen Yau.  Prediction of primate Splice Site Prediction Using Inhomogeneous Markov Chain and Neural Network.  DNA and Cell Biology, 26(7):477-483, 2007.
Jiang Xianyang, Ninghui Sun, Stephen Yau, Zhiwei Zu, Peiheng Zhang and Xinchun Liu.  Survey on index based homology search algorithms.  Journal of Supercomputing , Vol. 40(No.2):185-212, 2007.
Xi Wu, Lixing Jia, Amid Rasoulian and Stephen Yau.  Classification of all finite-dimensional nonlinear filter from lie algebraic point of view: state dimension 2 .  In 46th ieee cdc, new orleans, dec, (2007),, pages 813-817..  2007.
Stephen Yau and Ling Zhou.  Association rule and quantitative assoaciation rule mining among infrequent items.  In Proceedings of the 8th international workshop on multimedia data mining, pages 45-53.  2007.
Shiferaw Berhanu, Hua Chen, Jorge Hounie, Xiaojun Huang, Sheng-Li Tan and Stephen S.-T. Yau, editors.  Recent progress on some problems in several complex variables and partial differential equations, volume 400 of Contemporary Mathematics.  American Mathematical Society, Providence, RI, 2006. MR2172816
Wen-Lin Chiou, Woei-Ren Chiueh and Stephen S.-T. Yau.  Structure theorem for five-dimensional estimation algebras.  Systems Control Lett., 55(4):275--281, 2006. MR2202565
Xiaojun Huang, Hing-Sun Luk and Stephen S. T. Yau.  On a CR family of compact strongly pseudoconvex CR manifolds.  J. Differential Geom., 72(3):353--379, 2006. MR2219938
Hing Sun Luk, Stephen S.-T. Yau and Weitian Zang.  Complete invariant of a family of strongly pseudoconvex domains in $A_ 1$-singularity: Bergman function.  In Recent progress on some problems in several complex variables and partial differential equations, pages 161--171.  Amer. Math. Soc., Providence, RI, 2006. MR2222473
Xi Wu and Stephen S.-T. Yau.  Classification of estimation algebras with state dimension 2.  SIAM J. Control Optim., 45(3):1039--1073 (electronic), 2006. MR2247725
Ke-Pao Lin, Xi Wu, Stephen S.-T. Yau and Hing-Sun Luk.  A remark on lower bound of Milnor number and characterization of homogeneous hypersurface singularities.  Comm. Anal. Geom., 14(4):625--632, 2006. MR2273288
Stephen T. Yau and Letian Zhang.  An upper estimate of integral points in real simplices with an application to singularity theory.  Math. Res. Lett., 13(5-6):911--921, 2006. MR2280784
Salah Baouendi, Der-Chen Chang, Xiaojun Huang and Stephen S. T. Yau.  Preface [International Conference on the Theory of Functions of Several Complex Variables dedicated to Professor Sheng Gong on the occasion of his 75th birthday].  Sci. China Ser. A, 49(11):i, 2006. MR2288205
Kepao Lin, Zhenhan Tu and Stephen S. T. Yau.  Characterization of isolated homogeneous hypersurface singularities in $\mathbb C^ 4$.  Sci. China Ser. A, 49(11):1576--1592, 2006. MR2288215
J. Tang and S. S.-T. Yau.  Exotic option, stochastic volatility and incentive scheme.  In Computational finance and its applications II, pages 183--192.  WIT Press, Southampton, 2006. MR2334320
Changlin Yan and Stephen Yau.  A new suboptimal filter and numerical simulations for the cubic sensor problem.  IEEE ICNSC, 351--356, 2006.
Dongmin Cai and Stephen Yau.  Categorical clustering by converting associated information.  International Journal of Computer Science, 1:31--36, 2006.
Libin Liu, Yee-kin Ho and Stephen Yau.  Clustering DNA sequences by features vectors.  Molecular Phylogenetics and Evolution, 41:64--69, 2006.
Dongchul Yoo, Zhiqiang Gao and Stephen Yau.  On convergence of the linear extended state observer.  Proceedings of the 2006 IEEE International Symposium on Intelligent Control, 1645--1650, 2006.
Zhe Li and Stephen Yau.  Path dependent options: the case of high water mark provision for hedge funds.  Computational Finance and its Applications II, 43:393--400, 2006.
Jiuhong Tang and Stephen Yau.  The effects of different volatility and management free dynamics on high water mark option pricing.  In 45th ieee cdc,san diago, dec, pages 6696--6701.  2006.
Changchuan Yin, Yoo Dongchul and Stephen Yau.  Tracking the 3-base periodicity of protein coding regions by the nonlinear tracking differentiator.  In 45th ieee cdc, san diago, pages 2094--2097.  2006.
S. S.-T. Yau and G.-Q. Hu.  Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state-space dimension and Mitter conjecture.  Internat. J. Control, 78(10):689--705, 2005. MR2152444
Hon-Wing Cheng and Stephen S.-T. Yau.  Parallel computations for Yau filters.  Comput. Math. Appl., 50(5-6):881--893, 2005. MR2165645
Qing-Long Zhang and Stephen S.-T. Yau.  On intractability of spatial relationships in content-based image database systems.  Commun. Inf. Syst., 4(2):181--190, 2005. MR2165686
Stephen S.-T. Yau and Shing-Tung Yau.  Solution of filtering problem with nonlinear observations.  SIAM J. Control Optim., 44(3):1019--1039 (electronic), 2005. MR2178055
Ning Jin and Stephen S. T. Yau.  General finite type IFS and $M$-matrix.  Comm. Anal. Geom., 13(4):821--843, 2005. MR2191909
Stephen S.-T. Yau and Yung Yu.  Classification of 3-dimensional isolated rational hypersurface singularities with ${\bf C}^ \ast$-action.  Rocky Mountain J. Math., 35(5):1795--1809, 2005. MR2206037
Shaobo Wang and Stephen S.-T. Yau.  Rigidity of differentiable structure for new class of line arrangements.  Comm. Anal. Geom., 13(5):1057--1075, 2005. MR2216152
Qing-Long Zhang and Stephen S.-T. Yau.  Finding minimal and maximal sets of spatial relationships in pictorial retrieval systems.  Commun. Inf. Syst., 5(3):311--340, 2005. MR2230530
Qing-Long Zhang, Shi-Kuo Chang and Stephen S.-T. Yau.  On consistency checking of spatial relationships in content-based image database systems.  Commun. Inf. Syst., 5(3):341--366, 2005. MR2230531
ChangChuan Yin and Stephen Yau.  A fourier characteristic of coding sequences: origins and a non-fourier approximqation.  Journal of Computation Biology, 12:1153--1165, 2005.
Qing-Long Zhang and Stephen Yau.  A stepwise similarity approximation of spatial constraints for image retrieval.  In Proceedings of visual communications and image processing (Vcip2005), beijing, china, spie, pages 1550--1561.  2005.
Shing-Tung Yau and Stephen Yau.  Existence and uniqueness of solutions for duncan-mortensen-zakai equations.  In 44th ieee cdc, and ecc, seville, spain, dec., pages 536--541.  2005.
Stephen Yau and Lixing Jia.  Filtering problem with nonlinear observations and drift terms equal to gradient vector field plus affine vector field.  In 44th ieee cdc, and ecc, seville, spain, dec., pages 5865--5870.  2005.
Qing-Long Zhang and Stephen Yau.  On completeness of reasoning about planar spatial relationships in pictorial retrieval systems.  Communications in Information and Systems, , 4.3: 211-233., 2005.
Yi-Jing Xu and Stephen S.-T. Yau.  Lower estimate of multiplicity of isolated complete intersection singularities with applications in weakly elliptic singularities.  Math. Res. Lett., 11(1):59--71, 2004. MR2046200
Stephen S.-T. Yau.  Numerical characterization for affine varieties be a cone over nonsingular projective varieties.  In Complex analysis in several variables---Memorial Conference of Kiyoshi Oka's Centennial Birthday, pages 333--338.  Math. Soc. Japan, Tokyo, 2004. MR2087067
Ke-Pao Lin and Stephen S.-T. Yau.  Classification of affine varieties being cones over nonsingular projective varieties: hypersurface case.  Comm. Anal. Geom., 12(5):1201--1219, 2004. MR2103318
Stephen S.-T. Yau.  Computation of Fokker-Planck equation.  Quart. Appl. Math., 62(4):643--650, 2004. MR2104266
Stephen S.-T. Yau.  Global invariants for strongly pseudoconvex varieties with isolated singularities: Bergman functions.  Math. Res. Lett., 11(5-6):809--832, 2004. MR2106243
Zhigang Liang and Stephen S.-T. Yau.  Wavelet-Galerkin method for the Kolmogorov equation.  Math. Comput. Modelling, 40(9-10):1093--1121, 2004. MR2113839
Salah Baouendi, Joseph J. Kohn, Qi-keng Lu, Ngaiming Mok, Shing-Tung Yau and Stephen S. T. Yau.  Preface [Special issue dedicated to the 60th birthday of Yum-Tong Siu. Part II].  Asian J. Math., 8(1):iii, 2004. MR2128293
Salah Baouendi, Joseph J. Kohn, Qi-keng Lu, Ngaiming Mok, Shing-Tung Yau and Stephen S. T. Yau.  Preface [Special issue dedicated to the 60th birthday of Yum-Tong Siu. Part III].  Asian J. Math., 8(2):iii, 2004. MR2129534
Ning Jin and Stephen S. T. Yau.  Hausdorff dimension of invariant $C$-vector of M-matrix and self-affine fractal.  Asian J. Math., 8(2):259--285, 2004. MR2129537
Stephen S.-T. Yau and Qing-Long Zhang.  On completeness of reasoning about planar spatial relationships in pictorial retrieval systems.  Commun. Inf. Syst., 4(3):211--233, 2004. MR2200876
Stephen Yau and S.T. Yau.  Linear filtering with nonlinear observations.  In Proceeding of 43rd ieee cdc, atlantis paradise island, bahama, dec. 14-17, pages --.  2004.
Stephen Yau.  Numerical characterization for affine varieties be a cone over nonsingular projective varieties, complex analysis in several variables.  Kyoto/Nara. Memorial Conference of Kiyoshi Oka's Centennial Birthday. Advanced Studies in Pure Mathematics, 42:333--338, 2004.
Zhigang Liang and Stephen Yau.  Wavelet analysis on numerical solution to kolmogorov equation arising from linear filtering with non gaussian initial condition.  Mathematical and Computer Modelling, An International Journal, 40:1093--1121, 2004.
S.T. Yau and Stephen Yau.  Nonlinear filtering and time varying schrödinger equation i.  IEEE Transactions on Aerospace and Electronic Systems, 40:284--292, 2004.
Stephen S.-T. Yau and Yuen-Tai Lai.  Explicit solution of DMZ equation in nonlinear filtering via solution of ODEs.  IEEE Trans. Automat. Control, 48(3):505--508, 2003. MR1962262
Xiaojun Huang, Hing Sun Luk and Stephen S.-T. Yau.  Punctured local holomorphic de Rham cohomology.  J. Math. Soc. Japan, 55(3):633--640, 2003. MR1978213
Stephen S.-T. Yau.  Complete classification of finite-dimensional estimation algebras of maximal rank.  Internat. J. Control, 76(7):657--677, 2003. MR1979888
Ke-Pao Lin and Stephen S.-T. Yau.  Counting the number of integral points in general $n$-dimensional tetrahedra and Bernoulli polynomials.  Canad. Math. Bull., 46(2):229--241, 2003. MR1981677
Wing-Sum Cheung, Bun Wong and Stephen S.-T. Yau.  Some remarks on the local moduli of tangent bundles over complex surfaces.  Amer. J. Math., 125(5):1029--1035, 2003. MR2004427
Hing Sun Luk and Stephen S.-T. Yau.  Holomorphic de Rham cohomology of strongly pseudoconvex CR manifolds with $S^ 1$-actions.  J. Differential Geom., 63(1):155--170, 2003. MR2015263
Qing-Long Zhang and Stephen S.-T. Yau.  A general approach to indexing and retrieval of images in image databases.  Commun. Inf. Syst., 3(1):61--73, 2003. MR2042798
Salah Baouendi, Joseph J. Kohn, Qi-keng Lu, Ngaiming Mok, Shing-Tung Yau and Stephen S. T. Yau.  Preface [Special issue dedicated to Professor Yum-Tong Siu].  Asian J. Math., 7(4):iii, 2003. MR2073621
Qing-Long Zhang and Stephen S.-T. Yau.  A stepwise approximation of intractable spatial constraints in image queries.  Commun. Inf. Syst., 3(3):203--221 (2004), 2003. MR2131882
Stephen Yau, N. Jin and C.L. Yan.  Construction of finite-dimensional nonlinear filter via odes.  In Proceedings of the 2003 american control conference (Acc 2003), denver, colorad, june 4-6, pages 2447--2452.  2003.
Stephen Yau, J.S. Wang, A. Niknejad, C.X. Lu and Y.K. Ho.  Dna sequence representation without degeneracy.  Nucleic Acids Research, 31:3078--3080, 2003.
N. Jin and Stephen Yau.  Numerical solution of 1-d robust dmz equation.  In Proceedings of the 2003 ieee international symposium on intelligent control, houston, texas, oct. 5-8, 2003, pages 827--830.  2003.
W.-L. Chiou, W.-R. Chiueh and Stephen Yau.  Recent results on classification of low dimensional estimation algebras.  In Proceedings of 42nd ieee cdc, 2003, maui, hawaii, dec. 9-12, pages 5853--5858.  2003.
Stephen Yau.  Complete classification of finite-dimensional estimation algebras of maximal rank, .  International Journal of Control, , 76(7):657-677., 2003.
J.S. Wang, A. Niknejad, C.X. Lu, N. Jin, Y.K. Ho and Stephen Yau.  DNA sequence representation without degeneracy,.  Nucleic Acids Research, , 31(12):3078-3080, 2003.
Xiaojun Huang, Hing Sun Luk and Stephen Yau.  Punctured local holomorphic de-rham cohomology .  Journal of the Math. Soc. of Japan, 55(3):633-640, 2003.
Yuen-Tai Lai and Stephen Yau .  Explicit solution of dmz equation in nonlinear filtering via solution of odes.  IEEE Transaction on Automatic Control, , 48(3): 505-508, 2003.
Ke-Pao Lin and Stephen S.-T. Yau.  A sharp upper estimate of the number of integral points in a 5-dimensional tetrahedra [tetrahedron].  J. Number Theory, 93(2):207--234, 2002. MR1899303
Ke-Pao Lin and Stephen S.-T. Yau.  Analysis for a sharp polynomial upper estimate of the number of positive integral points in a 4-dimensional tetrahedron.  J. Reine Angew. Math., 547:191--205, 2002. MR1900141
Xi Wu, Stephen S.-T. Yau and Guo-Qing Hu.  Finite-dimensional filters with nonlinear drift. XII. Linear and constant structure of Wong-matrix.  In Stochastic theory and control (Lawrence, KS, 2001), pages 507--518.  Springer, Berlin, 2002. MR1931673
Stephen S.-T. Yau and Yung Yu.  Algebraic classification of rational CR structures on topological 5-sphere with transversal holomorphic $S^ 1$-action in $\mathbb C^ 4$.  Math. Nachr., 246/247:207--233, 2002. MR1944558
Yuen-Tai Lai and Stephen Yau.  Design of the ordinary differential equation solver in the yau filtering system.  In Proceedings of the american control conference, alaska, may, pages 5144--5149.  2002.
Guo-Qing Hu and Stephen Yau.  Finite dimensional filters with nonlinear drift xv: new direct method for construction of universal finite-dimensional filter.  IEEE Transactions on Aerospace and Electronic Systems, 38:50--57, 2002.
Stephen Yau.  On the under-determined partial differential equation in the nonlinear filtering problems.  In Proceedings of the american control conference, alaska, may, pages 907--908.  2002.
Stephen Yau, Xiaozhou Yang and Xi Wu.  Constant structure of wong's matrix in the maximal rank estimation algebra.  In International conference on control and automation, june 16-19, xiamen, china, pages 1950--1954.  2002.
Stephen S.-T. Yau and Guo-Qing Hu.  Finite-dimensional filters with nonlinear drift. X. Explicit solution of DMZ equation.  IEEE Trans. Automat. Control, 46(1):142--148, 2001. MR1809477
Xiaojun Huang, Shanyu Ji and Stephen S. T. Yau.  An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface.  Ark. Mat., 39(1):75--93, 2001. MR1821083
Tan Jiang, Stephen S.-T. Yau and Larn-Ying Yeh.  Simple geometric characterization of supersolvable arrangements.  Rocky Mountain J. Math., 31(1):303--312, 2001. MR1821382
Ke-Pao Lin and Stephen S.-T. Yau.  Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of homogeneous polynomials.  In First International Congress of Chinese Mathematicians (Beijing, 1998), pages 251--259.  Amer. Math. Soc., Providence, RI, 2001. MR1830181
Shing-Tung Yau and Stephen S.-T. Yau.  Real-time numerical solution to Duncan-Mortensen-Zakai equation.  In Foundations of computational mathematics (Oxford, 1999), pages 361--400.  Cambridge Univ. Press, Cambridge, 2001. MR1839150
Hing-Sun Luk, Stephen S. T. Yau and Larn-Ying Yeh.  Bergman kernels on resolutions of isolated singularities.  Math. Res. Lett., 8(3):303--319, 2001. MR1839480
Qing-Long Zhang, Shi-Kuo Chang and Stephen S.-T. Yau.  The consistency problem on content-based pictorial description in pictorial database systems.  Commun. Inf. Syst., 1(2):225--240, 2001. MR1907517
S.T. Yau and Stephen Yau.  Real time algorithm for nonlinear filtering problem.  In Proceedings of the 40th ieee conference on decision and control, orlando,, pages 2137-2142..  2001.
X. Wu and Stephen Yau.  Estimation algebras with state dimension 2.  In proceedings of the 40th ieee conference on decision and control, orlando, florida,, pages 2556-2561..  2001.
Jin Wang, Jie Huang and Stephen S. T. Yau.  Approximate nonlinear output regulation based on the universal approximation theorem.  Internat. J. Robust Nonlinear Control, 10(5):439--456, 2000. MR1760702
C. Fefferman.  Editor's note on papers by F. R. Harvey and H. B. Lawson, Jr.: ``On boundaries of complex analytic varieties. I'' [Ann. of Math. (2) 102 (1975), no. 2, 223--290; MR0425173 (54 \#13130)] and by H. S. Luk and S. S.-T. Yau: ``Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: an addendum to the paper of Harvey-Lawson'' [ibid. 148 (1998), no. 3, 1153--1154; MR1670081 (99j:32006)].  Ann. of Math. (2), 151(2):875, 2000. MR1765713
Mei Hui Chiu, Stephen S.-T. Yau and Yung Yu.  $Z_ 8$-cyclic codes and quadratic residue codes.  Adv. in Appl. Math., 25(1):12--33, 2000. MR1773191
Lei Guo and Stephen S.-T. Yau, editors.  Lectures on systems, control, and information, volume 17 of AMS/IP Studies in Advanced Mathematics.  American Mathematical Society, Providence, RI, 2000. MR1776016
Stephen S.-T. Yau.  Brockett's problem on nonlinear filtering theory.  In Lectures on systems, control, and information (Beijing, 1997), pages 177--212.  Amer. Math. Soc., Providence, RI, 2000. MR1776021
Hao Chen, Craig Seeley and Stephen S.-T. Yau.  Algebraic determination of isomorphism classes of the moduli algebras of $\~E_ 6$ singularities.  Math. Ann., 318(4):637--666, 2000. MR1802505
Shing-Tung Yau and Stephen S.-T. Yau.  Real time solution of nonlinear filtering problem without memory. I.  Math. Res. Lett., 7(5-6):671--693, 2000. MR1809293
Hao Chen and Stephen S.-T. Yau.  Moduli and modular groups of a class of Calabi-Yau $n$-dimensional manifolds, $n\geq 3$.  J. Differential Geom., 54(1):1--12, 2000. MR1815409
Guo-Qing Hu, Stephen S. T. Yau and Wen-Lin Chiou.  Finite-dimensional filters with nonlinear drift. XIII. Classification of finite-dimensional estimation algebras of maximal rank with state space dimension five.  Asian J. Math., 4(4):905--931, 2000. MR1870665
S.T. Yau and Stephen Yau.  Existence of solutions to time dependent parabolic equations with unbounded coefficients: application to duncan-mortensen-zakai equations.  In Proceedings of the american control conference, chicago, june,, pages 794-798.  2000.
Xi Wu and Stephen Yau.  linear filtering system with arbitrary initial conditions.  In Proceedings of the american control conference, chicago, pages 785-789.  2000.
Stephen Yau.  Solution to brockett's problem on finite dimensional estimation algebras of maximal rank in nonlinear filtering, .  In Proceedings of the 38th ieee conference on decision and control, sydney, australia,, pages 292-297..  2000.
X.J. Wang, Jie Huang and Stephen Yau.  A study of tracking-differentiator.  In Proceedings of the 39th ieee conference on decision and control, sydney, australia, , pages 4783-4788..  2000.
J. Chen X. Wu, W.L. Chiou and Stephen Yau.  new proof of the linear structure of wong matrix in nonlinear filtering .  In Proceedings of 19th chinese control conference, hong kong, , pages 384-388.  2000.
T. Bielecki, J. Chen, E. B. Lin and S. Yau.  Wavelet representations of general signals.  Nonlinear Anal., 35(1, Ser. B: Real World Appl.):125--141, 1999. MR1633962
Wing Shing Wong and Stephen S. T. Yau.  The estimation algebra of nonlinear filtering systems.  In Mathematical control theory, pages 33--65.  Springer, New York, 1999. MR1661469
Stephen S. T. Yau and Amid Rasoulian.  Classification of four-dimensional estimation algebras.  IEEE Trans. Automat. Control, 44(12):2312--2318, 1999. MR1728966
Stephen S.-T. Yau, Xi Wu and Wing-Shing Wong.  Hessian matrix non-decomposition theorem.  Math. Res. Lett., 6(5-6):663--673, 1999. MR1739223
Stephen Yau and Larn-Ying Yeh.  Lie algebraic method in nonlinear filtering with state space dimension up to 6.  In the 14th world congress of ifac, pages 97-102..  1999.
Jin Wang, Jie Huang and Stephen Yau.  Approximate nonlinear output regulation based on the universal approximation theorem .  In Proceedings of the world multiconference on systems, cybernetics and informations, orlando, florida,, pages 218-225.  1999.
Xi Wu and Stephen Yau.  explicit solution to generalized time-varying kolmogorov equation .  In proceedings of the 38th ieee conference on decision and control, phoenix,, pages 1897-1902..  1999.
Hao Chen, Hing Sun Luk and Stephen Yau.  Explicit computation of generalized Hamming weights for some algebraic geometric codes.  Adv. in Appl. Math., 21(1):124--145, 1998. MR1623345
Tan Jiang and Stephen S.-T. Yau.  Intersection lattices and topological structures of complements of arrangements in ${\bf C}{\rm P}^ 2$.  Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 26(2):357--381, 1998. MR1631597
Hing Sun Luk and Stephen S. T. Yau.  Explicit construction of graph invariant for strongly pseudoconvex compact $3$-dimensional rational CR manifolds.  Compositio Math., 114(1):77--111, 1998. MR1648535
Shing-Tung Yau and Stephen S. T. Yau.  Finite-dimensional filters with nonlinear drift. XI. Explicit solution of the generalized Kolmogorov equation in Brockett-Mitter program.  Adv. Math., 140(2):156--189, 1998. MR1658526
Hing Sun Luk and Stephen S.-T. Yau.  Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: an addendum to the paper of Harvey-Lawson.  Ann. of Math. (2), 148(3):1153--1154, 1998. MR1670081
Tan Jiang and Stephen S.-T. Yau.  Explicit computation of cohomological algebra of complement of arrangement of hyperplanes in ${\bf C}^ 3$ and new geometric characterization of supersolvable arrangements.  In Algebra and geometry (Taipei, 1995), pages 47--73.  Int. Press, Cambridge, MA, 1998. MR1697948
Shing-Tung Yau and Stephen S.-T. Yau.  Existence and decay estimates for time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation.  Asian J. Math., 2(4):1079--1149, 1998. MR1734138
Shing Tung Yau and Stephen Yau.  Addendum to "finite -dimensional filters with nonolinear drift": a response to f. daum's comments, .  IEEE Transactions on Aerospace and Electronic Systems, , 34(2): 57-58., 1998.
Guo-Qing Hu and Stephen Yau.  Recent results on classification of finite dimensional maximal rank estimation algebras with state space dimension up to 5 .  In Proceedings of the 37th ieee conference on decision and control, pages 1311-1312..  1998.
Xi Wu, Ke-Pao Lin and Stephen Yau.  Recent advance in computing kolmogorov equation arising from nonlinear filtering .  In Proceedings of the 37th ieee conference on decision and control, pages 2904-2905..  1998.
Amid Rasoulian and Stephen S.-T. Yau.  Finite-dimensional filters with non-linear drift. IX. Construction of finite-dimensional estimation algebras of non-maximal rank.  Systems Control Lett., 30(2-3):109--118, 1997. MR1449632
Hon-Wing Cheng and Stephen S.-T. Yau.  More explicit formulas for the matrix exponential.  Linear Algebra Appl., 262:131--163, 1997. MR1451772
Jie Chen and Stephen S.-T. Yau.  Finite-dimensional filters with nonlinear drift. VII. Mitter conjecture and structure of $\eta$.  SIAM J. Control Optim., 35(4):1116--1131, 1997. MR1453292
Jie Chen, Stephen S.-T. Yau and Chi-Wah Leung.  Finite-dimensional filters with nonlinear drift. VIII. Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension $4$.  SIAM J. Control Optim., 35(4):1132--1141, 1997. MR1453293
Hao Chen and Stephen S.-T. Yau.  Contribution to Munuera's problem on the main conjecture of geometric hyperelliptic MDS codes.  IEEE Trans. Inform. Theory, 43(4):1349--1354, 1997. MR1454971
Qi-keng Lu, Stephen S.-T. Yau and Anatoly Libgober, editors.  Singularities and complex geometry, volume 5 of AMS/IP Studies in Advanced Mathematics.  American Mathematical Society, Providence, RI, 1997. MR1468264
Tan Jiang and Stephen S.-T. Yau.  Complement of arrangement of hyperplanes.  In Singularities and complex geometry (Beijing, 1994), pages 93--104.  Amer. Math. Soc., Providence, RI, 1997. MR1468271
Hing Sun Luk and Stephen S.-T. Yau.  Complete algebraic CR invariants of real codimension $3$ strongly pseudoconvex CR manifolds.  In Singularities and complex geometry (Beijing, 1994), pages 175--182.  Amer. Math. Soc., Providence, RI, 1997. MR1468275
Hing Sun Luk and Stephen S. T. Yau.  Some remarks on compact strongly pseudoconvex CR manifolds.  In CR-geometry and overdetermined systems (Osaka, 1994), pages 237--246.  Math. Soc. Japan, Tokyo, 1997. MR1476246
Rui-Tao Dong, Wing Shing Wong and Stephen S.-T. Yau.  Filtering systems with finite-dimensional estimation algebras.  IEEE Trans. Automat. Control, 42(11):1601--1606, 1997. MR1479102
Shing Tung Yau and Stephen Yau.  Finite dimensional filters with nonlinear drift iii: duncan-mortenson-zakai equation with arbitrary initial condition for kalman-bucy filtering system and benes filtering system .  IEEE Transactions on Aerospace and Electronic Systems, , 33(4):1277-1294, 1997.
Zhigang Liang, Shing -Tung Yau and Stephen Yau.  Finite dimensional filter with nonlinear drift v: solution to kolmogorov equation arising from linear filtering with non gaussian initial condition .  IEEE Transactions on Aerospace and Electronic Systems, 33(4):1295-1308., 1997.
Qing-Long Zhang.  A new iconic indexing for 2d and 3d scenes .  In proceeding of the second chinese world congress on intelligent control and intelligent automation (Cwcicia 97), pages 1667-1672.  1997.
Guo-Qing Hu and Stephen Yau.  Explicit solution of dmz equation .  In Proceedings of the 36th ieee conference on decision and control, pages 4455-4459.  1997.
Jie Chen Chi-Wah Leung and Stephen Yau.  Explicit construction of finite-dimensional nonlinear filters with state space dimension 4 .  In Proceedings of the 36th ieee conference on decision and control, pages 4462-4466..  1997.
Qing-Long Zhang, Shi-Kuo Chang and Stephen Yau.  An experimental result in image indexing using gep-2d strings,.  Image Database and Multimedia Search, 127-146., 1997,.
Hing Sun Luk and Stephen S.-T. Yau.  Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real $(2n-1)$-dimensional CR manifolds in ${\bf C}^ N$.  J. Math. Soc. Japan, 48(1):61--68, 1996. MR1361547
Jie Chen, Stephen S.-T. Yau and Chi-Wah Leung.  Finite-dimensional filters with nonlinear drift. IV. Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension $3$.  SIAM J. Control Optim., 34(1):179--198, 1996. MR1372910
Yi-Jing Xu and Stephen S.-T. Yau.  Micro-local characterization of quasi-homogeneous singularities.  Amer. J. Math., 118(2):389--399, 1996. MR1385285
Yi-Jing Xu and Stephen S.-T. Yau.  A sharp estimate of the number of integral points in a $4$-dimensional tetrahedra [tetrahedron].  J. Reine Angew. Math., 473:1--23, 1996. MR1390680
S.-T. Yau and S. S.-T. Yau.  Explicit solution of a Kolmogorov equation.  Appl. Math. Optim., 34(3):231--266, 1996. MR1408739
Jie Chen and Stephen S.-T. Yau.  Finite-dimensional filters with nonlinear drift. VI. Linear structure of $\Omega$.  Math. Control Signals Systems, 9(4):370--385, 1996. MR1450359
Guo-QingHu and Stephen Yau .  Direct method without riccati equation for kalman-bucy filtering system with arbitrary initial condition.  In 13th world congress ifac, san francisco, june 30-july 5, volume h, (1996), , pages 469-474..  1996.
Qing-Long Zhang, Shi-Kuo Chang and Stephen Yau.  a unified approach to indexing images in image databases,.  In Proceedings of first international workshop on image databases and multi-media search,, pages 99-106..  1996,.
Amid Rasoulian and Stephen Yau.  The structure of $\omega$-matrix in nonlinear filters.  In Proceedings of the 35th conference on decision and control, kobe, japan, pages 1083-1087..  1996.
Ho-Wing Cheng and Stephen Yau.  Parallel ode-solvers for kalman-bucy filter with arbitrary initial .  In Conditionproceedings of the 35th conference on decision and control, kobe, japan, pages 4138-4145..  1996.
Guo-Qing Hu and Stephen Yau.  New direct method for yau filtering system with arbitrary initial conditions.  In proceedings of the 35th conference on decision and control, kobe, japan , pages 2539-2544..  1996.
Qing-Long Zhang, Shi-Kuo Chang and Stephen Yau.  A unified approach to iconic indexing, retrieval and maintenance of spatial relationships in image databases.  Journal of Visual Communication and Image Representation Vol. 7, No. 4 (Special Issue), , 307-324., 1996.
Hao Chen, Yi-Jing Xu and Stephen S.-T. Yau.  Nonexistence of negative weight derivation of moduli algebras of weighted homogeneous singularities.  J. Algebra, 172(2):243--254, 1995. MR1322403
Hing Sun Luk and Stephen S.-T. Yau.  Invariants of strongly pseudoconvex CR manifolds.  In Five decades as a mathematician and educator, pages 279--305.  World Sci. Publ., River Edge, NJ, 1995. MR1414723
Zhigang Liang and Stephen Yau.  Applying wavelet to kolmogorov equation.  In Proceeding of international conference on control and information, , pages 271-276..  1995.
Hon-wing Cheng and Stephen Yau .  A report on explicit formulas for exp(Ta), .  In proceeding of international conference on control and information, , pages 69-75.  1995.
Amid Rasoulian and Stephen Yau .  Recent results on classification of 4-dimensional estimation algebras .  In Proceeding of international conference on control and information, , pages 371-374.  1995.
Tomasz Bielecki; Man K. Kwong; Li M. Song and Stephen Yau.  Random wavelet transfrom, algebraic geometric coding and their applications in compression and de-noising of signals,.  In Proceeding of international conference on control and information, (1995),, pages 283-289..  1995.
Jie Chen, Chi-Wah Leungn and Stephen Yau.  Explicit construction of finite dimensional nonlinear filters with state space dimension 3, .  In Proceedings of the 34th ieee conference on decision and control, new orleans, louisiana, dec. 13-15, (1995), , pages 4030-4034..  1995.
Amid Rasoulian and Stephen Yau.  Construction of new finite dimensional nonlinear filters.  In proceedings of the 34th ieee conference on decision and control, new orleans, louisiana, , pages 4002-4005.  1995.
Wen Lin Chiou and Stephen S.-T. Yau.  Finite-dimensional filters with nonlinear drift. II. Brockett's problem on classification of finite-dimensional estimation algebras.  SIAM J. Control Optim., 32(1):297--310, 1994. MR1255972
Tan Jiang and Stephen S.-T. Yau.  Diffeomorphic types of the complements of arrangements of hyperplanes.  Compositio Math., 92(2):133--155, 1994. MR1283226
Stephen S.-T. Yau.  Finite-dimensional filters with nonlinear drift. I. A class of filters including both Kalman-Bucy filters and Benes filters.  J. Math. Systems Estim. Control, 4(2):181--203, 1994. MR1298555
Hing Sun Luk, Stephen S.-T. Yau and Yung Yu.  Algebraic classification and obstructions to embedding of strongly pseudoconvex compact $3$-dimensional CR manifolds in ${\bf C}^ 3$.  Math. Nachr., 170:183--200, 1994. MR1302374
Shing Tung Yau and Stephen Yau.  Explicit formal solution to generalized kolmogorov equation.  In Eleventh army conference on applied mathematics and computing, pages 133-155.  1994.
Hon Wing Cheng and Stephen Yau.  Computing the exponential of matrices.  In Proceedings of the american control conference, baltimore, maryland. june, (1994), , pages 3543-3547.  1994.
S.T. Yau and Stephen Yau.  New direct mehtod for kalman-bucy filtering system with arbitrary initial condition.  In proceedings of the 33rd ieee conference on decision and control, lake buena vista, florida,, pages 1221-1225..  1994.
Tomasz R.Bielecki, Jie Chen and Stephen Yau.  Random wavelet transformation and its properties.  In Spie proceedings on wavelet applications in signal and image processing ii, andrew laine and michael unser, eds,vol. 2303 july, (1994), , pages 345-353 .  1994.
Stephen S.-T. Yau and Yung Yu.  Gorenstein quotient singularities in dimension three.  Mem. Amer. Math. Soc., 105(505):viii+88, 1993. MR1169227
Tan Jiang and Stephen S.-T. Yau.  Topological invariance of intersection lattices of arrangements in ${\bf C}{\rm P}^ 2$.  Bull. Amer. Math. Soc. (N.S.), 29(1):88--93, 1993. MR1197426
Yi-Jing Xu and Stephen S.-T. Yau.  Durfee conjecture and coordinate free characterization of homogeneous singularities.  J. Differential Geom., 37(2):375--396, 1993. MR1205449
Tan Jiang and Stephen S.-T. Yau.  Topological and differentiable structures of the complement of an arrangement of hyperplanes.  In Differential geometry: geometry in mathematical physics and related topics (Los Angeles, CA, 1990), pages 337--357.  Amer. Math. Soc., Providence, RI, 1993. MR1216551
Stephen S.-T. Yau, Jie Chen and Chi-Wah Leung.  Finite-dimensional estimation algebras of maximal rank with dimension of state space equal to $3$.  In Transactions of the Tenth Army Conference on Applied Mathematics and Computing (West Point, NY, 1992), pages 337--344.  U.S. Army Res. Office, Research Triangle Park, NC, 1993. MR1224066
Hing Sun Luk and Stephen S.-T. Yau.  Cohomology and splitting criterion for holomorphic vector bundles on ${\bf C}{\rm P}^ n$.  Math. Nachr., 161:233--238, 1993. MR1251020
Stephen S.-T. Yau.  Complex hypersurface singularities with application in complex geometry, algebraic geometry and Lie algebra, volume 5 of Lecture Notes Series.  Seoul National University Research Institute of Mathematics Global Analysis Research Center, Seoul, 1993. MR1268890
J. Chen T. Bielecki, E. Lin and Stephen Yau.  Wavelet and wavelet stieltjes transforms.  In Proceedings of the 32nd conference on decision and control, san antonio, texas, dec, pages 3062-3063.  1993.
W. S. Wong Rui-Tao Dong and Stephen Yau.  Some pde problem: from estimation algebras.  In Proceedings on aerospace control systems, the first ieee regional conference, (1993), may 25-27,, pages 143-147.  1993.
Yi-Jing Xu and Stephen S.-T. Yau.  A sharp estimate of the number of integral points in a tetrahedron.  J. Reine Angew. Math., 423:199--219, 1992. MR1142487
Joseph Sampson, Stephen S.-T. Yau and Yung Yu.  Classification of gradient space as ${\rm sl}(2,\bold C)$ module. I.  Amer. J. Math., 114(5):1147--1161, 1992. MR1183535
Yi-Jing Xu and Stephen S.-T. Yau.  Topological types of seven classes of isolated singularities with ${\bf C}^ *$-action.  Rocky Mountain J. Math., 22(3):1147--1215, 1992. MR1183710
A. Libgober and S. Yau.  Erratum: ``An obstruction to smoothing of Gorenstein surface singularities'' [Comment. Math. Helv. 65 (1990), no. 3, 413--433; MR1069817 (91m:14005)].  Comment. Math. Helv., 67(4):670, 1992. MR1185815
Stephen S.-T. Yau.  A remark on moduli of complex hypersurfaces.  Amer. J. Math., 113(2):287--292, 1991. MR1099448
Rui-Tao Dong, Luen-Fai Tam, Wing Shing Wong and Stephen S.-T. Yau.  Structure and classification theorems of finite-dimensional exact estimation algebras.  SIAM J. Control Optim., 29(4):866--877, 1991. MR1111664
Hing Sun Luk and Stephen S.-T. Yau.  Obstructions to embedding of real $(2n-1)$-dimensional compact CR manifolds in ${\bf C}^ {n+1}$.  In Several complex variables and complex geometry, Part 3 (Santa Cruz, CA, 1989), pages 261--276.  Amer. Math. Soc., Providence, RI, 1991. MR1128600
Stephen S.-T. Yau.  Solvability of Lie algebras arising from isolated singularities and nonisolatedness of singularities defined by ${\rm sl}(2,{\bf C})$ invariant polynomials.  Amer. J. Math., 113(5):773--778, 1991. MR1129292
Stephen S.-T. Yau.  Regularity for the Harvey-Lawson solutions to the complex Plateau problem.  J. Differential Geom., 34(2):425--429, 1991. MR1131438
Craig Seeley and Stephen S.-T. Yau.  Algebraic methods in the study of simple-elliptic singularities.  In Algebraic geometry (Chicago, IL, 1989), pages 216--237.  Springer, Berlin, 1991. MR1181215
Craig Seeley and Stephen S.-T. Yau.  Variation of complex structures and variation of Lie algebras.  Invent. Math., 99(3):545--565, 1990. MR1032879
Luen-Fai Tam, Wing Shing Wong and Stephen S.-T. Yau.  On a necessary and sufficient condition for finite dimensionality of estimation algebras.  SIAM J. Control Optim., 28(1):173--185, 1990. MR1035978
Max Benson and Stephen S.-T. Yau.  Equivalences between isolated hypersurface singularities.  Math. Ann., 287(1):107--134, 1990. MR1048283
Anatoly Libgober and Stephen S.-T. Yau.  An obstruction for smoothing of Gorenstein surface singularities.  Comment. Math. Helv., 65(3):413--433, 1990. MR1069817
Yi-Jung Xu and Stephen S.-T. Yau.  The inequality $\mu\geq 12p_ g-4$ for hypersurface weakly elliptic singularities.  In Singularities (Iowa City, IA, 1986), pages 317--344.  Amer. Math. Soc., Providence, RI, 1989. MR1000609
Yi-Jing Xu and Stephen S.-T. Yau.  Classification of topological types of isolated quasi-homogeneous two-dimensional hypersurface singularities.  Manuscripta Math., 64(4):445--469, 1989. MR1005247
Stephen S.-T. Yau.  The multiplicity of isolated two-dimensional hypersurface singularities: Zariski problem.  Amer. J. Math., 111(5):753--767, 1989. MR1020827
Stephen S.-T. Yau.  Topological type of isolated hypersurface singularities.  In Recent developments in geometry (Los Angeles, CA, 1987), pages 303--321.  Amer. Math. Soc., Providence, RI, 1989. MR1034988
Stephen S.-T. Yau.  Classification of Jacobian ideals invariant by ${\rm sl}(2,{\bf C})$ actions.  Mem. Amer. Math. Soc., 72(384):iv+180, 1988. MR932689
Stephen S.-T. Yau.  Topological types and multiplicities of isolated quasihomogeneous surface singularities.  Bull. Amer. Math. Soc. (N.S.), 19(2):447--454, 1988. MR935021
Max Benson and Stephen S.-T. Yau.  Lie algebras and their representations arising from isolated singularities: computer method in calculating the Lie algebras and their cohomology.  In Complex analytic singularities, pages 3--58.  North-Holland, Amsterdam, 1987. MR894284
Stephen S.-T. Yau.  A necessary and sufficient condition for a local commutative algebra to be a moduli algebra: weighted homogeneous case.  In Complex analytic singularities, pages 687--697.  North-Holland, Amsterdam, 1987. MR894313
G. D. Mostow and Stephen S.-T. Yau.  Some surfaces covered by the ball and a problem in finite groups.  In Algebraic groups Utrecht 1986, pages 201--228.  Springer, Berlin, 1987. MR911141
H. Blaine Lawson, Jr. and Stephen S.-T. Yau.  Holomorphic symmetries.  Ann. Sci. École Norm. Sup. (4), 20(4):557--577, 1987. MR932798
Stephen S.-T. Yau.  Solvable Lie algebras and generalized Cartan matrices arising from isolated singularities.  Math. Z., 191(4):489--506, 1986. MR832806
Stephen S.-T. Yau.  Singularities defined by ${\rm sl}(2,{\bf C})$ invariant polynomials and solvability of Lie algebras arising from isolated singularities.  Amer. J. Math., 108(5):1215--1239, 1986. MR859777
I. M. Singer, Bun Wong, Shing-Tung Yau and Stephen S.-T. Yau.  An estimate of the gap of the first two eigenvalues in the Schrödinger operator.  Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12(2):319--333, 1985. MR829055
Stephen S.-T. Yau.  Criteria for right-left equivalence and right equivalence of holomorphic functions with isolated critical points.  In Complex analysis of several variables (Madison, Wis., 1982), pages 291--297.  Amer. Math. Soc., Providence, RI, 1984. MR740890
Paul C.-P. Yang and Stephen S.-T. Yau.  Riemann-Roch theorem for strongly pseudoconvex manifolds of dimension three.  In Several complex variables (Hangzhou, 1981), pages 257--267.  Birkhäuser Boston, Boston, MA, 1984. MR897605
Stephen S.-T. Yau.  Milnor algebras and equivalence relations among holomorphic functions.  Bull. Amer. Math. Soc. (N.S.), 9(2):235--239, 1983. MR707965
Stephen S.-T. Yau.  On irregularity and geometric genus of isolated singularities.  In Singularities, Part 2 (Arcata, Calif., 1981), pages 653--662.  Amer. Math. Soc., Providence, RI, 1983. MR713288
Stephen S. T. Yau.  Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities.  Proc. Nat. Acad. Sci. U.S.A., 80(24 i.):7694--7696, 1983. MR728666
Stephen S. T. Yau.  $s^{(n-1)}$ invariant for isolated $n$-dimensional singularities and its application to moduli problem.  Amer. J. Math., 104(4):829--841, 1982. MR667538
Bruce Bennett and Stephen S. T. Yau.  Milnor number and classification of isolated singularities of holomorphic maps.  In Harmonic maps (New Orleans, La., 1980), pages 1--34.  Springer, Berlin, 1982. MR673580
John N. Mather and Stephen S. T. Yau.  Classification of isolated hypersurface singularities by their moduli algebras.  Invent. Math., 69(2):243--251, 1982. MR674404
Stephen S. T. Yau.  Various numerical invariants for isolated singularities.  Amer. J. Math., 104(5):1063--1100, 1982. MR675310
Stephen S. T. Yau.  Kohn-Rossi cohomology and its application to the complex Plateau problem. I.  Ann. of Math. (2), 113(1):67--110, 1981. MR604043
Stephen S. T. Yau.  Deformations and equitopological deformations of strongly pseudoconvex manifolds.  Nagoya Math. J., 82:113--129, 1981. MR618811
Stephen S. T. Yau.  Sheaf cohomology in $1$-convex manifolds.  In Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979), pages 429--452.  Princeton Univ. Press, Princeton, N.J., 1981. MR627772
Stephen S. T. Yau.  Existence of $L^{2}$-integrable holomorphic forms and lower estimates of $T_{V}^{1}$.  Duke Math. J., 48(3):537--547, 1981. MR630584
John N. Mather and Stephen S.-T. Yau.  Criterion for biholomorphic equivalence of isolated hypersurface singularities.  Proc. Nat. Acad. Sci. U.S.A., 78(10, Phys. Sci.):5946--5947, 1981. MR773820
Stephen Shing Toung Yau.  On maximally elliptic singularities.  Trans. Amer. Math. Soc., 257(2):269--329, 1980. MR552260
Stephen S. T. Yau.  Index theory for the boundaries of complex analytic varieties.  Proc. Nat. Acad. Sci. U.S.A., 77(3, part 1):1248--1249, 1980. MR563635
Stephen Shing Toung Yau.  Hypersurface weighted dual graphs of normal singularities of surfaces.  Amer. J. Math., 101(4):761--812, 1979. MR536041
Stephen Shing Toung Yau.  Gorenstein singularities with geometric genus equal to two.  Amer. J. Math., 101(4):813--854, 1979. MR536042
Stephen Shing Toung Yau.  On strongly elliptic singularities.  Amer. J. Math., 101(4):855--884, 1979. MR536043
Stephen Shing Toung Yau.  Normal two-dimensional elliptic singularities.  Trans. Amer. Math. Soc., 254:117--134, 1979. MR539910
Stephen S. T. Yau.  The signature of Milnor fibres and duality theorem for strongly pseudoconvex manifolds.  Invent. Math., 46(1):81--97, 1978. MR0492391
Stephen Shing Toung Yau.  Normal singularities of surfaces.  In Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2, pages 195--198.  Amer. Math. Soc., Providence, R.I., 1978. MR520537
Stephen Shing Toung Yau.  On almost minimally elliptic singularities.  Bull. Amer. Math. Soc., 83(3):362--364, 1977. MR0432912
Stephen Shing Toung Yau.  The signature of smoothings of higher dimensional singularities.  Bull. Amer. Math. Soc., 83(6):1313--1315, 1977. MR0472813
Stephen S. T. Yau.  Two theorems on higher dimensional singularities.  Math. Ann., 231(1):55--59, 1977/78. MR0492389
update this page
HTML 5 CSS FAE
UIC LAS MSCS > people > publications