Selected Publications

Kwok Wai CHUNG Philippe G. CIARLET Felipe CUCKER Hui-Hui DAI
Daniel W. C. HO Benny Y. C. HON Chun Wah LI Kam Moon LIU
Ya Yan LU Tao LUO Stephen SMALE Weiwei SUN
Roderick S. C. WONG Jonathan WYLIE Tong YANG Qiang ZHANG
Ding-Xuan ZHOU

Kwok Wai CHUNG

  • K. W. CHUNG, H. S. Y. CHAN and B. N. WANG, Tessellations with Symmetries of the Wallpaper Groups and the Modular Group in the Hyperbolic 3-Space from Dynamics, Computers & Graphics, 25(2), 333–341, 2001.
  • K. W. CHUNG, H. S. Y. CHAN and B. N. WANG, Tessellations in Three-dimensional Hyperbolic Space from Dynamics and the Quaternions, Chaos, Solitons & Fractals, 12, 1181–97, 2001.
  • H. S. Y. CHAN, K. W. CHUNG and D. W. QI, Some Bifurcation Diagrams for Limit Cycles of Quadratic Differential Systems, International Journal of Bifurcation and Chaos, 11(1), 197–206, 2001.
  • S. X. YU, H. S. Y. CHAN and K. W. CHUNG, A Comparison of Sampling Designs in a Hainan Tropical Rain Forest, Communicty Ecology, 1(1), 81–87, 2000.
  • K. W. CHUNG, H. S. Y. CHAN and N. CHEN, General Mandelbrot Sets and Julia Sets with Colour Symmetry from Equivariant Mappings of the Modular Group, Computer & Graphics, 24(6) 911–918, 2000.

Philippe G. CIARLET

  • CIARLET, P.G.; MARDARE, C., Nonlinear Korn inequalities, J. Math. Pures Appl. 104 (2015), 1119-1134.
  • AMROUCHE, C.; CIARLET, P.G.; MARDARE, C., On a lemma of Jacques-Louis Lions and its relation to other fundamental results, J. Math. Pures Appl. 104 (2015), 207-226.
  • CIARLET, P.G.; IOSIFESCU, O., Donati compatibility conditions on a surface - Application to shell theory, J. Math. Pures Appl. 102 (2014), 173-202.
  • CIARLET, P.G.; GEYMONAT, G.; KRASUCKI, F., A new duality approach to elasticity, Math. Models Methods Appl. Sci. 22 (2012), 1150003 (21 pages).
  • CIARLET, P.G.; CIARLET, JR., P. Direct computation of stresses in planar linearized elasticity, Math. Models Methods Appl. Sci. 19 (2009), 1043-1064.

Felipe CUCKER

  • A Theory of Complexity, Condition, and Roundoff. Forum of Mathematics, Sigma, 3, e4, 2015.
  • On a Problem Posed by Steve Smale (with P. Bürgisser). Annals of Mathematics, 174, pp. 1785-1836, 2011.
  • Coverage Processes on Spheres and Condition Numbers for Linear Programming (with P. Bürgisser and M. Lotz). Annals of Probability, 38, pp. 570-604, 2010.
  • Emergent Behavior in Flocks, (with S. Smale). IEEE Trans. Autom. Control, 52, pp. 852-862, 2007.
  • On the mathematical foundations of learning, (with S. Smale). Bulletin Amer. Math. Soc. 39, pp. 1-49, 2002.

Hui-Hui DAI

  • H.-H. DAI and F.-F. Wang, Asymptotic bifurcation solutions for compressions of a clamped nonlinearly elastic rectangle: transition region and barreling to a corner-like profile, to appear in SIAM J. Appl. Math.
  • J. Wang and H.-H. Dai, Phase transitions induced by extension in a slender SMA cylinder: Analytical solutions for the hysteresis loop based on a quasi-3D contimuum model, Int. J. Plasticity, 26, 467–487, 2010.
  • H.-H. DAI and Z. CAI, Phase transitions in a slender cylinder composed of an incompressible elastic material. l., Proc. Roy. Soc. Lond. A-Mathematical Physical and Engineering Sciences. 462, pp. 75–95, 2006.
  • H.-H. DAI and Y. HUO, Solitary Waves in an Inhomogeneous Rod Composed of a General Hyperelastic Material, Wave Motion 35, pp. 55–69, 2002.
  • H.-H. DAI and Y. HUO, Solitary Shock Waves and Other Travelling Waves in a General Compressible Hyperelastic Rod, Proc. Roy. Soc. Lond. A. 456, pp. 331–363, 2000.

Daniel W. C. HO

  • Y. NIU, J. LAM, X. WANG and Daniel W. C. HO, Sliding Mode Control for Nonlinear Stated-delayed Systems Using Neural Network Approximation, IEE Proc Control Theory and Application, Vol. 150, No. 3, pp. 233–239, 2003.
  • Zidong WANG and Daniel W. C. HO, Variance – Constrained Filtering for Uncertain Stochastic Systems with Missing Measurements, IEEE Trans. Auto. Control, 48, 7, pp. 1254–1258, Jul 2003.
  • Daniel W. C. HO and Guoping LU, Robust Stabilization for a Class of Discrete-time Nonlinear Systems via Output Feedback: The Unified LMI Approach, International Journal of Control, Vol. 76, No. 2, pp. 105–115, 2003.
  • Zidong WANG and Daniel W. C. HO, Filtering on Nonlinear Time-delay Stochastic Systems, Automatica, 39, pp. 101–109, 2003.
  • D. W. C. HO, Ping-an ZHANG and Jinhua XU, Fuzzy Wavelet Networks for Function Learning, IEEE Trans on Fuzzy Systems, 9, 1, pp. 200–211, Feb 2001.

Benny Y. C. HON

  • J. CHENG, Y. C. HON and M. YAMAMOTO, Conditional Stability Estimation for an Inverse Boundary Problem with Non-smooth Boundary Data in R3, Transactions of the American Mathematical Society, Vol. 353, pp. 4123–4138, 2001, (31/145 – Mathematics).
  • Y. C. HON and T. WEI, Backus-Gilbert Algorithm for a Cauchy Problem of Laplace Equation, Inverse Problems, Vol. 17, pp. 261–271, 2001. (Ranking: 17/138 – Applied Mathematics Category).
  • M. SU, X. XU, J. ZHU and Y. C. HON, Numerical Simulation of Tidal Bore in Hangzhou Gulf and Qiantangjiang, International Journal for Numerical Methods in Fluids, Vol. 36, pp. 205–247, 2001. (64/138 – Applied Mathematics).
  • Y. C. HON and R. SCHABACK, On Unsymmetric Collocation by Radial Basis Functions, Applied Mathematics and Computations, Vol. 119, Nos. 2–3, pp. 177–186, 2001. (113/138 – Applied Mathematics).
  • Y. C. HON and Z. WU, A Numerical Computation for Inverse Boundary Determination Problems, Engineering Analysis with Boundary Element, Vol. 24, pp. 599–606, 2000, (57/138 – Applied Mathematics, 11/60 – Engineering).

Chun Wah LI

  • C. W. LI and Z. DONG, On Kernel Estimations and Invariant Measures of Stochastic Jump-diffusions, Dynamics of Continuous, Discrete and Impulsive Systems, Series A, Vol. 10, No. 1–3, pp. 373–387, 2003.
  • C. W. LI, Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps, Stochastic Inequalities and their Applications, Progress in Probability, Vol. 56, pp. 339–351, Birkhaüser Verlag, Basel, 2003.
  • C. W. LI, Z. DONG and R. SITU, Almost Sure Stability of Linear Stochastic Differential Equations with Jumps, Probab. Theory Relat. Fields, Vol. 123, pp. 121–155, 2002.

Kam Moon LIU

  • LIU, K.M., CHIM, K.C., CHUNG K.W. and HO, W.C., "Learning Undergraduate Mathematics in a Discovery-Enriched Approach", World Academy of Science, Engineering and Technology, Issue 72, December, 4 pages (2012).
  • HE, Y. and LIU, K.M., "Multi-level Spectral Galerkin Method for the Navier-Stokes Equations, II: Time Discretrization", Journal of Advances in Computational Mathematics, Vol. 25, pp. 403-433 (2006).
  • LIU K. M. and PAN, C. K., "The Automatic Solution to Systems of Ordinary Differential Equations by the Tau Method", Journal of Computers and Mathematics with Applications, Vol. 38, pp. 197-210, (1999).
  • LIU, K. M., "Numerical Solution of Differential Eigenvalue Problems with Variable Coefficients with the Tau-Collocation Method", Journal of Mathematical and Computer Modelling, Vol. 11, pp. 672-675 (1988).
  • LIU, K.M. and ORTIZ, E.L., "Numerical Solution of Eigenvalue Problems for Partial Differential Equations with the Tau-lines Method", Journal of Computers and Mathematics with Applications, Vol. 12B, pp. 1153-1168 (1986).

Ya Yan LU

Tao LUO

  • Luo, Tao. , Xin, Zhouping. & Zeng, Huihui, On Nonlinear Asymptotic Stability of The Lane-Emden Solutions for The Viscous Gaseous Star Problem. Advance in Mathematics. 291. 90 - 182 (2016). doi:10.1016/j.aim.2015.12.022
  • Federbush, Paul. , Luo, Tao. & Smoller, Joel, Existence of Magnetic Compressible Fluid Stars. Arch. Ration. Mech. Anal. 215/2. 611 - 631(2015).
  • Luo, Tao. & Zeng, Huihui, Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping. Comm. Pure Appl. Math. doi:10.1002/cpa.21562 (published online).
  • Luo, Tao. , XIn, Zhouping. & Zeng, Huihui, Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation. Arch. Ration. Mech. Anal. 213/2. 763 - 831(2014).
  • Luo, Tao. & Smoller, Joel. Nonlinear Dynamical Stability of Newtonian Rotating and Non-rotating White Dwarfs and Rotating Supermassive Stars. Commun. Math. Physics. 425 - 457 (2008).

Stephen SMALE

  • M. SHUB and S. SMALE, Complexity and Bezout's Theorem IV: Probability of Success, Extensions, to appear in SIAM J. of Numerical Analysis. Feb '96.
  • M. SHUB and S. SMALE, Complexity of Bezout's Theorem V: Polynomial time, Theoretical Computer Science, (1994) pp 141–164.
  • M. SHUB and S. SMALE, On the Intractability of Hilbert's Nullellensatz and an Algebraic Version of "NP ≠ P?", to appear in Duke Math. J. (special volume honoring John Nash).

Weiwei SUN

  • H. Gao and W. Sun, A new mixed formulation and numerical solution of Ginzburg-Landau equations under temperal gauge. SIAM J. Sci. Comput., accepted.
  • B. Li and W. Sun, Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra, Math. Comput., accepted.
  • B.Li and W.Sun, Regularity of the diffusion-dispersion tensor and error analysis of Galerkin FEMs for a porous medium flow, SIAM J. Numer. Anal., 53(2015), 1418--1413.
  • J. Wang, Z. Si and W. Sun, A new error analysis on characteristics-mixed FEMs for incompressible miscible flow in porous media SIAM J. Numer. Anal., 52(2014), 3000--3020.
  • B. Li and W. Sun, Unconditional convergence and optimal error estimate of Galerkin-mixed FEMs for incompressible flow in porous media, SIAM J. Numer. Anal., 51(2013), 1959--1977.

Roderick S. C. WONG

  • W.-Y. QIU and R. WONG, Uniform Asymptotic Formula for Orthogonal Polynomials with Exponential Weight, SIAM J. Math. Anal., 31 (2000), 992–1029.
  • C.-K. QU and R. WONG, "Best Possible" Upper and Lower Bounds for the Zeros of the Bessel Function, Trans. Amer. Math. Soc., 351 (1999), 2833–2859.
  • X.-H. JIANG and R. WONG, Justification of a Perturbation Approximation of the Klein-Gordon Equation, Studies Appl. Math., 102(1999), 375–417.
  • Y.-Q. ZHAO and R. WONG, Smoothing of Stokes Discontinuity for the Generalized Bessel Function II, Proc. Roy. Soc. Lond. Ser. A, 455 (1999), 3065–3804.
  • X.-S. JIN and R. WONG, Uniform Asymptotic Expansions for Meixner Polynomials, Constr. Approx., 14 (1998), 113–150.

Jonathan WYLIE

  • J. J. Wylie, B. H. Bradshaw-Hajek & Y. M. Stokes "The evolution of a viscous thread pulled with a prescribed speed" Journal of Fluid Mechanics 795, 380 (2016).
  • J. J. Wylie, H. Huang & R. M. Miura "Stretching of viscous threads at low Reynolds numbers" Journal of Fluid Mechanics 683, 212 (2011)
  • S. Ben Hariz, J. J. Wylie & Q. Zhang, "Optimal rate of convergence for nonparametric change-point estimators for non-stationary sequences", Annals of Statistics 35, 1802 (2007).
  • J. J. Wylie, Q. Zhang & X. X. Sun, "Anomalous Ritchmyer-Meshkov Fingering in Dissipative Particle Systems", Physical Review Letters 97, 104501 (2006).
  • J. J. Wylie, B. Voight & J. A. Whitehead, "Instability of magma flow with volatile-dependent viscosity", Science 285, 1883 (1999).

Tong YANG

  • Tong Yang and Hongjun Yu, Spectrum analysis of some kinetic equations, to appear in Archive for Rational Mechanics and Analysis.
  • Radjesvarane Alexandre, Yaguang Wang, Chao-Jiang Xu and Tong Yang, Well- posedness of The Prandtl Equation in Sobolev Spaces, Journal of American Mathematical Society, 28(3), 2015, 745-784.
  • Xulong Qin, Tong Yang, Zheng-an Yao and Wenshu Zhou, Vanishing shear viscosity and boundary layer for the Navier-Stokes equations with cylindrical symmetry, Archive for Rational Mechanics and Analysis, 216(2015), 1049-1086.
  • Zhouping Xin, Tong Yang and Hongjun Yu, The Boltzmann Equation with soft potentials near the Local Maxwellian, Archive for Rational Mechanics and Analysis, 206(2012), no. 1, 239-296.
  • Tai-Ping Liu and Tong Yang, L1 stability of weak solutions for 2 x 2 systems of hyperbolic conservation laws, Journal of American Mathematical Society, 12(1999), 729-774.

Qiang ZHANG

  • J. YAN, Q. ZHANG and S. ZHANG, Growth Optimal Portfolio in a Market Driven by Jump-Diffusion-Like Process or a Levy Process, Annals of Econ. and Fin., Vol. 1, pp. 101–116 (2000).
  • D. YANG and Q. ZHANG, Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices, J. of Business, Vol. 73, pp. 477–491 (2000).
  • Q. ZHANG, Analytical Solutions of Layzer-type Approach to Unstable Interfacial Fluid Mixing, Physical Review Letters, Vol. 81, pp. 3391–3394 (1998).
  • Q. ZHANG and M. J. GRAHAM, Scaling Laws for Unstable Interfacial Fluid Mixing Driven by Strong Shocks, Physical Review Letters, Vol. 79, pp. 2674–2677 (1997).
  • Q. ZHANG and S. SOHN, Nonlinear Theory of Unstable Fluid Mixing Driven by Shock Waves, Phys. of Fluids, Vol. 9, pp. 1106–1124 (1997).

Ding-Xuan ZHOU

  • Ding-Xuan ZHOU, Capacity of Reproducing Kernel Hilbert Spaces in Learning Theory, IEEE Trans. Inform. Theory Vol. 49, pp. 1743–1752, 2003.
  • S. SMALE and Ding-Xuan ZHOU, Estimating the Approximation Error in Learning Theory, Analysis and Applications Vol. 1, pp. 17–41, 2003.
  • Ding-Xuan ZHOU, The Covering Number in Learning Theory, J. Complexity Vol. 18, pp. 739–767, 2002.
  • Ding-Xuan ZHOU, Self-similar Lattice Tilings and Subdivision Schemes, SIAM J. Math. Anal. Vol. 33, pp. 1–15, 2001.
  • Gilbert STRANG and Ding-Xuan ZHOU, The Limits of Refinable Functions, Trans. Amer. Math. Soc. Vol. 353, pp. 1971–1984, 2001.

Last update: 17 May 2016