Publications

Differential Geometry and Topology

  • Weiqing Gu (1997), The Stable 4-dimensional Geometry of the Real Grassmann Manifolds. Duke Mathematical Journal, Vol. 93, No. 1, 155-178.
  • Weiqing Gu and Zhongmin Shen (1998), Lévy Concentration of Metric Measure Manifolds. Finslerian Geometries, Kluwer Academic Publishers, 169-177.
  • Weiqing Gu and Shenjun Jiang (1998), Knotty Matrices in Knots. The Journal of Knot Theory and its Ramifications, Vol. 8, No. 6, 701-707.
  • Daniel Grossman and Weiqing Gu (2001), Uniqueness of Volume-Minimizing Submanifolds Calibrated by the First Pontryagin Form. the Transactions of the American Mathematics Society, Vol. 353, No. 11, Pages 4319-4332. (Article also electronically published on June 14, 2001.)
  • Daniel Grossman and Weiqing Gu, The 4-Dimensional Calibrated Geometry of Complex Grassmannians. In preparation.
  • Herman Gluck and Weiqing Gu (2001), Volume-Preserving Great Circle Flows on the 3-Sphere, Geometriae Dedicata, Vol. 88, 2001, Pages 259-282.
  • Weiqing Gu and Christopher Pries, Examples of Cayley Manifolds in R8. Houston Journal of Mathematics. Electronic Edition Vol. 30, No. 1, 2004, pages 55-87. This is a publication with an undergraduate at HMC.
  • Weiqing Gu and Ian Weiner, Associative Manifolds Invariant Under 1-Parameter Subgroups of G2. Accepted by International Journal of Pure and Applied Mathematics.
  • Weiqing Gu and Christopher Pries, Classification of Symmetric Cayley Manifolds. Submitted to Houston Journal of Mathematics.
  • Weiqing Gu and Matt Holden, Volume Minimizing Cycles in R6 x S1 = R 7/Z. In preparation for submission.
  • Weiqing Gu and Jeff L. Jaurequi, Solving for Volume-Minimizing Cycles in G2-Manifolds. In preparation for submission.
  • Weiqing Gu and Ruben Arenas, A New Basis for Lie Algebra of G2. In preparation for submission.

Geometric Modeling and Design

  • Rida T. Farouki, Weiqing Gu, and Hwan Pyo Moon (2000), Geometry of Minkowski Roots. Geometric Modeling and Processing 2000, IEEE Computer Society Press, 287-300(2000).
  • Doug DeCarlo, Jean Gallier and Weiqing Gu, Fast and Simple Methods for Computing Control Points, Scientific Literature Digital Library, http://citeseer.ist.psu.edu/316748.htm1.
  • Philip D. Cha and Weiqing Gu (1999), Comparing the Perturbed Eigensolutions of a Generalized and a Standard Eigenvalue Problem. The Journal of Sound and Vibration, Vol. 227(5), 11 Nov, 99, 1122-1132.
  • Philip D. Cha and Weiqing Gu (1999), Model Updating Using an Incomplete set of Experimental Modes. The Journal of Sound and Vibration, Vol. 233(4), 2 Dec, 99, 587-600.
  • Philip D. Cha and Weiqing Gu, Perturbation Method for a Symmetrized Standard Eigenvalue Problem. International Journal of Computational and Numerical Analysis and Applications. Vol. 2, No. 3, 2002, 337-350.
  • Weiqing Gu and Ian Weiner, Minkowski Geometric Algebra of Quaternion Sets. International Journal of Pure and Applied Mathematics. Vol. 3, No. 4, 2002, 385-411. This is a publication with an undergraduate at HMC.
  • Weiqing Gu, Geometric Methods in Finding Complete Intersections of Quadratic Equations. In preparation for submission.
  • Weiqing Gu and Ronald N. Goldman, A New and Simple Scheme for Symmetrizing Multiaffine Polynomials. In preparation for submission.
  • Micah Smukler and Weiqing Gu, Minimal Symmetrizing Sets of Multiaffine Polynomials. In preparation.

Industrial Mathematics

  • Weiqing Gu, Using Elliptic Curves Over Finite Fields in Cryptography and Morc, currently VIASAT INC. CONFIDENTIAL: will be published after waiting a certain period since it is an extension of the math Clinic project with ViaSat Inc. supervised by myself on Using Elliptic Curve Cryptography for Secure Communication, which has been patented through ViaSat.
  • Weiqing Gu, Geometric Methods in Finding Intersections of Nonlinear Equations in Three Variables and Their Applications in Color-Imaging Technology. This document is HP CONFIDENTIAL.
  • Weiqing Gu and Ingeborg Tastl (2005), Analyzing and Comparing Interpolation Methods in Generating ICC Profiles. HP CONFIDENTIAL.
  • Weiqing Gu and Ingeborg Tastl (2005), An Iterative Method in Generating ICC Profiles. HP CONFIDENTIAL: in the process of patent through hp Invent. (The results from this research are being implemented by current hp Clinic team at Harvey Mudd.)
  • Weiqing Gu and Ingeborg Tastl (2005), Inventing a New Continuous Model irt. Generating ICC Profiles, HP CONFIDENTIAL, is in the process of patent through hp Invent.
  • Weiqing Gu and Ingeborg Tastl (2005), A New Method of Dealing With Subtle Color Regions Such As Gray and Skin-Tone. HP CONFIDENTIAL.
  • Weiqing Gu and Ingeborg Tastl (2005), Develop “Smart” CMM (Color Manager Model). In preparation, HP CONFIDENTIAL.

Applications in Math-Biology

  • Weiqing Gu and Helen Moore, A mathematical model for treatment-resistant mutations of HIV, Mathematical Biosciences and Engineering, Vol. 2, No. 2. April 2005, pp.363-380.
  • L. G. de Pillis, W. Gu, and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. Appearing soon in Journal of Theoretical Biology.
  • Weiqing Gu and Helen Moore, Optimal therapy regiments for treatment-resistant mutations of HIV, Submitted to Proceedings from the Joint Research Conference on Modeling the Dynamics of Human Diseases.
  • L. G. de Pillis, W. Gu, and F. Fister, Chemotherapy for Tumors: An Analysis of the Dynamics and a Study of Quadratic and Linear Optimal Controls. Submitted to Mathematical Biosciences.
  • Weiqing Gu, Lisette de Pillis, Will Chang, Eric Malm, An Immunotherapeutic Extension of the Jackson 3D Tumor Model. In preparation for submission.
  • Weiqing Gu and Jeffrey Jauregui, Applying Level Set Methods to the Modeling on Tumor Growth and Response to Chemotherapy. In preparation for submission.
  • L. G. de Pillis, W. Gu, and F. Fister, Optimal Control of Mixed Immunotherapy and Chemotherapy of Tumors. In preparation for submission.
  • L. G. de Pillis, W. Gu, and F. Fister, Seeking Bang-Bang Solutions in Mixed Imuno-Chemo-therapy of Tumors. In preparation.