Hongyou Wu

Schedule for Fall Semester 2008

Teaching

• Here are the information sheet for my Math 229 students.
  Sample tests: 1 & key; 2 & key.
  
• Here are the information sheet and syllabus for my Math 336 students.
  Old tests: 1 & key; 2 & key; 3 & key.
  Actual tests: 1 & key.
  Old finals: Fall 07; Spring 08 & key.
  

Published Research Papers

1. H. Wu: Particular solutions of nonhomogeneous recursive equations of second order with constant coefficients and periodicity of solutions. J. Chongqing University 1982, No.4, 111-117. (In Chinese, with English summary)
2. H. Wu: Symmetric properties of eigenfunctions of the Laplace operator on compact Riemannian manifolds. Michigan Math. J. 38 (1991), 129-139.
3. H. Wu: Non-linear partial differential equations via vector fields on homogeneous Banach manifolds. Ann. Global Anal. Geom. 10 (1992), 151-170.
4. H. Wu: Weingarten surfaces and nonlinear partial differential equations. Ann. Global Anal. Geom. 11 (1993), 49-64.
5. H. Wu: Banach manifolds of minimal surfaces in the 4-sphere. AMS Proc. of Symp. Pure Math. 54 (1993), 513-539.
6. J. Dorfmeister & H. Wu: Constant mean curvature surfaces and loop groups. J. reine angew. Math. 440 (1993), 43-76.
7. H. Wu: On Backlund transformations for nonlinear partial differential equations. J. Math. Anal. Appl. 192 (1995), 151-179.
8. F. Pedit & H. Wu: Discretizing constant curvature surfaces via loop group factorizations: the discrete sine- and sinh-Gordon equations. J. Geom. Phys. 17 (1995), 245-260.
9. J. Dorfmeister, I. McIntosh, F. Pedit & H. Wu: On the meromorphic potential for a harmonic surface in a k-symmetric space. Manuscripta Math. 92 (1997), 143-152.
10. Q. Kong, H. Wu & A. Zettl: Dependence of eigenvalues on the problem. Math. Nachr. 188 (1997), 173-201.
11. H. Wu: On the dressing action of loop groups on constant mean curvature surfaces. Tohoku Math. J. 49 (1997), 599-621.
12. H. Wu: Foliations on constant curvature surfaces and nonlinear partial differential equations. Houston J. Math. 24 (1998), 65-84.
13. J. Dorfmeister, F. Pedit & H. Wu: Weierstrass type representation of harmonic maps into symmetric spaces. Comm. Anal. Geom. 6 (1998), 633-668.
14. H. Wu: A simple way for determining the normalized potentials for harmonic maps. Ann. Global Anal. Geom. 17 (1999), 189-199.
15. M. S. P. Eastham, Q. Kong, H. Wu & A. Zettl: Inequalities among eigenvalues of Sturm-Liouville problems. J. Inequalities Appl. 3 (1999), 25-43.
16. H. Wu: A new characterization of normalized potentials in dimension two. Results in Math. 36 (1999), 184-194.
17. Q. Kong, H. Wu & A. Zettl: Dependence of the n-th Sturm-Liouville eigenvalues on the problem. J. Differential Equations 156 (1999), 328-354.
18. Q. Kong, H. Wu & A. Zettl: Inequalities among eigenvalues of singular Sturm-Liouville problems. Dynamic Systems & Appl. 8 (1999), 517-531.
19. Q.-S. Chi, L. Fernadez & H. Wu: Normalized potentials of minimal surfaces in spheres. Nagoya Math. J. 156 (1999), 187-214.
20. Q. Kong, Q. Lin, H. Wu & A. Zettl: A new proof of the inequalities among Sturm-Liouville eigenvalues. PanAmerican Math. J. 10 (2000), no. 2, 1-10.
21. Q. Kong, H. Wu & A. Zettl: Geometric aspects of Sturm-Liouville problems, I. Structures on spaces of boundary conditions. Royal Soc. Edinburgh Proc. 130A (2000), 561-589.
22. E. Behr, J. Necas & H. Wu: On blow-up of solution for Euler equations. Modelisation Math. Anal. Numerique 35 (2001), 229-238.
23. Q. Kong, H. Wu & A. Zettl: Left-definite Sturm-Liouville problems. J. Differential Equations 177 (2001), 1-26.
24. Q. Kong, H. Wu & A. Zettl: Sturm-Liouville problems with finite spectrum. J. Math. Anal. Appl. 263 (2001), 748-762.
25. H. Wu: Denseness of plain constant mean curvature surfaces in dressing orbits. Contemporary Math. 308 (2002), 341-349.
26. P. Bailey, J. Billingham, R. Cooper, W. Everitt, A. King, Q. Kong, H. Wu & A. Zettl: On some eigenvalue problems in fuel-cell dynamics. Proc. Royal Soc. London 459A (2003), 241-261.
27. X. Cao, Q. Kong, H. Wu & A. Zettl: Sturm-Liouville problems whose leading coefficient function changes sign. Canadian J. Math. 55 (2003), 724-749.
28. Q. Kong, M. Moller, H. Wu & A. Zettl: Indefinite Sturm-Liouville problems. Proc. Royal Soc. Edinburgh 133A (2003), 639-652.
29. K. Haertzen, Q. Kong, H. Wu & A. Zettl: Geometric aspects of Sturm-Liouville problems, II. Space of boundary conditions for left-definiteness. Trans. American Math Soc. 356 (2004), 135-157.
30. X. Cao & H. Wu: Geometric aspects of high order eigenvalue problems, I. Structures on spaces of boundary conditions. International J. Math. Math Sci. 2004 (2004), 647-678.
31. L. Kong, Q. Kong, H. Wu & A. Zettl: Regular approximations of singular Sturm-Liouville problems in the limit-circle case. Results in Math. 45 (2004), 274-292.
32. Q. Kong, H. Wu & A. Zettl: Multiplicity of Sturm-Liouville eigenvalues. J. Comp. Appl. Math. 171 (2004), 291-309.
33. Q. Kong, H. Wu & A. Zettl: Singular left-definite Sturm-Liouville problems. J. Differential Equations 206 (2004), 1-29.
34. Z. Wang & H. Wu: Equality of multiplicities of Sturm-Liouville eigenvalue. J. Math. Anal. Appl. 306 (2005), 540-547.
35. H. Wu: On boundary value problems for nonlinear ordinary differential equations, I. Undamped equations with Dirichlet type boundary conditions. Media-Enhanced Math. 2005 September 12.
36. W. Peng, M. Racovitan & H. Wu: Geometric aspects of Sturm-Liouville problems, V. Natural loops of boundary conditions for monotonicity of eigenvalues and their applications. J. Spectral Math. Appl. 2006.
37. Z. Wang & H. Wu: Dissipative non-self-adjoint Sturm-Liouville operators and completeness of their eigenfunctions. J. Spectral Math. Appl. 2006.
38. W. Ma & H. Wu: Time-space integrable decompositions of nonlinear evolution equations. J. Math. Analysis Appl. 324 (2006), 134-149.
39. X. Cao, H. Wu & C. Xu: On Miura transformations among nonlinear partial differential equations. J. Math. Phys. 47 (2006), 083515.
40. W. Ma, H. Wu & J. He: Partial differential equations possessing Frobenius integrable decompositions. Phys. Lett. A 364 (2007), 29-32.
41. G. Wang, Z. Wang & H. Wu: Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions. J. Math. Analysis Appl. 336 (2007), 1061-1072.
42. X. Cao, Q. Kong, H. Wu & A. Zettl: Geometric aspects of Sturm-Liouville problems, III. Level surfaces of the n-th eigenvalue. J. Comp. Appl. Math. 208 (2007), 176-193.
43. Z. Wang & H. Wu: Geometric aspects of Sturm-Liouville problems, VI. Arcs of boundary conditions for equalities in eigenvalue inequalities. Pacific J. Appl. Math. 1 (2007), 1-25.
44. J. Dorfmeister & H. Wu: Unitarization of loop group representations of fundamental groups. Nagoya Math. J. 187 (2007), 1-33.
45. J. Dorfmeister & H. Wu: Construction of constant mean curvature n-noids from holomorphic potentials. Math. Z. 258 (2008), 773-803.
46. Q. Kong, H. Wu & A. Zettl: Limits of Sturm-Liouville eigenvalues when the interval shrinks to an end point. Royal Soc. Edinburgh Proc. 138A (2008), 323-338.
47. G. Wang, Z. Wang & H. Wu: Computing the indices of Sturm-Liouville eigenvalues for coupled boundary conditions (the EIGENIND-SLP codes). J. Comp. Appl. Math. 220 (2008), 490-507.

Research Paper(s) Accepted for Publication

• Z. Wang & H. Wu: Sturm-Liouville problems with limit-circle end points, I. Structures on spaces of problems and their applications. Pacific J. Appl. Math., to appear.
• Z. Wang & H. Wu: The index problem for eigenvalues for coupled boundary conditions and Fulton's conjecture. Monatsh. Math., to appear.
• G. Shi & H. Wu: Spectral theory of Sturm-Liouville difference operators. Linear Algebra Appl., to appear.

Research Paper(s) Submitted for Publication

• X. Cao, Z. Wang & H. Wu: On boundary conditions in self-adjoint multi-interval Sturm-Liouville problems. Preprint, February 2007.
• J. Huang, Alatancang & H. Wu: Descriptions of spectra of infinite dimensional Hamiltonian operators and their applications. Preprint, April 2007.
• S. Sun, Y. Shi & H. Wu: On discrete Sturm-Liouville problems, I. Structures on spaces of problems and their applications. Preprint, June 2007.
• S. Sun, Y. Shi & H. Wu: On discrete Sturm-Liouville problems, II. Dependence of the n-th eigenvalue on the problem. Preprint, July 2007.
• Y. Shi, S. Sun & H. Wu: On discrete Sturm-Liouville problems, IV. The index problem for eigenvalues for coupled boundary conditions. Preprint, September 2008.
• J. Qi & H. Wu: Interlacing eigenvalue intervals for Sturm-Liouville problems. Preprint, October 2008.

Research Preprint(s)

• J. Dorfmeister & H. Wu: Construction of constant mean curvature trinoids from holomorphic potentials. Preprint, 2000 April 29.

Research Announcement(s)

• J. Dorfmeister & H. Wu: Banach manifolds of constant mean curvature surfaces. Geometry and Topology of Submanifolds, III (Leeds, 1990), 153-162, World Sci. Publishing, River Edge, NJ, 1991.

Research Exposition(s)

• H. Wu: The PDE describing constant mean curvature surfaces. Math. Bohem. 126 (2001), 531-540.

Geometry Resources on the WorldWideWeb

• Mathematical Sciences Research Institute, Berkeley
• School of Mathematics, Institute for Advanced Studies, Princeton
• American Institute of Mathematics
• The International Centre for Mathematical Sciences, Edinburgh, Scotland
• Pacisfic Institute of the Mathematical Sciences, Canada
• The Center for Geometry, Analysis, Numerics and Graphics, University of Massachusetts at Amherst
• Sonderforschungsbereich 288, Technical University of Berlin
• Sonderforschungsbereich 256, University of Bonn
• Some geometers not at the above institutions
• Some books on geometry

Spectrum Resources on the WorldWideWeb

• An introduction to Sturm-Liouville problems
• Some books on spectra
• Some papers on spectra
• Journal of Spectral Mathematics and its Applications
• Mathematica codes EIGENIND-SLP

Soliton Resources on the WorldWideWeb

• Some books on solitons
• Some papers on solitons

More Mathematics Resources on the WorldWideWeb

• Some mathematics departments not mentioned above
• Some universities (not in China) not mentioned above
• Some universities in China not mentioned above
• Other books on mathematics
• Some mathematics journals
• Some publishers
• Others

Some Papers by Others

Educational Services on the WorldWideWeb

• Educational test services

Others

• Finance and Investment
• Tavel sites

Go to the WorldWideWeb page of the Department of Mathematical Sciences at Northern Illinois University.