US Patent

Mirrored disk partition with disk partition modification contemporaneous with client application access (with J. Jones, M. Ng, and L. Suen)

Selected Publications (out of about 140)

  1. On Opial's inequality with an integral condition, submitted
  2. Cone fixed point theorems and BVP of second-order DE, submitted
  3. On Krasnoselskii's cone fixed point theorem, submitted
  4. A non-oscillation theorem for superlinear Emden-Fowler equations with near-critical coefficients, submitted
  5. Integral criteria for second-order linear oscillation, Electronic J. Qual. Theory Diff. Equ. 8, 2006, 1-18
  6. Some extensions of the Brouwer-Petryshyn fixed point theorem, J. Nonl. Functional Anal. Diff. Equ. to appear
  7. On the Nonoscillation of Sublinear Emden-Fowler Equations, Dynamics of Continuous, Discrete and Impulsive Systems, to appear
  8. Second Order Oscillations, A Case History, (with James S.W. Wong), Canadian Appl. Math. Quart., Proceedings for the Midwest Pacific Diff Equ Conference 2005, to appear
  9. The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE, Electronic J. Qual. Theory Diff. Equ. 6, 2006, 1-14
  10. On the oscillation of Hill's equations under periodic forcing (with James S.W. Wong), J. Math. Anal. Appl. 320, 2006, 37-55
  11. A survey of results on the ground state of semilinear elliptic equations, to appear in Proceedings of the International Congress of Chinese Mathematicians, 2004
  12. Oscillation and nonoscillation of Hill's equation with periodic damping (with James S.W. Wong) J. Math. Anal. Appl., 288, 2003, 15-19
  13. An alternate proof of Kato's inequality Evolution Equations (with A. Zettl) Dekker Series of Lecture Notes in Pure and Applied Maths., vol. 234, 2003, 275-279
  14. A comparison result and elliptic equations involving subcritical exponents, Nonlinear Diffusion Equations and Their Equilibrium States,3} ed. by N.G. Lloyd et al., Birkh\"auser, Boston, 1992, 299-318.
  15. Integral criteria for second-order linear oscillation Math. Inequal. Appl. 2, 1999, 55-71.
  16. Simulating vortex motion in superconducting films with the time-dependent Ginzburg-Landau equations, (with Erhan Coskun) Nonlinearity 10, 1997, 579-593.
  17. The existence of multiple solutions for a Ginzburg-Landau type model of superconductivity, (with S.P. Hastings and W. C. Troy) European J. Appl. Math. 7, 1996, 559-574.
  18. A Picard method without Lipschitz continuity for some ordinary differential equations, (with F. Bernis) Ann. Fac. Sci. Toulouse Math 6, 1996, 577-585.
  19. On the One-dimensional Ginzburg-Landau BVPs, Differential and Integral Equations 6,} 1995, 1395-1405.
  20. Vortex configurations in Type-II superconducting films, (with H.G. Kaper) J. Computational Physics 119, 1995, 120-131.
  21. Asymptotics of a free boundary problem, (with F.V. Atkinson, H.G. Kaper) Methods Appl. of Analysis 2, 1995, 466-474.
  22. W-transform matrices for feature-oriented multiresolution image retrieval, (with Frank Biqun Lin) Proceedings of SPIE Conference, Orlando, FA April, 1995. Also MCS Preprint MCS-P489-0195
  23. W-Matrices, Nonorthogonal Multiresolution Analysis, and Finite Signals of Arbitrary Length, with Peter Tang Preprint MCS-P449-0794.
  24. A real-time MPEG software decoder using a portable message-passing library retrieval, with Frank Biqun Lin and P. T. Peter Tang, MCS Preprint MCS-P506-0195
  25. Random wavelet transforms, algebraic geometric coding, and their applications in signal compression and de-noising, with T. Bielecki, L. M. Song, and Stephen S. T. Yau, Proc. International Conference on Control and Information, Hong Kong, June, 1995, the Chinese University Press, 283-289.
  26. High-Performance Image Analysis and Visualization Engine for Three-dimensional Light Microscopy, with J. Chen, M. Griem, J. Aarsvold, C. T. Chen, T. Disz, R. Hudson, Biquan Lin, MSC Preprint 526
  27. Orthogonally compensated W-multiresolution analysis and signal processing, (Proc. of ICIAM 95, Hamburg, Germany), also as MSC Preprint 528
  28. MATLAB Implementation of $ W $-Matrix Multiresolution Analyses, Preprint MCS-P462-0894.
  29. A remark on a weighted landau inequality of Kwong and Zettl, with R.C. Brown and D. Hinton, Canadian Math. Bull. 38, 1995, 34-41.
  30. On the best constant for the inequality $ \int^\infty _0 y^{\prime\, 2}\le K\left(\int_0^\infty|y|\right)\max\limits_{(0,\infty)} |y^{\prime\prime}| $, with R.C. Brown, World Scientific Series in Applicable Analysis 3,} 1994, 103-121.
  31. Symmetry results for reaction-diffusion equations, with H.G. Kaper and Y. Li, Differential and Integral Equations 6, 1993, 1045-1056.
  32. Sweeping algorithm for inverting the discrete Ginzburg-Landau operator, Applied Math. and Computations, 53, 1993, 129-150.
  33. Domain decomposition: a blowup problem and the Ginzburg-Landau equations, Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, Proceedings of the NATO Advanced Research Workshop held in Beaune, France, May 1992, H.G. Kaper and M. Garbey, eds., Kluwer Academic Publishers, Cordrecht, 1993, 106-122.
  34. Asymptotically constant functions and second order linear oscillation, with A. Zettl, J. Math. Anal. Appl. 93, 1983, 475-494.
  35. A review of MATLAB 4.0, SIAM News 26, \#2, March 1993
  36. The influence of nonlocal nonlinearities on the long-time behavior of solutions of Burgers' equation, with K. Deng and H. A. Levine, Quarterly of Applied Mathematics, 50, 1992, 173-200.
  37. (Editor for) Proc. of the Organized Sessions ``Nonlinear Problems in Superconductivity,'' and ``Blow-up and Dead-core in Nonlinear Parabolic Equations,''First World Congress of Nonlinear Analysts,} ed. with C.Y. Chan, 1993.
  38. Ground state solutions of $ -\Delta u=u^p-u^q $ , with J.B. McLeod, L.A. Peletier, and W.C. Troy, J. of Differential Equations, 95, 1992, 218-239.
  39. Uniqueness of radial solutions of semilinear elliptic equations, with Y. Li, Trans. Amer. Math. Soc. 333, 1992, 339-363.
  40. On two conjectures concerning the multiplicity of solutions of a Dirichlet problem, with H. G. Kaper, SIAM J. Math. Anal., 23, 1992, 571-578.
  41. On the unboundedness of the number of solutions of a Dirichlet problem, Nonlinear Anal., 18, 1992, 993-1001.
  42. A Dirichlet problem with infinite multiplicity, World Scientific Series in Applicable Analysis, 1, 1992, 393-402.
  43. Proceedings of the First World Congress of Nonlinear Analysts, Tampa, Florida, Aug. 1992, edited with C. Y. Chan
  44. Uniqueness of the positive solution of $ \Delta u+f(u)=0 $ in an annulus, with Liqun Zhang, Differential and Integral Equations 4, 1991, 583-599.
  45. Uniqueness results for Emden-Fowler boundary value problems, Nonlinear Analysis 16, 1991, 435-454.
  46. Oscillation of first-order delay equations, J. Math. Anal. Appl., 156, 1991, 274-286.
  47. Norm inequalities for the powers of a matrix, with A. Zettl, Amer. Math. Monthly 98, 1991, 533-538.
  48. <=a href=>On the Kolodner-Coffman method for the uniqueness problem of Emden-Fowler BVP, J. Appl. Math. Physics (ZAMP), 41, 1990, 79-104.<=/a>
  49. Sturm comparison theorems for second-order delay equations, with M. Du, J. Math. Anal. Appl., 152, 1990, 305-323.
  50. On the positive solutions of the free-boundary problem for Emden-Fowler type equations, with H.G. Kaper and Y. Li, Partial Differential Equations with Minimal Smoothness and Applications, IMA Volumes in Mathematics and its Applications, 42, 163-172, Edited by B. Dahlberg et al, Springer-Verlag, 1992.
  51. Existence results of steady-states of semilinear reaction-diffusion equations and their applications, with C.Y. Chan, J. Diff. Eq. 77, 1989, 304-321.
  52. <=a href=>Semilinear elliptic problems in annular domains, with C. Bandle, J. Appl. Math. Physics (ZAMP), 40, 1989, 245-257.<=/a>
  53. Uniqueness of positive solutions of $\Delta u - u + u^p =0 $ in $R^n$, Arch. Rat. Mech. 105, 1989, 243-266.
  54. On a result on the problem of quenching, with C.Y. Chan, Nonlinear Analysis 12, 1988, 1377-1383.
  55. Uniqueness for a class of nonlinear initial value problems, with H.G. Kaper, J. Math. Anal. Appl. 130, 1988, 467-473.
  56. A non-oscillation theorem for the Emden-Fowler equation: ground states for semilinear elliptic equations with critical exponents, with H.G. Kaper, J. Diff. Eq. 75, 1988, 158-185.
  57. Landau's inequality for the difference operator, with A. Zettl, Proc. Am. Math. Soc. 104, 1988, 201-206.
  58. Comparison Theorems for First Order Linear Delay Equations, with W.T. Patula, J. Diff. Eq. 70, 1987, 275-292.
  59. Uniqueness results for some nonlinear initial and boundary value problems, with H.G. Kaper, Arch. Rat. Mech. 102, 1988, 45-56.
  60. <=a href=>Oscillatory second order linear difference equations and Riccati equations, with J.W. Hooker and W.T. Patula, SIAM J. Math. Anal. 18, 1987, 54-63.<=/a>
  61. Weighted means and oscillation conditions for second order matrix differential equations, with R. Byers and B.J. Harris, J. Diff. Eq. 61, 1986, 164-177.
  62. <=a href=>Characterization of the Friedrich extensions of singular Sturm-Liouville expressions, with H. Kaper and A. Zettl, SIAM J. Math. Anal. 17, 1986, 772-777.<=/a>
  63. Oscillation of two-dimensional linear second order differential systems, with H. Kaper, J. Diff. Eq. 56, 1985, 195-205.
  64. Riccati type transformations for second-order linear difference equations, II, with J.W. Hooker and W.T. Patula, J. Math. Anal. Appl. 107, 1985, 182-196.
  65. An oscillation criterion for linear second-order differential systems, with F.V. Atkinson and H. Kaper, Proc. Amer. Math. Soc. 94, 1985, 91-96.
  66. Hermitian matrix inequalities - a conjecture, with N.N. Chan, Am. Math. Monthly 92, 1985, 533-541.
  67. Differential operators and quadratic inequalities with a degenerate weight, with W.N. Everitt and A. Zettl, J. Math. Anal. Appl. 98, 1984, 378-399.
  68. <=a href=>Regularizing transformations for certain singular Sturm-Liouville boundary value problems, with H.G. Kaper and A. Zettl, SIAM J. Math. Anal. 15, 1984, 957-963.<=/a>
  69. Oscillation of linear second order differential systems, with H. Kaper, K. Akiyama, and A.B. Mingarelli, Proc. Am. Math. Soc. 91, 1984, 85-91.
  70. Lower bounds for the spectrum of ordinary differential equations, with W.D. Evans and A. Zettl, J. Diff. Eq. 48, 1983, 123-155.
  71. Weighted Landau inequalities, with J. Goldstein and A. Zettl, J. Math. Anal. Appl. 95, 1983, 20-28.
  72. <=a href=>On an oscillation theorem of Belohorec, with J.S.W. Wong, SIAM J. Math. Anal. 14, 1983, 474-476.<=/a>
  73. Linearization of second order nonlinear oscillation theorems, with J.S.W. Wong, Trans. Am. Math. Soc. 279, 1983, 705-722.
  74. Oscillation of second order hyperbolic equations with non-integrable coefficients, with W. Hsiang, Proc. Roy. Soc. Edinburgh 91A, 1982, 305-313.
  75. Differential and integral inequalities and second order linear oscillation, with A. Zettl, J. Diff. Eq. 45, 1982, 16-23.
  76. On certain Riccati integral equations and second order linear oscillation, J. Math. Anal. Appl. 82, 1982, 315-330.
  77. An application of integral inequality of second order nonlinear oscillation, with J.S.W. Wong, J. Diff. Eq. 45, 1982, 63-77.
  78. On certain comparison theorems for second order linear oscillation, Proc. Am. Math. Soc. 84, 1982, 539-542.
  79. On the oscillation and nonoscillation of second order sublinear equations, with J.S.W. Wong, Proc. Am. Math. Soc. 85, 1982, 547-551.
  80. On Lyapunov's inequality for disfocality, J. Math. Anal. Appl., 83, 1981, 486-494.
  81. Discreteness conditions for the spectrum of ordinary differential operators, with A. Zettl, J. Diff. Eq. 40, 1981, 53-70.
  82. Solution to problem S13 (dedicated to Emory P. Starke): matrix with non-negative entries, proposed by H. Kestelman, American Mathematical Monthly, 87, 1980, p. 670
  83. Inequalities for the powers of nonnegative Hermitian operators, Proc. Am. Math. Soc. 51, 1975, 401-406.
  84. On the boundedness of solutions of second order differential equations in the limit circle case, Proc. Am. Math. Soc. 52, 1975, 242-246.