Patrick M. Fitzpatrick

Articles in Scholarly Journals [Incomplete List]

  1. Bounds on Codes Derived by Counting Components in Varshamov Graphs
    Designs, Codes and Cryptography, vol. 39, no. 3, pp. 387–396, 2006
  2. Algorithm and architecture for a Galois field multiplicative arithmetic processor
    IEEE Transactions on Information Theory, vol. 49, no. 12, pp. 3303–3307, 2003
  3. Hamming metric decoding of alternant codes over Galois rings
    IEEE Transactions on Information Theory, vol. 48, no. 3, pp. 683–694, 2002
  4. Gröbner basis solutions of constrained interpolation problems
    Linear Algebra and its Applications, vol. 351-352, pp. 533–551, 2002
  5. Algebraic structure of quasicyclic codes
    Discrete Applied Mathematics, vol. 111, no. 1-2, pp. 157–175, 2001
  6. Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes
    Journal of Symbolic Computation, vol. 31, no. 5, pp. 565–584, 2001
  7. Spectral Flow and Bifurcation of Critical Points of Strongly Indefinite Functionals Part II. Bifurcation of Periodic Orbits of Hamiltonian Systems
    Journal of Differential Equations, vol. 163, no. 1, pp. 18–40, 2000
  8. Uniqueness of spectral flow
    Mathematical and Computer Modelling, vol. 32, no. 11-13, pp. 1495–1501, 2000
  9. Spectral Flow and Bifurcation of Critical Points of Strongly-Indefinite Functionals Part I. General Theory
    Journal of Functional Analysis, vol. 162, no. 1, pp. 52–95, 1999
  10. Comparison of Two Algorithms for Decoding Alternant Codes
    Applicable Algebra in Engineering, Communication and Computing, vol. 9, no. 3, pp. 211–220, 1998
  11. Solving a Multivariable Congruence by Change of Term Order
    Journal of Symbolic Computation, vol. 24, no. 5, pp. 575–589, 1997
  12. Extending backward error assertions to tolerance of large errors in floating point computations
    IEEE Transactions on Computers, vol. 46, no. 4, pp. 505–510, 1997
  13. Spectral flow and bifurcation of critical points
    Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, vol. 325, no. 7, pp. 743–747, 1997
  14. On the scalar rational interpolation problem
    Mathematics of Control, Signals, and Systems, vol. 9, no. 4, pp. 352–369, 1996
  15. The Berlekamp-Massey Algorithm and Linear Recurring Sequences Over a Factorial Domain
    Applicable Algebra in Engineering, Communication and Computing, vol. 6, no. 4-5, pp. 309–323, 1995
  16. On the key equation
    IEEE Transactions on Information Theory, vol. 41, no. 5, pp. 1290–1302, 1995
  17. Orientability of Fredholm Families and Topological Degree for Orientable Nonlinear Fredholm Mappings
    Journal of Functional Analysis, vol. 124, no. 1, pp. 1–39, 1994
  18. Nonorientability of the index bundle and several-parameter bifurcation
    Journal of Functional Analysis, vol. 98, no. 1, pp. 42–58, 1991
  19. Parity and Generalized Multiplicity
    Transactions of the American Mathematical Society, vol. 326, no. 1, p. 281, 1991
  20. Shorter Notes: A Remark on a Paper of Ji-Shou
    Proceedings of the American Mathematical Society, vol. 112, no. 2, p. 601, 1991
  21. A Local Bifurcation Theorem for C 1 -Fredholm Maps
    Proceedings of the American Mathematical Society, vol. 109, no. 4, p. 995, 1990
  22. Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence
    IEEE Transactions on Information Theory, vol. 36, no. 6, pp. 1480–1487, 1990
  23. Homotopy, linearization, and bifurcation
    Nonlinear Analysis, vol. 12, no. 2, pp. 171–184, 1988
  24. On the Covering Dimension of the Set of Solutions of Some Nonlinear Equations
    Transactions of the American Mathematical Society, vol. 296, no. 2, p. 777, 1986
  25. Global several-parameter bifurcation and continuation theorems: a unified approach via complementing maps
    Mathematische Annalen, vol. 263, no. 1, pp. 61–73, 1983
  26. The homotopy of certain spaces of nonlinear operators, and its relation to global bifurcation of the fixed points of parametrized condensing operators
    Journal of Functional Analysis, vol. 34, no. 1, pp. 87–106, 1979
  27. Some applications of A-proper mappings
    Nonlinear Analysis, vol. 3, no. 4, pp. 525–532, 1979
  28. Galerkin Methods in the Constructive Solvability of Nonlinear Hammerstein Equations with Applications to Differential Equations
    Transactions of the American Mathematical Society, vol. 238, p. 321, 1978
  29. Existence results for equations involving noncompact perturbations of Fredholm mappings with applications to differential equations
    Journal of Mathematical Analysis and Applications, vol. 66, no. 1, pp. 151–177, 1978
  30. Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators
    Journal of Differential Equations, vol. 22, no. 2, pp. 428–441, 1976
  31. Fixed-point theorems for multivalued noncompact inward maps
    Journal of Mathematical Analysis and Applications, vol. 46, no. 3, pp. 756–767, 1974
  32. On the Structure of the Set of Solutions of Equations Involving A-Proper Mappings
    Transactions of the American Mathematical Society, vol. 189, p. 107, 1974
  33. Subjectivity results for non-linear mappings from a Banach space to it's dual
    Mathematische Annalen, vol. 204, no. 3, pp. 177–188, 1973
  34. A generalized degree for uniform limits of A-proper mappings
    Journal of Mathematical Analysis and Applications, vol. 35, no. 3, pp. 536–552, 1971
  35. New Existence Theorems for Nonlinear Equations of Hammerstein Type
    Transactions of the American Mathematical Society, vol. 160, p. 39, 1971