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Patrick M. Fitzpatrick
Articles in Scholarly Journals [Incomplete List]
Bounds on Codes Derived by Counting Components in Varshamov Graphs
Designs, Codes and Cryptography, vol. 39, no. 3, pp. 387–396, 2006
Algorithm and architecture for a Galois field multiplicative arithmetic processor
IEEE Transactions on Information Theory, vol. 49, no. 12, pp. 3303–3307, 2003
Hamming metric decoding of alternant codes over Galois rings
IEEE Transactions on Information Theory, vol. 48, no. 3, pp. 683–694, 2002
Gröbner basis solutions of constrained interpolation problems
Linear Algebra and its Applications, vol. 351-352, pp. 533–551, 2002
Algebraic structure of quasicyclic codes
Discrete Applied Mathematics, vol. 111, no. 1-2, pp. 157–175, 2001
Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes
Journal of Symbolic Computation, vol. 31, no. 5, pp. 565–584, 2001
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
Uniqueness of spectral flow
Mathematical and Computer Modelling, vol. 32, no. 11-13, pp. 1495–1501, 2000
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
Comparison of Two Algorithms for Decoding Alternant Codes
Applicable Algebra in Engineering, Communication and Computing, vol. 9, no. 3, pp. 211–220, 1998
Solving a Multivariable Congruence by Change of Term Order
Journal of Symbolic Computation, vol. 24, no. 5, pp. 575–589, 1997
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
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
On the scalar rational interpolation problem
Mathematics of Control, Signals, and Systems, vol. 9, no. 4, pp. 352–369, 1996
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
On the key equation
IEEE Transactions on Information Theory, vol. 41, no. 5, pp. 1290–1302, 1995
Orientability of Fredholm Families and Topological Degree for Orientable Nonlinear Fredholm Mappings
Journal of Functional Analysis, vol. 124, no. 1, pp. 1–39, 1994
Nonorientability of the index bundle and several-parameter bifurcation
Journal of Functional Analysis, vol. 98, no. 1, pp. 42–58, 1991
Parity and Generalized Multiplicity
Transactions of the American Mathematical Society, vol. 326, no. 1, p. 281, 1991
Shorter Notes: A Remark on a Paper of Ji-Shou
Proceedings of the American Mathematical Society, vol. 112, no. 2, p. 601, 1991
A Local Bifurcation Theorem for C 1 -Fredholm Maps
Proceedings of the American Mathematical Society, vol. 109, no. 4, p. 995, 1990
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
Homotopy, linearization, and bifurcation
Nonlinear Analysis, vol. 12, no. 2, pp. 171–184, 1988
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
Global several-parameter bifurcation and continuation theorems: a unified approach via complementing maps
Mathematische Annalen, vol. 263, no. 1, pp. 61–73, 1983
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
Some applications of A-proper mappings
Nonlinear Analysis, vol. 3, no. 4, pp. 525–532, 1979
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
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
Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators
Journal of Differential Equations, vol. 22, no. 2, pp. 428–441, 1976
Fixed-point theorems for multivalued noncompact inward maps
Journal of Mathematical Analysis and Applications, vol. 46, no. 3, pp. 756–767, 1974
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
Subjectivity results for non-linear mappings from a Banach space to it's dual
Mathematische Annalen, vol. 204, no. 3, pp. 177–188, 1973
A generalized degree for uniform limits of A-proper mappings
Journal of Mathematical Analysis and Applications, vol. 35, no. 3, pp. 536–552, 1971
New Existence Theorems for Nonlinear Equations of Hammerstein Type
Transactions of the American Mathematical Society, vol. 160, p. 39, 1971