Theses - Mathematics
http://hdl.handle.net/1721.1/7842
Tue, 16 Jan 2018 08:02:14 GMT2018-01-16T08:02:14ZContributions to recursion theory on higher types (or, a proof of Harrington's conjecture),
http://hdl.handle.net/1721.1/113187
Contributions to recursion theory on higher types (or, a proof of Harrington's conjecture),
Harrington, Leo Anthony
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.; Vita.; Bibliography: leaves 93-95.
Mon, 01 Jan 1973 00:00:00 GMThttp://hdl.handle.net/1721.1/1131871973-01-01T00:00:00ZOn the equivalence of two continuous homology theories
http://hdl.handle.net/1721.1/113186
On the equivalence of two continuous homology theories
Giever, John Bertram, 1919-
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1948.; Vita.; Includes bibliographical references (leaf 44).
Thu, 01 Jan 1948 00:00:00 GMThttp://hdl.handle.net/1721.1/1131861948-01-01T00:00:00ZOn the formula of de JonquiÃ¨res for multiple contacts.
http://hdl.handle.net/1721.1/113166
On the formula of de JonquiÃ¨res for multiple contacts.
Vainsencher, Israel
Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Includes bibliographical references.
Sat, 01 Jan 1977 00:00:00 GMThttp://hdl.handle.net/1721.1/1131661977-01-01T00:00:00ZRational matrix differential operators and integrable systems of PDEs
http://hdl.handle.net/1721.1/112909
Rational matrix differential operators and integrable systems of PDEs
Carpentier, Sylvain, Ph. D. Massachusetts Institute of Technology
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra bracket {F, G} = XF(G) - XG(F), where XF denotes the evolutionnary vector field attached to F. In all known examples, these hierarchies are constructed by means of Lenard-Magri sequences: one can find a pair of matrix differential operators (A(a), B(a)) and a sequence (G.n)>n>0,[epsilon] Vl such that ** F = B(GN) for some N >/= 0, ** {B(Gn), B(Gm)} = 0 for all n, m >/= 0, ** B(G,+1 ) = A(G) for all n,m >/= 0. We show that in the scalar case l = 1 a necessary condition for a pair of differential operators (A, B) to generate a Lenard-Magri sequence is that for all constants [lambda], the family C[lambda] = A + [lambda]B must satisfy for all F, G [epsilon]V {C[lambda](F), C[lambda](G)} [epsilon] ImC[lambda]. We call such pairs integrable. We give a sufficient condition on an integrable pair of matrix differential operators (A, B) to generate an infinite Lenard- Magri sequence when the rational matrix differential operator L = AB-1 is weakly non-local and the algebra of differential functions V is either Z or Z/2Z-graded. This is applied to many systems of evolution PDEs to prove their integrability.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 129-133).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1721.1/1129092017-01-01T00:00:00Z