http://hdl.handle.net/1721.1/7604 http://hdl.handle.net/1721.1/49623 Generalized long-wave evolution equations Šipčić, Radica, 1972- Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998. Includes bibliographical references (p. 84-86). http://hdl.handle.net/1721.1/49622 Local-rules based topological modeling of tetrahedral ceramic network structures Jesurum, Caroline Esther, 1969- Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998. Includes bibliographical references (p. 147-156). http://hdl.handle.net/1721.1/49577 Kähler structures on cotangent bundles of real analytic Riemannian manifolds Stenzel, Matthew B. (Matthew Briggs) Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1990. Includes bibliographical references (leaves 134-136). http://hdl.handle.net/1721.1/47899 Differential posets and dual graded graphs Qing, Yulan, S.M. Massachusetts Institute of Technology In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the growth and classification of differential posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the second part of the thesis, we present a series of new examples of dual graded graphs that are not isomorphic to the ones presented in Fomin's original paper. Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. Includes bibliographical references (leaf 53).