By Shujie Li, Paul H Rabinowitz, Haim Brezis
ICM 2002 satellite tv for pc convention on Nonlinear research used to be held within the interval: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This convention used to be equipped by way of Mathematical tuition of Peking college, Academy of arithmetic and process Sciences of chinese language Academy of Sciences, Mathematical institution of Nankai collage, and division of arithmetic of Shanxi college, and used to be subsidized via Shanxi Province schooling Committee, Tian Yuan arithmetic starting place, and Shanxi University.166 mathematicians from 21 international locations and components on the planet attended the convention. fifty three invited audio system and 30 members offered their lectures. This convention goals at an summary of the new improvement in nonlinear research. It covers the next subject matters: variational tools, topological equipment, mounted element conception, bifurcations, nonlinear spectral concept, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian platforms, significant configuration in N-body difficulties and variational difficulties coming up in geometry and physics
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Additional resources for Topological Methods, Variational Methods and Their Applications - Proceedings of the Icm2002 Satellite Conference on Nonlinear Functional Analysis
Example text
In O, respectively. For 2 hdom set P ´ 2W P . /. P /op . 4 BGG reciprocity and quasi-hereditary structure A module N 2 O is said to have a standard filtration or Verma flag if there is a filtration of N whose subquotients are Verma modules. /. 5 (BGG reciprocity). (a) Every projective module in O has a standard filtration. (b) If some N 2 O has a standard filtration, then for any 2 h the multiplicity ŒN W M. / of M. / as a subquotient of a standard filtration of N does not depend on the choice of such filtration.
0 (a) For every W -antidominant 2 W there is a unique indecomposable projective functor  ; such that  ; . / D P . /. (b) Every indecomposable projective functor from O to O 0 is isomorphic to  ; for some W -antidominant 2 W 0 . 2 implies that an indecomposable projective functor  is completely determined by its value  . / on the corresponding dominant Verma module . /. Moreover, as  . / is projective and projective modules form a basis of ŒO 0 (as O 0 , being quasi-hereditary, has finite global dimension), the functor  is already uniquely determined by ŒÂ .
8. For every 2 h there is a unique (up to isomorphism) indecomposable module T . r/ such that . / T . / and the cokernel of this inclusion admits a standard filtration. L For 2 hdom the module T ´ 2W T . / is called the characteristic tilting module. 9. The module T is ext-selforthogonal, has finite projective dimension and there is an exact sequence 0 ! P ! Q0 ! Q1 ! Qk ! T / for all i. The (opposite of the) endomorphism algebra of T is called the Ringel dual of B . The Ringel dual is defined for any quasi-hereditary algebra and is again a quasihereditary algebra.