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MARKOV CHAINS Card shuffling, Ehrenfest urns [JT98] HYDRODYNAMIC STABILITY AND TURBULENCE Surveys [Sch00], [SH01] Compressible boundary layers (Schmid, et al., 1993) Orr-Sommerfeld operator [RSH93] Plane Poiseuille and Couette flow [RH93], [TTRD93] Pipe flow [TTS99], [MT00], [MT02] Airy operator [RSH93] Ginzburg-Landau equations [CC97] Control of turbulence [Bew00] Gravitational jets [dLCC02] MAGNETOHYDRODYNAMICS Instability in ionosphere [FST99] Alfvén waves [Bor94], [Dor03] Vlasov equation [Cra97] OTHER FLUID MECHANICS Flow down inclined plane [OH95] Papkovitch-Fadle problem [Tre97] Aerodynamic flutter (Braconnier, Chatelin, & Dunyach, 1995) LASERS Free-electron lasers [Lan77] Unstable resonators [Lan76] FUNCTIONAL ANALYSIS Operator approximation [BM01], [Har98a], [Wol01] C*-algebras [Bot00], [HRS00], [RS96] Hille-Phillips and Zabczyk operators [Bag94], [Tre97] NUMERICAL LINEAR ALGEBRA Convergence of Krylov subspace iterations [Emb99], [HL97], [Nev93], [NRT92a], [NRT92b], [Sim96], [Sim98], [SG96], [Toh96], [Tre90] Convergence of eigenvalue algorithms [BER01], [Sor02] Computation of the matrix exponential [HL97] Rounding errors (Godunov, Malyshev, and colleagues) [CF96], [CTT00], [God98], [HK95], [KR95] Ill-conditioned invariant subspaces and "sep" [Bea00], [Bor01], [Dem87b], [Var79] Directionality effects in SOR and Gauss-Seidel (Pathria & Trefethen, unpublished) Preconditioners for fluid mechanics [DS96] Condition number estimation [HT00] NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS General stability theory [DKS93] Stability of spectral methods [RT90], [Ren97] Stability of the method of lines [RT92a] Stiffness of ordinary differential equations [HT93] Runge-Kutta methods [VSH95] Waveform relaxation [JOW98], [JW00], [LW97b] Absorbing boundary conditions [DT96] GKS-instability (Pierce, unpublished) DIFFERENTIAL OPERATORS AND EQUATIONS Non-self-adjoint differential operators [Dav00b], [Red93], [Tre97] Convection-diffusion operators [RT94] Reaction-convection-diffusion equations [HO96] Lewy non-existence [Zwo01], [Zwo02] TOEPLITZ MATRICES AND OPERATORS Toeplitz matrices and operators [Böt94], [Böt96], [BET00], [BG00c], [BS99], [BW97], [Lan75], [RT92] Block Toeplitz matrices [LW97a] INTEGRAL OPERATORS Wiener-Hopf operators [Böt94], [BGS97], [Red93], [Roc00], [Toh96] Abel integral operators [Pla97] Multi-dimensional integral operators [KS99] CONTROL THEORY Distance to controllability and stability [Dem87a], [HK93], [HP92], [HP94] Optimization of pseudospectral abscissa [BLO02], [BLO03], [BLO04a], [BLO04b] Lyapunov equations [RS00], [TM99] MATRIX THEORY AND APPLICATIONS Polynomial zerofinding [TT94] Chebyshev polynomials of matrices [TT99a] Distance to multiple eigenvalues, Jordan blocks [GG00], [Gra00], [GH99], [Wil86] Pseudospectra of generalized eigenvalue problems [Dor97], [FGNT96] [Rie94] Pseudospectra of polynomial eigenvalue problems [HT02], [TH01] Pseudospectra of rectangular matrices [WT02] RANDOM MATRICES AND OPERATORS Dense random matrices [Tre92] Triangular random matrices (Embree & Trefethen, in preparation) Bidiagonal random matrices [TCE01] NON-HERMITIAN QUANTUM MECHANICS Complex Schrödinger operators [AD00], [Dav99a], [Dav99b], [Dav00b], [Red00], [Red01] Localization-delocalization transition [TCE01] SOME FURTHER APPLICATIONS OF NON-NORMALITY Boundary layers (Butler & Farrell) Geophysical dynamo (Farrell & Ioannou) Granular flow (Schmid & Kytomaa) Viscoelastic flow (Brown & Covert) Driven contact lines (Bertozzi & Brenner) Trailing line vortex flow (Schmid, et al., 1993) Cyclogenesis (Farrell) Unstable resonators (Siegmann) Dense random matrices (Chalker & Mehlig) Complex Schrödinger operators (Bender) Localization-delocalization transition (Hatano & Nelson; Feinberg & Zee; Davies) Neutron transport (Lehner) Food webs and ecology (Neubert; Cohen)