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2. Dense Fast Random Projections and Lean Walsh Transforms

3. MHD Channel Flows

4. DRBEM Solutions of Unsteady MHD Convection and Inductionless Flows

5. The Equations of Magnetohydrodynamics

6. Boundary Element Solution of Potential Flow Problems

7. Fundamental Solution to Coupled MHD Flow Equations

8. Examples

9. Framework

10. Strain and Stress

11. Conservation

12. Objectivity

13. Quasi-Periodic Solutions and Tori

14. Approximations on Timescales Longer than

15. Second Order Periodic Averaging

16. Averaging over Spatial Variables

17. Periodic Solutions

18. Hamiltonian Resonances

19. First Order Periodic Averaging

20. Introduction

21. First Order General Averaging

22. Averaging for Partial Differential Equations

23. Basic Examples

24. Design Choices

25. The Lean Proof Assistant

26. Abstraction and Prototyping

27. Anisotropic Error Estimates in Polyhedral Domains

28. Error Estimates in Polygonal Domains

29. Regularity Estimates and Graded Meshes in Polyhedral Domains

30. The Function Space

31. The Finite Element Method

32. Singularities and Graded Mesh Algorithms

33. Mode-2 Waves

34. Exact Internal Hydraulics

35. Exact Internal Solitary Waves

36. Using Linear and Weakly Nonlinear Theory

37. Derivations: Linear, Weakly Nonlinear, and Conjugate Flow Theory

38. Background and Equation Summaries

39. Concluding Thoughts

40. Non-trigonometric Waveform and Iterated KMD

41. Crossing Frequencies, Vanishing Modes, and Noise

42. Review

43. Appendix

44. Unknown Base Waveforms

45. Additional Programming Modules and Squeezing

46. Introduction

47. Kernel Mode Decomposition Networks (KMDNets)

48. The Mode Decomposition Problem

49. Modeling Complex Interactions

50. Applications

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