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26 Jun 2024:  2 Z+ (2.20). This is interesting. We have an example where a parameter in an action can only. ... freedom w() and the Lagrange multiplier (). First, we ask: how can we see the quantisation condition of  (2.20) in the path.

27 Dec 2023: 𝜁 = 𝐷𝑒(1 𝜂) = 𝐷𝑒𝜂 for 𝜂 1, (3.20)382. so that 𝐷𝑒(1 𝜂2) = 𝜁(2 𝜂) 2𝜁. ... Specifically, substituting (3.1) into (2.20)412yields at 𝑂(𝛽) the pressure drop Δ𝑃1,413.

10 Jun 2024: ζ = De(1 η) = Deη̃ for η̃ 1, (3.20)so that De(1 η2) = ζ (2 η̃) 2ζ. ... Specifically, substituting(3.1) into (2.20) yields at O(β̃) the pressure drop P1,.

26 Jun 2024: conditions, Sθ can only take values of the form. Sθ = θN with N Z (1.20). ... 22cNe2. Sθ = θN with N = nn′ Z. which is our promised result (1.20).

24 Jul 2023: 20] N. Darnton, L. Turner, K. Breuer, and H. C. Berg, Moving fluid with bacterial carpets, Biophys.

15 Jul 2023: 20] Colbrook, Matthew, Andrew Horning, and Alex Townsend. "Resolvent-based techniques for computing the discrete and continuous spectrum of differential operators." XXI Householder Symposium on Numerical Linear. ... Slide 19: Example 1: One-dimensional

26 Jun 2024: The. infinitesimal action of the vector rotation! ei is. = i , ̄ = i (3.20). ... tions dier. For the vector transformation (3.20), we have = i and ̄ = i ̄.This extra minus sign means that the Jacobian factors for and ̄ have the form.

31 May 2024: 6. Black Holes. Black holes are among the most enigmatic objects in the universe. They are described. by deceptively simple solutions to the Einstein equations, yet hold a host of insights. and surprises, from the meaning of causal structure, to

31 May 2024: X0 = R sinh(/R) and Xi = R cosh(/R)yi (4.20). where the yi, with i = 1, 2, 3, 4, obeyP.

15 Jul 2023: 20] Colbrook, Matthew J. "The mpEDMD algorithm for data-driven computations of measure-preserving dynamical systems." SIAM Journal on Numerical Analysis 61.3 (2023): 1585-1608. ... Slide 18. Slide 19: Residuals implies avoid spectral pollution! Slide 20: