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8 Mar 2024: ii) In the case k > 0, we define a new time coordinate η bydη. ... Deduce that if fα is chosen to satisfyfα = hαβ,β, then in the new coordinates the gauge condition hαβ,β = 0 holds.

4 Oct 2023: .  ,. where ǫ > 0. You should find that the (2, 3) element of the new matrix is O(ǫ3) and that the newmatrix has exactly the same trace as A.

6 Oct 2023: Define new variables. ξ = x y , η = x ,. and evaluate the partial derivatives of x and y with respect to ξ and η.

31 Jan 2024: Show that, by changing to a new parameter λ(µ), any geodesic can be affinely parametrized.

4 Oct 2023: Show that subsequently it evolves tobecome the new coherent state eiωt/2 |eiωtα〉.

1 Oct 2023: A2 (t B)2 and using the new.

5 Jan 2024: All positions in the new frame are related to positions in the old frame byx′ = f(x, t). ... Consider, in particular,the transformations (a) – (c) listed below. In each case obtain an equation for mẍ′(t′).Note that ′ denotes the new frame and

24 Nov 2023: Evaluate thecommutation relations of these generators. By choosing a new basis consistingof sums and differences of pairs of L(SO(3)) generators, show that L(SO(4)) =L(SO(3))

23 Oct 2023: 22 p. 21 p. 22. ),. determine the new Hamiltonian H(Q,P). ... Explainwhy the theory of adiabatic invariants cannot be used to calculate the new orbit.

22 Feb 2024: Iserles, "A new simulation technique for RF oscillators", Electronics Letters (2011) 47 13. ... Wozniakowski, ed.), Academic Press, New York (1993), 97–112.). A. Iserles, "On the generalized pantograph functional-differential equation'', Europ.