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16 Oct 2021: X. Y. (. X. (. f. ). ). Y. This is not linear in the second argument, which is one of the requirements of a tensor. ... d. J. =. 0. which is the requirement of current conservation expressed in the language of forms.

18 Oct 2021: In fact, our normalisability requirement (3.62) can be restated in terms of the inner product. ⟨. ... a. =. 1. ,. 2. ,. 3. The requirement that the wavefunctions are single valued functions then tells us that.

16 Oct 2021: 𝐒. 1. But this coordinate does not meet our requirements to be a chart because it is not an open set. ... μ. |. p. :=. x. μ. |. p. which acts on functions as shown in (2.57) obeys all the requirements of a tangent vector.

9 Jun 2021: in which the entries of J are again partial derivatives at afixed point ðu; v; wÞ of the homogeneous system. ... However, why thethreshold should be “large” in the first place remainsunclear; this does not follow from the requirement ofunequal

8 Oct 2021: the inner product is antilinear in its first entry, it’s important that our chosen element. ... 6The requirement that the space be complete in the norm (2.14) is rather subtle.

16 Oct 2021: This is the UV cut-off. Λ. Recall that, implicit in our construction of the theory is the requirement that the Fourier modes.

29 Oct 2021: Residence time of buffer with blood was 2 minutesprior to chamber entry; adequate mixing had already beendetermined by preliminary experiments using fluorescein-stained coagulation buffer. ... mM). Chamber width doubles at thepoint of quenching buffer

16 Oct 2021: One then writes down the most general Landau-Ginzburg free energy, subject to the requirement that it is invariant under. ... 2. ϵ. This does not affect the eigenvalues which are given by the diagonal entries,.

18 Oct 2021: It matters whether the time of entry occurs during the radiation or matter dominated eras. ... For a given mode. 𝐤. , the scale factor at horizon entry is given by.

18 Oct 2021: 1 The Expanding Universe. 1 The Expanding Universe. Our goal in this section is an ambitious one: we wish to construct, and then solve, the equations that govern the evolution of the entire universe. When describing any system in physics, the trick