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If a suffix appears twice in a term it is a dummy suffix and is summed over, whereas free suffices appear once in every term. ... T. 1322. = T. 52. ). This is very useful as we can display every tensor up to 4th rank as a single two-dimensional matrix,

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8 Aug 2022: And sometimes you’re just in awe because it’s so gorgeous; every now and then the sun will be shining on a building and I think, ‘Wow, I’m living ... You don’t have to have a perfectly tuned answer to every question, you’re not going to know

i) There exist a,b > 0 such that a ‖en‖,‖en‖ b for every n N,(ii) ek(en) = δkn for every k,n N,. ... We say that B is monotone whether Kb = 1. Along the paper we will refer to every such B simply as a basis.

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23 May 2001: by setting f(v)=1 and f(w)=0 for every other w in B. ... since every element of V. is a linear combination of elements of B in a unique way.) Since f(e.

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b) = b for every b B. That is, f is an idempotent polymorphism ofB. ... 1. u(y) P Cb {b} for every b B and y P Cb ,2.

4 Oct 2001: i. = lambda b. i. for every i', but this introduces an unknown constant lambda, and it will make our proof harder later on if we have to find this lambda. ... i. b. j. = a. j. b. i. for every pair i,j.

Suppose γ Sand take B(β,γ) satisfying (i) and (ii). Then Bα Aγ is finite for every α < γ, α S andtherefore. ... Then we choose a decreasing sequence (ank)k such that(a) ank an0 , ank yn for every k(b) limk λ(a.