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28 Nov 2012: F maps some neighbourhood U of x dif-feomorphically onto a neighbourhood V of (y,T(x)). ... for some function τ(s). (Note that 〈b, ḃ〉 = 0 since b has unit norm.).

28 Nov 2012: F maps some neighbourhood U of x dif-feomorphically onto a neighbourhood V of (y,T(x)). ... for some function τ(s). (Note that 〈b, ḃ〉 = 0 since b has unit norm.).

14 May 2012: 2.4. Microlocalisation. We recall some basic results in the theory of algebraicmicrolocalisation. ... the form Ân,K for some almost commutative R-algebra A, provided that |q1| < 1.

19 Jul 2012: This miraculous geometric structure, however, in some sense obscures two other,equally fundamental aspects of (1):. ... 17) β = B(u, ϑ)r4 log r O(r4),. for some B(u, ϑ) which possibly vanishes.

27 Nov 2012: that says that these objects are, in some sense, two dimensional, i.e. ... Ric (n1)kg. for some k > 0. Then the diameter of M satisfies.

26 Apr 2012: Then. necessarily ρ(0) = idV , and ρ(1) is some invertible linear map f on V. ... V is irreducible then Schur’s Lemma tells us that ϕ = λ idV for some.

27 Nov 2012: Proposition 2.2shows that Ax = Bx v for some B O(2) and some vector v R2. ... Then Proposition 2.2 shows that A maps a vector x RN to thevector Bx v for some B O(N ) and v RN.

28 Nov 2012: Then. necessarily ρ(0) = idV , and ρ(1) is some invertible linear map f on V. ... Then ρ(r) has a eigenvector v, say. Soρ(r)v = λv for some λ 6= 0.