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11 Mar 2024: f(B) then y = f(a) for some a A andy = f(b) for some b B but then f(a) = y = f(b) so a = b A Band y ... If y f(A) f(B) then y = f(a) for some a A and y = f(b) for someb B.

17 May 2024: C93. “Combining information from different sources: Some surprising phenomena,” with B. ... C95. “Mutual information, synergy and some curious phenomena for simple channels,” with B.

17 May 2024: C93. “Combining information from different sources: Some surprising phenomena,” with B. ... C95. “Mutual information, synergy and some curious phenomena for simple channels,” with B.

8 Mar 2024: a1α1. adαdq. for some a1,. ,ad Z. Proof. We take. q =(disc(α1,. , ... In what follows, we will exhibit asuitable α, but this requires some preparations.

16 Jan 2024: γABA′B′ = φABεA′B′ ψA′B′εAB. for some symmetric spinors φ an ψ. ... for some complex Zα, α = 0, 1, 2, 3, where Z2 6= 0.

22 Jan 2024: 2 Background on quadratic formsWe collect together some standard definitions and results on quadratic forms. ... and henceto see that they satisfy some interesting symmetries (see Corollary 5.8).

31 Jan 2024: 223.4 The Galois correspondence. 25. 4 Some group theory 284.1 Free groups and presentations. ... H|{y0}[i/N,(i1)/N] : {y0} [iN ,. i1N ] X. lies entirely inside some Uα.

31 Jan 2024: If g2H = g′2H, then we know g. ′2 = g2 h for some h H. ... So we have to show p - ||. This is just some basic counting: we have. ||

5 Jun 2024: For injectivity, let τ NFalg(A)n be a cyclesuch that ψ[τ] = 0, i.e., τ(n1,⟨0⟩) = b (1)n1b for some b A. ... By the firststep in the proof of Proposition 3.18, τW = τb+(1)dn b for some b Wh(M).

29 May 2024: 0. for some valuation v. Then v(p q) = 1 and v(p r) = 0. ... Finally, assume that dom(f) 6= X. Then dom(f) = Ix for some x X.