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22 Oct 2020: However, if G is residually split, thenfor [b] B(G,{µ}), all the straight representatives of [b] lie in the admissible set for µ. ... In particularthese are all open in X({µ},b)K and one cannot connect points in different strata.

4 Mar 2020: Suppose given, for each A B X with B finite, a real numberµ (UA,B) 6 1 and assume that all the consistency relations are satisfied (c.f. ... subse-quence (using a diagonal argument) such that (µn (UA,B))n>1 converges to some real number µ (UA,B)for

5 Jun 2020: In all our experiments in [12][14] and in the results presented in the followingsection we set B = 1000, which, as discussed below, appears to have been sufficiently largefor the central ... variables {Xn}, where the the Xi are independentand all have

5 Jun 2020: such that for all y V we have. ess infx. P Xr y j x. ... type condition there exists an integer r and a real such that for all y V we.

9 Nov 2020: 3. (i) Show that the function ψ(A,B) = tr(ABT ) is a symmetric positive definite bilinear form on the spaceMatn(R) of all nn real matrices. ... sn forms a basis for Pn.(iii) For all 1 k n, sk spans the orthogonal complement of Pk1 in Pk.(iv) sk is an

5 Jun 2020: Assigning to all the other elements of An binary strings oflength equal to. ... Therefore,. P[log2 X log2(1 MX (2a )). ] = P [ı X (X ) a] (74)Moreover, because of (51), for all b 0,.

5 Jun 2020: All Rights Reserved. ii. I certify that I have read this dissertation and that in. ... Mike Harrison and George Papanicolaou for being on my Orals committee and for all.

5 Jun 2020: T0 is v-separable for all r.1 The fact that this is indeed weaker than the assumption in(DV3) (ii) follows from Lemma B.3 in the Appendix. ... for all r, where v = eV. (b) The kernel P T0 is v0-separable for some unbounded function v0 : X [1,).

6 May 2020: It follows that, for all t,t′ [a,b],. (c′|[t,t′]. ) d. (c′(t),c′ ([t]0). ) ... ii) For all (a,b) , (a′,b′) R, we have |dA (a,a′) dB (b,b′)| ε.

8 Jun 2020: vii) f(gh) = (fg)h for all A h B g C f D. ... 0, |A|}, so we get a weakly initial set in (A U) by considering a fixedset B of this cardinality, all possible subsets B′ of B, all possible group structures on

6 May 2020: ii) For all (a,b) , (a′,b′) R, we have |dA (a,a′) dB (b,b′)| ε. ... dX (ϕn(p)a,pa) 2δ. It follows in particular that, for all a,b θn,.

9 Nov 2020: 5. (i) Let X be the set of all prime ideals of R. ... closure of A in L. Show that σ(B) = B for all σ G and that A = BG.

2 Dec 2020: G1) For all a,b,c G we have (a b) c = a (b c). ... A group (G, ,e) is abelian2 if for all a,b G we have a b = b a.

5 Jun 2020: Pt(x,A) > 0, for all t sufficiently large. It follows that there is a countable covering of the state space by small sets [7, Prop. ... Γ‖f = sup. g(t,y)Γ(dt,dy),. where the supremum is over all g satisfying |g(t,y)| f(t,y) for all t,y.

30 May 2020: ahomotopy s.t. ϕ(t, ) is a homeomorphism for all t [0, 1]. ... It suffices to check that, for all β B, wehave α β α1 ' δαδ1αβ.

28 May 2020: 0 Coker fi2fi1 Ai. fi Ker fi1 0. is exact for all i. ... X f Y = (X qY ) / ,where is the equivalence relation given by b f(b) for all b B.

3 Jun 2020: a d(x,y) 6 d (f(x),f(y)) 6 b d(x,y), (). for all x,y M. ... B|〈x,ω〉|p dλ(ω). is the same for all x S – call it α.

22 Oct 2020: This allows us to prove that all Newton strata are non-empty for these models. ... Indeed when p is inverted, all the Λmi coincide and the choice of Fm0 Λm0,F determinesthe other Fmi.

11 Feb 2020: every z C, |f(z) b| > ε.(iii) f = u iv and |u(z)| > |v(z)| for all z C.4. ... 11. (i) Let w C, and let γ, δ : [0, 1] C be closed curves such that for all t [0, 1],|γ(t) δ(t)| < |γ(t) w|.

5 Jun 2020: 1. None of the Yi dominate the sum, i.e., their parameterspi = Pr{Yi 6= 0} are all appropriately small;. ... Eµ[eθ|g| log+ |g|] < ,. for all θ > 0 small enough, where log+ x = max{log x, 0}.