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22 Oct 2020: For some examples of cases when connectedparahorics arise in the study of Shimura varieties we refer to [PR09, 1.b.3] for the case of ramifiedunitary groups and [PR05] for cases ... We assume G isof the form Gx for some x B(G,Qp).

4 Feb 2020: Prove that there exists some c [0, 1]with f(c) = c. ... Show that thereis some c (a,b) with f ′(c) = k.

5 Jun 2020: iii) There exists a closed, small set C and an extended-valued non-negative function Vsatisfying V (x0) < for some x0 X, such that Condition (V3) holds. ... Theorem 5.3 of [9] implies that (1.3) will holdif f is subject to this additional bound: For some

23 Jan 2020: 5. Let f : B B be a continuous function from the open disc B = {(x,y) R2 :x2 y2 < 1} to itself. ... 11. Suppose f : R R has the intermediate value property that if a,b R andf(a) < c < f(b), then f(y) = c for some y between a and b.

9 Nov 2020: The square matrices A and B over the field F are congruent if B = PTAP for some invertible matrixP over F. ... for some λ,µ,ν R (which should turn out in this example to be integers).Does there exist a linear transformation which reduces the pair of

5 Jun 2020: In 1989, in an attempt to understand the exact compression performance of some. ... Lm(D) = supf 1 : yj+j1 2 B(x1;D); for some j = 0; 1; : : : ;m 1g:.

5 Feb 2020: a) g(z) = z for some z S1.(b) g(z) = z for some z S1.

24 Feb 2020: Euclidean domain. Could there be some other Euclidean function φ making Z[3]. ... iii) Show that if R is a PID, the gcd of elements a and b exists and can be written asra sb for some r,s R.

5 Jun 2020: linear programwhose value bounds the right hand sideof (14). Write γ = γ1 Q for some transition kernelQ. ... 15] P. Glynn and R. Szechtman. Some new perspectives on themethod of control variates.

16 Nov 2020: b) [Needs some topological knowledge.] First project S2 onto its equatorial plane by(x,y,z) 7 ζ = xiy. ... Show that χ(g) = 0 for some g G. [Hint: partition G into equivalence classes bycalling two elements of G equivalent if they generate the same