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9 May 2023: Juul, N. Looper, M. Manes, B. Thompson, L. Walton), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. ... Some consequences of Schanuel's conjecture (with C. Cheng, B. Dietel, M.

21 Nov 2023: 10. Let f: R2 R and (a,b) R2. (a) Suppose that D1f exists and is continuous in some open ball around (a,b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a,b), and.

12 Oct 2023: a, b], and suppose that fn converges pointwise to a continuous function f. ... Show that there is some subinterval [a, b] of [0, 1] with a < b on which (fn) is uniformly.

24 Nov 2023: 10. Let f: R2 R and (a,b) R2. (a) Suppose that D1f exists and is continuous in some open ball around (a,b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a,b), and.

21 Nov 2023: 4. Let K be a field containing a primitive mth root of unity for some m > 1. ... Showthat f and g have the same splitting field if and only if b = cmar for some c Kand r N with gcd(r,m) = 1.

12 Oct 2023: 6. By considering the singularity at or otherwise, show that any injective holo-morphic map f C C has the form f(z) = az b, for some a C and b ... 0,1,a} to be conformallyequivalent to C{0,1,b}, where a,b C{0,1}.[Don’t forget the cross ratio from IB -

12 Oct 2023: a, b], and suppose that fn converges pointwise to a continuous function f. ... Show that there is some subinterval [a, b] of [0, 1] with a < b on which (fn) is uniformly.

19 Apr 2023: Juul, N. Looper, M. Manes, B. Thompson, L. WaltonTo appear in Research Directions in Number Theory - Women in Numbers 4. ... 23, 5498-5525. 2. 2009 Some Consequences of Schanuel’s Conjecture,with C. Cheng, B.

24 Nov 2023: 4. Let K be a field containing a primitive mth root of unity for some m > 1. ... Showthat f and g have the same splitting field if and only if b = cmar for some c Kand r N with gcd(r,m) = 1.

11 Oct 2023: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1. 2. 1.9. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0.

6 Mar 2023: Hence deduce that two analytic toriC/Λ1 and C/Λ2 are conformally equivalent if and only if the lattices are relatedby Λ2 = λΛ1 for some λ C. ... τ2 = aτ1 b. cτ1 d. for some matrix (a bc d. )

6 Mar 2023: Hence deduce that two analytic toriC/Λ1 and C/Λ2 are conformally equivalent if and only if the lattices are relatedby Λ2 = λΛ1 for some λ C. ... τ2 = aτ1 b. cτ1 d. for some matrix (a bc d. )

24 Nov 2023: 1. The square matrices A and B over the field F are congruent if B = PT AP for some invertible matrixP over F. ... 7. Let S be an n n real symmetric matrix with Sk = I for some k 1.

6 Mar 2023: By considering the singularity at or otherwise, show that any injective an-alytic map f C C has the form f(z) = az b, for some a C and b ... 9. Define an equivalence relation on C by z w iff z = 2sw for some s Z.Show that the quotient space R = C/ has

6 Mar 2023: By considering the singularity at or otherwise, show that any injective an-alytic map f C C has the form f(z) = az b, for some a C and b ... 9. Define an equivalence relation on C by z w iff z = 2sw for some s Z.Show that the quotient space R = C/ has

25 Nov 2023: Some more questions. 15. Show that the direct sum A B of C-algebras A and B is a C-algebra withcoordinate-wise operations and with ‖(x,y)‖ = max. ... norm ‖‖. Let ‖‖1 be some (possibly incomplete) algebra-normon A. Show that ‖f‖6 ‖f‖1

2 Oct 2023: What happensif Θ = [a,b] for some 0 < a < b <? 9. Let X be multivariate normal N(θ,I), where θ Θ = Rp,p 3, and I is the pp identitymatrix. ... a) Show that the James-Stein estimator θ̃(1) dominates all estimators θ̃(c),c 6= 1.(b) Let θ̂ be the

24 Jan 2023: domain. Could there be some other Euclidean function φ making Z[3] into a Euclidean. ... ra sb for some r,s R. Give an example to show that this is not always the case ina UFD.

27 Nov 2023: ni=1. µ̂i =. ni=1. Yi. 2. Suppose that for some strictly increasing function f, we have. ... for some β that you should specify. (b) How can we estimate β from the data (Yi, xi)ni=1?

16 Feb 2023: 5. Consider the (2,3)-Baumslag–Solitar group BS(2, 3) = 〈a,b | ba2b1a3〉. ... You may use the simplicial approximation theoremwithout proof.]. (b) By considering the preimage of the midpoint of I in the disc, provethat some term ai or bi of g is