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10 Jan 2017: δ is abelian.(c) Assume that δ(g) = 1 for some g G. ... irreducible. 3 Find an example of a representation of some finite group over some field of charac-teristic p, which is not completely reducible.

23 Feb 2017: Could there be some other Euclidean function φ making Z[3] into a Euclidean domain? ... iii) Show that if R is a PID, the gcd of elements a and b exists and can be written as rasbfor some r,s R.

22 Mar 2017: in the planning conditions for the North West Cambridge development. b) Transport: A co-ordinated approach to transport for clubs would reduce risk and take some burden. ... but greater knowledge is needed as to actual and potential participation levels

6 Oct 2017: ii) m n a b (n m) [(a = 1) (b = 1) (ab 6= n)]Is (ii) true? ... 5. How large can the product of some (not necessarily distinct) natural numbers be, if their sumis 100?

7 Mar 2017: 0 πb. ),. for some integers a,b 0. Replacing F by an OK-equivalent form, it follows that. ... Lemma 2.5. Let F be an integral (2, 2)-form. If some pair (a,b) is admissible for.

12 Oct 2017: 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 ... 1.8. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0.

20 Jan 2017: Xn be independent Poisson random variables, with Xi having meaniθ, for some θ > 0. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).

22 Nov 2017: 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

8 Mar 2017: Now let us assume that Gk1,I is measurable, for some k N, and any open intervalI = (a,b):. ... the above summation is always greater than some c > 0.5, when xis outside of the set B(0,r).

18 Jan 2017: Some important continuous distributions: Uniform. Some important continuous distributions: Uniform. X has a uniform distribution on [a, b], X U [a, b] ( < a < b < ), if it haspdf. ... Some important continuous distributions: Exponential. Some Gamma