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30 Aug 2019: Definition. The vector space IndGHV is defined to be the space with basis givenby the abstract symbols tj vi where t1,. , ... is given by g (tj vi) := ts hvi where ts is the unique coset representative suchthat gtj tsH, and h = t1s gtj.

10 May 2024: 2012). 109,. 268102. (doi:Modelling lateral manoeuvres in fish. K Singh, TJ Pedley. – ... 2010). 82,. 021408. (doi:Instability of uniform micro-organism suspensions revisited. TJ Pedley. –

10 May 2024: PW Mote, TJ Dunkerton, ME McIntyre, EA Ray, PH Haynes, JM Russell. –

10 May 2024: Enterria, M Diefenthaler, M Fucilla, MV Garzelli, M Guzzi, M Hentschinski, TJ Hobbs, J Huston, J Isaacson, SR Klein, F Kling, P Kotko et al.

10 May 2024: D Frankel, M Davies, B Bhushan, Y Kulaberoglu, P Urriola-Munoz, J Bertrand-Michel, MR Pergande, AA Smith, S Preet, TJ Park, M Vendruscolo, KS Rankin, SM Cologna, JR Kumita, N

17 Jun 2019: for j 6= i. Prove that the random vectors Yj AjX are independent, and thatY (Y T1 ,. ,Y TJ )T has a multivariate normal distribution.[ Hint: Random vectors are independent if

30 Aug 2019: Deduce that for every n 1,. Tn =d1j=1. cn(j)Tj. 2 Define the Weierstrass -function (z) associated to a lattice Λ.

30 Aug 2019: the space of splines of degree k1 spanned by the B-splines (Nj )nj=1on a knot sequence = (tj )nkj=1 such that tj < tjk. ... Prove that‖Qf‖C[tj ,tj1] ck‖f‖C[tj1k,tjk] ,. hence derive that‖f Qf‖ = O(|t|k) f Ck[a, b],.

30 Aug 2019: Justify your answers. Suppose now that, in addition to the delay Dj(yj), users of link j incur a traffic-dependent toll Tj(yj), and suppose each user selects a route ... Show that it is possible to choose the functions Tj() sothat the equilibrium flow

30 Aug 2019: i)B (t). (c) tj and tk are times of consecutive events (tj < tk) in a relative survival dataset.Describe the behaviour of F̂E (t) for tj < t < tk. ... Describe an example of a situation whereF̂E (tK ) might be greater than F̂E (tj ). END OF PAPER.

30 Aug 2019: Justify your answers. Suppose now that, in addition to the delay Dj (yj ), users of link j incur a traffic-dependent toll Tj(yj ), and suppose each user selects a route

30 Aug 2019: sequence = (tj ). nkj=1 such that tj < tjk.

30 Aug 2019: where Si1, Si2 correspond respectively to the swimming times of the strong swimmer andthe not so strong swimmer in the ith pair, for 1 6 i 6 3, and Tj corresponds ... a) Show that for j = 4,. 8, Tj has probability density function.

30 Aug 2019: State the dual Cauchy identity. Let F (t) =. j>0 fj tj be a formal power series, where f0 = 1.

19 Jun 2019: The variable tj (j = 1,. , 3) records the time interval under observationand takes the values 2, 4 or 6 months. ... logE(Yij|zi; xi; tj ). 1 E(Yij|zi; xi; tj )= α φZi βT xi δtj , (i = 1,. ,

30 Aug 2019: The variable tj (j = 1,. , 3) records the time interval under observationand takes the values 2, 4 or 6 months. ... logE(Yij|zi; xi; tj ). 1 E(Yij|zi; xi; tj )= α φZi βT xi δtj , (i = 1,. ,

30 Aug 2019: connected to nodes ti and tj with arcs of infinite capacity, and each nodeti is connected to a node s′ with an arc of capacity w wi 1 and w = wn.

30 Aug 2019: Define f(tj) and h(tj) to be theprobability mass function and discrete hazard function of failing at tj respectively. ... Thelatter corresponds to the conditional probability of failing at tj, given still alive beyond theprevious failure time point tj1.

30 Aug 2019: Part III, Paper 61. 5. 5. 1) Let = (tj)nkj=1 be a knot sequence such that tj < tjk, and let Sk() be the.

30 Aug 2019: the space of splines of degree k1 spanned by the L-normalizedB-splines (Nj )nj=1, on a knot sequence = (tj ). nkj=1 , where tj < tjk. Let x = (xi). ni=1