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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

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

30 Aug 2019: Part III, Paper 69. 3. 3. 1) Let Sk() be 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.

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: Show that the action of the left-invariant vector fields,. Tj (u) = iµji(u). ... ui,. on the matrix A is given by Tj A(u) = A(u) σj , and hence that Ti are generators of the.

19 Jun 2019: dependent toll Tj(yj ), and suppose each user selects a route in an attempt to mini-. ... Tj () so that the equilibrium flow pattern minimizes the average delay in the network.

30 Aug 2019: y1,j = f(tj) g1(tj) ǫ1,j. y2,j = f(tj t) m g2(tj) ǫ2,j.

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: 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

19 Jun 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.