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17 Jun 2019: Assume p > q. Let Tj = inf{n > 1 : Xn = j} if this is finite, and Tj = otherwise.

4 Aug 2022: Writedown operators which are a finite product. N. j=1. exp[sjA(tj)] (for appropriate {sj} and {tj}).

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: 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.

19 Jun 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.

17 Jun 2019: Let Ti = inf{n > 1 : Xn = i}. For each i 6= j letqij = P(Tj < Ti | X0 = i) and mij = E(Tj | X0 = i).

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.