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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: The effects of recombination in the segment may be ignored.The time for which the sample has j distinct ancestors is denoted by Tj , j = 2, 3,. ,

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],.

17 Jun 2019: Find the probability-generating functions of the random variables Hj and Tj.

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

17 Jun 2019: Show that if g(s, x) is a real-valued function of realvariables s, x, and Tj are the jump times of (Nt, t > 0) then. ... E[exp. {θ. Nt. j=1. g(Tj, Xj). }]= exp. {λ. t. 0(E(eθg(s,X)) 1)ds. },.

17 Jun 2019: Show that if g(s, x) is a real-valued function of realvariables s, x, and Tj are the jump times of (Nt, t > 0) then. ... E[exp. {θ. Nt. j=1. g(Tj, Xj). }]= exp. {λ. t. 0(E(eθg(s,X)) 1)ds. },.

30 Aug 2019: Theeffects of recombination in the segment may be ignored. The time for which the samplehas j distinct ancestors is denoted by Tj , j = 2, 3,. ,

17 Jun 2019: minimise g(t) =n. i=1. ci Πmj=1 taijj. subject to tj > 0 j = 1,.

30 Aug 2019: tjk1 x), and τ is any point in [tj, tjk], can be used tofind the coefficients of the B-spline expansion of f as an element of S. ... that tj < tjk, and let x = (xi)ni=1 be interpolation points obeying the conditions.