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20 Sep 2011: Kenyon, J.B. Orlin, P.W. Shor and R.R. Weber. , in Proc. ... In addition, we present a ran- domized O(nB log B)-time on-line algorithm SS , based on SS, whose expected behavior is essentially optimal for all discrete distributions.

26 Oct 2011: B(x,r δ) π(C(π1(x),r)) B(x,r δ), for all R > R0. (2.5). ... Also for all A π1(B(0,K)) we have that. µ(A) vol(π(A)) 0, as R.

22 Aug 2011: 3. adjust the divisor d in such a way that the sum of the seatnumbers of all Member States equals the given Parliament-size. ... 2. Suppose, at some stage, that State i has been allocated ai seatsin all.

17 Feb 2011: Wenext prove fk B(s, L) for all k and suitable c′, η. ... 3.5. Proof of Theorem 4. For simplicity of notation, we suppress the supremaover B(s, L) in most of what follows—uniformity of the bound follows from track-ing all

30 Nov 2011: Trans-mission is assumed to occur simultaneously through all resources on route i. ... By Proposition 4.3,there exists a compact set B(R) in RI+ such that n(t) B(R) for all t 0 for anyfluid model solution n satisfying |n(0)|

8 Jun 2011: pt =1011 for all t. {c(0),c(1),c(2),c(3),c(4),. } = {0, 316,12,1,1,. }. Note that c(i)2 c(i 1)c(i 1) ... Adv Appl Probab 42(3):795–815. Bartroff J, Goldstein L, Samuel-Cahn E (2010b) The spend-it-all regionand small time results for the continuous

26 Oct 2011: 1 P(Ψ(B) > 0)). 1 exp(BΛ. P(Ψ(B) > 0)). Taking sup over all Λ Γ of type 1, we deduce that P(Ψ(X) > 0) = 1. • ... Pu(B hits A) > 0,for all starting points u. By neighborhood recurrence of Brownian motion, we get that thisprobability is indeed

20 Jan 2011: This is the same as requiring an equal sizeof resource contribution from all participants. ... So N B(n 1, 1 αq). Theexpected net benefit of all the agents is.

25 Oct 2011: µqA(B) := q. Rd. Ex[eqTA 1{XTAB}. ]dx for all B B(Rd). ... 8.2& 8.4], provided we replace Gq by. G0(y,B) :=. 0. Py(Xt B) dt for all B B(Rd), (1.21).

9 May 2011: We write. g(x) z = b, z 0. It will frequently be mathematically useful to turn all our constraints into equalities. ... You can confirm for all b thatprimal and dual here have the same optimal values.

15 Sep 2011: In this case any bidder can obtain greater profits by bidding bA E on A, b E on B, and 0 on all other items. ... for all c and N. For c > 2 and p > 1.5, 1 - I/p seems very close to B.

21 Oct 2011: The Invincible Fighter Problem corresponds to the investment problem of Derman et al andso (A), (B) and (C) all hold. ... We summarise in Table 1 the status of (A), (B) and (C) for the set of problems discussed above,all of which are defined by cases of

15 Sep 2011: As ν , all states are eventually in S2. The solution tothe ν-wage problem can be succinctly described in terms of the 2n indices producedby the algorithm. ... Also, bi < b for all states i in which theactive action is taken.

15 Sep 2011: Using this heuristic limfl-0o( 1/S)log P(B) < - 5 if and only if I{c a)/a > 5for all a. ... because it is unlikely that any theoretical model is rich enough to adequatelymodel all traffic classes.

18 Sep 2011: fa i 1u r era t ere pair s t rat e gy rna x i rn i z e s for all t the pro b a biIi t y ... 352 P. NASH AND R. R. VEBER. B)O, and the result follows by taking c as a vector which is in the component corresponding to all jobs complete and 1

15 Sep 2011: This is the same as requiring an equal sizeof resource contribution from all participants. ... So N B(n 1, 1 αq). Theexpected net benefit of all the agents is.

15 Sep 2011: We desire to stabilize t > l e system by ensuring t h a t for all i a,nd t we have E ( z i ( t ) ) < B for some R. ... Similarly, r = {x : Bx 2 0) for sonie B with coefficients t h a t a,re all -1, 0 or 1.

15 Sep 2011: We desire to stabilize the system by ensuring that for all i and t we have E(xi(t)) < B for some B. ... Similarly, = f x Bx? O} for some B with coefficients that are all -1, 0, or 1.

15 Sep 2011: Thus, we need to establish the optimality of 7r, amongst all dispatching functions. ... That is, B, is the set of states for which the confining of all future Cj job assignments to P,,. "? ",

15 Sep 2011: So for all m_. mo we have [b m(c6 - p,, (6))] > b and. ... Thus I(c, b)? bH(c) for all b. Moreover, for those b for which b =. m(cp'(H(c))-c), m= 1, 2,--., we have I(c, b)=bH(c).

15 Sep 2011: Denote by F, = F ( N n r B n , c n ) the current fraction of cells lost a t buffer n, for all buffers n in the network. ... Under these assumptions, D will have a negligible dependence on B as well (for large B ). Consequently, the probability t h a t

15 Sep 2011: Thus the. expected wasted space is bounded by some B for all t. ... Thus the wasted space satisfies I B' I|1/N < Wt' | I B' I|1N for all possible packings.

31 Oct 2011: From the above, the minimum subsidy that makes (1, 1)passive also makes all states passive. ... 1. We shallprove by induction on s that that for all valid state vectors(ω̄1, y, ω̄2, ω̄3).

15 Sep 2011: Note that not all n customers will choose a dynamic contract, butwe will address this issue later on. ... of band-width, while with probability 1pi he does not buy nothing at all, with pi beinguniform in [0, a/b].

15 Sep 2011: Mtisfies (b) for all StMM with a 111-ponent of value k or bigger by (2.2) and the fact that M isk-liiited. ... The newfunction has all positive coefficients and will continue tosatisfy (b) with y replaced by y/2 >0.

15 Sep 2011: manner until all machines are assigned or all jobs are allocated to machines. ... The uniform, exponential, hyperex- ponential, gamma, and folded-normal distributions all have sc2 densities.

15 Sep 2011: 1, 0, 2).Let PS,b denote the set of all perfect packing configurations for a given S and b. ... LetΛS,b be the convex cone in Rd spanned by all nonnegative linear combinations ofconfigurations in PS,b.

15 Sep 2011: Then 7r minimizes E[ J', cj Uj] amongst all the static list policies. ... All the jobs are present at time 0, so T7 = SJ Qr ,dt.

15 Sep 2011: b) The worst possible growth rate for expected waste. of FFD over all pairs j,k is n1624 = (.00160. ) ... 1,0,2). Let P,B denote the set of all perfect packing. configurations for a given S and B.

15 Sep 2011: Only the first two customers purchasecontracts. If we have wanted to ensure that all three customers. ... An important question thatmay rise is how the shape of the utility function affects all theaforementioned results.

31 Oct 2011: simultaneously. The parametersof the contracts become finalized once all agents have madetheir bids. ... post ones, eitherfor C3, or for C1 and C2, but not for all.

15 Sep 2011: This distribution is known to all agents, butthe value of is known to agent alone. ... this denotes all the preferences parameters apart from. Theproblem is to maximize expected social welfare.

15 Sep 2011: terms of maintaining guaranteedservice to all customers) as two units of service A. ... This is the charging method which is adopted by an all-you-can-eat restaurant.

15 Sep 2011: Place the next item so as to minimize P1i<B n(g)2.For all the discrete distributions we have tested, SS appears to produce sublinearexpected waste whenever the optimal expected ... assume that all discrete distributions have beenscaled up by an

15 Sep 2011: If there is a function V : Z [1, ),constants b < , β > 0, and a finite subset C Z such that for all x Z,. ... that (a) sS µ(s) = 1 and (b) for all states s′ S,µ(s′) =. sS µ(s)ps(s. ′). If we let sn denote the state after n steps, then

15 Sep 2011: there exists a bin-packing algorithm whose use guarantees the expected wasted space is less than B for all t. ... Thus the expected wasted space is bounded by some B for all t.

15 Sep 2011: All the services are deter- ministic, with a duration of 1 time unit. ... It can now be shown that the whole expression is maximized over the range -a < b - a by b = 0 for all 0 < a < 1/2.

15 Sep 2011: We define a system to be stabilizable if, for any arrivalprocess in L{), a policy exists under which E[xt(t)] < B < <x> for all times t.A system is/-stabilizable ... When a bin is filled with all the type a items itcan store, it is immediately filled

15 Sep 2011: By m o v i n g a j o b all the w a y a r o u n d the cycle, f r o m n o d ... All these decisions are to be m a d e dynamically as a function of the n u m b e r o f jobs.

15 Sep 2011: a) [Initial Bound Hypothesis]. E[bφ(X1). ]<. (b) [Bounded Variation Hypothesis]. For all N 1, |φ(XN1)φ(XN)|. ... tation. The state space S is the set of all length-(B 1) vectors of non-negativeintegers x̄= 〈x1,x2,.

15 Sep 2011: From d(z - ii)/dt = Ai(2 - ) we see that ifz(t) - n for all. ... All the following matrix calculations were carried out using the software PC-MATLAB 3.10. -

29 Sep 2011: f>(0) = lim nl logE[exp(n0TZ„)],n-oo. existsfor all 0, possibly as oo. ... For example,if the definition of a slot doubles, then c, ptand y,- all double.

21 Oct 2011: on all the past history Fn. The optimal t! will then choose to. ... Fn = B(xn) and zn = g{xn) 'l'There g is Fn- measurable, all n.