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26 Aug 2010: for all open balls B Rd, where Qd is the countable set of vectors in Rd with rationalcoordinates. ... Lemma 3.1. Consider a sequence of measurable functions ξn : B Rd such that supn |ξn(ω)| < for all ω B.

18 May 2015: Random-sign hashing. Choose random sign assignments {1,. ,p}{1, 1} : k 7 Ψklindependently for all columns l = 1,. ... Example: When X is binary κ(δ) = 1/δ effectively scales all xi to.

15 Jan 2021: F t (i) =. F t (j ) for all i = j and t 1.(b) If (F1(i) : i S) are independent and uniformly distributed on S, then. ... Furthermore,. kt (. f ) = k(f ) and kt (. f ) = k(f ) for all large t.(b) Let F = (Fs : s N) be independent and identically

17 Aug 2010: and for all v I(Ka,b),. Pp(v oo in Ka,b) > 0. ... and for all v I(Ka,b),. Pp(v a in Ka,b) > 0.

14 Mar 2012: k and V. 1m = B. 1m for all m. Continuing in the same way, i.e. ... uniformly in the ball B(0,R). Using Lemma 4.1 we deduce that, for all k,.

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.

2 Sep 2008: v η(v). where |δ(v)| 0 as τ , and there exist constants A and B such that |η(v)| AB log(v)for all large enough τ. ... E[( Stτ. St K. )|Ft] = E[(Sτ K)].for almost all K > 0.

9 Jan 2012: Proposition 4(a) extendsTheorem 1(b) to more general configurations than the all-1 configuration. ... a) all sites in [[1, n]]d1 {1} have color ;(b) all sites in [[1, n]]d1 {m} have color ; and(c) no site of color is adjacent in G to

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.

27 Jul 2012: E[(vol(Va(I,δ))). 2] 2E[vol(Va(I,δ))]2. (6.4). For all x define τx = inf{t I : Xt at B(x,δ)}. ... that for all ε sufficiently small. vol({Ψ > 0}) 12 log(1/ε).

18 Aug 2017: It turnsout that all clusters of the infinite-volume limit are almost surely finite. ... Each vertex has degreeeither 1 or 2, and therefore all components are either paths orcycles.

22 Jan 2024: b) E(λX) = λE(X) for all λ [0,) and all X F+,. ... am b = f(m) and ax b f(x) for all x I.

3 Aug 2012: constants. We then show that for all d 1 theMinkowski dimension of (B f)(A) is at least the maximum of the Minkowski dimension off(A) and that of B(A). ... The balls of radius ε centered at (B f)(ti) might not all be disjoint; the followinglemma

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

5 May 2022: 12 GEOFFREY R. GRIMMETT AND ZHONGYANG LI. (a) for all e and all ω E, we have ω {e} f(e, ω),(b) for all e and all ω, the difference ... a) for all e and all ω E, we have ω {e} h(e, ω),(b) for all e and all ω, the difference [ω {e}] h(e, ω) is

26 Aug 2013: b) If µ(v) = µ for some v V , then µ(v) = µ for all v V. ... We have thatµ(G) < 1 if either. (a) G is -regular and contains a cycle, or(b) deg(v) for all v V , and there exists w V with deg(w).

8 Jul 2009: Theorem 3. (a) The constant word of length n is M-seen in Y if and only if τk Mfor all 1 k n.(b) The alternating word An of length ... As Tn mn by Proposition 6, this impliesτi M for all i n.

6 Sep 2012: x. The unique value x maximizing the form is a stable point of thesystem to which all trajectories converge. ... a link between nodes b and c followed by routing adaptation to theextra capacity reduces the throughput of all connections.

24 Apr 2014: 6. Proof. We already noticed that Mt is adapted to Ft for all t. ... t for all x B(0, 2t), by using the Markov property we can deduce.

6 Oct 2021: Note that µ is increasing andµ() = 0. Let us say that A E is µ-measurable if, for all B E,. ... all sets of theform A N, where A B and N B for some B B with µ(B) = 0.